text
stringlengths 100
500k
| subset
stringclasses 4
values |
|---|---|
Definition: An equation in the form $a_0 + a_1x_1 + a_2x_2 + ... + a_nx_n = 0$ is called a Linear Equation of the $n$-variables $x_1, x_2, ..., x_n$.
If we are dealing with equations of two variables, we will often use $x$ and $y$ instead of $x_1$ and $x_2$. For example, the equation $2 + 3x + 4y = 0$ is a linear equation. If we are dealing with equations of three variables, we will often use $x$, $y$ and $z$ instead of $x_1$, $x_2$, and $x_3$. For example, the equation $1 + 3x - 5y + 4z = 0$ is a linear equation. If we are dealing with equations of $n$-many variables, we will often use the former notation. For example, the equation $2 + 3x_1 + x_2 - 4x^3 + 0x^5 = 0$ represents a linear equation of $5$ variables (although the variable $x^4$ is not present in this linear equation).
We will now review what linear equations of 2 variables and 3 variables represent geometrically. | CommonCrawl |
Jerry L. Bona, Henrik Kalisch. Models for internal waves in deep water. Discrete & Continuous Dynamical Systems - A, 2000, 6(1): 1-20. doi: 10.3934\/dcds.2000.6.1.
Alberto Bressan, Wen Shen. BV estimates for multicomponent chromatography with relaxation. Discrete & Continuous Dynamical Systems - A, 2000, 6(1): 21-38. doi: 10.3934\/dcds.2000.6.21.
E. N. Dancer, Shusen Yan. On the existence of multipeak solutions for nonlinear field equations on $R^N$. Discrete & Continuous Dynamical Systems - A, 2000, 6(1): 39-50. doi: 10.3934\/dcds.2000.6.39.
John Erik Forn\u00E6ss. Infinite dimensional complex dynamics: Quasiconjugacies, localization and quantum chaos. Discrete & Continuous Dynamical Systems - A, 2000, 6(1): 51-60. doi: 10.3934\/dcds.2000.6.51.
Roland Gunesch, Anatole Katok. Construction of weakly mixing diffeomorphisms preserving measurable Riemannian metric and smooth measure. Discrete & Continuous Dynamical Systems - A, 2000, 6(1): 61-88. doi: 10.3934\/dcds.2000.6.61.
V. M. Gundlach, Yu. Kifer. Expansiveness, specification, and equilibrium states for random bundle transformations. Discrete & Continuous Dynamical Systems - A, 2000, 6(1): 89-120. doi: 10.3934\/dcds.2000.6.89.
Fanghua Lin, Ping Zhang. On the hydrodynamic limit of Ginzburg-Landau vortices. Discrete & Continuous Dynamical Systems - A, 2000, 6(1): 121-142. doi: 10.3934\/dcds.2000.6.121.
Tai-Ping Liu, Shih-Hsien Yu. Hyperbolic conservation laws and dynamic systems. Discrete & Continuous Dynamical Systems - A, 2000, 6(1): 143-145. doi: 10.3934\/dcds.2000.6.143.
Mark Pollicott. $\\mathbb Z^d$-covers of horosphere foliations. Discrete & Continuous Dynamical Systems - A, 2000, 6(1): 147-154. doi: 10.3934\/dcds.2000.6.147.
Marek Fila, Hiroshi Matano. Connecting equilibria by blow-up solutions. Discrete & Continuous Dynamical Systems - A, 2000, 6(1): 155-164. doi: 10.3934\/dcds.2000.6.155.
Alexander Krasnosel\'skii, Jean Mawhin. The index at infinity for some vector fields with oscillating nonlinearities. Discrete & Continuous Dynamical Systems - A, 2000, 6(1): 165-174. doi: 10.3934\/dcds.2000.6.165.
Yuan Lou, Salom\u00E9 Mart\u00EDnez, Wei-Ming Ni. On $3\\times 3$ Lotka-Volterra competition systems with cross-diffusion. Discrete & Continuous Dynamical Systems - A, 2000, 6(1): 175-190. doi: 10.3934\/dcds.2000.6.175.
I. Moise, Roger Temam. Renormalization group method: Application to Navier-Stokes equation. Discrete & Continuous Dynamical Systems - A, 2000, 6(1): 191-210. doi: 10.3934\/dcds.2000.6.191.
Gang Tian. Bott-Chern forms and geometric stability. Discrete & Continuous Dynamical Systems - A, 2000, 6(1): 211-220. doi: 10.3934\/dcds.2000.6.211.
P. Magal, G. F. Webb. Mutation, selection, and recombination in a model of phenotype evolution. Discrete & Continuous Dynamical Systems - A, 2000, 6(1): 221-236. doi: 10.3934\/dcds.2000.6.221.
Lan Wen. On the preperiodic set. Discrete & Continuous Dynamical Systems - A, 2000, 6(1): 237-241. doi: 10.3934\/dcds.2000.6.237.
Zhihong Xia. Homoclinic points and intersections of Lagrangian submanifold. Discrete & Continuous Dynamical Systems - A, 2000, 6(1): 243-253. doi: 10.3934\/dcds.2000.6.243. | CommonCrawl |
If $X$ and $Y$ are topological vector spaces over $\mathbb R$, then a map $f:X\to Y$ is called uniformly continuous if for each neighborhood $V\subseteq Y$ of $0\in Y$, there exists a neighborhood $W\subseteq X$ of $0\in X$ such that for any $x,y\in X$ satisfying $x-y\in W$, it follows that $f(x)-f(y)\in V$.
It is not difficult to show that addition $+:X\times X\to X$ is a uniformly continuous function when $X\times X$ is endowed with the product topology. Also, for a given $\alpha\in\mathbb R$, the map $x\mapsto \alpha x$ is a uniformly continuous function from $X$ to $X$.
However, I suspect that scalar multiplication $\cdot:\mathbb R\times X\to X$ is not necessarily uniformly continuous when $\mathbb R$ is endowed with the usual topology and $\mathbb R\times X$ is endowed with the product tvs structure. Indeed, if $X=\mathbb R$ under the usual topology, then the function $(\alpha,x)\mapsto \alpha x$ from $\mathbb R^2$ to $\mathbb R$ is clearly not uniformly continuous.
Can anybody confirm this? I'm asking because several textbook references on topological vector spaces claim that both addition and multiplication are uniformly continuous functions, but I suspect uniform continuity of scalar multiplication can only be established in a restricted sense, i.e., when it is interpreted for a given scalar and not when $\mathbb R$ is considered as a tvs in its own right to be multiplied with $X$ to form a product tvs. In particular, I'm confused as to which of these two notions of "scalar multiplication" is appropriate when one is talking about the uniform continuity of such an operation.
You're right, as can be seen in the example you mention, multiplication $\mathbb R\times\mathbb R \to\mathbb R$. And you say this is "clearly" not uniformly continuous, so I don't know if you have a question about proving it. You can take as $V$ the interval $(-1,1)$. Each open $W\subset \mathbb R\times \mathbb R$ containing $(0,0)$ also contains $(\delta,0)$ for some $\delta>0$, but $\left(\frac1\delta+\delta\right)\cdot\frac1\delta - \frac1\delta\cdot\frac1\delta = 1\not\in (-1,1)$ even though $\left(\frac1\delta+\delta,\frac1\delta\right)-\left(\frac1\delta,\frac1\delta\right)\in W$.
You might want to consider for which subsets $A\subset \mathbb R$ the restriction $A\times X\to X$ is uniformly continuous. It is necessary and sufficient that $A$ be bounded.
Not the answer you're looking for? Browse other questions tagged general-topology functional-analysis vector-spaces continuity or ask your own question.
Completability of a uniform space, metric space and topological vector space? | CommonCrawl |
Abstract: Given a direct system of Hilbert spaces $s\mapsto \mathcal H_s$ (with isometric inclusion maps $\iota_s^t:\mathcal H_s\rightarrow \mathcal H_t$ for $s\leq t$) corresponding to quantum systems on scales $s$, we define notions of scale invariant and weakly scale invariant operators. Is some cases of quantum spin chains we find conditions for transfer matrices and nearest neighbour Hamiltonians to be scale invariant or weakly so. Scale invariance forces spatial inhomogeneity of the spectral parameter. But weakly scale invariant transfer matrices may be spatially homogeneous in which case the change of spectral parameter from one scale to another is governed by a classical dynamical system exhibiting fractal behaviour. | CommonCrawl |
Pre algebra calculator, poems to help remember algebra, factoring algebraic expressions calculator, algebra in life, glencoe algebra 2, prentice hall mathematics answers.
Why Do I need algebra?, glencoe mathematics algebra 2 answers key, algebra graphing program, adding radicals, Elementary Algebra pearson, ninth grade algebra help.
Algebra expressions for kids, calculator for factoring trinomials, glencoe math book, calculator algebra2, Poem, or jingle for solving equation, algebra standard form.
Help with freshmen algebra, 4th grade algebra expressions, merrill math textbooks, process algebra tutorial, algebraic formula.
Pizzazz algebra, 10th grade algebra, modulus inequalities, pre algebra an accelerated course answers, Middle School Math With Pizzazz Book E-52, Algebraic equations poem, algebra using rational expressiona and factoring in real life.
Intermediate algebra textbook Prentice hall, first year algebra problems, prentice hall mathematics algebra 1 teachers edition, prentice hall algebra 2 book answers.
Answers for algebra 2 workbook, quadratic equation writer, get algebra awnsers, simplifying a complex fraction calculator, times, x, dummies guide to alebra, mathcad calculating sign post.
Algebra for class 8, algebra 2 plato answers, Algebra 2 Trigonometry answers of test 3, Free Math Answers.
Glencoe algebra 1 homework answers, AJmain, FREE ONLINE solving equations with rational numbers calculator, basic algebra rules.
Algebra ii glencoe mathomatics practice book, glencoe answer key for algebra 1b, algebra mapping, algebra linear inequalities pictues.
Free word problem solvers for college math, radical equations extraneous solutions, algebra used daily life, cheat sheet pre geometry, accelerated math help, nth term algebra, algebra 1 honors help.
Order of operation two steps (1) Answer, impossible math problems, prentice hall mathematics algebra 1 free answers, Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule., algebra solver that shows steps, answers to holt pre algebra.
9th grade algebra help, role of operations inequalities, balancing calculator, prentice hall algebra 2 answers chapter 11, algebra multiplying radicals helper, alg 2 cheat, algebra in aptitude test.
Practice workbook lesson 3-7 answer, who uses algebra, orleans hanna prognosis test, directly related inversely, algebra 2 practice workbook answers, collegealgebra for dummies, developmental mathematics 4th edition.
How to solve f x problems, how to unfoil, algebra helper, 3X3 matrix multiplication tutorial, chinese remainder theorem for groups, variable fractions.
Find quadratic equation from table, differential solver, why do you need a common denominator, algebra 1 book answers, Algebra for Dummies, algebra structure and method book 1.
Online algebra tile program, ac quadratic equation, algebraic properties of equations, explanatoin laws of exponents, Algebra Answers, 7th grade simplifying radicals.
ALGEBRA 2 FOERSTER, algebra LCm calculator, difficult algebraic equations, free printable exponent worksheets, algebra calculator that shows work, algebra practice problems.
Writing summation notation fractions, problem solver geometry, College Algebra for Dummies, linear algebra otto solutions, identifying coefficients in fractions, solve my equation online.
Equations having more than one variable, math decomposition, advanced mathematics by richard g. brown, algebrator free, solve adding exponents, algebra calculator with work.
Download algebrator, saxon algebra 2 2nd edition, solve my math problems for me for free, hardest algebra problem in the world.
View Solutions prentice hall mathematics for Pre-Algebra (2004 Edition), how to do basic probabilities, algebra ERB, lcd of complex fractions, algebra 1 glencoe workbook help!.
Abstract algebra mathematicians, prentice hall mathematics algebra 2, word problem solver calculator, .157 to fraction.
How do you turn ratios into fractions?, algebraic formulas list, orleans-hanna sample test, electrical math problems, online word problem solver, algebra formulas and equations, logarithmic equation solver.
What is a expression in math, Answers to glencoe algebra 1 worksheets, free algebra solver, answers for Algebra Structure and Method Book 1, how to do hard algebra.
What do learn in 11 grade math, algebra 2 test 1 answerkey, formula s in pre alg, 7th Grade Prealgebra exponential graph, Who Invented Algebra.
Applications of quadratic equations in daily life, algebra and trigonometry book 2 answers, solving algebra solution sets.
Algebra 2 answers for practice A 5.7 worksheet, glencoe algebra 1 book, solving quadratic equations in everyday life.
College algebra cheat sheet, algebra answers word problems, online fraction calculator.
Beginning algebra 4th edition, exponent fraction calculator, glencoe pre algebra answers, math simplification rules.
Practice workbook algebra 1 answers, east way to factor, prentice hall mathematics algebra 1 answers key, pre algebra espanol, answers to algebra textbook, i WANT TO KNOW MORE ABOUT ALGEBRA.
Rational number equations calculator, basketball algebra, complex order of operations, Algebra pretest, equations of the hyperbola problems and solutions, finite math help, why is algebra important.
T86 calculator, how to turn a decimal into a fraction, math worksheet on open sentences.
Math tutors and baltimore, answers to glencoe algebra test, Algebra Testing for Ninth Grade, glencoe mathematics pre algebra teacher's edition.
Math refresher for adults, how to remember geometry equations, prentice hall mathematics algebra 2 answers, 8th grade algebra word problems, answer book for elementary and tintermediate algebra.
Rearrange equations online calculator, how to do a quadratic, compass algebra help, steps for algerbra.
Parent fuction+algerbra, intermediate algebra concepts, 1st year algebra, middle school math with pizzazz book e, Middle School Math with Pizzazz, rational equations real life examples, algerbrasolver.
Algebra for beginners, how to cheat an algebra test, Algebra 2 McDougal Littell Online, pictures of triangles in everyday life, distributive property step by step help, radical rules, algebra print outs.
Simplify using positive exponets, algebrator review, math steps algebra.
Advanced algebra trivia, how to do algebraic pyramids, unFOIL, "charges $600 for a seminar", McDougal Littell algebra 2 Chapter 7 test answer, prentice hall mathematics algebra 2 textbook.
Contemporary math college class, samples of college word problems, cheat on algebra, Algebra: Structure and Method Book I, easy way to solve fractions.
Prenticehall workbook, finding common denominators with variables, quadratic equations in algebra 1 workbook answer, text symbol on ti 82.
Algebra solving for an exponent, practice eog math for the 7th grade, factoring trinomials calculator.
Why should we clear decimals when solving linear equations and inequalities, how to solve distributive property, maths real life graphs, sho me how to simplify.
Steps on how to learn algebra, algebra 1 glencoe answers, algebraic model, www.solvemymathproblem.com, Saxon Algebra 2 test answers.
Learn algebra formulaes, prentice hall mathematics algebra 2 online book, 8th grade made worksheets.
Graphing linear equations with 3 variables, Prentice Hall Mathematics Algebra 1 answers, Instant Algebra Answers, i need answers to algebraic equations, answers to math free, algebraic proofs, algebra 2 answer key mcdougal.
Algebra answer worksheet, math answers for free, pictures of linear graphs, math tutors in baltimore, problem solving for Algebra.com, learning algerba, Algebra principles.
Rational Expressions Solver, online simplifying rational calculator free, how do you solve matrices, math tutor in columbia sc.
Practice worksheet 7-4, Glencoe Algebra 2 Answers, what website will give free answers to polynomials?, how to learn calculas.
Linear programming application high school, I have pre algebra skill and need to learn about logarithms, Algerbra Answers, algebra tutoring online free, how to enter trig intigrals in a ti 89, what are some similarities for quadratic , linear, and exponentail functions.
How to easily understand rational expressions, algebra nth term, learn intermediate algebra, what to know for college algebra.
Fraction in a radical, hard algebra problems, prentice hall answers, algebra with pizzazz website, helping students learn how to solve problems by solving them step by step, how to solve geometry problems, decimal to radical form..
Help with 7th grade polynomials, myalgebrahomework.com, hard pre algebra problems, glencoe converting algebra 1, math with pizzazz answers, plato test answer keys algebra 2a, how do you solve equivalent standard form.
Algebra I final, quadratic simultaneous equations questions, math solutions software, algerbra formulas, developing skills in algebra book c page 117, math problem solver algebra 2, algebra for dummies.
Easiest way to factor, Algebra and trigonometry books 2 answers, equation simplification.
Samples of polynomials, problem solving using rational equations, how to solve multiplying monomials.
Easy way to factor, math inequalities help, simple algebraic proofs.
How to find alegbra amswer, cubic graph solver, understanding functions in algebra, expressions with positive exponents, algebra facts, help doing algebra problems.
Hyperbola helper, Algebra test maker, expanding algebraic products exercises.
Answers to prentice hall mathematics algebra 1, cheat sheet for algebra, 6th grade algebra word problems, set summation, Enter Math Problems for Answers.
How to teach algebra, prentice hall mathematics geometry book answers, intermediate algebra tips, Alegebra 1, easy ways to factor.
Mathturbo, algebra least common multiple calculator, online simplifying rational calculator, glencoe math books.
Algebra 2 calculator online shows steps, solver range, 10 MINUTES TURNED INTO FRACTION, solving equations with variables on both sides with fractions, how to use algebrator, rational expressions algebra solver.
How to work on algebra, glencoe test anwsers, factor negative exponent, algebra examples and answers.
Www.freecollegealgebra.com, synthetic division online solving calculator, polynomials with negative exponents, geometry problem solver, florida algebra 2 state test, refers to the degree of exactness, algebra 101.
My alegbra, algebraic equations with a double variable, best way to understand algebra, a poem about algebra, algebra vocabulary.
7th grade eog math practice, california state standards: algebra 2, algebraic terms, algebra 1 answers prentice hall, changing to standard form, times or x.
Sqare root of exponets, eureka math, pre-algebra study guide, developing skills in algebra book c.
Work out geometry problems, solving radical equations with extraneous solutions, algebra calculator show steps, Algebra 2 solution key Prentice Hall, lowest common denominator finder, free math helper algebra.
Solving fractions, show your work calculator, step by step simplifying rational expressions.
Algebraic expressions and equations, solve triginometry, equation transformation, Algebrator free, how to work out an algebra problem, reversed algebraic sign.
Logrithem tutor, finding the least common denominator with variables, difference quotient calculator, why do we need algebra 1, Algebra for colleges 5th edition, Uses of Algebra.
Teachers answer key to Glenco Algebra 2, preparing for college algebra, simultaneous equations general formula, graphing inequalities 6th grade math.
Saxon math algebra 2 test answers, expression multiplier, simplifying different integers, quadratic exercises, pizzazz math answers, algebraic equations formulas, algebra 2 texas math book.
Cheap DIVE Algebra I, Algebra, 2nd Edition (purple book), geometry radicals, Math Makes Sense online book, unfoil math, math tutors for adults.
Elementary algebra free help, transforming formulas worksheet algebra 1, solving shadow word problems, exponential and radical simplify expressions, complex numbers to standard form calculator online, Algebra: Structure and Method biik 1hotfile, rewriting expressions without radicals.
Holt rinehart and winston algebra 1, graphing three variables, algebra problems in life, algebra tiles worksheets, pre algebra media enhanced cheats, prentice hall mathematics algebra 1 answers, solving variables on both sides with MS Calculator.
How is algebra used today, how do you solve quarktic equations, factoring problem, glencoe algebra 2 test answers, Free Math Solver with steps, prealgebra calculator.
Algebra with pizzazz answers, pass algebra 2 app, algebra structure and method book 1 answers, how to do college algebra on ti83, online algebra solver, dividing rational expressions solver, denominator algebra.
Factoring fractions algebra, logarithms explanation, algebra, angel..., rational number calculator, Algebra 2 Answer Key, orleans-hannah algebra diagnostic test for 7th graders, algebra en espanol.
Triginometry, beginning algebra workbook, free algebra answers.
Algebra textbook for 9th grader, algerbraic fraction solver, solving hard transfer function, writing algebraic equation, teaching linear equations to ninth graders, simplify complex fraction calculator.
Multiplying a polynomial by a monomial calculator, Triginometry, Algebra 2: An Integrated Approach.
McDougal littell algebra 2 2004, GCF helper, solving algebraic expressions calculator, algebra for dummies download, prentice hall algebra 2 with trigonometry answer key, tutor pay in minnesota, 5th grade algebra equations unknowns.
Iowa aptitude test, algebra for idiots, online algebraic fraction calculator, 8th grade algebra examples.
Orleans hanna algebra prognosis test, algebra drills, step showing calculator, algebra 1b problems, proof algebra help, 7th grade math scale factor, LCM 5th grade.
What does algebra have to do with real life, how algebra help change your life, simplifyingpowers of i, algebra 1 study guide, teach me algebra, free freaking algebrator.
Algebra terms, algebra math problems and answers, how to write algebraic equations, Is there a difference between solving a system of equations by the algebraic method and the graphical method? Why or why not, Algebrator, algebra factoring worksheets, prentice hall algerbra 2.
Who invented algebra, mcdougal littell algebra 1 teachers edition online, quadratic formula worksheet.
Algebra substitution method, algebra 1 mcdougal littell vocabulary, best precalculus software, Algebra textbook answers.
Algebra factoring square roots, solve my math problems, algebra homework solvers, how to learn algebra fast.
Algebraic fractions calculator, how to do well in algebra, why should we clear fractions when solving linear equations and inequalities.
Answer key for teachers, algebraic fractions questions, conjugate method calculus, Online Free simplying Radical Equation Calculator, math problem helper.
Equation for transformation, setup for mathematical induction, algebra with pizzazz printables no answers, finding vertices of inequalities.
Holt pre algebra, prentice hall pre algebra answer key, graphs in real life.
Allgebra, MCDOUGAL algebra 1 smartboard lessons, how to solve and graph inequalities on a number line.
What does x mean in algebra, NJBST, algerbra pizzaz, gustafson frisk college algebra answers, how to solve fractions with variables, Math Extrapolation, Algebra 2: Prentice Hall Mathematics.
Simplifying complex Fractions Calculator, real life quadratic function examples, algebra 2 parent functions, exponential equations and its applications to real life, why should we clear decimals when solving linear equations and inequalities, PreAlgebra multiple choice.
Inequality algebra calculator, how does algebra 2 relate to everyday life?, 9th grade algebra 1 problems, exponential rule.
Math simplify calculator, how to do algebra year 7, how to do fractions on a scientific calculator, distance, rate & time elementary algebra.
Writing algebraic expression worksheets, free printable exponents worksheets, algebra 1 workbooks, russian algebra.
Glencoe mathamtics, algebra variables fractions, how to learn algebra the easy way, variable e, verbal model.
Answers to the algebra 2 practice workbook, solve algebra problem and show work, trinomial solver, Algebra Symbolic method, step by step how to solve algebra, college math problems.
Algebra polynomials used in real life, purdue tutor, Algebra with Pizzazz, rudin chapter 3 solution, rational expressions used in real life.
Where can i solve special products of binomials?, linear algebra and its applications answers, agebra, math definitions for algebra, operations with rational expressions check homework.
Www.printablesalberaworksheets.com, Turn a Decimal into a Fraction, evaluating calculator, linear equations and real life problems, sat cheats.
Eqations with eqations on both sides calculator, how to do inequalities, applications polynomials daily life, +CALCULATOR MUTIPLYING BINOMIALS USING FOIL.
Prentice hall mathematics algebra 1 online textbook, 7th grade pre algebra problems, graphing algebraic inequalities, algebraic thinking tasks, simple algebraic formula, examples of algebraic equations related to real life, what does the x mean in algebra.
Differential equation calculator, double variable equations, intermediate algebra answers, algebra 2 final exam study guide, learn algebra fast.
Expressing summation notation with fractions, on-line tutorials for beginning algebra, songs on algebraic equations, solving differential equations online, teaching lowest common denominator, alegebra with pizzazz.
Algebra tests with answers, algebra percent change, answers for elimnation problems for algebra, blitzer college algebra 4th edition.
Algebrator download, how to factor problems, solving perfect square trinomials, rudin mathematical analysis solutions, algebra 2 simplifaction.
Linear equations and inequalities help, final exam for college algebra by sullivan and sullivan, Examples of equation poems, 9th grade algebra, algebra made easy, Principles of Mathematical Analysis- SOLUTION MANUAL.
Lessons on functions, confusing jr high algebra problems, gcf equation, freshman algebra for dummies.
Solving multi-step equations calculator, use a caculator that shows your work, free algebrator, math with pizzazz genius test.
Free online algebra 2 problem solver, dilation algebra problem, merrill pre algebra, Workingout algebra, all of the answeres to the florida adition pre algebra math book., mcdougal littell algebra 2 answer key, Hungerford Abstract Algebra Solutions.
Ti-89 sat, free algebra word problems, interesting algebra facts, 4x+-3+-2x awnser solve binomials, why should we clear decimals when solving linear eqautions and inequalities.
College algebra story problem help, algebra sequences helper, new orleans hanna test, free finite math help, Algrebra.
Algebra II factoring, pre algebra calculater, algebra eoc practice, 6th grade equations, 2 square root times x, all algebraic identities, solving multi step equations calculator.
Myalgebra.com, Free Online Algebra Solver, solving two step equations.
Solve finite math problems, factoring a polynomial tool, preliminary mathematics formula list, beginning and intermediate algebra 4th edition, teach me algebra for free, simplified fraction radical, elementary algebra word problems examples.
ALGEBRA EXPRESS calculator, Multiplying Radicals, algebra1problem solver.com, Algebra transforming formulas, saxon math problem set template.
Saxon Algebra 2 Answer Keys, algebra prognosis test, nth term solver.
Learn inequalities, ti study cards, dividing linear equations with exponents, Algebra Structure and Method Book 1, the steps in algebra, Easy trinomial factoring, step by step math solutions.
Operations with rational exponents, algebra 2 problem solver, multiplication worksheets with arrays, solve for a fraction inequality, help with finite math, algebrator.
Simplify radical expressions fractions calculator, online differencial, how to solve algebraic functions.
Easy method to teach algebra, Create an example of a real-life word problem which can be solved using algebraic inequalities.Write the problem, and solve the problem. Show the algebraic inequalities that are involved including all necessary steps taken to get the answer., 6th grade math dilation, explain a algebra problem.
What type of math is used for cryptography, college algebra calculator, binomial theorem homework checker.
Textbook answer keys, how to use algebrator software, algebra 2 saxon book online, calculators that show work, tests algebra structure and method book 1, College Algebra Formulas, holt OHIO MATH answer key.
Henry borenson, best algebra calculator, can cheat with ti 89 on sat math, middle school math with pizzazz, exponent problems, how to explain equations.
Adv algebra, ready for algebra 2 quiz, algebra 2 solver.
My algedra.com, online differential equation solver, answers to algebra 1 textbook, algebra 2 summation notation, how do you solve quarctic equations, range symbol.
8th grade free printables for algebra and answer sheets, algebra 1 calculator online, simplify algebra step by step, free college algebra tutor program, writing equation worksheets, mathematic-simplification, math simplification algebra ii.
Solve my math, differential equation online solver, 8th grade algebra help, algebrA multistep equation worksheet, algebra made simple, free algebra solutions, how to factor polynomials dumbed down.
Method of decomposition math, boolean algebra simplification tutorials, how to change radicals to degrees, solving polynomial with negative exponents.
Open sentence math worksheets, impossible to solve math problems, exponent exercises, math calculator that shows work, saxon math course 2 answers.
Exponent is fraction, hungerford algebra solution, SIMPLE ALGEBRA PROBLEMS TO FIND X FOR 5TH GRADE, glencoe algebra 2 answer key, algebra writing expressions.
What is the difference between intermediate and college algebra, math interpolation, how do to algebra, how can i understand algebra 1, algebra x times x.
Algebra 2 list of formulas, learn algebra step by step, funny algebra equations, glencoe algebra 2 book answer keys, MCAS formula sheet.
Algebra 1: Explorations and Applications,, algebra homework answers, calculator with work shown.
Advanced algebra projects, show work calculator, online book for algebra 1 concepts and skills.
Paul A Foerster, free worksheets on linear equations, Algebra Poems, summer practice for algebra 1, algebra 1 pre test, symbol for range.
Free pre algebra tutoring, algebraic simplification, learning distributive property, step-by-step algebra softwear, illinois algebra book glencoe, exponential algebra dilation.
Practical application of fractions, algebra fun, middleschoolmathwithpizzazz.
Glencoe Algebra 2, mcdougal littell algebra i an integrated approach, dividing rational expressions calculator, probability problems middle school math with pizzazz Book E, algebra and explanation, saxon algebra 2 test solutions.
How to interpolate math, poems about algebra, solve algebra 2 problems online free.
Learn how to do algebra, solve my algebra problem, equations used in everyday life, free college algebra practice test.
Foerster calculus, factoring calculator, simplifying radical expressions with fractions, t eighty three online calculator, simplify radical expressions calculator, Algebra EOC help.
Worlds hardest algebra problem, pre algebra textbooks by pearson c, Help with 10th Grade Biology, algebra surface area.
Math workbooks for 9th grade, impossible math problem, rudin solutions ch3, chicago style math, Algebra 1 Answers, monomials solver, beginner algerbra.
Year 11 algebra, a penny a day problem solution, math for dummies online, poems on algebraic equations, freshman algebra problems, geometry problems.
Middle School Math with Pizzazz Book C, teavh me hot to do pre algebra, teach me basic alebra, 7th grade math eog practice, expression simplifying calculator, pearson prentice hall geometry answers, california orkbook pages algebra 1.
Prealgebra 4th edition, algebra answer, rudin analysis solutions, algebra one glencoe florida edition, 5th grade permutation problems, math help algebra 3.
Jlab algebra 2 answer keys, college algebra for dummies, algebra open ended questions, pre algebra study guide, algebra math solver.
Solve math for me, how to solve a finite series, how to solve square roots.
Algebra for 9th graders, What is disjunction in algebra?, math story problem solver, simplification calculator, Matrices made simple.
How to use algebrator?, slove daigrams of algebra, free college algebra software, algebra factoring trinomials help, algerbra.
Mathematical induction solver, the 4th root of 1.927, I want to learn algebra.
Contemporary abstract algebra answer, 2 step algebra equation calculator, Saxon Algebra 2 helps, simplify x3-27, the best of simultaneous equations, Why is it important to simplify radical expressions before adding or subtracting? How is adding radical expressions similar to adding polynomial expressions? How is it different? Provide a radical expression for your classmates to simplify., glencoe algebra.
Show steps for algebra, college algebra formulas, Prentice Hall Mathematics Algebra 1 Answers, math answers free.
Interval notation solver, prentice hall algebra tools for a changing world answers, rearrange algebraic equations.
Inequality calculator, алгебратор, what is the answer to algebra problems, what is a sample of the Iowa alegebra aptitude test, graphing radicals, radical rules algebra, algebra exponent rules.
Saxon math homework answers, algebra1 463-464 answer key, how to learn to do ratios, 9th grade algebra textbook, decimals to mixed numbers calculator, Factoring Polynomials Calculator, 8TH GRADE ALGEBRA PROBLEMS AND ANSWERS.
Algrebra 1 Pennsylvania Prentice Hall, how to do parent functions, ks3 maths free worksheets, i don't understand algebra, free solver for word problems, Free Algebra Answers, Algebra 2 answers for free.
Nonlinear algeba, what is interest in algebra, equation for perfect square trinomials, Algebra Equation Solving Calculator, software library lie algebra.
Algebra cartoons, answers to prenctice- hall algebra, algebra rediness test review, interval notation help, prentice hall algebra 1 textbook online, houghton mifflin trigonometry.
Cpm algebra 1 answers, solve graphing problems, algebra symbols.
Synthetic Division Worksheet, solution solver, what is the domain in alegabra, TI83 cheat, algebra readiness test review, free step by step algebra problem solver.
Distributive property fun problems, algebra begining, factor polynomials for me.
Holt rinehart winston algebra 2, how to pass algebra 2, writing equations worksheets.
University of chicago algebra, algebraic geometry examples, algebracheats.com.
Answer key for glencoe mathbooks, prentice hall algebra 1 answers, mcdougal littell algebra 2 answer keys.
Mcas formula sheet, 2010 taks practise for 6th grader, ti 83 calculator cheats, real life application of quadratic function.
Algebra made easy doc, radical equation simplifier, difficult Multi-step equations, algebra squares for 8 years old.
Orlean hanna algebra prognosis test, If you are looking at a graph of a quadratic equation, how do you determine where the solutions are?, how do i add fractions in algebra.
Free Answer Algebra Problems Calculator, algebra help for 9th graders, radicals (cube roots), apexvs key asnwers for literature, integrated math help, Answers For Glencoe Algebra 1 Book, algrebra.
Pattern and algebra homework, algebra 2 worksheet review logarithms, how to do quadratics, algebra 2 exam.
Prentice hall geometry book answers, Jacobson basic algebra, 5th grade free math worksheets.
Ti 83 algebra downloads, college algebra practice test, fun algebra projects mathematics.
Algebra for dummies pdf, pre algebra brain teasers, basic finite math, sample test of orleans-hannah, free math word problem solver, McDougal Littell Algebra 1 Answer Key, algebra 1 answer key.
Algebra poems mathematics, intermediate algebra seventh edition, pre-algebra readiness test.
Need answers to math problems, what comes after college algebra?, solving multi step inequalities, Munem and West, Applications of quadratic equaltions in our daily lives, formula to test for symmetry algebra, practice workbook answers.
Equivalent form algebra, how to do algebra problems step by step, 1st year Algebra, rationalizing problems, algebra.
Algebra-1 final exam, showing work calculator, free algebra program, Basic Algebra Concepts, trinomial factoring calculator, modern algebra proofs, mcdougal littell answer key for algebra 1b.
Algebra 1 test prep, everyday equations, calculate covariance on ti 83, need help with algebra, mcdougal littell algebra answers.
The university of chicago school mathematics project algebra, California Algebra 1 2009 edition problems, glencoe algebra 2 workbook answers, free pre algebra workbook, Free Algebra 2 Answers.
Algebra with pizzaz, how is algebra used in architecture, algebra 1 teacher acces code, explain algebra.
Algebra 2 workbook answers pearson prentice hall, free math answers algebra 2, show work on algebra, how to explain algebra, factor a problem for me, Help with 9th Grade Algebra.
Distributie property, recurrent decimal, online adding and subtracting rational expressions calculator, distributive property of inequities.
Writing algebraic expressions worksheets, Algebra 1 Lesson plans, Free Algebra Solver, algebra 1 answers, equations used everyday, basic graphing rules.
Carol hannah algebra test, learning algebra 2, simple algEbrA math formulas, Best algebra websites, idiots guide to algebra, basicGeometry final Exam.
Radical expression calculator, an algebra problem worked out, dilation algebra, algebra puzzles, solution rudin chapter 11.
How to work out algebra, example of algebra problem, how to learn intermediate algebra, clearing algebraic fractions.
Substituting values in algebraic expressions, math book answers, operational systems algebra, what is f x in algebra.
Series solver, How to pass an algebra 2 final, Math Textbook Answers.
Can you do fractions on a scientific calculator, algebraic expressions definition, contemporary abstract algebra solution, thinkwell reviews, cat number system pdf download free.
How to do algebra, algebra find rule, excel algebra, how hard is finite math.
Glencoe algebra test, solving funny equations, simplifying algebraic expressions worksheets, rewrite the following expression with positive exponents, Texas Algebra 2 EOC review, college algebra math answers.
Saxon math pre algebra helper, fractions with exponent calculator, what is algebra used for in life, how to solve algebra proofs, rationals solver, free math equation solver, rational number equivalent solver.
College algebra introduction, math software symbols, best work book for math, complex factoring, online solver of differential equation, algebra with pizzazz.
How to work out algebra equations, algebra charts, Fractions Homework KS2, TI85 online, square root variables, write a quadratic function in matlab.
Fraction to decimal chart, c# math symbol &, algebra if8762 answers multiplying a polynomial by a monomial, number line eighths, algebrator inverse, cramers rule 4x4 matrix.pdf, wave equation for beginners.
Applying algebraic factorisation to simplify algebraic fractions, pizzazz worksheets free, Third Grade Distributive Property Worksheet.
\math forumula for percentage, slope worksheets that answer A riddle, functional equations in matlab, alegebrator, Krystal bought a refrigerator from a rental center for $1,050. She makes 16 monthly payments of $112.75 with her credit card. The rental center charges $1.25 for every payment made with a credit card. What is the total cost of the refrigerator?, free online foil calculator.
Algebraic calculator online compound inequality, automatic simplifier, multiplying negative decimals worksheet.
Free algebra software program, math word problems with negaative slopes, subtraction inequalities calculater, pdf exercices maths solve by factoring and completing square, apex algebra 1 answers.
Math Formula for Percentage, 19, rearrange formula calculator, chessboard ks2 perimeter answer.
Excel intercept explained, remainder theorem solver, find the possible general nth term calculator, calculator long equations, difficult acceleration worksheets.
Quadratic simultaneous equation solver, Simplify Complex Radicals, glencoe, lesson 3-1, graphing linear equations worksheet and answers;, nonlinear ode calculator, complex rational expressions worksheet.
Directrix calculator, factoring in middle school, nth term calculator, in multiplying or dividing, should you report the answer with the greatest or the least number of significant numbers in the equation?, linear equations fun.
Download algebrator, Java MathBasic, laplace calculator step by step, bisection calculator online, multiplying two monomials worksheets, Develop a system of equations that would provide the number of single rooms and double rooms and show the solution of these equations, Linear equation activity sheet tes.
Solve two simultaneous equations of third degree, geometry equations, poem with algebraic expression, matrix factorization where c is of the form +matlab, mit advanced college algebra mixture word problems, radical expressions calculator.
Contrast solving a linear equation with moving weights between the two sides of a balance scale., ti 84 consecutive numbers programs, PROBLEM SOLVING FOR PERCENTAGE BASE AND RATE, Orleans-Hanna Algebra Prognosis Test, a(b+c)=ab+ac, exponents, multiplying square roots calculator.
Kuta software infinite algebra 1 absolute value inequalities answers, convert fraction into decimal, practice book answers pg151.
Code le la route algerien +pdf, TI Calculator that solves Laplace, teorema algebra solver, adding subtracting multiplying integers, adding and subtracting trig identities tangent.
Sample kumon worksheets, algebrator, Fractions in Simplest Form Calculator, factors and mu;tiples worksheet, powerpoint on ordered pairs, Pictures of Quadratic Graphs worksheet, two step equations fun worksheets.
Algebra ks3, holt algebra 1 workbook answers, simlplify fractions using exponents worksheets, +algelbra least common denominator calculator, multiplying and dividing rational expressions free calculator, the algebrator.
Answer key to Review What You Know About Solving Linear Systems p. 76, solving simultaneous trig equations using matlab, it and mit aptitude test past papers in moratuwa, prentice hall algebra 1 practice workbook answers chicago, 7th Grade Math For Dummies, simultaneous equations solver quadratic and linear.
Adding fraction equations precalculus, example of mathematical software, kuta software infinite algebra 2 finding slope from a graph answers, balancing equations, a interesting project on arithmetic progression in daily life, work book to solve c programs yahoo, primary software.
Rational Focal Point date expressions, contemporary math lessons, ptt conceptual problemsfirst order differential equation.
+sample word problems on finding the base, percentage, rate, 2007 Holt Algebra 2 Michigan Answer Key, negative number ruler, addition table for binary number.
Consumer theory exam book +Pdf, exponential equations multiple choice, mymathlab cheating, Algebrator, complex rational fractions calculator, long hand multiplication calculator.
"homeworks and solutions" "matlab" fileytype=pdf, fraction integer graph, printable glencoe radical and roots quiz with answers.
Two step word problems on addition and subtraction of decimals, year 3 optional sats papers 1998, math trivia algebra question and answer, chemistry addison wesley fifth edition answers.
Grade three free maths first term test paper, solving math tough math problems, kuta software infinite algebra 2 resource master, multiply mixed numbers, that shows fractions.
Examples of math poems, pre calcalus math solver, kuta software algebra 2 solving systems of equations by substitution, pre algebra worksheet DISTRIBUTIVE PROPERTY and INEQUALITIES.
Matlab functional equation, 11th grade math problems worksheets, solve algebra equations with radicals calculator, mathematics investigatory, solving for the given variable calculator, Convert scientific notation to decimal MATLAB.
Numerical methods for chemical engineers: flash separator calculation +pdf, algebrator free download, Math equasions worksheet works pdf, problems of solutionsfrequency and distribution and graph.
One step inequalities+worksheets, dividing rational expressions calculator, decimal fraction chart, solving differential equations ti-89, rational root calculator, gaussian elimination vectors, absolute value and exponents worksheet.
Free prealgebra software, free 5th grade worksheet of square root, tree quarters of one percet as a decimel, simplifly maple, xlwt Formula ctrl+shift+enter, high school math maple worksheet.
Ebook of limit maths, worksheets on finding the percentage rate and base, death calculator +formula, formula to fit a 2nd order curve, hard u substitution problems, A certain mountain has an elevation of, algebrator download.
Simplifying a ratio of polynomials, pre-algebra with pizzazz 241 worksheet, example ladder programming example +pdf.
Boolean algebra reduction online calculator, "find x" mathematics "free worksheets" "grade 7", free ks2 worksheets writing brackets, partial quotients printable worksheets, Least Common Multiple Chart, answer to the chapter 4 test a mcdougal littell math course 2, based on the information given for each of the following studies.
Glencoe radical and roots quiz with answers, long hand multiplication decimals calculator, least common denominator calculator, linear inequalities summary, communtive property of multiplcation free work sheets.
Zero factor property calculator free, differential equation + worksheet + doc, proof for "cauchy-euler system", logarithms for dummies, Rational Expressions Calculator solver multiplying, ordered pair linear system calculator.
Kuta algebra for 10 grade with solutions, name 3 states that have the mississippi river as the border, simplifying radicals with radical prison, Asymptotes notes and printable worksheets.
Decimal multiplication integers homework, free linear equations worksheets, define addition and subtraction,multiplication and divisionof fracions to class 4th, example of symmetric property, free algebra cheats, 9-1 Skills practice Multiplying and Dividing Rational Expressions Glencoe Algebra 2, algebraic calculator with inequalities.
Holt algebra 1 answer key, Kuta Software-Infinite Algebra 2 Simplifying Radicals answer sheet1-34, year 8 maths programme, least common denominators for rational expressions calculator, math worksheet stretching machines, what is the dictionary meang of 'problems' and 'challenges' +pdf +powerpoint.
Literal factor algebra, factorization of algebraic espression using hcf for juniors, pre-algebra with pizzazz test of knowledge, how matlab solving differential equations +pdf, addition of radical expression lesson plan, List of All Fractions, dividing mixed integers.
Adding subtracting multiplying and dividing integers, kumonworksheets, calculus with applications, adding and subtracting radicals calculator, factorization questions, rational exponents 9th grade.
Divide polynomials calculator, 2558708, abstract algebra ppt.
Arithmetic with Polynomials and Rational Expressions assessment plan, quadratic equations & quadratic inequalities calculator, printable study guide and Orleans-Hanna Algebra Prognosis.
Convert decimal to octadecimal, math equation and problem solving revission paper,, level 14, algebra 2 - quadratic expressions calculator, translating sentences into variable expressions calcultor.
Modeling with one-variable linear equations and inequalites packet jed, logrhythm spiral formula, stem leaf plot worksheet word problem, example ladder programming operation example +pdf, solve math differential equations calculator.
Algebraic calculator with inequalities online, exponential function, holt rinehart and winston algebra 1 answers, algebra 1 practice workbook online answer, solving system of linear equations with Excel, second order differential equation in matlab, gce a math december 2000.
Bbc maths LCM fractions, elementary algebra practice problems, codigo para calculo de factorial con una funcion factorial(int x)+c++, algebra structure and method pdf.
Solution "difference equation using matlab", simplify radicals using cake walk, free slope puzzle, kuta software infinite algebra 2 systems of two equations answers.
Dividing negative numbers, factoring difference of squares worksheet hard, how do you write one eights on calculator, Prentice Hall Mathematics free printable Answer Key to graphing equations in slope-intercept form, explain math worksheets.
Zero and negative exponent worksheets, what is 125 +CUBED v, equivalent fraCTIONS.
Inequality multiple choice worksheets, "Worlds hardest chemical equation", binomial theorem program, 4 bit binary multiplication, trigonometric equations with factorising worksheet.
Lcd calculator, beginning trigonometry worksheets with answer key, rational expressions calculator, 4, holt physics solutions 2c, calculate Nelson Complex number.
Absolute value of complex numbers worksheet, solve function online, gcm in math, The President's Council on Fitness asked adults who exercise if they walk, run or stretch. Here is the Venn diagram of the results., where does bearing +mathematics.
Comarision between synthetic and analytical thinking +PDF, algebra dimonds, Funny Algebra jokes finding x, math factoring.
9th grade algebra problems, finding the perimeter of radicals, square root method formula.
Excess 3 to BCD conversion Using Gates, 7, algebrator for mac, excel matrix operation, trinomial cube formula, offset slider-crank calculations.
Algebratopr, solving compound inequalities prerequisites, negative distributive property worksheet, Converting irrational expressions, solver for rationalize denominatior, Rational Expressions Calculator with Steps, tick matlab.
Number line to 100, directed numbers worksheet, list of algebra formulas, Solve the inequality and enter your solution as an inequality comparing the variable to a number..
Subtracting equations worksheets, solution manual on cost accounting 7 edition by matz usry +PDF free download, free algebra calculator online, trigonomic rules, math photo.algebra.
Expression for 2,4,8,16, how to multiply fractions, scale factor worksheet, how do you say multiply and divide in spanish, free pre made lesson plans polynomials, fractional exponents with radicals calculator, multiple variable polynomial division C langague programming.
Multiplying monomials and polynomials worksheet, distributive property calculator, how to convert a radicals to decimals, multiplying and dividing rational expressions calculator for free, full subtractor truth table, rational equations calculator.
Progress monitoring 2 minute time test, change standard form to slope intercept form filetypeppt, batticaloa and paton beach, weegy . comq-1/2 > 2/3 what is the inequality and graphing the solution, math interactive games " literal equations".
Matematical excersices, simplifying positive and negative fractions worksheet, +how to calculate the value of p+2p.
Examples and exercises with solution on Special Products and Factoring pdf, maple print to 2 decimal places, cube model problems second grade, +ks3 high school answer sheet for 2R homework booklet, hundredths grid.
In order to find the x intercepts of a ratinal function of the form f(x) =p(x)/q(x), that is in its simplist or reduced form, one should?, base five addition table, solving linear equations worksheet, addition regrouping worksheets 5th grade.
How to factor x^3+3x+1, math story problems with negaative slopes, powerpoint presentation in trigonometric function, mathematic accounting examples, fistin math, engineering equation solver, plenty thanks graph.
Java big decimal/compound interest examples, henderson hasselbalch calculator, content, adding subtracting multiplying and dividing with scientific notation.
Solution algebra hungerford chapter 4.5, square roots with exponents, mathematics worksheets parabola, how to find zero without knowing the equation in matlab 2010.
Multiplying and dividing decimals worksheets, برنامج لحل مسائل الجبر, math games for kids.cybe, holt algebra 1 answer key free, proportion to solve ratio solver, prentice hall algebra 1 workbook answers, +how can i divide useing partial quotients.
Rational functions and simplifying rational expressions, maple worksheet, high school math, difficulty to understan is it adding or multiplying word problems, banking applications of arithmetic sequence, 3,3,6,18,72 - grade 7 math, LCD calculator.
Math trivia with answers, pyramid algebra, igcse math long division, leaner equation, +sum of factorial in fractionn programs in c++ using function.
How do we use polynomials in real life, radical and roots quiz with answers, When would you use factoring?, graph the linear inequality generator, more about quadratic equations, dumitt, modern algebra pdf .
Multipliing decimals calculator, kg car slams on the brakes locking the wheels. A total retarding force of, quick free test for 9 yr old, adding subtracting multiplying and dividing fractions.
Algebra inequality calculator, explanation of euler about arithmetic progression in daily life, "subtracting a fraction from 1" worksheet, intermediate math quick images, decimal into quotient of integers 5.98..., excel, CTRL+SHIFT+ENTER.
Synthetic substitution practice, mathematics, o-level, exam problems, simplifying cubic root equations, algebra word problems worksheets with answers, proportionality equation - use graph to find exponent, free online dividing polynomials calculator.
Math formulas for the gre, linear equalities in 2 unknown, permutation problems and solutions, free expotential and like term math worksheets, factorization of algebraic binomials using hcf for juniors.
8 is what percent of 40, equivalent fractions, absolute value and exponents, what kind a think comes in add number.
3, parabola primary worksheet, simplify exponents algerbra.
ribe the proocedures for solving linear inequalities using a graphing method.
"two variable linear programming"+"solved problems"
a square garden plot measures 125 square feet. A second square garden plot measures 405 square feet. How many more feet of fence will the second garden plot require over that required for the first garden plot?
free essay five paragraph essay math story/ application problems addition,subtraction,multiplication,and division "add,subtract,multiply,divide"
"christmas worksheets for 8th graders"
Diamond method math, 9th math vocabulary definitions algebra 1, simplifying radicals worksheets, integers quiz grade 7, distributive property worksheet, geometry tiling, mcdougal littell algebra 2 answers.
Nth term solver, inverse formula 9th grade math, radical form calculator, combination method, algebra worksheets for 5th grade.
Online math for 7th graders, simpllify algebra, iowa algebra readiness test and sixth grade algebra.
How to simplify givrn answers in exponential form, how to solve aptitude questions quickly, Assignment 08.06 - Solving Equations with Radicals, double integral problems and answers, 10 easy polynomial problem solver, six grade math problems worksheets, Solving Cubic Equation in Excel.
How to solve factorial equations, 9th grade geometry worksheets, solve algebra problems with fractional exponents, excel solver polynomial, imperfect square roots.
Year 9 online math tests, online trinomial factorer, slope intercept form worksheets, probability worksheet 2nd grade, 9th grade biology tests, synthetic division mathtype.
Gee 10 grade math, homework sheets to do online, algebra substitution method calculator, rearranging formula calculator, online Holt, Rinehart and Winston Algebra 1 teachers edition online resource, logs of fractions, Plotting Points worksheets.
Factor finder online, 9th grade algebra games, operations with radical expressions calculator, factorisation calculator, algebra de baldor, math shading worksheets, trigonomic identities solver.
Simple proportion, worksheets for 5th grade math and ratios, Solving for Radius, 7th grade simplifying radicals, holt math 6th grade workbook, partial fractions calculator.
Permutations and combinations Free worksheets, how u find square root and cube root, two-step equation worksheets.
Quadratic factoringcalculator, applet factors of polynomials, texas taks 6th grade math 2010 PRACTICE TEST, quadratic formula table, 100 7th grade integers questions, matrix solver step by step, Math transformations.
Factorising quadratics calculator, ks3 formulas, solving squares, quadratic binomial, radical equations worksheet, formulas of mathematics of class 10th.
Grade 5 mathematics exercise, combinations and permutations matlab, relating algebra to real life.
Math type 5.0 equation, finding LCM +formula, multistep equation worksheet, 9 grade history game.
Hot to do multiplication of monomials and binomials, algebra de baldor online, simplify radicals worksheet, multiplying binomials game.
9th Grade Math Practice Worksheet, solving aptitude questions, calculating square meters to running meters, graphing simple compound inequalities printable worksheet, equivalent expressions worksheet, adding and subtracting radicals homework.
Online radical calculator, formula for expanding brackets, Calculator that can factorise quadratics, solve system of equations by graphing using math cad, exponent +simplifyer, factorial equations to solve.
9th grade math questions and answers, dividing binomials by binomials calculator, square cube formula, 7th Grade Math Worksheets, polinomials.
Algebra 1 permuations and combinations worksheets, adding and subtracting integers worksheets, algebra chart TAKS, gre formula sheet.
Linear equation calculator, 2nd grade volume worksheet, equation graph maker.
Two step equations worksheet, step by step derivative solver, how simplify radical 1690, online radical simplifier, volume worksheets 4th grade, transposition of formula calculator, how to find the eigenvalues of a matrix ti 83.
Laplace calculator, trigonomic identities, Math TAKS formula chart, what is a second grade function formula, equation grade 9 -12.
Inequality number lines, proportion worksheets sixth grade math, solving complex fractions algebra, "taks" exponent questions logs, 10 class maths formulas.
9th grade word games, expand function calculator, trig identiites calculator, trinomial factor solver, factoring linear equations, factoring quadratics worksheet, radical math excel.
Converting radicals into entire form, matlab quadratic form plot, limit solver step by step, ez grader online, completing the square practice sheets, how to do radical form worksheets, permutation and combination properties.
Evaluating expressions ti 89, free worksheets combinations, multiplying and dividing monomials worksheet.
Combinations work sheet, Formula for Scale Factor, log solver online, printable maths mat, transformation worksheets 4th grade, laplace calculator online, 6th grade math homework sheets.
Simultaneous linear equations in three and four variables, inequality simplifier, rationalize the denominator online].
Boolean expression simplifier online, highest common factor and lowest common multiple worksheet, simplifying products of radicals, solve my math problems for me.
Statistics equations cheat sheet, online scientific calculator ti-84, oxidation numbers worksheet, standard form calculator solver, monomials solver.
Ks2 maths worksheets, substitution calculator online, 63 simplied radical form.
Radical form definition, factorial equation, factoring worksheets, second grade, simultaneous equations, transformations math grade 6, factoring polynomials worksheet, hands on equations quiz.
Simple equations worksheet, factoring using the distributive property worksheet, 10th grade geometry formulas, easy combining like terms worksheet, laplace transform online.
Factoring cubed equations, boolean algebra online, online percentage solver, factor machine online.
Parabola problem solvers, college algebra formulas, how do add fractions and simple radical numbers, probability for 7th grade, factoring binomials cubed, binary division step by step.
Cube root formula, Holt, Rinehart and Winston Algebra 1 teachers edition online resource, which binomial is a facter for the quadratic, pre algebra charts pdf, how to adding binomials and monomials, formula chart geometry.
Simplyfying radicals worksheets, caculater, ordered pairs worksheet fun.
Rearranging formulae questions, how to find log on ti 89, factoring complex numbers, the function machine, algebra factoring chart, tape measure cheat sheet.
Percentage equation solver, substitution calculator algebra, online chemistry solver, taks math formula chart mathematics.
Computing with fractions, algebraic expressions worksheet, permutation and combination for sixth grade, grade 9 algebra worksheets, 9th grade geometry.
Percentage sums, rearranging equations solver, 6th grade printouts, graphing Absolute-Value Inequalities in excel.
Double integration solver, dividing binomials, circle printouts, ti30 calculator online, 3rd grade math answers, equation domain finder.
Divisibility printable worksheets, polynomial divider, standard form solver.
8th taks formula chart, grade 9 mathematics exam papers, Permutation & Combination equation, SIMPLE ALGEBRA PROBLEMS TO FIND X FOR 5TH GRADE.
Practise SAT papers algebra, free permutations combinations worksheets, transforming formulas algebra, math worksheets 6th grade, multiplying expressions calculator.
Math books for 7th graders, copies pre algebra reference sheets, 5th grade exponent worksheet, symmetry worksheets for 2nd grade, holt mathematics 6th grade, algebra readiness test, "decimals exercises".
College algebra math problems, holt pre algebra test masters, Guide to transposition of formulae, multiplacation.com, 10th class maths formulas, 4th grade trivia.
алгебратор онлайн, Improper integration calculator, texas taks 6th grade math PRACTICE TEST2010, online trig identity solver, algebra honors 7th grade worksheets.
Math games proportions, step by step instructions to predicting products of chemical reactions, ordering integers calculator.
TAKS 3rd Grade Reading Worksheet, integral calculator online step by step, factoring polynomials solver.
Tenth grade geometry final test, only formula maths 10 class, iaat test practice, trivias about math.
Square root property, is there a dividing radical calculator, 6th grade math eog help, exponential power problem simplifier, proportion worksheet ks2, factorization of trinomials worksheets, simple algebra worksheets grade 3.
Comulative property, Simplify radical y10th, log2 calculator, gcf of monomials calculator.
Scale factor problems solving powerpoint, algebra, fraction to percent, algebra formula chart.
Algebrator free download, printable algebra readiness test, Printable Math Worksheet for 8th Graders, fraction solver.
Thing to know algebra1, quadratic equation simplification, exponent simplifier, factor binomial calculator, easy permutations and combinations worksheet, factoring binomials worksheet.
Easy steps for solving Aptitudes beginners, quadratic graphs with fractions, linear algebra simplified.
Expand radicals, trigonometric identities calculator online, 9th grade division problems, Aptitude simple equations, 6th grade math taks requirements in texas, taks 8th grade math formula chart, polynomial calculator solver.
Rationalize radicals calculator, rearrange equations online calculator, rearrange formula calculator, ratio solver online, foil calculator, 7th grade pre algebra test.
Simplify logarithms calculator, radical calculators, online algebraic mcqs, online chemistry problem solver, Subtracting Radicals, online radical expressions calculator.
Factor polynomial calculator, math solver, alegbra grade 4.
Proving trig identities calculator, texas 8th grade algebra test online, matlab quadratic equation, quadratic relations grade 10.
Divide fractions worksheets, linear equations and worksheet and 6th grade, practice 6th grade algebra tests, formula of 10th math, mcdougal littell algebra 1 answers, solve by square root property calculator.
Rational equations worksheet, prove trig identities solver, 10th class formula.
Factorise quadratics calculator, percentage math solver, trivia about trigonometry, interpolation online.
Mcdougal littell inc answers algebra, compound interest math worksheet, 9th grade geometry games, expanding function calculator.
8th grade algebra test, maths equations year 8, 5th grade measurement worksheet, grade 5 intergers, mathematics formula chart, seventh grade algebra.
Tslib quadratic plugin, gre math formulas, algibra, holt 2004 algebra 1 book download, multiplying radical expressions.
How to find the vertex algebra, dividing radicals worksheet, factoring cubic polynomials worksheets, divide radicals steps, easy equations fourth grade.
Factorise machine, 7th grade math eog practice, line plot worksheet elementary, online simplifier.
"funny math function", algebra worksheets for grade 8, multiplying radical calculator, linear equations for 5th graders, 9th gradeGeometry games, solving nonlinear equations in matlab.
Multi-step equation generator, trig identity proofs solver, 6th grade geometry test online.
7th grade eog practice worksheets, online double integral calculator, factoring calculator for polynomials, kumon practice, proportion worksheets pdf.
Funny percentage formulas, free middle school math worksheets, Formula for calculating square metre, quadratic equations in daily life, solving cubic functions in excel, ks3 maths printable worksheets.
Online chemical equation solver, polynomial simplification calculator, definition of percent and formula, quadratic ganes, 6th class maths new syllabus.
Improper integrals calculator, rotation worksheets, grade 9 algebra test.
Quadratic formula game, understand function machine algebra, online calculator for identities, radical expressions calculator online, transformations grade 6, ppt on linear differential equation, MATH PROBLEMS FOR 8 GRADERS.
Daily use of rational number, quadratic equation simplifier, ucsmp advanced algebra, radical quiz, quadratic fractions, combinations 6th grade worksheet.
Math dilations worksheet, factorising equations online, geometry for 1st grade, math topic sheets.
Algebra calculator trinomials, calculator to solve the equation by the square root property, algebra percent problems, monomials worksheet, math quizzes for 9th graders.
Sample math 8th grade, eighth grade fraction worksheets, proof solver, simplifying complex exponants, linear equations calculator, 10th grade geometry, algebra test for year 8.
Everything i need to know in 7th grade workbooks, quadratic sequence solver, trigonometry worksheet [doc], Glencoe nc math sample problems grade 5, algebra inequalitie word problems, formula sheet for pre algebra.
Zero property calculator, simplifying radicals online calculator, 8th grade math for dummies, draw ellipse in matlab.
Plotting pointsworksheets, online factor finder, online calculator that shows work, grade mnine maths, matlab combination, free math worksheets with combinations, rewriting linear equations.
Simplifying a complex fraction calculator, factoring trinomials solver, McDougal Littel books online, simplifying rational expressions calculator online, solving quadratic polynomials for dummies, figure out quadratics caclator.
Equation fraction worksheets, integrated algebra worksheets, trigonometric functions solver, rearranging formulas calculator, integration solver, FIFTH get to know you worksheets.
Formula rearranger, do math worksheets for 5th graders, online equation grapher, understanding non linear inequalities.
Linear function solver, online quadratic finder, online integral calculator step by step, algebraic equations worksheets, compound interest math worksheets, algebra problem solver.
How to make a curved graph on mastering physics, 6th grade holt math book answers, exponential algebra dilation, exponents worksheets grade 9, exanded notation calculator, Double Radical Equations, kumon pricing in austin, tx.
Arcsin calculator, 3 degree equation solving software, what is the hardest formula of any math, ratio proportion worksheets, partial fractions solver, solve equations online polynomials, eog practice tests for 7th grade math.
Operations with Radical Expressions Solver, who invented the quadratic equation, line graph worksheets, polynomial factory solver, solving complex fractions, algebraic equations solver.
6th grade science worksheets, printable SOL tests for fifth grade, 7th grade spelling worksheets, substitution calculator, solve redicals, complex percent formula, questions on graphing inequalities 6th grade math.
Ppt exercises on multiplying monomials, rearrange equation calculator, Operations with radical expressions, integer online calculator, online partial fraction calculator, mathtype 5.0 download, declaring bigdecimal.
4th order equation solver, calculator that shows work, show me how to do geometry formulas, Geometry cheat sheet, online matrix solver, algebrator free.
Polynomials Factor calculators, simplifying exponent worksheets, seventh grade math eog's online, mathematical formula chart, trig proof solver.
Expand and simplify polynomial, where to buy kumon material, free printable factor tree worksheets, formula chart for geometry, formula chart mathematics, ez grader on line.
Root solver, solving radical equations activity, formula chart for algebra, second grade equation, 9th grade algebra worksheets online.
Algebra scale factor, rational equation simplifier, algebaic expressions for 6th graders, linear graphs worksheets, how to solve for x on ti 84, teaching in radicals, simple equations worksheet.
Fraction word problems calculator, java linear system solver, solve equations with square roots, 10th standard maths formulas, calculus problem solver online.
Algebra math test online 6th grade, georgia algebra1 eoc, laplace transform calculator.
Finding volume worksheets, online algebra calculator, area and perimeter fifth grade test, class 10th maths formulas, what is standard radical form, Integer Worksheets for 7th Grade.
Solve polynomials online, simultaneous equations worksheet, simultaneous equations solver, exponential inequalities, vertex solver, solving complex radicals geometry.
Simplifying quotients with radicals, inequalities square root, gr 9 matrics.
Kumon Worksheets Online, how to plot a ellipse matlab, simplifying radical expressions with fractions, quadratic sequences solver.
Algebra baldor, trig identity calculator with working, application of quadratic equations in daily life, basic college algebra formulas, converting to radical form, online formula rearranger, radical simplification calculator.
Online boolean calculator, 7th grade EOG math worksheets, math percentage equations, Factors Year 6, geometry worksheets gr. 14.
Solving logarithmic inequalities, graph creator from equation, Dividing Radicals, interpolation online calculator, compound inequalities worksheets, 6th grade printable math sheets, free printable ratio/proportion worksheets.
Creative ways to teach algebra, math worksheets + ratios, algebraic expressions free worksheet, need a graph for cube root function for equation of an inequality, matrix differential equations in matlab.
Inverse quadratic equation, algebra tiles online, 5th Grade Math Worksheets, worksheets, finding slope printable, factoring polynomials online calculator, algebra worksheets 7th grade.
Algebra 1 formulas, Algebra EOC help, polynomial factor calculator, trig trivia, algebra 2 parabolas free answers.
Math venn diagram worksheet, online factor polynomials, 2nd grade everyday math.
How to solve aptitude problems, hard math trivia, solve quadratic equation matlab, iowa algebra readciness, multiple square roots.
7th grade math sheets, holt algebra 1 online textbook, prime factorization worksheets, equatest.
Test for math for 6th graders, Word problems with Radicals, kumon worksheet, writing in radical form, simplest radical form calculator.
Math tutor scaling, HISTORY OF FORMULA PIE, fraction into decimal, ohio 7th grade math worksheets, fraction tiles printable.
7th grade slope test, formula chart for 8th grade, algebra inequalities worksheet, equivalent fractions solver, equations of circles ellipses chapter test, function factorize tool.
My alegbra, iaat sample test, simplifying radicals ti-83, summation calculator.
Math problem solving for six graders that are worksheets, formulas of mathematics for 10th matric, 7th grade algebra worksheets, formulas in aptitude.
Graphing parabolas online calculator, geometry formula chart, taks exponent questions, graphing linear equations online test, graphing inequalities 6th grade math.
Algebra EOC, solve binomial factors, rationalizing denominators, 9th grade biology quiz, maths printable worksheets ks3.
9th Grade Algebra Sample Problems, 6th grade math worksheets, college algebra worksheets.
STANDARD RADICAL FORM, algebra with pizzazz, 6th grade intege, calculating scale worksheets, binomial pdf, algebra projects for sixth graders.
Printable homework for 5th and 6th grade, EXPONETIAL CALCULATOR, free worksheets for third grade teaching volume, inequality 7th grade worksheets, booleaanse algebra online.
Y-intercept calculator, foiling radicals, dilations math worksheet.
X intercept calculator, difference of two squares worksheet, combining like terms worksheet.
Quadratic functions solutions flowchart, laplace transform online calculator, elimination calculator online algebra, free algebra factoring test, predicting products of chemical reactions, using matlab to rearrange an equation, TAKS algebra formula chart.
How to figure the ntop of parabla, volume worksheets for 4th grade, partial fraction calculator.
Physics formula worksheet, educational 9th grade games online, gee 10 grade math tests and examples, how to calculate a radical in excel.
Factorisation A=LU+homework, simplifying radical with similarity ratio, XTHMATHS FORMULA, radical expressions solver, expending calculator, simplifying square roots worksheet, math cheat machine.
Graphing complex numbers, algebra solver, printouts for 3th math, solving exressions with integers worksheet, complex fractions and the LCM calculator.
How to solve triple inequalities, Adding compatible numbers worksheet, applet to solve second order differential equations, online factoring calculator polynomials, trig identity calculator.
Simplifying integers calculator, Texas 7th grade math worksheets, partial fraction calculator online, extrapolation online calculator, algebra de baldor on line, factorising calculator, cool maths for kids algebra.
Trig identities calculator, prentice hall algebra 2 online textbook, exponentials and radicals, math trivia questions, Seventh Grade Math Slope, gauss elimination using TI-89 step by step -jordan, simplifying complex fractions with variables calculator.
8th grade geometry worksheets, Hyperbola in Real Life, quadratic formula worksheet, how to solve factorial problems.
Complex system of linear equations in real life, factor equation c#, algebra graphing linear equations worksheet.
Algebra solver step by step, dividing polynomials by binomials, free math worksheet on permutations and combinations, grade 11 half-life math problems, Step by step break down of linear equations, trigonometric identities printable page, contemporary abstract algebra solution.
Algebra tiles worksheet, 8th grade inequality help, integer worksheets, step by step integral calculator online, TI-84 plus online, free radical equation solver.
Seventh grade proportions, Exponents and square roots worksheets, example of quadratic polynomial.
Equations fractions calculator, probability solver, linear graphing worksheets.
Hands on equations worksheet 11, math for dummies online, fraction word problem for 3rd graders, laplace online transform, TAKS MATH TEST, are all liner equations functions.
Dividing cube roots, fraction subtractor, combining like terms calculator, 6th grade scale factor, factoring binomial calculator, how to solve nonhomogeneous system, grade 10 exponents test sheet.
Binomial factorization, algebra in third grade? why?, 4th grade fractions questions, free permutations and combinations worksheet, slope of a quadratic equation, expression worksheets+math+grade8.
Powerpoints and equations and pre algebra, 8th grade taks chart, computing fractions, worksheets of hands on equations, 4TH GRADE GEOMETRY MATH WORKSHEETS, combinations worksheets 5th grade.
5th grade variables worksheet, cool mathforkids.com, solving subtraction equations worksheet.
Triangle linear interpolation java, 6th grade glencoe math, 6th grade pre algebra.
Free combining like terms worksheets, compound fractions calculator, factoring calculator step by step, math practice for 7th grade EOG.
10th grade geometry problems, logarithmic equation solver in matlab, Quadratic equation c#, parabolas solver, booleaanse algebra onine, standard form of a linear equation calculator, distributive property worksheets.
Optional mathematics question solver, online alrgebra graphing program, seventh grade pre-algebra online book.
Trigonometry for dummies online, Permutations worksheets, algebra for 7th graders, What are some examples from real life in which you might use polynomial division?, algebra graphing linear equations calculator.
Maths mcqs, long division calculator shows work, online ti-83 emulator, glencoe pre-algebra practice workbook answers.
Worksheet square number ks2, solve radicals online, basic rules of graphing an equation or inequality, eighth grade print outs, Fourth Grade Geometry Worksheets.
Cube root tricks, inverse proportion worksheet, expression simplifying calculator, test on polynomials grade 9, multiplication ladders, simplifying trigonomic identities calculator, www.algebra.com.
A list of fractions from least to greatest, www.learnlogarithmsonline.com, inequality solver, helpful statistics cheat sheet, printable 7th grade math sheets, 6th grade printable math worksheets, 7th grade math taks test.
Expanding calculator, standard to vertex form calculator, evaluate formula algebra, solve triginometry, ged algebra worksheets.
Plotting fractions on a number line, plot a quadratic form, 7th grade math slope.
Math solver: rationalizing denominators, 8th grade math formula chart, boolean expression simplifier, tenth maths formulas, expand calculator, 9th class math book free download, 5th grade solving equation.
Monomial equations, how to solve equivalent expression, calculator that shows working out, ratio and proportion worksheet with answers.
Partial sums algorithm worksheet, radical multiplier, algebra worksheets ks2, Online EZ Grader, Statistical Formulas Cheat Sheet, trial and error problem solving activity sheets.
Math worksheets 5th grade lattice, online integer calculator, arcsin online calculator, transposing trigonometry, simplifying the radical expressions fractions, divisor fourth grade.
Ks3 maths printout worksheets, trig identity solver, integers worksheets, 1st grade math sheets, algebra simplifier, calculate integers, multiply square roots calculator.
Permutation and combination worksheet, arcsin Calculator, linear equations range, online logarithm solver, how to simplify exponent algebraic equations, integer puzzles, geometry cheat sheet.
Free adding integers quiz "adding" -subtracting -multiplying -dividing, polynomial factoring calculator, formula chart 8th grade.
Multiplying square roots calculator, inventor of quadratic equation, how do you foil with 3rd degree, referece sheets for hard algebra, formula in getting percentage.
Algebra change linear units, polynom solver, quadratic expression factoring calculator.
Decimal to fraction ti89, mathematics formula pdf, solve simultaneous exponential equations "exponential", ti 84 synthetic division how to program, rearranging formulas.
Basic algebra explained, linear equations generator, calculations, pie formula, algebra formulas sheet free, polynomials in real life, linear algebra cheat sheet.
Algebra math shading worksheets, compounding interest worksheets, gre math formula sheet, calculator with pie, iowa algebra readiness, ti 84 plus algebra programs.
Factoring binomials calculator, nonlinear differential equation with MAPLE, simultaneous equations matlab, binomials worksheet, mathtype 5.0 equation, ti 84 radical expressions.
Trinomial to binomial, simplify radical expressions with fractions, trigonometric identities calculator, logarithmic equation solver, es on factors and multiples.
Dilation worksheets, algebra step by step, math games for 9th graders online, online simplify radicals calculator, algebraic factorization, show work on algebra, taks mathematics formula chart.
Algebra test, laplace calculate, algebrator online, 7th grade proportions, 9th grade taks test review.
Geometry Test 10 grade, algebra 1 answers for mcdougal littell workbook, Printable Number Line Worksheet, trig formula chart, pre-algebra textbook online, math 6th grade printable.
Ratio proportion ks2, 2 grade homework sheets, algebra with pizzazz worksheet p 115, www.algebra-test.com, Effortless maths game, kumon worksheets online, 5th grader worksheet printouts.
Simplify online, formula transposition calculator, activities to teach fractions to grade7.
Ez grader download, 6th grade multiplying integers, algebra formulas pdf.
Mathematics formula chart 10th grade, 9th grade Geometry games, formula rearranging calculator, really hard quadratic math problems, hands on equations worksheets answers.
7th grade Integers quiz, homework cheater, problem with fraction homework sheet.
Graping x cubed, DAILY use of rational numbers, strategies for problem solving workbook, simplifying square root fractions, standard radical form, boolean algebra solver.
YEAR 8 MATHS TEST, complex radical slover, pre-algebra formula chart, taks test formula chart, maths formulas for 10th class, simplify inequalities calculator, 10th grade geometry assessment.
Gauss elimination using TI-89, algebra inequality problems, balancing equations powerpoint, how to solve cube problem in aptitude, line plot elementary, 8th grade math formula chart, free algebrator download.
Trigonometry basic ppts, factorising equations calculator, how to slove a liner system, factor finder, free 3rd grade ebooks, how to do divison.
Glencoe algebra II resource master download, multiply radicals calculator, practice math for 9th grade, subtracting integers worksheet, graphing integers worksheet, sat 6th grade printable worksheets, 5th grade algebra worksheets.
Solving radical equations worksheet, easy trig equations worksheet, volume worksheets.
Adding and subtracting square roots worksheet, zero factor property calculator, grade 6 transformational worksheet, online summation calculator.
Buy holt algebra I textbook, simplest form fractions calculator, decomposition math, worksheet and division of radicals, calculate venn diagramm online.
Complete the square ti-89, "Geometry cheat sheet", permutation matlab, online math for 8th graders, algebra help substitution calculator, geometry 8th grade.
Matlab rearrange equation, online equation solver chemistry, investigatory project in math, "linear algebra worksheets", download a ez grader, 4th grade volume worksheets.
Square roots matlab, algebra simple and math solver, domain and range in linear functions, download algebrator.
Balance math equation worksheets printable, online calculator arcsin, radical equation solver.
3 degree equation solver, solve quadratic equation in matlab, decimal multiply and divide worksheets, 9th grade algebra word problems 10 items.
Simplifying exponential form math problems, 3rd grade decimal activities, double integral solver, 9th grade pre algebra worksheets.
6th grade math printouts, 3rd grade math printouts, eigenvalues TI-84.
Prentice hall algebra 2 textbook online, simple interest power point presentation, How do you solve simplest radical form, e-z grader online.
Expanding cubes, 10th grade Geometry, 8th grade pre-algebra formulas, how to evaluate expression on ti-89, algebra substitution formula, add positive and negative numbers worksheet, solving equations online calculator.
Fractional exponent calculator, 10th maths formulas, lowest common denominator calculator, step by step radical expressions calculator, fourth order equation solver, 8th grade taks math chart, 6th Grade Math Worksheets.
Grade 7 math pl, rules of transposition of formula, ratio and proportion worksheets ks2, simplifying radical fraction similarity ratio, venn diagram worksheets, lu factorization calculator.
Instant Algebra Answers, formular for doing fractions, 9th grade algebra worksheets, radical expressions fractions, improper intergral calculator, factoring trinomials with a decimal square.
8th grade percent worksheets, adding binomials and monomials calculator, ti 89 simplify equations, algebra 1 formulas sheet, prentice hall chemistry workbook answers, 3RD GRADE PRINTOUTS.
7th grade math slope, exponent expression simplifier, scale factor powerpoint, fraction simplifier, combination solver, c# interpolation function, dilation + practice sheets + math.
Online calculators with remainders, 7th grade advanced pre algebra practice tests, logbase on ti-89, online algebra test.
Algebra-test.com, holt worksheets for math 7th grade, linear extrapolation calculator, factoring in java, division problems for seven year old, algebra even root property.
Equa test for grade 6, gcf and lcm worksheets, algebra help for sixth graders, multiple integral calculator online.
Simplest form fraction calculator, prentice hall algebra 2 book online, solve triginometry functions online.
Short answer questions on graphing inequalities 6th grade math, Grade 9 equations, scale math problems, free two step equations worksheet.
2010 taks practise for 6th grade, Formula for calculating square meter please, rearranging equations calculator, factorising quadratics interactive, function machines worksheet, facing math worksheets solving multi step equations, inequalities worksheets 6th grade.
Difficult Multi-step binomial equations, Trinomial Factor online, 7th Grade Prealgebra exponential graph.
Transforming formulas worksheet algebra 1, factor tree worksheets equations, graphing ordered pairs worksheets.
LCM 5th grade, how to do slope in math 7th grade, convert to radical form.
Converting decimals to radicals, fourth grade greatest common factor worksheets, work it out solving equation.
Online equation simplifier, taks practice page 46 math, canadian algebra test grade eight, boolean equation solver, rational expressions unit test help.
CHART OF ACCOUNT UK, solving polynomial equations, word formulae and equations ks2, 3rd power formula.
5 degree slope test pad, math fun worksheets 7th grade shade in, exponents and square roots worksheets, solving equations with x cubed, hands on equations worksheets.
Linear inequalities solver, how to do 8th grade math slopes, vertex form calculator, business algebra problems, trig identities, multiplying monomials worksheets, complete the identity trigonometry.
4th grade equation, 1st grade math review printable, How to Solve Binomials, online equation rearranger, 7th grade factoring worksheets.
Worksheet and simplifying radicals, prentice hall algebra 2 book answers, fractions on ti-86, third order polynomial calculator, factoring worksheets for fourth grade, decimal to radical calculator, maths problem printouts.
Linear extrapolation calculation, simplifying number expressions worksheets, grade 9 linear algebra problems, factoring polynomials calculator online.
Standard form to vertex form calculator, multiplying radicals calculator, chemical equation solver, square root property calculator, step by step partial fractions calculator, lattice multiplication worksheet, range of a quadratic equation.
Linear equations and real life problems, examples of quadratic equations in real life, simplify complex fraction calculator, trinomial equation solver, adding radical solver, geometry worksheets 9th grade, three step algebra equations.
Rules for linear equations, factor tree worksheets, all trigonomic identities, cheat sheet pre geometry, math percent formula, trig proof calculator, online slope and y-intercept calculator.
Online ti89, Triple Integral Calculator, ratio and proportion information and worksheet, online trinomials factoring, year 9 algebra worksheets.
1994 algebra game, online factor equation program, 9th grade algebra problems.
Quadratic equations for beginners, algebra solving for an exponent, Algebra 1 teks for 2002, log equation solver, explanation of rational exponent.
Hardest equation ever, online summation, double integral calculator online, equa testing, Trigonometric sample formula question, linear equations worksheets, dividing fractions with exponents.
Multiply expressions calculator, 6th grade math worksheet, algebra slope calculator, step by step to midpoint formula, algebrasolve.com.
Physics the physical setting answer key prentice hall, when using polynomials can you combine negative numbers, how to do long division, polynomials, linear equations worksheets, algebra 2 solver, algebra 1 answers.
Synthetic long division algebra calculator, how to do quadratic equations, quadratic formula.
Algebra 2 practice workbook answers, solves math problems step by step online, step by step way to solve rational expressions with addition.
College algebra help for dummies, Algebra Solve for X and Y, polynomial functions, ALGEBRA GRAFTING, do algebra problems online.
Solving exponential equations, algerba solvers, algebra 1 calculator.
Online graphing linear equations calculator, what is lcm in algebra, "fundamentals of cost accounting 2nd edition answer key", How is doing operations adding, subtracting, multiplying, and dividing with rational expressions similar to or different from, practice workbook McDougal little Algebra 2 answers.
Adding and subtracting rational expressions, graphing quadratic equations worksheets, math for dummys, best algebra software.
Algebra solvers, synthetic division calculator, how to solve this linear equation 3x+-4=12, multiplying rational xpressions solver, In which direction does the parabola for the quadratic equation y = x2 + 5x + 17 open, Algebra Solver.
Free online algebra calculator, solve polynomal inequlities steps easy problem, Free Online Algebra Problem Solver, McDougal Littell Algebra 2 practice workbook Answers, find the value of x in fractions.
Www.algerbra.com, algebra solver software, scale factor games, college algebra for idiots, printable positive and negative integer line sheet.
Algerbrasolver, Algebra SOLUTIONS, imaginary solutions.
Matrices solver, what term identifies the designated portion of this quadratic trinomia 3x^2 ?, partial fraction decomposition calculator, solve this inequality -9≤3/2z+3≤-3, algebra 2 connections volume 1, rational expressions, X^2 +5x=7.
4, pre algebra graphing linear equations, how to solve 3+2(x-6)=3x+8, adding and subtracting rational expressions, solve 5x-2.
Step by step algebra solver, calculator for algebra, algebrasolves.com, algebra for idiots, gRAPHING qUADRATIC iNEQUALITIES, grad 10 algebra.
Scale factor word problem worksheet, Solving and Graphing Linear Inequalities, Algebra 2 workbook Answers, algebra buster, graphing inequalities for dummies, scale factor word problem, linear equation solver.
Linear ALgebra, linear system solver, algebra graphing linear equations, college algebra worksheets, How to Solve Linear Inequalities, foil method calculator, what is a algebraic expression that can be used to find any term in this squence. 1,4,10,19,31.
Holt algebra 1 worksheets, algebra solve, algebrasolver.com, What is a free online calculator for rational expressions?, factoring polynomials, solving by elimination calculator.
+algebraic fractions solver, a. Solve the equation for r.When solving for r, you should first change the r-2 into an exponent with a positive power by moving the r2 to the denominator. Then, multiply both sides of the equations by r2. This will rid the problem of the denominator. You sh, readicals, simplifying radical expressions √(9+25), what calculators are used for algebra, solving linear equations online calculator, examples of mathematics trivia.
Matrices, algebra equation solving calculator, vertex solver.
Algebra help on solving absolute value equations step by step, what is the quadratic formula, basic algebra worksheets, I have never had algebra before help, Solution: (3+2)(6-2)(7+1) = (4+4)(x). What is the value of x?, algebra solvers.com.
Simplify a radical expression, algebra help, step by step on solving equation.
Monomials, algebra and Trig I practice problems, algebra solver demo.
Free 6th grade curriculm and schooling, solve by elimination calculator, [6.03] What is the value of the x variable in the solution to the following system of equations?2x + 3y = 4x - 2y = -5, matrices calculator, algebra calculator for pocket pc, Radicals, adding and subtractin rational expressions.
Rational numbers, polynomial, ninth grade math percentages, algebra 2 skills practice workbook answers, algebra solver, myalgebra.com, simplifying radicals solver.
Find the difference: (-x2 + 8x – 7) – (-9x2 – 5x – 7), how do i solve multiplication and division equations, radical mathematics, step by step algebra solver.
Quadratic calculator, how to solve for y, Algebra 1 Textbook Answers, how to simplify radicals on a TI-83 plus, google/algebra worksheete with answers, Translate this phrase into an algebraic expression For more than four-sevenths of Mabel's height.
Working out sixth grade word math problem with answers, Algebrator, whar are some algebraic expressions containing radicals and absolute values?, |x + 3| > -2.
Simplifying complex rational expressions, math disability waiver college, operations with polynomials, linear algebra, quadratic calulator, I=40 P=800 R=2.5 T=? SOLVE.
Solve absolute value inequalities using ti-83 calculator, Prentice Hall Mathematics Algebra 1 Answers, online algebra solver, www.algebrasolver.com.
College basic algebra, solve x+5y=39 -x+4y=15, simplifying radicals.
Inequalities, algebra problem solver, HOLT CA Algebra II, algebrator on megaupload, solving radical expressions.
How to rationalize the denominator, solve algebra problems free online, conceptual physics think and solve answers, solving quadratic equations.
Solve a linear equation, algebra equation solver, f1 maths exercise, math factor sheet, advanced math calculator to find the value of x, factoring quadratic equations.
How to solve algebraic radicals, algebra answers, compound inequalities, algebra solver, compound inequality, math for dummies.
Agebra 2 software, examples of equations with imaginary solutions, algebrator, Free College Algebra For Dummies.
Free algebra for dummies mathematics online, adding radical expression calculator, Algerbra for 10th graders, solving algebra task, quiero aprender algebra 1 intermediario, Real Life Example of Polynomial division, ti-84 emulator download.
How to solve agbria, step by step algebra equation solver, +examples of mathematics trivia, how to solve parabolas and their roots worksheets.
Difficult quadratic inequalities word problems, what does x and y mean in math, equations containing fractions worksheets.
Formula chart, solve for z: x=19-5(y-z), agebraic maths problem solve - 8x + 5x - 11x =, how to factor polynomials completely.
Parabola, SOLVE FOR R (5.6X/R)=(3.64X/(2+R)), simplify radicals, simplifying radicals worksheet, free algebra 2 calculator online.
Free algebra solver, math trivia with answers, algebra calculator, parabola worksheets for algebra 1, Graph Solving Equation Free.
How to solve graphing linear equations in two variables, division online calculator, phillis wheatley. | CommonCrawl |
(1) Plot the graph of the function $y=f(x)$ where $f(x) = \sin x +|\sin x|$. Find the first derivative of this function and say where it is defined and where it is not defined.
(2) Express the function $f(x) = \sin x + \cos x$ in the form $f(x)=A\sin (x+\alpha)$, find $A$ and $\alpha$ and plot the graph of this function. Similarly express the function $g(x) = \sin x - \cos x$ in the form $g(x) = B\sin (x +\beta)$ where $-\pi /2 < \beta < \pi /2$, and plot its graph on the same axes.
(3) Plot the graph of the function $y=f(x)$ where $f(x)= \sin x + |\cos x|$. Find the first derivative of this function and say where it is defined and where it is not defined.
These graphs are not monsters. They are humpy because the functions are periodic and involve sines, cosines and absolute values. This problem calls for you to describe and explain the features of the graphs.
First think about the features of the graphs and try to sketch them for yourself, then it may help to use a graphic calculator or graphing software.
Andrei from Romania chose this problem for the NRICH 10th Anniversary special collection. He said "The problems you are posting on the site are usually, at least for me, far from the problems we solve in school or in other activities related to school."
We would like to hear from other students. Is this your experience?
Andrei says "It's a difficult task to choose the problems I liked most, and to choose one seems impossible." So he also chose Over-booking and Wobbler.
Graph plotters. Trigonometric functions and graphs. Maths Supporting SET. Differentiation. Transformation of functions. Engineering. Investigations. Trigonometric identities. Graphs. Sine, cosine, tangent. | CommonCrawl |
Basic Notions: Barry Simon "More Tales of our Forefathers (Part II)"
This is not a mathematics talk but it is a talk for mathematicians. Too often, we think of historical mathematicians as only names assigned to theorems. With vignettes and anecdotes, I'll convince you they were also human beings and that, as the Chinese say, "May you live in interesting times" really is a curse. Among the mathematicians with vignettes are Riemann, Newton, Poincare, von Neumann, Kato, Loewner, Krein and Noether.
Amitsur Symposium: Tsachik Gelander - "Local rigidity of uniform lattices"
We establish topological local rigidity for uniform lattices in compactly generated groups, extending the result of Weil from the realm of Lie groups. We generalize the classical local rigidity theorem of Selberg, Calabi and Weil to irreducible uniform lattices in Isom(X) where X is a proper CAT(0) space with no Euclidian factors, not isometric to the hyperbolic plane. We deduce an analog of Wang's finiteness theorem for certain non-positively curved metric spaces. This is a joint work with Arie Levit.
Amitsur Symposium: Amiram Braun - "The polynomial question in modular invariant theory, old and new"
Let G be a finite group, V a finite dimensional G- module over a field F, and S(V) the symmetric algebra of V. The above problem seeks to determine when is the ring of invariants S(V)^G , a polynomial ring. In the non-modular case (i.e. char(F) being prime to order(G)), this was settled in the Shephard-Todd-Chevalley theorem. The modular case (i.e. char(F) divides order (G) ), is still wide open. I shall discuss some older results due to Serre, Nakajima , Kemper-Malle and explain some new results, mostly in dimension 3.
Amitsur Symposium: Lev Glebsky - "Approximations of groups by finite and linear groups"
The sofic groups and hyperlinear groups are groups approximable by finite symmetric and by unitary groups, respectively. I recall their definitions and discuss why those classes of groups are interesting. Then I consider approximations by other classes of groups and review some results, including rather recent ones by N. Nikolov, J. Schneider, A.Thom, https://arxiv.org/abs/1703.06092 . If time permits I'll speak about stability and its relations with approximability.
Amitsur Symposium: Arye Juhasz - "On the center of Artin groups"
Let A be an Artin group. It is known that if A is spherical (of finite type) and irreducible (not a direct sum), then it has infinite cyclic center. It is conjectured that all other irreducible Artin groups have trivial center. I prove this conjecture under a stronger assumption that not being spherical namely, if there is a standard generator which is not contained in any 3-generated spherical standard parabolic subgroup. The main tool is relative presentations of Artin groups.
Amitsur Symposium: Yael Algom-Kfir - "The metric completion of an asymmetric metric space"
The Teichmuller space with the Thurston metric and Outer Space with the Lipschitz metric are two examples of spaces with an asymmetric metric i.e. d(x,y) eq d(y,x). The latter case is also incomplete: There exist Cauchy sequences that do not have a limit. We develop the theory of the completion of an asymmetric space and give lots of examples. Time permitting we will describe the case of Outer Space.
Amitsur Symposium: Alex Lubotzky - "First order rigidity of high-rank arithmetic groups"
The family of high rank arithmetic groups is a class of groups playing an important role in various areas of mathematics. It includes SL(n,Z), for n>2 , SL(n, Z[1/p] ) for n>1, their finite index subgroups and many more. A number of remarkable results about them have been proven including; Mostow rigidity, Margulis Super rigidity and the Quasi-isometric rigidity.
Amitsur Symposium: Chloe Perin - "Forking independence in the free group"
Model theorists define, in structures whose first-order theory is "stable" (i.e. suitably nice), a notion of independence between elements. This notion coincides for example with linear independence when the structure considered is a vector space, and with algebraic independence when it is an algebraically closed field. Sela showed that the theory of the free group is stable. In a joint work with Rizos Sklinos, we give an interpretation of this model theoretic notion of independence in the free group using Grushko and JSJ decompositions.
Amitsur Symposium: Aner Shalev - "The length and depth of finite groups, algebraic groups and Lie groups"
The length of a finite group G is defined to be the maximal length of an unrefinable chain of subgroups going from G to 1. This notion was studied by many authors since the 1940s. Recently there is growing interest also in the depth of G, which is the minimal length of such a chain. Moreover, similar notions were defined and studied for important families of infinite groups, such as connected algebraic groups and connected Lie groups.
Amitsur Symposium: Malka Schaps - "Symmetric Kashivara crystals of type A in low rank"
The basis of elements of the highest weight representations of affine Lie algebra of type A can be labeled in three different ways, my multipartitions, by piecewise linear paths in the weight space, and by canonical basis elements. The entire infinite basis is recursively generated from the highest weight vector of operators f_i from the Chevalley basis of the affine Lie algebra, and organized into a crystal called a Kashiwara crystal. We describe cases where one can move between the different labelings in a non-recursive fashion, particularly when the crystal has some symmetry.
Logic Seminar - Assaf Shani - "Borel equivalence relations and symmetric models"
We develop a correspondence between the study of Borel equivalence relations induced by closed subgroups of $S_\infty$, and the study of symmetric models of set theory without choice, and apply it to prove a conjecture of Hjorth-Kechris-Louveau (1998).
Title for the day: "Quantum ergodicity and spectral theory with a discrete flavour"
9:00-10:50: Shimon Brooks (Bar Ilan), "Delocalization of Graph Eigenfunctions"
14:00-15:50: Elon Lindenstrauss (HUJI), "Quantum ergodicity on graphs and beyond"
See also the Basic Notions by Elon Lindenstrauss @ Ross 70 (16:30).
NT&AG: Gal Porat (HUJI), "Induction and Restriction of $(\varphi,\Gamma)$-Modules"
Abstract. Let L be a non-archimedean local field of characteristic 0. In this talk we will present a variant of the theory of (\varphi,\Gamma)-modules associated with Lubin-Tate groups, developed by Kisin and Ren, in which we replace the Lubin-Tate tower by the maximal abelian extension \Gamma=Gal (L^ab/L). This variation allows us to compute the functors of induction and restriction for (\varphi,\Gamma)-modules, when the ground field L changes. If time permits, we will also discuss the Cherbonnier-Colmez theorem on overconvergence in our setting. Joint work with Ehud de Shalit.
T&G: Yaron Ostrover (Tel Aviv), Quantitative symplectic geometry in the classical phase space.
We shall discuss several topics regarding symplectic measurements in the classical phase space. In particular: Viterbo's volume-capacity conjecture and its relation with Mahler conjecture, the symplectic size of random convex bodies, the EHZ capacity of convex polytopes (following the work of Pazit Haim-Kislev), and (if time permits) also computational complexity aspects of estimating symplectic capacities. | CommonCrawl |
What are the essential characteristics of asset prices?
I think the question has already been asked about stylized facts of asset returns; this question regards the essential characteristics and normative assumptions used to evaluate asset prices. I.e., given that the economic value of a generic asset is its discounted expected utility, what are some assumptions by which an economic stakeholder may assess a claim's worth?
Price is an expressed belief of value.
The efficient market hypothesis (EMH): the market acts as a price discovery mechanism in which market prices reflect participants' capital-weighted expectation. It should be difficult to prove that the market price is not "correct". "Price is what you pay -- value is what you get" applies only in cases where the market is not efficient.
The fundamental theorem of asset pricing (FTAP) which posits (i) a risk-neutral measure equal to a probabilistic measure which can only be rigorously demonstrated given (ii) complete markets.
FTAP's correlary to EMH: in an efficient market place, any price which reflects a $\mathbb P$ (i.e., "acturial" and/or "real-world") expectation that does not have a different $\mathbb Q$ ("risk-neutral") measure can be considered an efficient price. I.e., any "no-arbitrage" price is permitted under EMH.
Asset prices cannot be negative (or can they???). Since maximum loss is (typically) constrained to principal invested, asset prices cannot theoretically be negative -- but, in practice, investors may assign them negative values (vis-a-vis, the "drag" on value whereby the inclusion of an asset causes a portfolio to be valued less than it if were dis-included).
Corollary of requirement that prices be supported over the domain $\left[0, \infty \right]$: price paid determines both expected return as well as maximum loss (à la Seth Klarman's synthesis regarding Warren Buffet-esque "Margin of Safety").
The fair price of any generic asset is equal to the expected net present value of the discounted cash flows that it is expected to generate.
Time value of money (TVM): Time is money. Time has monetary value which can be expressed as a utility function. Utility is usually interchangeably expressed as a discount factor or an interest rate which represents an expected and/or required rate of return based on an investor's intertemporal preferences regarding consumption and risk. Rational utility should always be a monotonically decreasing utility function with respect to time -- i.e.,"a dollar today is always worth more than a dollar at any time in the future". Therefore, discount rates cannot be negative (or can they???). Also, a discounting function need not be an exponential/geometric (i.e., normative) function, continuous, symmetrical, or time-invariant.
Modigliani-Miller's postulates on (i) the value of a firm and (ii) the irrelevance of capital structure inform the intuition that -- under a broad range of regulatory frameworks -- capital structuring decisions are not a major factor in determining an asset's enterprise value.
Corollary to MM II: it is simpler to price the firm's underlying assets in totality (and then allocate value to claims in order of seniority) vice value each class of claim individually, vis-a-vis "in order to value a company's stock, one must first value the company itself" (attribution needed).
Arbitrage Theory of Pricing's (APT) statement that asset prices are reflexively a transformed function of returns.
The Capital Asset Pricing Model's (CAPM) application of APT which states that asset prices are a function of diversifiable and non-systemic risk under a mean-variance framework.
Equity is analogous to a long call option on a firm's value; debt is analogous to short put option on a firm's value. A position which is long equity and long debt is a synthetic long position on the firm's underlying assets.
Good responses should add depth to and/or expand upon those characteristics already identified. I also would appreciate any relevant references including compendia and/or primers.
I appreciate your thoughts and references.
Browse other questions tagged returns arbitrage asset-pricing actuarial-science or ask your own question.
Have any new stylized facts of asset returns been discovered since 2001?
Critique against consumption-based asset pricing theory?
What is the Most Efficient Way to Calculate the Internal Rate of Return IRR?
What is a standard model of convergence when looking at negative stub values?
How to calculate an option porfolio cost and payoff function? | CommonCrawl |
I have a randomForest object in R, and am trying to extract prescriptive insights, as I would with a tree. This is for a binary classification problem.
Given this setting, my main question is: How can I make sense of what values of what features are associated with each classification? For example, is there a way I can analyze the randomForest object to understand that values of feature1 between 0.5 and 0.8 are likely associated with a classification of "1"?
I would imagine there is something I could do using the votes for each object (given its feature values), or the feature importance for each feature in the forest?
There are a number of model-agnostic ways of interpreting complex machine learning models. Model-agnostic means that it can be applied to all sorts of models, including the random forest.
Christoph Molnar put his entire book Interpretable Machine Learning: A Guide for Making Black Box Models Explainable on the internet, and he devotes an entire chapter to model-agnostic methods.
Two popular methods are LIME (which stands for local interpretable model-agnostic explanations) and Shapley values. Both of these are described in the Molnar book listed above.
Crudely put, LIME looks at a specific prediction, makes slight variations on your data to see predictions around that space and to learn about how the model makes predictions in that local space, and then trains an interpretable model (such as linear regression) based on this information. I'm not recalling precisely how Shapley values work—other than remembering it is a clever extrapolation of a metric from game theory: Features are treated as cooperating in making predictions, and features receive a higher Shapley value for contributing to the prediction more.
A talk of Molnar's on these methods, found at YouTube.
The Data Skeptic podcast episode on LIME.
Two episodes of the Linear Digressions podcast on Shapley values. The two webpages (here and here) have lots of other links to the original papers, use-case write-ups, and other episodes of theirs on LIME and model interpretation.
Apologies for not going too in depth on these methods, but these resources should point you in the right direction.
For a variety of reasons, this is very hard to do for random forests, or most blackbox methods with complex interactions. Remember that a random forest is basically taking the average over a large number of decisions trees that are all trained to perfectly fit their subset of the data. Understanding even a single one of these saturated trees is nearly impossible, and now to "understand" the average of a large number of them is not a reasonable human task.
With that in mind, the simplest approach I would advise is to use a model in which the feature effects are much easier to understand, like an elastic net model. If the predictive ability is close to that of the random forest, then one might pick the elastic net model just due to interpretability over a random forest, even though the random forest might have slightly higher accuracy.
Finally, if one does find that the interpretable models are unacceptably worse in predictions than the non-interpretable model, then one way to answer your question is to simply plug feature values into your fitted model and see how the outcome changes. However, this is actually slightly more challenging than it looks; remember that in a random forest, the model allows for interactions between variables. So it is possible that if $x_1 = 0$, high values of $x_2$ lead to high probabilities of success in the outcome, but if $x_1 = 1$, low values of $x_2$ lead to high probabilities of success in the outcome.
One way to summarize this might be to plug in all rows of your data, except that you change your feature of interest into something like "low", "medium" and "high". Then compare the estimated probabilities given the different levels for your feature given several representative values of all the other covariates.
Finally, just a word of caution in general when interpreting feature effects from a predictive model. Note that you are interpreting how the model makes a decision, which is different than the actual relation between a feature and the outcome. For example, if there's very little evidence for an effect from a given feature, then the elastic net model will likely set this estimated coefficient to 0 due to the $L_1$ penalty term. However, lack of evidence is not the same as evidence of lack; if $x_1 = 0$ for 99.9% of your data, then you have very little evidence about the effect of $x_1$, and so the elastic net model is likely to set this coefficient to 0, even though the effect may be large.
Not the answer you're looking for? Browse other questions tagged r classification random-forest or ask your own question.
How do you calculate variable importance p-values using the randomForest package in R?
In a random forest algorithm, how can one intrepret the importance of each feature?
Random Forest - Is it a good approach to bin categories to reduce the size of the model? | CommonCrawl |
Kristian Ranestad (Universitetet i Oslo).
Inquires should be directed to Joachim Jelisiejew, (jj277546 at students mimuw edu pl).
Registration deadline was: June 15th, 2013.
Program of the meeting is posted here.
Worldwide, the study of tensor and polynomial decompositions from the geometric point of view is a very active area of science and has significant applications outside of pure mathematics. The underlying geometric problems have been often studied by mathematicians since 19th century, and it is a part of Italian mathematical tradition to investigate these objects. To illustrate, two fundamental varieties used as the main tool in this subject are named after two Italian mathematicians, Giuseppe Veronese and Corrado Segre. In Poland, the subject is relatively new, but a research group founded by Weronika Buczyńska and Jarosław Buczyński is growing and is very active in the subject. The school will be an opportunity for Polish students and researchers to learn about fundamental recent and classical achievements from world class experts, and to establish long lasting mathematical collaborations with European and extra-European scientists.
Given a homogeneous polynomial (a form) $F$ of degree $d$ over a field of characteristic $0$ (usually, complex numbers), one can write $F$ as a sum of powers of linear forms $F= l_1^d + ... + l_r^d$. The minimal $r$ allowing such power sum decomposition is called the rank of $F$ (also called Waring rank, or symmetric tensor rank). A decomposition $F= l_1^d + ...+ l_r^d$ with $r$ equal to the rank of $F$ is called a Waring decompostion of $F$. Generally, the Waring problem is to find bounds for the rank of $F$, but nowadays it has many variants. For instance, one can ask what is the rank of a general (random) form in a fixed number of variables and of a fixed degree. This is solved by the famous Alexander-Hirschowitz theorem. One can ask what is the rank of a particular $F$, such as monomial (solved recently by Enrico Carlini, Maria Virginia Catalisano, Anthony Geramita), or a determinant of a matrix, with variables as entries (unknown even for $3 \times 3$ matrix). One can also ask about possible forms of a Waring decomposition, is it unique, or if not, how to describe the space of all possible Waring decompositions (essentially this space is called the variety of sums of powers of $F$)?
During the school, we will concentrate on algebro-geometric methods and approaches to the Waring-type problems.
(iii) for a given form.
From a geometric point of view they correspond to (i) finding a bound for the maximum rank, (ii) the computation of the dimension of certain secant varieties of Veronese varieties and (iii) finding a generalization of the classical Sylvester algorithm. While the computation of the maximum rank of forms is still the most difficult problem, the two other ones can be successfully tackled via Apolarity and Inverse Systems. Such tools allow to translate these problems in terms of linear systems of hypersurfaces through fat points and Gorenstein $0$-dimensional schemes of minimal length.
Any tensor can be decomposed as a sum of decomposable tensors. In the symmetric case, this is the Waring decomposition of a polynomial as a sum of powers. This decomposition of a tensor is particularly useful in applications when it is unique, in this case we say the tensor is identifiable. We study results and criteria which guarantee that a tensor is identifiable. One of the most important is related to the geometric notion of weak defectiveness introduced by Chiantini and Ciliberto. If time allows, I will continue with applications of vector bundles (nonabelian apolarity).
For an arithmetic Gorenstein variety of dimension $n$, one may associate an apolar form to the general codimension $n+1 $ linear section. The variety of sums of powers of the apolar form may be studied in this setup, and yields interesting and often surprising results for general forms in a number of special examples of arithmetic Gorenstein varieties.
Suggested preparatory reading: from Kristian Ranestad and Frank-Olaf Schreyer: "Varieties of Sums of Powers", J. reine angew. Math. 525 (2000), 147-181: sections 1,2,3.
The school will take place in a Warsaw University pension in Łukęcin (look here for more information), on Western part of Polish Baltic sea shore. Participants are expected to arrive on Sunday, September 1st, evening. Lectures are Monday to Friday and Saturday is the departure day.
The accommodation (full board, double room) costs about 125 złoty (PLN) a day. 1 Euro $\simeq$ 4.2 złoty (approximately), but the exchange rate is not fixed.
A small registration fee of 60 złoty per person will apply. The fee is not covered by the financial support.
Graduate students and young researchers with inadequate support from their home institutions are encouraged to apply for accommodation cost waiver. Please indicate your need for support in the registration form. You will need to provide the name of your scientific adviser and we may ask you to provide an additional letter of recommendation. The organizers will not pay for participants' travel, nor for the registration fee.
Click map of Autumn School in Algebraic Geometry, Łukęcin, Poland for a larger map.
The organizers will provide a conference bus from Szczecin Główny train station to Łukęcin which will depart on Sunday, Sept 1st in the afternoon. Suggested departure time is 17:30. More details about this bus will be posted at a later time.
Other possibilities to get from Szczecin to Łukecin are a minibus, see e.g. KSKBus, or Ober-Trans, or a taxi.
There will be a bus provided by organizers on the departure day, Saturday, Sept. 7th, which will arrive to Szczecin Główny train station around 11:00.
There is also a small airport in Heringsdorf, near Świnoujście, see here. It is located about 65 km from Łukęcin and it has a few flights from Germany, Austria, Switzerland and Poland. We have no information about arriving to and from this airport.
Visa information: Polish Ministry of Foreign Affairs. | CommonCrawl |
Consider the following protocol, meant to authenticate $A$ (Alice) to $B$ (Bob) and vice versa.
$R$ is a random nonce.
$K$ is a pre-shared symmetric key.
$E(m, K)$ means $m$ encrypted with $K$.
$\langle m_1, \ldots, m_n\rangle$ means an assemblage of the $m_i$'s that can be decoded unambiguously ($n$ is encoded unambiguously as well).
We assume that the cryptographic algorithms are secure and implemented correctly.
An attacker (Trudy) wants to convince Bob to accept her payload $P_T$ as coming from Alice (in lieu of $P_A$). Can Trudy thus impersonate Alice? How?
This is a follow-up to Break an authentication protocol based on a pre-shared symmetric key.
is Alice. Each time she generates such a chipertext, the last component is $P_A$. If $E$ is a strong enough encryption (non malleable), then Trudy will not be able to generate by herself a an encryption $E(m)$ of a massage in the formt $m=\langle 2,R,P_T \rangle $ that Bob would accept (except with negligible probability).
Not the answer you're looking for? Browse other questions tagged cryptography protocols authentication or ask your own question. | CommonCrawl |
Is there a neat formula for the volume of a tetrahedron on $S^3$?
There is a nice formula for the area of a triangle on the 2-dimensional sphere; If the triangle is the intersection of three half spheres, and has angles $\alpha$, $\beta$ and $\gamma$, and we normalize the area of the whole sphere to be $4\pi$ then the area of the triangle is $$ \alpha + \beta + \gamma - \pi. $$ The proof is a cute application of inclusion-exclusion of three sets, and involves the fact that the area we want to calculate appears on both sides of the equation, but with opposite signs.
However, when trying to copy the proof to the three dimensional sphere the parity goes the wrong way and you get 0=0.
Is there a simple formula for the volume of the intersection of four half-spheres of $S^3$ in terms of the 6 angles between the four bounding hyperplanes?
Note that the 3-dimensional formula has to be much more complicated. The 2-dimensional formula comes from Euler characteristic and Gauss-Bonnet, but the Euler characteristic of the 3-sphere, or any odd-dimensional manifold, vanishes. In fact every characteristic class of a 3-sphere vanishes, because the tangent bundle is trivial. There can't be a purely linear treatment of volumes in isotropic spaces in odd dimensions. In even dimensions, there is always a purely linear extension from lower dimensions using generalized Gauss-Bonnet.
Nice answer, Greg. I looked at the linked paper and was sufficiently intimidated. I just want to point out, again, that for those (like me) who have a phobia of differential geometry, and hence don't want to use (generalized)Gauss-Bonnet, it is easy to see, using inclusion-exclusion, that the formula in even dimensions is a neat linear combination of the formulas in lower dimensions.
Not the answer you're looking for? Browse other questions tagged mg.metric-geometry or ask your own question.
Is there a general formula for calculating the volume of elliptical simplex on the surface of $S^n$?
Is there a similar formula in spherical and hyperbolic geometry as Euclidean Geometry? | CommonCrawl |
There are some chapters which don't have quizzes for the community to work on and they need your help. You can help Brilliant by contributing some good problems in those chapters. The list of those chapters can be found when you click on "Publish" button as you can see below.
You are free to post all level problems. And you can see your good enough problems in the challenge quizzes of the community. I will also contribute the problems to get the Brilliant with more amazing problems. And I'm looking forward for your contributions too.
I've posted a problem in Percentages chapter. You would love it: What is your LCM?
And it will be displayed as Name of the problem.
@Worranat Pakornrat – Great! Nice problem, thanks!
@Sandeep Bhardwaj – @Sandeep Bhardwaj , I want to contribute in quadratic discriminant , should I share link of problem here ?
@A Brilliant Member – Not compulsory, but you can if you wish.
Thanks :) umm I have question. Is there any place where I can see the complete formula/equations list? Or a link where I can improve my skills in using \(Latex\) kind of fonts.
You can get a lot of Latex guides from Daniel's note: Beginner LaTex Guide. And if you're looking for the complete guide, then refer to the wikipedia page: LaTex/Mathematics.
Hope it will be helpful. Thanks!
@Julius Adrian – Here is an extensive guide to using \(\LaTeX\). Except the points 1 and 2, all the other points are universally applicable wherever you use \(\LaTeX\)/MathJax.
The alternative to point 1 in this site is to hover your mouse cursor over the equations to see the raw \(\LaTeX\) code or use the "Toggle \(\LaTeX\)" option from the pop-down menu in the top right area (click on the small circled profile pic area).
The alternative to point 2 in this site is use \(\backslash(\ldots\backslash)\) instead of \(\$\ldots\$\) and to use \(\backslash[\ldots\backslash]\) instead of \(\$\$\ldots\$\$\).
The answer posts on that post further elaborate on how to make tables, matrices, etc.
I've just posted a new problem on the Triangle Chapter: Lucky Star Number 7 .
I do not understand it inEnglish.May it be inLituanian or inRusian language? | CommonCrawl |
The goal is to tile rectangles as small as possible with the given heptomino, in this case number 7 of the 108 heptominoes (see example below). We allow the addition of copies of a rectangle. For each rectangle $a\times b$, find the smallest area larger rectangle that copies of $a\times b$ plus at least one of the given heptomino will tile.
I found only 7 more. I considered component rectangles of width 1 through 11 and length to 31 but my search may not be complete.
These could all be tiled by hand, of course the bigger ones will be challenging. I'm making this one a 'hand tiling only' puzzle. In other words, use a computer to do anything except look up or compute the arrangements.
I found a solution for the $2\times5$. It obviously also works for $1\times5$.
Here is a better $1\times5$ solution. | CommonCrawl |
Abstract: The model of a stationary universe and the notion of local times presented in are reviewed with some alternative formulation of the consistent unification of the Riemannian and Euclidean geometries of general relativity and quantum mechanics. The method of unification adopted in the present paper is by constructing a vector bundle $X\times R^6$ or $X\times R^4$ with $X$ being the observer's reference frame and $R^6$ or $R^4$ being the unobservable inner space(-time) within each observer's local system. Some applications of our theory to two concrete examples of human size and of cosmological size are discussed, as well as the uncertainty of time in our context is calculated. | CommonCrawl |
A $d$-broadcast primitive is a communication primitive that allows a sender to send a value from a domain of size $d$ to a set of parties. A broadcast protocol emulates the $d$-broadcast primitive using only point-to-point channels, even if some of the parties cheat, in the sense that all correct recipients agree on the same value $v$ (consistency), and if the sender is correct, then $v$ is the value sent by the sender (validity). A celebrated result by Pease, Shostak and Lamport states that such a broadcast protocol exists if and only if $t < n/3$, where $n$ denotes the total number of parties and $t$ denotes the upper bound on the number of cheaters.
This paper is concerned with broadcast protocols for any number of cheaters ($t<n$), which can be possible only if, in addition to point-to-point channels, another primitive is available. Broadcast amplification is the problem of achieving $d$-broadcast when $d'$-broadcast can be used once, for $d'<d$. Let $\phi_n(d)$ denote the minimal such $d'$ for domain size $d$.
We show that for $n=3$ parties, broadcast for any domain size is possible if only a single $3$-broadcast is available, and broadcast of a single bit ($d'=2$) is not sufficient, i.e., $\phi_3(d)=3$ for any $d\geq 3$. In contrast, for $n > 3$ no broadcast amplification is possible, i.e., $\phi_n(d)=d$ for any $d$.
However, if other parties than the sender can also broadcast some short messages, then broadcast amplification is possible for any $n$. Let $\phi^*_n(d)$ denote the minimal $d'$ such that $d$-broadcast can be constructed from primitives $d'_1$-broadcast, \ldots, $d'_k$-broadcast, where $d'=\prod_i d'_i$ (i.e., $\log d'=\sum_i \log d'_i$). Note that $\phi^*_n(d)\leq\phi_n(d)$. We show that broadcasting $8n\log n$ bits in total suffices, independently of $d$, and that at least $n-2$ parties, including the sender, must broadcast at least one bit. Hence $\min(\log d,n-2) \leq \log \phi^*_n(d) \leq 8n\log n$. | CommonCrawl |
cylinder ⋆ 100% Private Proxies - Fast, Anonymous, Quality, Unlimited USA Private Proxy!
I am lost with that problem, and I cannot continue.
But is that the best way to do that with surface integrals? Seems, that integral gives a lot of job. Plese help me.
Definable subsets of $ \mathbb N$ in the language of Presburger arithmetic are exactly the eventually periodic sets.
In communication complexity the interpretation is more on intersection and union of combinatorial rectangles or complements of combinatorial cylinder intersections which does not seem to be as nice as what comes from geometric interpretation of Presburger.
Is there an arithmetic that corresponds to definable sets in communication complexity?
Would it be reasonable to expect something?
How to find the vole of a cube remaining after drilling a cylinder with a diameter larger than the cube's side length?
So, for example, say there's a cube with side length L, and you drill a cylinder with a diameter larger than L through the cube, what volume remains? | CommonCrawl |
Finding Vertical Asymptotes. There are two main ways to find vertical asymptotes for problems on the AP Calculus AB exam, graphically (from the graph itself) and analytically (from the equation for a function).... A function can have a slant asymptote and a horizontal asymptote. For example, it might approach a horizontal line as $\,x\rightarrow\infty\,$, and a slanted line as $\,x\rightarrow -\infty\,$.
To Find Horizontal Asymptotes: 1) Put equation or function in standard form. 2) Remove everything except the biggest exponents of x found in the numerator and denominator.... - [Voiceover] We're asked to describe the behavior of the function q around its vertical asymptote at x = -3, and like always, if you're familiar with this, I encourage you to pause it and see if you can get some practice, and if you're not, well, I'm about to do it with you.
Explanation: An exponential equation of the form has only one asymptote - a horizontal one at . In the given function, , so its one and only asymptote is . how to find acceleration with velocity and time - [Voiceover] We're asked to describe the behavior of the function q around its vertical asymptote at x = -3, and like always, if you're familiar with this, I encourage you to pause it and see if you can get some practice, and if you're not, well, I'm about to do it with you.
The graph has a horizontal asymptote at y = 0, because 2 x > 0 for all x. It passes through the point (0, 1). We can translate this graph. For example, we can shift the graph down 3 units and left 5 units.
To Find Horizontal Asymptotes: 1) Put equation or function in standard form. 2) Remove everything except the biggest exponents of x found in the numerator and denominator.
Introduction to asymptotes of exponential functions. In certain functions, either the value of the function tends to infinity (or –infinity) for an input variable or the function tends to a constant value at an infinitely small (or large) value of the input variable. | CommonCrawl |
Here you will find the final sage project. Feel free to discuss the questions and answers.
1. Find the determinant of this matrix. Is this matrix nonsingular?
2. Find the characteristic polynomial of this matrix. Use this polynomial to determine the eigenvalues.
3. Use Sage to find the eigenvalues and eigenvectors of this matrix.
6. Optional: Use Sage to find the expanded formula for a generic $4\times 4$ matrix. How many terms are there in this formula. Do you have a guess as to how to generalize the determinant formula for $n\times n$ matrices.
You can change the 10 to change the size of the matrix and you can change the 9 to create a different number down the diagonals.
You can always create really large pattern-filled matrices using two for loops. | CommonCrawl |
Can you figure out where each of these four products appears in the different methods?
Can you deconstruct $246 \times 34$ in the same way?
Multiplication & division. Addition & subtraction. Video. Algorithms. Place value. Mathematical reasoning & proof. Creating and manipulating expressions and formulae. Factors and multiples. Integers. Divisibility. | CommonCrawl |
Because of their connections with public-key cryptography, trapdoor functions are surrounded by a lot of mystery. While one-way functions (functions that are easy to compute, yet hard to invert) like integer multiplication are familiar and intuitive, the idea of a function that is hard to invert except if one possesses some secret, the "trapdoor", seems a more remote possibility. The few such functions suitable for cryptographic purposes that have been found (like the modular exponentiation functions as used by the RSA and Rabin cryptosystems) unsurprisingly require heavy use of number theory to understand and analyze.
For every $m \in \mathbb N$ there exists a (not necessarily unique) $n \in \mathbb N$ such that $f_N(n) = m$.
For every $m > 0$, finding any $n$ with $f_N(n) = m$ is equivalent to factoring $N$.
What at first glance might appear incomprehensible is actually a rather simple decision procedure, obfuscated through arithmetic.
Since the factorization is nontrivial and preimages for any values of $g$ and $h$ are readily found, it follows that knowing the prime factors $p$ and $q$ of $N$ is both necessary and sufficient for making the original function $f_N$ produce any value other than $0$. | CommonCrawl |
Phenol has a $\mathrm pK_\mathrm a$ approximately equal to $9.9$.
First of all, chlorophenols are more acidic than phenol, due the negative inductive effect (−I) of chlorine, that reduces the negative charge, located on the oxygen of the phenolate anion.
Among the different chlorophenols, the observed trend is explained by the fact that the stabilizing −I effect of chlorine decreases with the distance from oxygen.
In this case, the methyl group yields a positive inductive effect (+I), thus increasing the negative charge on phenolate oxygen. That's why cresols are less acidic than phenol. One can further realize that the meta compound is more acidic, and this is due to the resonance structures which show a negative charge in ortho and para, but not in meta.
I would appreciate to learn whether such a reasoning, for these two type of substituted phenols, is plausible or whether further more solid arguments should be invoked.
In particular, I would appreciate to understand why the difference in acidity between 2- and 4-chlorophenols is much more pronounced than the same difference between o- and p-cresols.
Your reasoning seems generally well thought out. You clearly have a good understanding of inductive effects and you mention resonance effects in the cresol series. Structural effects don't play a role with these compounds, but let me mention them for completeness. If we have a compound such as I with a carbonyl ortho to the hydroxyl substituent, then in addition to inductive (stabilizes the anion) and resonance (stabilizes the anion) effects, we should also consider hydrogen bonding; which , in this case would stabilize the phenol making it less acidic. On the other hand, in compound 2, the bulky t-butyl group would force the ester carbonyl to twist out of the plane of the benzene ring. In II, the inductive effect of the carbonyl would still operate, but the resonance and hydrogen bonding effects on acidity would be diminished.
This link discusses electrophilic aromatic substitution, where again both inductive and resonance effects need to be considered. About two-thirds of the way down the page we see that chlorobenzene undergoes electrophilic nitration about 30 times slower than benzene, but is still ortho-para directing. We also see that toluene reacts about 25 times faster than benzene and is also ortho-para directing. From these and other examples we learn that chlorine donates electrons weakly by resonance and withdraws electrons strongly through its inductive effect; and that a methyl group is a mild electron donor through resonance (hyperconjugation), while its inductive effect is also electron donating, but is small.
Let's apply these concepts from electrophilic aromatic substitution to your two phenol series. In the chlorophenols, we would expect the chloro substituent to influence the series primarily through a strong electron withdrawing inductive effect. Indeed, as the chlorine moves closer to the hydroxyl substituent, the inductive electron withdrawal increases in power and the $\mathrm pK_\mathrm a$ increases dramatically. On the other hand, in the methyl series we expect mild resonance (hyperconjugation) effects to dominate (even though the inductive effect is in the same direction), therefore in the ortho- and para-cresols we expect the anion to be weakly destabilized and consequently a bit less acidic than phenol itself; while the meta isomer, with minimal resonance and inductive effects affecting the anion, should have an acidity close to phenol.
Not the answer you're looking for? Browse other questions tagged organic-chemistry acid-base quantum-chemistry resonance phenols or ask your own question.
Why is p-methoxyphenol more acidic than p-methylphenol?
Why is o-fluorophenol a stronger acid than p-fluorophenol?
Why is acetic acid more acidic than phenol?
Why is phenol more acidic than aniline? | CommonCrawl |
The role for proteoglycans in acetylcholine receptor clustering on cultured muscle.
The present dissertation investigated the possible role of proteoglycans (PGs) in acetycholine receptor (AChR) clustering on cultured C2 myotubes. Analysis of variant muscle cell lines and their hybrid products supported the hypothesis that PGs are required for the clustering of AChRs. Three PG-defective genetic variants derived from the C2 cell line form myotubes but fail to spontaneously cluster AChRs. The three variants show different broad-spectrum defects in glycosaminoglycan (GAG) biosynthesis and are especially deficient in the synthesis of chondroitin sulfate (CS) chain. Formation of heterokaryon myotubes containing nuclei from two different variants spontaneously clustered AChRs and recovered synthesis of GAGs, especially of CS. It strongly suggests that there is a requirement for proper GAG biosynthesis in AChR clustering. Chlorate was found to inhibit both GAG synthesis and the clustering of AChRs in a dose-dependent manner. When extracellular calcium was raised from 1.8 to 6.8 mM in cultures of wild type C2 myotubes, both the frequency of spontaneous AChR clusters and the level of CS were increased. Culture of wild type C2 myotubes in the presence of chondroitinase ABC eliminated CS and prevented the formation of AChR clusters. Treatment with chondroitinase ABC only prevented AChR clustering if begun prior to the formation of spontaneous clusters. This suggests that CS is required in the initiation but not the maintenance of AChR clusters. Agrin-induced AChR clustering was dramatically reduced by digestion of CS. Unlike calcium, however, agrin action on AChR clustering did not affect levels of CS. Also, agrin-induced AChR clustering was restored on S27 myotubes by adding calcium-treated C2 conditioned medium. The IIH6 monoclonal antibody against α-dystroglycan, laminin, and agrin all bound to a specific fraction of C2 cell extracts separated on ion exchange chromatography. Also IIH6, laminin, and agrin affinity-precipitations showed a smeared sulfate labelled band above 120kD which is close in molecular weight to that of $\alpha$-dystroglycan. The band disappeared after chondroitinase ABC treatment. Protease-digested IIH6 immunoprecipitate eluted corresponding to CS. This result strongly suggests that CS is required for agrin activity on AChR clustering. | CommonCrawl |
calculus linear-approximation share|cite|improve this question asked Dec 9 '15 at 14:52 AleksandrH 1978 add a comment| 1 Answer 1 active oldest votes up vote 1 down vote accepted For a cube Can anyone point me in the proper direction? Answer Questions Determine if S is in the Vector Space? More questions Calculus percent error from linear approximation?
Cara · 6 months ago 0 Thumbs up 0 Thumbs down Comment Add a comment Submit · just now Report Abuse This Site Might Help You. Linear approximation says $f(x) \approx f(x_0) + f'(x_0)(x-x_0)$ for $x$ close to $x_0$. (This is the most important formula in differential calculus, in my opinion.) So in this case $6x^2 \approx Linear Approximation & Determining Percentage Error!!? Browse other questions tagged calculus linear-approximation or ask your own question.
Add your answer Source Submit Cancel Report Abuse I think this question violates the Community Guidelines Chat or rant, adult content, spam, insulting other members,show more I think this question violates Any help with the logic or steps behind this would be greatly appreciated. Its is 1-4x. The system returned: (22) Invalid argument The remote host or network may be down.
This feature is not available right now. Since we know f(x) we can find f''(x) by differentiation. How do we do that? Sign in to make your opinion count.
Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the Often |f''| is greatest at x=a or x=b in which case we take the appropriate value. f(x)= x / x+2 ; a=1; f(1.1) I've gotten so far as to a) f(x)~L(x)=(1/3)+(2/9)(x-1) b) was graphing, I got the graph correct c) f(1.1)~.356 everything above was correct, however part For instance, if you are measuring the radius of a ball bearing, you might measure it repeatedly and obtain slightly differing results.
Follow 1 answer 1 Report Abuse Are you sure you want to delete this answer? [email protected] 2,996 views 48:19 Differentials Tangent Line Approximation Propagated Error - Duration: 58:11. The Taylor series says that the error depends a value of f'' somewhere within the interval. Multiply this value with 100 to fing %age error.
Russell Reply With Quote 07-02-2013,03:37 PM #3 StintedVisions View Profile View Forum Posts Private Message New Member Join Date Jul 2013 Posts 11 I did |(.356-1.1) / 1.1| * 100 and Okay here's the problem: Assume that the measurement of x is accurate within 2%. All rights reserved. Sign in Transcript Statistics 6,889 views 14 Like this video?
Your cache administrator is webmaster. Powered by vBulletin Version 4.2.2 Copyright © 2016 vBulletin Solutions, Inc. rdavisedcc 50,860 views 9:27 Linear Approximation Square Root Example - Duration: 13:50. Expand» Details Details Existing questions More Tell us some more Upload in Progress Upload failed.
What's New? Working... Is there any algebraic way to solve this problem, though? Sign in Share More Report Need to report the video?
Compute both the error and percentage error of linear approximation? Please upload a file larger than 100x100 pixels We are experiencing some problems, please try again. I know how Linear Approximation works and sort of understand percentage error. Expand» Details Details Existing questions More Tell us some more Upload in Progress Upload failed.
f'(x)=12x² m=f'(1.5)=27 L(x)=27x-27 So, 4x^3≈27x-27 when x≈1.5 If we wanted to estimate f(1.52), we could find L(1.52)=27*1.52 - 27 =14.04. Okay here's the problem: Assume that the measurement of x is accurate within 2%. Polynomial question? | CommonCrawl |
Abstract. Given two selfadjoint operators $H_0$ and $V=V_+-V_-$, we study the motion of the spectrum of the operator $H(\alpha)=H_0+\alpha V$ as $\alpha$ increases. Let $\lambda$ be a real number. We consider the quantity $\xi(\lambda,H(\alpha),H_0)$ defined as a generalization of Krein's spectral shift function of the pair $H(\alpha),\ H_0$. We study the asymptotic behavior of $\xi(\lambda,H(\alpha),H_0)$ as $\alpha\to \infty.$ Applications to differential operators are given. | CommonCrawl |
I'm trying to rotate a tesseract in 4D space for a project.
This shows I can use bivectors to "to generate rotations in four dimensions." Following exterior algebra and finding the wedge product, I've managed to get a 6D vector that supposedly describes my 4D rotation. This is great, except I have no idea how to use the 6D vector to rotate my 4D object.
I've looked at many links but none describe how to actually do the rotation using the wedge product. I'd like to stay away from matrix rotations.
Rotating a 4 dimensional point?
How can I use the 6D vector to rotate the 4D object?
Browse other questions tagged rotations exterior-algebra dimension-theory or ask your own question.
how to perform a rotation around a point which itself is rotating?
Find an angle to rotate a vector around a ray so that the vector gets as close as possible to another vector.
Can the "symmetric algebra" over $\mathbb R^n$ be defined from an infinite-dimensional exterior algebra?
Are all bivectors in three dimensions simple? | CommonCrawl |
Let $*: G \times X \to X$ be a group action.
where $*$ denotes the group action.
Some authors use $G_x$ for the stabilizer of $x$ by $G$.
The stabilizer of $x$ is also known as the isotropy group of $x$.
That it is in fact a group, thus justifying its name, is demonstrated in Stabilizer is Subgroup.
Results about stabilizers can be found here.
The British English spelling for stabilizer is stabiliser. | CommonCrawl |
What goes into a model?
Last time, I'd pointed out how many people think that it's blatantly obvious that statistical models should be expressed in code as an object (as opposed to an ad hoc aggregation of functions, environments, and whatever else seems necessary at the moment).
So what methods should go into that object?
There's a balancing to be done: too many elements and you have a mess where some parts are inapplicable to some models and every week somebody else thinks of something new that a model should do; too few elements gives up on the object concept.
One definition (herein the 'small' definition) is that a model is a parameterized likelihood function. You give me data and a parameter set (like $\mu$ and $\sigma$ for a Normal distribution), and I give you a likelihood. That is, given the parameter space $\params$ and data space $\datas$, the model is a function $L: \params\times \datas \to \Re$.
I called it the 'small' definition because I'd like to widen it. The small definition is a category, a collection of sets and mappings between those sets, with only one mapping, $\params \times \datas \to \Re$. But what about others? You can probably think of a few useful functions associated with a model for mapping $\datas\to\params$, like estimating the optimal parameters from data, or from $\params \to \datas$, like an expected value or random draw function.
CDF (cumulative distribution function, $CDF:\params\times\datas \to [0, 1]$).
The fun thing about categories is that if you have mappings between them, then (set of categories, morphisms from category set to category set) is itself a category. More on that next time. But for now, some discussion of why the 'larger' definition is worth having.
I see the statistics literature as a broad framework plus a long list of little results about efficiencies we can gain given certain special models. Some models (like the logit or probit) are described as having some loss function, and then we expect the computer to use it to find the optimal parameters; some models (like OLS) have parameters that can be solved in closed form, and it would be folly to waste time on an explicit optimization search. Custom leans heavily on those models where there is a closed form solution.
So the model should accommodate this, with default methods for any black-box model, and hooks for all the special methods as they come up. The estimation routine, then, is a plain black-box optimizer unless you tell me otherwise.
Here's a little demo wherein we use the model struct as a plain optimizer. This example isn't even a statistical model, but declares an objective function representing $-(x-2)(x+3)$. This 'model' has one parameter; i.e., its parameter set is a $1\times 1$ matrix. Having declared the model, finding its optimum is the one-liner it should be.
You'll need to have Apophenia installed to run the demo code; see Apophenia's setup page for details.
Because the model has only a probability method defined, the estimate function knows to call the optimizing routines.
For many well-known models, it's folly to use an optimizer. The maximum likelihood estimator for the $\mu$ parameter of a Normal distribution is the mean of the input data, so it would be folly to call an optimizer, and the next example explicitly specifies the estimate routine. This model has parameters in a vector of size 2. The key point to these two demo snippets is that the object structure already works: the apop_estimate call doesn't really change even though one model had an explicit estimate routine and the other didn't.
So that's the basic thinking here: we should have a slot where we can put a known method from the literature whenever possible, but if we don't have a method, there should be a default to put in. The same goes in other directions too: given a log likelihood, I should be able to produce an RNG; given an RNG, I should be able to produce a CDF; et cetera.
By the way, verifying numeric estimation routines is a real challenge. You can check corner cases that can be calculated by hand, but knowing that my OLS routine works for a set of points that are neatly arranged so that I can do the math by hand is not reassuring. However, if the results of a hand-written method using nontrivial data match the results from a default routine, then that's a much stronger indication that both are correct. You're using the same default method over and over, so be sure to do this on a dozen or so models so that you can raise confidence in the default itself.
The first thing to note is that the estimate routine doesn't have a signature $\datas\to\params$, but $\datas\times \models \to \models$, because it takes in a model with no parameters (inmodel.parameters==NULL) and returns a copy of that model with parameters set.
Functions that are boilerplate for objects: print, prep (more-or-less what gets called for a new model), and a single char for error codes. I think every object should have an error element, so you can ask the object itself if it ran into glitches in processing.
Things that are technically necessary for a coherent model, like a slot for the size of the parameters (so an MLE knows how big a space to search, for example) and a list of model-specific settings.
Things that, if I knew then what's so obvious now, would be external functions, including the score (dlog liklelihood) and a prediction function.
That last part deserves further note, which I will get to in a few entries if anybody requests it. There are all sorts of things that need to behave differently for certain models, including Bayesian updating, entropy calculations, or expected value. I wound up making this happen via a virtual table method (yes, this reimplements a C++ feature, but in a manner more appropriate to the situation). You call the apop_update function with a beta model and a binomial model; it looks in its lookup table and sees that the beta-binomial has a closed-form posterior; it calls the associated function that makes that happen. Taking this to the extreme, one could implement a model as little more than a label, and then every function above (CDF, RNG, estimate, update, …) all have hooks that allow different behaviors depending on the label sent in. You could write functions that do a similar sort of per-model dispatch for entropy, expected value, Kullback-Leibler divergence, and who knows what else.
Above, I presented one point where one could put the break between between things that should be taken as inherently part of the model and those that are functions that behave differently given different model inputs. There are a continuum of others, inlcuding small definitions that basically move every special method outside the object to a lookup table. | CommonCrawl |
Abstract: Eff is a programming language based on the algebraic approach to computational effects, in which effects are viewed as algebraic operations and effect handlers as homomorphisms from free algebras. Eff supports first-class effects and handlers through which we may easily define new computational effects, seamlessly combine existing ones, and handle them in novel ways. We give a denotational semantics of eff and discuss a prototype implementation based on it. Through examples we demonstrate how the standard effects are treated in eff, and how eff supports programming techniques that use various forms of delimited continuations, such as backtracking, breadth-first search, selection functionals, cooperative multi-threading, and others.
To read more about eff, visit the eff page.
This looks fascinating! Is it straightforward to explain why Eff could not simply be implemented within the syntax of an existing language, say Haskell or ML?
Well, ML has handlers just for exceptions and those cannot be used to get general handlers. I suppose you could emulate eff in ML with delimited continuations, but I think you would end up with a "deep" embedding of eff.
People have tried to get something in Haskell, e.g., effects on Hackage. Judge for yourself.
I fail to understand why ressources have a different syntax than regular handler. Intuitively I would have thought they were just "handlers declared at toplevel for your convenience", but it seems like I missed something here.
Resources do not have access to the continuation, while ordinary handlers do.
It makes little sense for a "top-level handler" to be able to manipulate the continuation, since the continuation is open-ended in nature, i.e., it is not delimited. But this is not why we defined resources. We defined resources as a direct implementation of the theoretical idea of co-models.
Well, you could have continuation that map to the empty type as toplevel continuations, but it still makes sense to consider these not too valuable.
On the other hand, I don't see how comodels play in that picture. Am I missing something obvious?
A top-level continuation that maps to the empty type? Where would that come from? Or are you suggesting that there be a top-level "abort" operation (although that is an _operation_ whose return type is empty). I'll let Matija explain the comodels.
This is what I had in mind yes.
I have advocated a top-level abort operation, but was unable to convince Matija. So far.
3. random_int (say) takes integer bounds, generates a random integer according to the state of the pseudo-random generator, sets the new state, and yields the generated integer.
In general, an operation $op : A \to B$ takes a parameter of type $A$, interacts with the "real-world", and yields a result of type $B$.
If you take $W$ to be the set of all possible worlds, operations correspond to maps $A \times W \to B \times W$ – they take the parameter and the current world state, and yield a result and the new world state. And this is exactly what comodels for a given collection of operations are: sets $W$ equipped with a map $A \times W \to B \times W$ for each operation $op : A \to B$. As a bonus, comodels are dual to models and thus a natural extension of the algebraic theory of effects.
Comodels are dubbed resources in eff and are implemented slightly differently. The main reason is that there is, of course, no datatype you can use to represent the set of all worlds $W$. For this reason, I was at first inclined to drop any explicit mention of $W$. Instead, only special built-in effects (for example standard I/O channel) would have resources and those resources would be implemented in effectful OCaml code, making $W$ implicit. Andrej argued that a programmer would still want to write her own resources, for example to implement a pseudo-random number generator. Thus, we decided to equip each resource with a state only it can access, and provided a syntax with which a programmer defines the desired behaviour.
What about toplevel handlers or other alternatives to resources? First imagine how a handler should handle a toplevel (non-delimited) continuation. As soon as a handler applies it to some value, the continuation never yields back control and whatever follows it in the handler is discarded. Furthermore, the continuation should be called at least once (I'll discuss this later), otherwise eff would abruptly exit.
Thus, each toplevel handler is more or less some computation followed by an application of the continuation to a given value. What if this computation triggers some operations? Since these operations happen at the toplevel, we cannot handle them as they have escaped all handlers. We had an implementation that worked like this for some time, but there were no obvious advantages, all while the implementation was hacked together, the behaviour was wildly unpredictable, and the (pretty neat, we probably agree) abstraction of effects that eff provides was broken.
In the end, we decided to allow only pure computations at the top-level. So, you have some pure computation that in the end passes a result to the toplevel continuation. But this is exactly what a resource does, except that you only compute the result while the passing to the continuation is implicit.
What if you do not call the continuation, but instead call some special toplevel abort operation? What exactly should this operation be, if it is not a standard exception?
1. If it is a special extension of eff that can be used only in resources, why would we use it? One reason was that for some exceptions, you want to have a nicer error message than the usual "Uncaught operation …#raise …". For this reason, we have a built-in function exception (declared in the pervasives) that generates exceptions with resources that do just that. So we can get the same benefit without any extensions.
2. If it is a special extension that can be used everywhere, it again breaks the abstraction of effects, as there is a way to perform effects without operations.
Thank you for the precisions.
1. It's unnecessarily confusing that you use c for built-in constants and computations, esp. since there is only a short phrase mentioning the first. Can you choose another metavariable for constants?
2. I'm confused about the typing of e#op, both in its own rule and in the handler rule. The only way to get an effect type E seems to be by introducing a computation with new, which is typed with the $\vdash_c$ judgment, but the aforementioned rules with e#op require typing the effect e with $\vdash_e$ judgment.
@Sean: Thanks for the comments. Regarding constants, yes of course, that is an unecessary slip up on our part. Regarding your second point: you are right, so the typical way of getting a e#op is to write something like let x = new E in .... x#op ... What did you expect? You could write (new E)#op in concrete syntax, but that would be useless and also it would be desugared into let x = new E in x#op.
Ah, okay. So, you're assuming a variable will be used as the expression e in e#op. I was missing where the coercion from computation to expression was taking place. It might be helpful to mention that, since you already mention val for coercing an expression to a computation.
It appears that let is the only way to get an expression with an E type. Is it possible to have a non-variable expression in e? If not, perhaps it's a simplification (and clarification) to directly use a variable, as in x#op.
I am not "assuming" that a variable will be used in e#op. Rather, this is a consequence of the fact that the syntax does not have any exprssions of effect types, other than variables. I don't think anything would be simplified if we restricted e in e#op to variables. We would just break orthogonality, so this does not sound like a good idea to me.
I said "assuming" because you said "typical." If it's a consequence, then it's not the typical way, it's the only way. Since it's the only way, I don't see the orthogonality that is broken.
Anyway, this is all very nitpicky. We read your paper in our reading club at Utrecht, and one of the comments that came up was that it was fuzzy how computations and expressions were distinguished. Now that I understand how you get from a computation to an expression, it's more clear. But I think something could possibly be improved in the explanation.
I you have a suggestion, I'd be very happy to hear. Perhaps an example earlier in the paper? Video lecutures? | CommonCrawl |
Random walk on thin ice?
My Question: Is the stochastic process which is described below a (special case of a) well-studied model? What kind of properties are known under which assumptions?
Let's think of a random walker on a frozen lake. Obviously, this lake is a subset $E$ of $\mathbb Z^n$. The ice isn't too stable, though, and therefore our poor walker can occupy each vertex only $k\in\mathbb N$ times before the ice collapses. Luckily, the walker is quick and agile enough to leave the vertex before she is swallowed by the lake. However, she will no longer be able to visit this vertex, changing the rules for the future of her odyssey.
Obvious questions about this process: What's the probability that the walker will eventually get trapped between collapsed vertices? If e.g. the lake $E$ is finite, the probability is obviously one. What about the expected time for this to happen? If $E=\mathbb Z^n$, which recurrence properties (or general asymptotic properties) does the process have and in which sense?
I would appreciate it very much, if anyone could give me a hint where to look for answers.
PS: For the inspiration for this question, look here.
$(1)$ The probability the random walker survives $n$ steps without being trapped decreases exponentially in $n$.
They remark that $(1)$ holds for higher dimensional lattices with arbitrary probabilities. The argument is essentially that the walker always has a non-zero probability of being trapped on its first visit to a given hypercube in the lattice. In 2D, this looks like a 'G' shape. I don't see why this wouldn't hold if $k > 1$. Calculating the expected number of steps before getting trapped is completely beyond me though.
Not the answer you're looking for? Browse other questions tagged probability-theory reference-request stochastic-processes random-walk random-graphs or ask your own question. | CommonCrawl |
I have a histogram showing the distribution of reaction times from $100$ trials worth of data. The range in times is measured in ms and ranges from $70$ ms to $420$ ms. The frequency is displayed on the left y-axis with the max peaking at $28$ occurrences in the $175-210$ ms bin range. The bin sizes, as you could guess, are in $35$ ms sized boxes. I have to add a probability y-axis and a probability density y-axis to the same graph, but I'm not sure how to calculate the probability to see how high in value the axis should go. My lab describes calculating this amount by dividing the scale of the "first axis" by the total number of measurements of my histogram.
I thought it would simply by $35$ for the scale of the "first axis", which I'm assuming is the x-axis, divided by $100$, the number of trials I conducted, but when I start to calculate the probability density, I have to divide the scale for probability by the interval width.
So basically I have to solve the first to solve the second. The problem is I don't know what is the difference between the scale of the first axis and the interval width.
With the assumption of $35/100 = 0.35$ becomes my max for the probability axis, but this doesn't exactly make sense because then the next equation would just be $0.35/35$, which means I'm calling the scale of the first axis the same thing as the interval width.
Could anyone provide some clarification on how I should identify what is the first axis, and how do I find its scale? What's the difference from the interval width?
Assuming that the different scales are multiples of each other and that the original plot has a vertical axis in the count scale, just use the definitions of the probability and probability density scales.
Let the sample size be $n$ and the values for each bin are $c_i$, $p_i$, and $d_i$ (for $i=1,2,\ldots,n$) for the count, probability, and probability density scale. That each are multiples of the other we can write $p_i=w c_i$ and $d_i=v c_i$.
The maximum count occurs at 28 so "nice" tick marks can occur at 0, 5, 10, 15, 20, 25, and 30. The maximum probability occurs at $28 w=28/100=0.28$ so "nice" tick marks are 0.00, 0.05, 0.10, 0.15, 0.20, 0.25, and 0.30. The maximum probability density occurs at $28 v=28/(35*100)=0.008$ so "nice" tick marks will be 0.000, 0.001, ..., 0.009.
Now we find the corresponding counts to those sets of tick marks. That will be 0, 5, 10, 15, 20, 25, 30 for the probability axis and 0, 3.5, 7, 10.5, 14, 17.5, 21, 24.5, 28, 31.5 for the probability density axis.
Not the answer you're looking for? Browse other questions tagged probability statistics graphing-functions or ask your own question.
What is the correct way to plot histogram?
How to normalize histogram well?
What methods are there to determine Bin Width for Frequency Tables given the number of bins in Mixed Intervals?
How can "relative frequency histogram" become a "probability density curve"? | CommonCrawl |
While theoretical efforts continue to explore possible explanations for the late-time cosmic acceleration, as well as the problem of the cosmological constant, we expect future cosmological surveys to judge against or for many of the proposed theories. In this talk, I will first review the status of models of dark energy provided by fundamental physics (supergravity and string theory) by presenting, as an example, a recently discovered class of $\alpha$-attractor models of quintessential inflation which combine dark energy and inflation in a unified framework.
Teleparallel gravity (TEGR) as a gauge theory: Translation or Cartan connection?
Lire la suite de Teleparallel gravity (TEGR) as a gauge theory: Translation or Cartan connection?
I will provide a general introduction to tensor models and their applications to quantum gravity. Initially developed in the context of random geometry, as a generalization of the matrix models approach to 2d quantum gravity, tensor models and their large N expansion have more recently been taken advantage of in the context of holography. In particular, the "near AdS_2 / near CFT_1 correspondence" establishes a connection between strongly-coupled and explicitly solvable large N quantum mechanics and Jackiw-Teitelboim gravity in d=2. | CommonCrawl |
I have research work where I need to compute a matrix inversion. The matrix has a size $31300\times31300$. I am using a universal java matrix package to invert this matrix. But as the dimension of the matrix is huge, it throws error memory out of scope. Cpu cannot allocate huge memory space.
So, to find out a solution I came to know about GPU(Graphical Processing Unit). But in every search about GPU, it is described that GPU is used to speed up a process.
So my doubt is that the computation that failed to compute by CPU, is it possible to be computed by GPU? Or GPU only used for those processes which take of time to compute in CPU, they can compute in GPU for speedup.
Unfortunately, GPUs will be of no help to you in this particular situation. Your problem is in the memory limitation; thus, you just do not have enough RAM resources to allocate/factorize/solve the system. GPUs usually have a much smaller amount of memory available on them, so they are not used to help with memory-limited problems.
It looks like you are trying to allocate $31300\times 31300$ matrix which implies you are solving a dense linear algebra problem. Make sure that the matrix you work with is not sparse (in this case, there are efficient sparse linear algebra solvers).
There are out-of-core linear algebra solvers (which are, of course, significantly slower) which will allow you to solve larger problems within your RAM limitations by using your hard drive to store intermediate/final results.
Use efficient LAPACK linear algebra, say Intel MKL.
Try using a machine with a larger amount of memory (Amazon EC2 has cheap options available).
Not the answer you're looking for? Browse other questions tagged linear-solver gpu memory-management .
What kinds of problems lend themselves well to GPU computing?
Can I convert CUDA core to CPU core and use it as cpu core while running any program? | CommonCrawl |
If X and Y are independent, Y and Z are independent, and so are X and Z, one might be tempted to conclude that X, Y, and Z are independent. But it has long been known in classical probability theory that, intuitive as it may seem, this is not true in general. In quantum mechanics one can ask whether analogous statistics can emerge for configurations of particles in certain types of entangled states. The explicit construction of such states, along with the specification of suitable sets of observables that have the purported statistical properties, is not entirely straightforward. We show that an example of such a configuration arises in the case of an N-particle GHZ state, and we are able to identify a family of observables with the property that the associated measurement outcomes are independent for any choice of $2,3,\ldots ,N-1$ of the particles, even though the measurement outcomes for all N particles are not independent. Although such states are highly entangled, the entanglement turns out to be 'fragile', i.e. the associated density matrix has the property that if one traces out the freedom associated with even a single particle, the resulting reduced density matrix is separable. | CommonCrawl |
Assume there would be $x_1 < x_2$ such that $f(x_1) = f(x_2)$.
The function $f$ is continuous and differentiable on $[x_1,x_2]$.
By Rolle's Theorem there exists $c$ in $(x_1,x_2)$ with $f'(c) = 0$.
This is a contradiction since $f'(x) = \pause 3x^2 + 1 \pause \ge 1$ for all $x$.
There no $x_1 < x_2$ such that $f(x_1) = f(x_2)$. Thus $f$ is one-to-one. | CommonCrawl |
Purpose: In this tutorial, you will learn how to optimize a general crystal structure. An explicit example is given for hexagonal structures. Here, you will set up and execute a series of calculations for different volumes (at constant c/a ratio) and for different c/a ratios (at constant volume) for Be in the hexagonal structure. The tools which are used in this tutorial are applicable for any crystal type.
Read the following paragraphs before starting with the rest of this tutorial!
Before starting, be sure that relevant shell variables are already defined and that the excitingscripts directory has already been downloaded, as specified in Tutorial scripts and environment variables. Here is a list of the scripts which are relevant for this tutorial with a short description.
OPTIMIZE-lattice.py: Python script. A manager program which calls the setup and analyze scripts.
OPTIMIZE-setup.py: Python script for generating structures at different volume/strains. This script is used within the lattice script.
OPTIMIZE-analyze.py: Python script for fitting the energy-vs-volume and energy-vs-strain curves. This script is called by the lattice script.
OPTIMIZE-submit.sh: (Bash) shell script for running a series of exciting calculations.
OPTIMIZE-clean.sh: (Bash) shell script for cleaning unnecessary files.
exciting2sgroup.xsl: xsl script for converting an exciting input file to an input file for the program sgroup.
Requirements: Bash shell. Python numpy, lxml, matplotlib.pyplot, and sys libraries.
The scripts in this tutorial use the sgroup tool. If you have not done before, this tool should be downloaded and installed. The code sgroup is a utility which allows to determine the space group and symmetry operations of a crystal structure.
After the download, you will get a tar.gz file, go to the directory where you saved this file and execute the following commands.
Now, you have everything you need for starting and performing general lattice optimization.
The lattice of a general crystal structure is determined by giving six lattice parameters, $a, b, c, \alpha, \beta,$ and $\gamma$. The first 3 parameters are connected with the length of the 3 primitive vectors of the crystal; the last 3 are the angles between the primitive vectors.
In order to perform the optimization of the energy of a crystal with respect to all lattice parameters, we can use an iterative cyclic procedure where in turns one parameter is varied and the remaining 5 are kept fixed. The procedure can be repeated until the obtained equilibrium parameters do not vary anymore within a desired accuracy. In particular, the minimization procedure as performed by the script OPTIMIZE-lattice.py will contain the following cycles.
Minimization with respect to the volume $V$ (by applying an isotropic strain).
Minimization with respect to the $b/a$ ratio (all other parameter are fixed).
Minimization with respect to the $c/a$ ratio (all other parameter are fixed).
Minimization with respect to the angle $\alpha$ between the $b$ and $c$ axes (all other parameter are fixed).
Minimization with respect to the angle $\beta$ between the $a$ and $c$ axes (all other parameter are fixed).
Minimization with respect to the angle $\gamma$ between the $a$ and $b$ axes (all other parameter are fixed).
In the example reported in this tutorial, we consider a crystal with hexagonal crystal structure. In this case there are only two free parameters, the volume $V$ and the $c/a$ ratio. In the next, we show how to perform the lattice optimization with respect to these two parameters.
The first step is to create a directory for the system that you want to investigate. In this tutorial, we consider as an example the calculation of energy-vs-volume and energy-vs-strain curves for Be in the hexagonal structure. Therefore, we create a directory Be_OPT and we move inside it.
Inside this directory, we create or copy an exciting input file for hexagonal Be with the name Be_opt.xml name. This file could look like the following.
This file can be saved with any name. In this tutorial is not necessary to rename the exciting input file as input.xml, because this file is the input of the script OPTIMIZE-lattice.py and not of exciting itself. Please, notice that the input file for a direct exciting calculation must be always called input.xml.
In the next, we illustrate the iterative procedure for performing the optimization of the crystal stucture of hexagonal Beryllium. The only relevant parameters in this case are the volume of the unit cell and the $c/a$ ratio.
At the first step, we optimize the energy with respect to the volume. In order to generate input files for a series of volumes you have to use the script OPTIMIZE-lattice.py.
Entry values must be typed on the screen when requested. In this case, entries are the following.
Be_opt.xml, the name of the input file you have created.
1, the type of optimization you choose.
0.010, the absolute value of the maximum strain for which we want to perform the calculation.
5, the number of deformed structures equally spaced in strain, which are generated between the maximum negative strain and the maximum positive one.
To execute the calculations, you have to run the script OPTIMIZE-submit.sh. If you do so, you see the following messages on the screen.
When calculations finished to run, results can be analyzed. In order to do this, you have to run again the OPTIMIZE-lattice.py python script in the current directory.
At this point, the script is asking whether you desire to use a Murnaghan (M) or Birch-Murnaghan (B) equation of state for extracting the equilibrium parameters such as the equilibrium volume and the bulk modulus. For more details about the equation of state see here.
Moreover, the script generates a plot (PostScript file vol.ps) which looks like the following.
On this plot, you can also find the optimized values of the parameters appearing in the equation of state (minimum energy, equilibrium volume, bulk modulus, and bulk modulus pressure derivative.
Please note: The bulk modulus and bulk modulus pressure derivative which are derived here have to be interpreted only as fitting parameters. They do not coincide with the "exact" bulk modulus and bulk modulus pressure derivative of the crystal. Indeed, these "exact" values should be obtained by fitting, with an equation of state (Birch or Murnaghan), the function E=E(V), where for each volume V, E(V) is the energy obtained by optimizing, at that given V, all other lattice and internal parameters.
A file corresponding to an exciting input file for the optimized geometry is created with the name vol-optimized.xml. If you are interested to check how accurate are the calculated equilibrium parameters at this step, you can find more information here.
At this point, you have performed the first optimization step by varying only the volume. In order to be prepared for the next step, you should move now to the parent directory and rename the VOL directory to 1-VOL (first step, optimizing only the volume). Then, you should copy the vol-optimized.xml file to the current directory with the new name 1-VOL.xml. This file will be used as the input file in the next step.
In order to perform the next optimization step, you have to run again OPTIMIZE-lattice.py in the Be_OPT directory, typing entries like in the following.
Now, move to the COA directory and run OPTIMIZE-submit.sh.
When calculations are finished, run again OPTIMIZE-lattice.py.
In this case, the optimization is performed using a fourth-order polynomial fit for calculating the minimum energy and the corresponding strain. The resulting plot (also available as PostScript file as coa.ps) should look like the following.
At this point, you have completed the second optimization step (by varying only the $c/a$ ratio). The optimized structure is saved in the coa-optimized.xml file. Similar to the previous step, you should move out to the parent directory, rename COA to 2-COA (second optimization step, varying only $c/a$). Then, copy the coa-optimized.xml file to the current directory with the name 2-COA.xml.
Notice: Due to the fact that the volume and $c/a$ ratio have been already optimized once, we can choose smaller range of distortion for the next steps.
Repeat now the procedure already explained in STEP1 using the following entries.
After having performed the calculation, you run OPTIMIZE-lattice.py and get the following plot.
At this point, you have optimized the volume for the second time. Follow the last part of STEP1 and copy the file vol-optimized.xml to the parent directory under the name 3-VOL.xml.
Repeat the procedure in STEP2 with the following input.
In a similar way to STEP2, you will end up with the following plot.
At this point, the second optimization of the $c/a$ ratio has been completed and the new optimized structure has been saved in coa-optimized.xml.
In the following table you find a summary of the result of the first 4 optimization steps.
As you can see from the previous table, at the 4-th iteration you reached the following convergence.
The c/a ratio is converged within 2$\times$10-4.
The energy at the minimum is converged within 10-3 [mHa].
If these results correspond to the desired accuracy you can stop the optimization procedure. Otherwise, you proceed with the next step and, using the new results, you check again the convergence behaviour of the equilibrium parameters. | CommonCrawl |
Question 1: What's a (nice) way to characterize data $\theta_i$, $\ell_i$, $\kappa_i$ that describes a valid circular triangle?
Question 2: Can all circular triangles be expressed as the image of geodesic triangles from some "nice" space under some "nice" map?
For instance, one can study the subset of circular triangles coming from spherical geometry (via stereographic projection) or hyperbolic geometry (via the Poincaré model). What about the rest?
Question 4: Is there another name for this object? What else is known?
Any pointers are appreciated. Thanks!
A. Schonflies, Ueber Kreisbogendreiecke und Kreisbogenvierecke, Math. Ann., 44 (1894) 105--124.
F. Klein, Ueber die Nullstellen der hypergeometrischen Reihe, Math. Ann., 37 (1890) 573--590.
F. Klein, Vorlesungen uber die hypergeometrische Funktion, 1933, reprint: Springer-Verlag, Berlin-New York, 1981.
There is a complete classification and description of the moduli space. The connection with hypergeometric function is the following. Let $y^"+Py=0$ be a hypergeometric equation with real coefficients. Let $y_1,y_2$ be two linearly independent solutions. Then $f=y_1/y_2$ maps the upper half-plane conformally onto a spherical triangle (region bounded by 3 arcs of circles). And every spherical triangle (region, surface) is obtained in this way.
Of course, your definition of the spherical triangle is different: your triangle is just a curve. But classification of triangles-curves is simpler that classification of triangles-regions, and it can be found in those papers I mentioned.
Notice also that fractional-linear transformations of the Riemann sphere act on the set of circular triangles. By a fractional-linear transformation, every triangle can be sent to a triangle with vertices $0,1,\infty$. Then two sides are straight, and one, $(0,1)$ is straight or circle. This leads to a simple classification.
What are trig classes like within a universe that's "noticeably" hyperbolic?
Are all Dehn invariants achievable?
If a triangle can be displaced without distortion, must the surface have constant curvature? | CommonCrawl |
What Am I and What Do I Do?
I know what I am - I'm an actuary. But how many other people know what an actuary is?
It all started (as we keep saying) with the Greeks. In this case with a certain Eubulides, philosopher-about-town in Athens of the 4th century BC.
Since 15 across is a 2 digit cube, and an integer, it is either 27 or 64. Assume that it is 64.
Alice's and Bert's ages combined total 11016 days.
Q.840 (i) Let $\alpha ,\beta$ be two distinct solutions of $$x^3 - x^2 - x + c = 0.$$ Simplify $\alpha^2\beta + \alpha\beta^2 - \alpha\beta$.
Q.829 (i) let $c$ be any integer. Show that the remainder when $c^2$ is divide by $4$ cannot be either $2$ or $3$. | CommonCrawl |
Matrix functions of the form $f(A)v$, where $A$ is a large symmetric matrix, $f$ is afunction, and $v\\ne 0$ is a vector, are commonly approximated by first applying a few,say $n$, steps of the symmetric Lanczos process to $A$ with the initial vector $v$ in order todetermine an orthogonal section of $A$. The latter is represented by a (small)$n\\times n$ tridiagonal matrix to which $f$ is applied. This approach uses the $n$ firstLanczos vectors provided by the Lanczos process. However, $n$ steps of the Lanczosprocess yield $n+1$ Lanczos vectors. This paper discusses how the $(n+1)$stLanczos vector can be used to improve the quality of the computed approximation of$f(A)v$. Also the approximation of expressions of the form $v^Tf(A)v$ is considered. | CommonCrawl |
The stiffness matrix of $Ax=B$ system of linear equations, where $A$ is an $n\times n$ symmetric matrix stored in the form of symmetric skyline matrix, that is associated with a finite element model of 3-D elastic solids, when reordered with the reverse Cuthill–McKee algorithm doesn't result in a skyline matrix with limited RAM storage space requirements as would happen with a 2-D problem.
What is the best algorithm for the 3-D case?
For direct solution in 3D, you should probably be using some flavor of nested dissection (ND) or minimum degree (MD). These attack the storage requirements of A=LL' factorization directly, not the bandwidth (which has only an indirect effect on fill-in). On it's own, bandwidth reduction is just not strong enough to make 3D direct solve tractable.
Good ND codes to try are METIS or Scotch, while AMD is easiest to access MD code. Many sparse direct solvers will expose/reference these reordering packages directly among their input parameters.
For a good "turn-key" package that hides/handles all this detail for you, I'd recommend Intel's MKL PARDISO. Although it is closed-source, binaries are available under pretty liberal license terms.
Not the answer you're looking for? Browse other questions tagged finite-element linear-solver sparse memory-management or ask your own question.
Is reduced stiffness matrix positive definite too? | CommonCrawl |
take the last 16 bytes of the shared secret byte array (do not use the first 16 bytes — those are not as uniformly distributed as the last 16 bytes!).
Why are the last 16 bytes more random than the first 16?
Is this specific to the secp224r1 curve, or is it general to the elliptic curve version of the Diffie-Hellman algorithm?
There are at most $n$ distinct values of $(x, y) = [\alpha \beta]G$ where $\alpha$ and $\beta$ are secret scalars in $\mathbb Z/n\mathbb Z$ and $G$ is the standard base point, all satisfying this equation.
If you choose uniformly among them, e.g. by choosing $\alpha$ and $\beta$ independently uniformly at random, and encode the pair $(x, y)$ into a $2 \lceil\log_2 p\rceil$-bit string, there is a trivial algorithm to distinguish the resulting string from a uniform random $2 \lceil\log_2 p\rceil$-bit string: decode it as a pair of integers $x$ and $y$ and test whether $y^2 \equiv x^3 + a x + b \pmod p$. So not only do the encoded values of $(x, y)$ cover a tiny fraction of the space of $2 \lceil\log_2 p\rceil$-bit strings—square root of the number of all such strings of that length—but they're trivial to distinguish from uniform random.
But that's partly because for each $x$, there's only at most two values of $\pm y$, so we can compress it into a much shorter $(1 + \lceil\log_2 p\rceil)$-bit string by storing only a bit to discriminate between the two possible values of $y$. Is that uniform random? No! If you decode $x$, you can test whether $x^3 + a x + b$ is a quadratic residue modulo $p$, which only about half of the integers are.
Distinguishers for the encoding of uniform random elliptic curve points were some of the first problems documented publicly in Dual_EC_DRBG, before everyone realized it was an obvious vector for a back door.
In general, when a random string is readily distinguishable from uniform like this, it is unfit to be used as a secret key in a cryptosystem whose contract demands a uniform random key—if you violate the security contract, it is null and void. But if the random string, while not uniform, nevertheless has high min-entropy, you can effectively get a uniform random string by hashing it, say with SHAKE256—what this means is that the best an adversary can do is test a guess about what the input might have been.
As for the low-order or high-order bits of $x$ and $y$? Don't bother; just hash them all. The cost of computing a hash like SHAKE256 is negligible compared to the cost of computing an elliptic curve scalar multiplication even on a small curve like secp224r1.
Not the answer you're looking for? Browse other questions tagged key-exchange diffie-hellman elliptic-curves or ask your own question.
Besides key and ciphertext sizes what are other advantages of elliptic curve versions of various protocols?
Security of Diffie-Hellman with multiplication for secret derivation? | CommonCrawl |
For the grand opening of the algorithmic games in NlogNsglow, a row of tower blocks is set to be demolished in a grand demonstration of renewal. Originally the plan was to accomplish this with controlled explosions, one for each tower block, but time constraints now require a hastier solution.
To help you remove the blocks more rapidly you have been given the use of a Universal Kinetic / Incandescent Energy Particle Cannon (UKIEPC). On a single charge, this cutting-edge contraption can remove either all of the floors in a single tower block, or all the $x$-th floors in all the blocks simultaneously, for user's choice of the floor number $x$. In the latter case, the blocks that are less than $x$ floors high are left untouched, while for blocks having more than $x$ floors, all the floors above the removed $x$-th one fall down by one level.
Given the number of floors of all towers, output the minimum number of charges needed to eliminate all floors of all blocks.
The first line of input contains the number of blocks $n$, where $2 \leq n \leq 100\, 000$. The second line contains $n$ consecutive block heights $h_ i$ for $i=1,2,\ldots ,n$, where $1 \leq h_ i \leq 1\, 000\, 000$.
Output one line containing one integer: the minimum number of charges needed to tear down all the blocks. | CommonCrawl |
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:5600-5609, 2018.
We present first massively parallel (MPC) algorithms and hardness of approximation results for computing Single-Linkage Clustering of n input d-dimensional vectors under Hamming, $\ell_1, \ell_2$ and $\ell_\infty$ distances. All our algorithms run in O(log n) rounds of MPC for any fixed d and achieve (1+\epsilon)-approximation for all distances (except Hamming for which we show an exact algorithm). We also show constant-factor inapproximability results for o(\log n)-round algorithms under standard MPC hardness assumptions (for sufficiently large dimension depending on the distance used). Efficiency of implementation of our algorithms in Apache Spark is demonstrated through experiments on the largest available vector datasets from the UCI machine learning repository exhibiting speedups of several orders of magnitude.
%X We present first massively parallel (MPC) algorithms and hardness of approximation results for computing Single-Linkage Clustering of n input d-dimensional vectors under Hamming, $\ell_1, \ell_2$ and $\ell_\infty$ distances. All our algorithms run in O(log n) rounds of MPC for any fixed d and achieve (1+\epsilon)-approximation for all distances (except Hamming for which we show an exact algorithm). We also show constant-factor inapproximability results for o(\log n)-round algorithms under standard MPC hardness assumptions (for sufficiently large dimension depending on the distance used). Efficiency of implementation of our algorithms in Apache Spark is demonstrated through experiments on the largest available vector datasets from the UCI machine learning repository exhibiting speedups of several orders of magnitude. | CommonCrawl |
Exceptional complex Lie groups have become increasingly important in various fields of mathematics and physics. As a result, there has been interest in expanding the representation theory of finite groups to include embeddings into the exceptional Lie groups. Cohen, Griess, Lisser, Ryba, Serre and Wales have pioneered this area, classifying the finite simple and quasisimple subgroups that embed in the exceptional complex Lie groups.
This work contains the first major results concerning conjugacy classes of embeddings of finite subgroups of an exceptional complex Lie group in which there are large numbers of classes. The approach developed in this work is character theoretic, taking advantage of the classical subgroups of $E_8 (\mathbb C)$. The machinery used is relatively elementary and has been used by the author and others to solve other conjugacy problems. The results presented here are very explicit. Each known conjugacy class is listed by its fusion pattern with an explicit character afforded by an embedding in that class.
The Heavens and the Earth is a groundbreaking new textbook designed for the undergraduate, non-science major. Thoroughly Biblical in approach and content, it is the only college-level textbook in Earth and space sciences that advocates Biblical, young-Earth creationism while also fairly and respectfully presenting naturalistic views of history.
FIVE SOULS, huddled against the aching cold of the Alaskan wilderness. On a hunt for truth amid the shrieks of wild animals, the clouds, overhead race swiftly by?. Adventures from left to right: Mike Liston, Buddy Davis, Dan Specht, George Detwiler, and John Whitmore.
LOCKED in a remote, frozen wasteland where man has rarely been lie remains of creatures so mysterious, science can scarcely believe the truth.
A team of scientists and researchers endured incredible hardships to reach a site many would rather avoid?the Alaskan wilderness?and in the process, uncovered unfossilized dinosaur bones. The implications are enormous, for how can dinosaurs be 65 million years old if their bones are still unfossilized?
Join the team and thrill at the photographs and tales of danger, as The Great Alaskan Dinosaur Adventure drops a bombshell on the scientific community. | CommonCrawl |
Abstract: We propose a Las Vegas probabilistic algorithm to compute the zeta function of a genus-3 hyperelliptic curve defined over a finite field $\mathbb F_q$, with explicit real multiplication by an order $\mathbb Z[\eta]$ in a totally real cubic field. Our main result states that this algorithm requires an expected number of $\widetilde O((\log q)^6)$ bit-operations, where the constant in the $\widetilde O()$ depends on the ring $\mathbb Z[\eta]$ and on the degrees of polynomials representing the endomorphism $\eta$. As a proof-of-concept, we compute the zeta function of a curve defined over a 64-bit prime field, with explicit real multiplication by $\mathbb Z[2\cos(2\pi/7)]$. | CommonCrawl |
Lemma 5.28.7. Let $X$ be a topological space. Suppose $X = T_1 \cup \ldots \cup T_ n$ is written as a union of constructible subsets. There exists a finite stratification $X = \coprod X_ i$ with each $X_ i$ constructible such that each $T_ k$ is a union of strata.
In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 09Y4. Beware of the difference between the letter 'O' and the digit '0'.
The tag you filled in for the captcha is wrong. You need to write 09Y4, in case you are confused. | CommonCrawl |
Let $\Pi$ denote a portfolio consisting of a long position of 100 dollars face value in each bond, i.e. $\Pi$ has a value of 2 × 90 = 180.
I am asked to calculate the Expected Shorfall for the portfolio $\Pi$ as a function of $\alpha\in(0,0.5)$. How can it be done?
Browse other questions tagged value-at-risk default cvar or ask your own question.
What is the difference between these two Expected Shortfall definitions?
Where can I find Value at Risk & Expected shortfall for ETF's?
How do I compute Value at Risk of a European call option? | CommonCrawl |
Just received my handibot today and encountered a few problems.
After that did a bit of debugging and I found that the home tool appears to move to the right by 1/2" after reaching the far left. *But* this causes the dust collector to collide with the motor if moved to the right by 6". Looking at the code for the macro it looks like it hasn't changed in a while so I'm not sure what is going on. I can remove the dust cover for the Z-Zero *but* I will still get the collision during milling if I use the full 6" in X.
For the test cut being deep I believe that is because the Z-Zero does not set the zero and it needs the Resume during the home to set it (I must have clicked on quit instead of resume; have not tried again). Just a guess though.
Try this: in your macro editor (folder icon on left side bag bar in FabMo) edit macro #3. In that macro there is a variable at the top called $x_backoff. It should be set to 0.075–change it to 0.25 and save the macro. Run the homing routine again and see if the spacing is correct.
For the test cut—yes you should update the z home location. Do you have a scrap piece of wood on which you can run the test cut again? You can also send the z axis to z=0 with the manual controls to check if the bit is touching the material after homing.
Yeah I will edit the macro#3 to change my home a little more to the left. The Z-Zero also looks like it has it's own code to home the X so I will also edit that code and test.
I did the zero and then checked the Z and yes it is indeed on the top of the material (so that is working). For the test cut I will do that later today (after work).
1) If I did leave the zero at the homing location it would have milled in the air and not further down into the material. So seems like I did zero it.
2) When I do a preview of the job that was submitted it shows a Z of 0.92"
How do I interpret this 0.92"?
I would have interpreted it as 0.92" deep from the zero point. But that would have gone right through the material so I assume it is the max Z travel for the cut and since I don't know where the cuts starts the 0.92" doesn't mean much to me.
How deep is the test cut suppose to be from the zero point?
0.92" is the total range of travel in the Z axis for the cut--though max Z depth would be a more helpful measure I agree. In the test cut, the Z first jogs to a safe height of 0.8"--then at the point in the cut where the letters are being VCarved, it reaches a depth of -0.12"--giving the range of 0.92" throughout the cut file.
I'm trying to piece together why the cut went too deep on your first attempt--If you had selected "quit" when prompted in the homing routine, it would have left z zero just 0.075" from the very top of travel. When Z jogged to 0.8" at the start of the file, it would have hit the top hard stop and lost position--shifting the Z zero down by 0.725" Still not enough to cause the cut to be too deep.
I've never really tried to work out a relationship between time of year and certain tech support issues, but I imagine the hot-cold-hot-cold-hot of winter shipping can put strain on the aluminum joints of the tool.
2) I did find that the router wasn't perfectly vertical. So removed it and adjusted the holder. Even with that the dust adapter still hits the stepper. So still need the offset adjust in home.
I will give the test program another try when my daughter isn't waiting.
Actually just had an idea for maybe why it was too deep. When doing the tour it has you zero it out first (and then do the home). That first zero attempt the dust collector was on and when that collided with the stepper if that caused it to not lower (but it thought it was lowering) then it would think the zero is inside the material. Then in the home I would have done resume and then the cut would be too deep.
The size thing sounds like something going on in the actual design of the file--maybe the choice of "inside" vs "outside" in the profile cut that cuts out the part?
Still curious about the cutting in the air issue with the test cut. You're checking that when z=0, the bit is touching the material--then when the cut is run and the z axis is driven to some negative value, the bit is above the material...somehow that position must be getting lost. To rule out mechanical causes, we should try slowing the tool waaaay down. In the Axis tab on the configuration menu there are max-federate values for all three axes and max jog speeds. If you set all of these to 60 inches per minute--both jog and federate. Plus set the "maximum jerk" very low for all three axes. A value of 25 should do it. See if you can run the file with those settings--then we can rule out software issues at least. | CommonCrawl |
Investigate other $3\times 3$ squares.
Now try with $2\times 2$ squares and $4\times 4$ squares.
Can you predict your answers? What is happening?
Addition & subtraction. Generalising. Mathematical reasoning & proof. Properties of numbers. Visualising. Games. Working systematically. Creating and manipulating expressions and formulae. Factors and multiples. Multiplication & division. | CommonCrawl |
Each of the two chapters in this dissertation is based on a game theory paper. Although the topic of each chapter is different, they are linked by the question: How do players coordinate their actions through communication? Each chapter develops a communication schema, depicts equilibrium strategies, and responds to this inquiry. In the first chapter, I study a collective action problem in a setting of discounted repeated coordination games in which players know their neighbors' inclination to participate as well as monitor their neighbors' past actions. I define strong connectedness to characterize those states in which, for every two players who incline to participate, there is a path consisting of players with the same inclination to connect them. Given that the networks are fixed, finite, connected, commonly known, undirected and without cycles, I show that if the priors have full support on the strong connectedness states, there is a weak sequential equilibrium in which the ex-post efficient outcome repeats after a finite time $T$ in the path when discount factor is sufficiently high. This equilibrium is constructive and does not depend on public or private signals other than players' actions. In the second chapter, I consider the three-player complete information games augmented with pre-play communication. Players can privately communicate with others, but not through a mediator. I implement correlated equilibria by letting players be able to authenticate their messages and forward the authenticated messages during communication. Authenticated messages, such as letters with signatures, cannot be duplicated but can be sent or received by players. With authenticated messages, I show that, if a game $G$ has a worst Nash equilibrium $\alpha$, then any correlated equilibrium distribution in $G$, which has rational components and gives each player higher payoff than what $\alpha$ does, can be implemented by a pre-play communication. The proposed communication protocol does not publicly expose players' messages in any stage during communication. | CommonCrawl |
François Loeser and I just uploaded a paper on arXiv about Motivic height zeta functions. That such a thing could be possible is quite funny, so I'll take this opportunity to break a long silence on this blog.
In Diophantine geometry, an established and important game consists in saying as much as possible of the solutions of diophantine equations. In algebraic terms, this means proving qualitative or quantitative properties of the set of integer solutions of polynomial equations with integral coefficients. In fact, one can only understand something by making the geometry more apparent; then, one is interested in integral points of schemes $X$ of finite type over the ring $\mathbf Z$ of integers. There are in fact two sub-games: one in which one tries to prove that such solutions are scarce, for example when $X$ is smooth and of general type (conjecture of Mordell=Faltings's theorem, conjecture of Lang) ; the other in which one tries to prove that there are many solutions —then, one can even try to count how many solutions there are of given height, a measure of their size. There is a conjecture of Manin predicting what would happen, and our work belongs to this field of thought.
Many methods exist to understand rational points or integral points of varieties. When the scheme carries an action of an algebraic group, it is tempting to try to use harmonic analysis. In fact, this has been done since the beginnings of Manin's conjecture when Franke, Manin, Tschinkel showed that when the variety is a generalized flag variety ($G/P$, where $G$ is semi-simple, $P$ a parabolic subgroup, for example projective spaces, grassmannians, quadrics,...), the solution of Manin's question was already given by Langlands's theory of Eisenstein series. Later, Batyrev and Tschinkel proved the case of toric varieties, and again with Tschinkel, I studied the analogue of toric varieties when the group is not a torus but a vector space. In these two cases, the main idea consists in introducing a generating series of our counting problem, the height zeta function, and establishing its analytic properties. In fact, this zeta function is a sum over rational points of a height function defined on the adelic space of the group, and the Poisson summation formula rewrites this sum as the integral of the Fourier transform of the height function over the group of topological characters. What makes the analysis possible is the fact that, essentially, the trivial character carries all the relevant information; it is nevertheless quite technical to establish what happens for other characters, and then to check that the behavior of the whole integral is indeed governed by the trivial character.
In mathematics, analogy often leads to interesting results. The analogy between number fields and function fields suggests that diophantine equations over the integers have a geometric analogue, which consists in studying morphisms from a curve to a given variety. If the ground field of the function field is finite, the dictionary goes quite far; for example, Manin's question has been studied a lot by Bourqui who established the case of toric varieties. But when the ground field is infinite, it is no more possible to count solutions of given height since they will generally be infinite.
However, as remarked by Peyre around 2000, all these solutions, which are morphisms from a curve to a scheme, form themselves a scheme of finite type. So the question is to understand the behavior of these schemes, when the height parameter grows to infinity. In fact, in an influential but unpublished paper, Kapranov had already established the case of flag varieties (without noticing)! The height zeta function is now a formal power series whose coefficients are algebraic varieties; one viewes them as elements of the Grothendieck ring of varieties, the universal ring generated by varieties with addition given by cutting-and-pasting, and multiplication given by the product of varieties. This ring is a standard tool of motivic integration (as invented by Kontsevich and developed by Denef and Loeser, and many people since). That's why this height zeta function is called motivic.
What we proved with François is a rationality theorem for such a motivic height function, when the variety is an equivariant compactification of a vector group. This means that all this spaces of morphisms, indexed by some integer, satisfy a linear dependence relation in the Grothendieck ring of varieties! To prove this result, we rely crucially on an analogue of the Poisson summation formula in motivic integration, due to Hrushovski and Kazhdan, which allows us to perform a similar analysis to the one I had done with Tschinkel in a paper that appeared last year in Duke Math. J. | CommonCrawl |
Morgana is learning computer vision, and he likes cats, too. One day he wants to find the cat movement from a cat video. To do this, he extracts cat features in each frame. A cat feature is a two-dimension vector <$x$, $y$>. If $x_i$ = $x_j$ and $y_i$ = $y_j$, then <$x_i$, $y_i$> <$x_j$, $y_j$> are same features.
So if cat features are moving, we can think the cat is moving. If feature <$a$, $b$> is appeared in continuous frames, it will form features movement. For example, feature <$a$ , $b$ > is appeared in frame $2,3,4,7,8$, then it forms two features movement $2-3-4$ and $7-8$ .
Now given the features in each frames, the number of features may be different, Morgana wants to find the longest features movement.
First line contains one integer $T(1 \le T \le 10)$ , giving the test cases.
In The next $n$ lines, each line contains one integer $k_i$ ( the number of features) and $2k_i$ intergers describe $k_i$ features in ith frame.(The first two integers describe the first feature, the $3$rd and $4$th integer describe the second feature, and so on).
In each test case the sum number of features $N$ will satisfy $N \le 100000$ .
For each cases, output one line with one integers represents the longest length of features movement. | CommonCrawl |
(this may also be rotated by several right turns, or horizontally reflected or vertically reflected).
As suggested by Slepz in comments, it is clear that no corner cell may be covered, and no two adjacent edge cells may be covered. It follows that at most 5 of the 9 non-corner cells on each long edge may be covered, and at most 4 of the 8 non-corner cells on each short edge may be covered. This gives an upper bound of 5+5+4+4=18 for the number of covered edge cells.
Proof: Following the same logic as the previous paragraph, 5+5+4+4 would be the only possible way to achieve 18. By inspection we can see that the only way to cover 5 squares on the long edge is the green-yellow pattern in Jeff B's answer (with two possible orientations).
However, note that each yellow cross actually eliminates 2 non-corner cells on each short edge. Considering both yellow crosses on one short edge, this means only the two central cells of the short edge remain. Since they are adjacent only at most one can be covered.
So we have shown that if 5 cells are covered on both long edges, then at most 3 cells may be covered on either short edge. This proves the lemma and reduces our upper bound for edge square coverage to 16.
Finally, since there are 8 x 9 = 72 non-edge squares, 72 + 16 = 88 is now the upper bound on coverage for all squares; therefore placing 15 crosses (which would cover 90 squares) is not possible.
Seeing what seemed to be wasted space, I tried rotating a few (e.g., the leftmost bluish cross), but couldn't get any more in.
Corners are out. Since the shape has... let's call them "jutty-out parts"... none can be packed flat against a side, so there will necessarily be unused squares on every single side. Packing them as closely as possible (as I have at the bottom), each long side will have the previously-mentioned $2$ unused corner squares as well as $4$ unused squares which alternate with the end bits of the crosses. Each short side will have the previously-mentioned $2$ unused corner squares and at least $4$ other unused squares. This alone (unusable side squares) gives us a maximum $90$ squares that could contain parts of crosses. If we could rearrange that remaining space, and if, instead of crosses, we were trying to pack $3\times2$ rectangles in that remaining space, then we could fit exactly $15$ of them in there.
This, in combination with the reasoning given in @M.M's post, shows that $14$ is the largest number of crosses that can be contained entirely within a $10\times11$ grid.
extremely arnold schwarzenegger voice remember when I said I would never do another math puzzle again. i lied.
I cannot manage a better arrangement.
Not the answer you're looking for? Browse other questions tagged mathematics combinatorics checkerboard or ask your own question. | CommonCrawl |
The publication first conscientiously develops the speculation of reproducing kernel Hilbert areas. The authors then speak about the choose challenge of discovering the functionality of smallest $H^\infty$ norm that has distinct values at a finite variety of issues within the disk. Their point of view is to think about $H^\infty$ because the multiplier algebra of the Hardy area and to exploit Hilbert house ideas to resolve the matter.
Maestro Benedetto In 1463, Benedetto of Florence completed his great work "Trattato di praticha d'arismetica", consisting of 500 large pergament pages. For us, the most interesting parts of this work are the books 13, 14, and 15, which deal with algebraic equations. Benedetto starts with the welI-known "reghola de algebra amuchable", that is, with the solution of the six types of linear and quadratic equations x 2 =px x 2 =q px=q x 2 +px=q x 2 +q=px x 2 =px+q. According to Franci and Toti Rigatelli (Historia Math.
Cajori: A History of Mathematics, p. 271. In 1240, the republic of Pisa awarded the "serious and learned Master Leonardo Bigolli" a yearly salary of 20 pounds silver "in addition to the usual From Leonardo da Pisa 10 Luca Pacioli 35 allowances, in recognition of his usefulness to the city and its citizens through his teaching and devoted services". We shall now discuss the extant works of Leonardo. 1. The "Liber Abbaci" The Italian masters of computation were called "maestri d'abbaco". In this sense the title of Leonardo's most influential work is to be understood.
I shall now describe their work, wh ich is of fundamental import an ce for the history of algebra. Scipione deZ Ferro The general cubic equation The Solution of Cubic and Biquadratic Equations 53 ean be redueed, by introdueting a new variable x'=x+ta, to the simpler form If only positive eoeffieients and positive values of x are admitted, there are 3 types x 3 +px=q (1) (2) x 3 =px+q (3) x 3 +q=px. The first to solve equation (1) was Seipione deI Ferro, who was professor at the university of Bologna until his death in 1526. | CommonCrawl |
Proceedings of ICML Workshop on Unsupervised and Transfer Learning, PMLR 27:145-153, 2012.
Multi-task learning aims at transferring knowledge between similar tasks. The multi-task Gaussian process framework of Bonilla et al. models (incomplete) responses of $C$ data points for $R$ tasks (e.g., the responses are given by an $R \times C$ matrix) by using a Gaussian process; the covariance function takes its form as the product of a covariance function defined on input-specific features and an inter-task covariance matrix (which is empirically estimated as a model parameter). We extend this framework by incorporating a novel similarity measurement, which allows for the representation of much more complex data structures. The proposed framework also enables us to exploit additional information (e.g., the input-specific features) when constructing the covariance matrices by combining additional information with the covariance function. We also derive an efficient learning algorithm which uses an iterative method to make predictions. Finally, we apply our model to a real data set of recommender systems and show that the proposed method achieves the best prediction accuracy on the data set.
%X Multi-task learning aims at transferring knowledge between similar tasks. The multi-task Gaussian process framework of Bonilla et al. models (incomplete) responses of $C$ data points for $R$ tasks (e.g., the responses are given by an $R \times C$ matrix) by using a Gaussian process; the covariance function takes its form as the product of a covariance function defined on input-specific features and an inter-task covariance matrix (which is empirically estimated as a model parameter). We extend this framework by incorporating a novel similarity measurement, which allows for the representation of much more complex data structures. The proposed framework also enables us to exploit additional information (e.g., the input-specific features) when constructing the covariance matrices by combining additional information with the covariance function. We also derive an efficient learning algorithm which uses an iterative method to make predictions. Finally, we apply our model to a real data set of recommender systems and show that the proposed method achieves the best prediction accuracy on the data set.
AB - Multi-task learning aims at transferring knowledge between similar tasks. The multi-task Gaussian process framework of Bonilla et al. models (incomplete) responses of $C$ data points for $R$ tasks (e.g., the responses are given by an $R \times C$ matrix) by using a Gaussian process; the covariance function takes its form as the product of a covariance function defined on input-specific features and an inter-task covariance matrix (which is empirically estimated as a model parameter). We extend this framework by incorporating a novel similarity measurement, which allows for the representation of much more complex data structures. The proposed framework also enables us to exploit additional information (e.g., the input-specific features) when constructing the covariance matrices by combining additional information with the covariance function. We also derive an efficient learning algorithm which uses an iterative method to make predictions. Finally, we apply our model to a real data set of recommender systems and show that the proposed method achieves the best prediction accuracy on the data set. | CommonCrawl |
This study deals with the transition toward quasi-periodicity of buoyant convection generated by a horizontal temperature gradient in a three-dimensional parallelepipedic cavity with dimensions $4\times2\times1$ (length$\,\times\,$width$\,\times\,$height). Numerical continuation techniques, coupled with an Arnoldi method, are used to locate the steady and Hopf bifurcation points as well as the different steady and periodic flow branches emerging from them for Prandtl numbers ranging from 0 to 0.025 (liquid metals). Our results highlight the existence of two steady states along with many periodic cycles, all with different symmetries. The bifurcation scenarios consist of complex paths between these different solutions, giving a succession of stable flow states as the Grashof number is increased, from steady to periodic and quasi-periodic. The change of these scenarios with the Prandtl number, in connection with the crossing of bifurcation points, was carefully analysed. | CommonCrawl |
The information complexity of a function $f$ is the minimum amount of information Alice and Bob need to exchange to compute the function $f$. In this paper we provide an algorithm for approximating the information complexity of an arbitrary function $f$ to within any additive error $\alpha>0$, thus resolving an open question as to whether information complexity is computable.
In the process, we give the first explicit upper bound on the rate of convergence of the information complexity of $f$ when restricted to $b$-bit protocols to the (unrestricted) information complexity of $f$. | CommonCrawl |
I am trying to solve for the allowed wavefunctions and energies for a 1D quartic potential well.
where left means integration from x = 0 to x = patch, and right means integration from x = end to x = patch.
When I inspect the minimizing function that I find the roots of, I see that it does not cross zero at low energies.
I suspect the issue for this is that in the deeper well, the two potential wells can be considered separately because there is so little wavefunction overlap. I would, however, like my solver to be robust enough to find the isolated wavefunctions, or at the very least recognize when the two potential wells can be considered separately. I would also like my solver to solve asymmetric wells, which I am not sure it can do right now. Is there a way I can adapt my code to solve these two issues?
Also, here is the MATLAB code reproduced below. The main function is the first code block and is the script.
% % the wells are too seperate, consider them as isolated!!
%% Two pass patching, now we do it again...having found the optimal patching where the agreement is closest. Necessary?
% the division will make it nonzero because zero will go to inf!!
While I cannot help you with your specific implementation, I want to point out to an alternative method (as already indicated in a comment to phil's answer) : Marston's "Fourier Grid Hamiltonian" (FGH).
The FGH is a pseudo-spectral method and yields a simple recipe for constructing the discretized Hamiltonian matrix for bound systems. As usual, eigenvectors and eigenvalues of the discrete Hamiltonian represent discrete wavefunctions and corresponding energies. For the FGH, the Hamiltonian $H = T+V$ is split in a kinetic energy part $T$ and the potential part $V$. In position space the matrix elements $\left< x\vert V\vert x'\right>$ are just $V(x)\delta(x- x')$, so the potential energy contributes only the Hamiltonian matrix' diagonal. For the matrix elements of the kinetic energy operator, a band-limited (discrete $x_i$!) plane wave basis is used and the matrix elements $\left< x_i\vert T\vert x_j\right>$ are computed analytically.
You'll find a great discussion of this and various related Fourier methods in David Tannor's book "Introduction to Quantum Mechanics: a time-dependent perspective". Original references are also given there.
You'll find a Jupyter notebook with a simple Python/Cython implementation that tackles a quartic potential here. To change the potential you work with, find the line with pot = lambda x: x**4 - 20*x**2 and change it to any other potential you're interested in. Make sure to compute only bound states for which $\left<\psi\vert\psi\right>$ has decayed to zero close to the boundary of your $x$ domain.
The standard way to find the eigenvalues of the Schrodinger equation is called "imaginary time propagation". You change the coordinates, t=-i\tau, and integrate in the \tau direction. Any random initial condition will converge to the lowest energy eigenstate. The resulting equation is solved by splitting methods: First propagate the kinetic energy using Fast Fourier Transforms and then propagate the potential. This is possible since the solution decays fast (exponentially) as |x| grows and you can effectively replace your boundary conditions by periodic ones.
Since you want more eigenstates, there are several procedures: 1: iteration. compute the first eigenstate. Then, you restart the procedure, but in every step, you subtract the projection to this state. E.g. for the second state psi_2, in each step you write psi_2 = psi_2 - *psi_1.
As a complete alternative, you can discretize the Laplacian using finite differences (or use again FFTs) and then use the inverse power method. given your Hamiltonian H, iterate over n: (H-\lambda^(-1)I)^(-1)\psi_(n+1) = \psi_n for some guess of the eigenvalue \lambda. You can find details on wikipedia.
Not the answer you're looking for? Browse other questions tagged finite-difference eigenvalues eigensystem quantum-mechanics or ask your own question. | CommonCrawl |
Is every uniformizable topology induced by a Heine-Borel uniformity?
This is a follow-up to my question here. A subset $A$ of a uniform space is said to be bounded if for each entourage $V$, $A$ is a subset of $V^n[F]$ for some natural number $n$ and some finite set $F$. Just like for metric spaces, a compact subset of a uniform space is always closed and bounded, but the converse need not be true. A uniformity has the Heine-Borel property if a set is compact if and only if it is closed and bounded.
Suppose $X$ is a uniformizable topological space, AKA a completely regular topological space. My question is, is it necessarily the case that the topology on $X$ is induced by some Heine-Borel uniformity?
Now this answer shows that a metrizable topology is induced a metric with the Heine-Borel property if and only if it is locally compact and separable. But that doesn't answer this question, because even if we take a topology which isn't locally compact or isn't separable, it's possible that such a topology is induced by a non-metrizable uniformity with the Heine-Borel property.
A space $X$ is pseudocompact if any continuous $X\to\mathbb R$ is bounded. There exist completely regular non-compact pseudocompact spaces $X$ such as the long line (there are other examples at π-Base). By pseudocompactness, $X$ is bounded in any continuous pseudometric. By the positive answer to your previous question Is a set bounded in every metric for a uniformity bounded in the uniformity?, noting that the answers also work for pseudometrics in non-metrisable spaces, $X$ is bounded in every uniformity. So $X$ does not admit any Heine-Borel uniformity.
Not the answer you're looking for? Browse other questions tagged general-topology metric-spaces compactness examples-counterexamples uniform-spaces or ask your own question.
Is a set bounded in every metric for a uniformity bounded in the uniformity?
Is every metrizable topology induced by a Heine-Borel metric?
When is a bornology on a uniformizable space induced by a uniformity?
Is every uniformity for a metrizable topology metrizable?
Does Cauchy Completeness imply the Heine-Borel theorem generally? | CommonCrawl |
Some R-codes, class notes and tutorials produced by our team and collaborators. We are glad to share them as they are, of course without any warranty that they are all running properly.
On line syllabus from our graduate course on using R in ecology. In portuguese.
Tutorials on basic use of the R environment, from our graduate course on using R in ecology. In portuguese.
quick R tutorial on model fiting by the maximum likelihood method. In portuguese.
Our graduate course on statistical modelling: nice R tutorials and study notes. In portuguese.
The R package vegan has functions for individual-based permutation tests of additive diversity partitioning (sensu Crist et al. 2003).
Here we provide a code for the sample-based tests (Crist et al. 2003), where sample units of a given level are shuffled within units of the level above.
This code is an improved version of code used by Ribeiro et al. (2008). Apart code fine-tuning, in this version average diversity indexes are not weighted (see Crist et al. 2003).
Test data: birds in Southern Bahia (Pardini et al. 2009).
An introductory tutorial in R of additive diversity partitioning, from a graduate course (in portuguese).
Compound generalized linear models of Pardini et al. (2010).
Different combinations of Poisson and negative binomial linear models were used to predict number of species (or individuals) of small mammals in three landscapes that differ in the remaining forest cover. Each of these combinations represents alternative hypotheses on the interaction between landscape context and patch-area in fragmented landscapes.
Alonso, D., Ostling, A., & Etienne, R. S. (2008). The implicit assumption of symmetry and the species abundance distribution. Ecology Letters, 11, 93-105.
Bulmer, M. G. (1974). On fitting the Poisson lognormal distribution to species abundance data. Biometrics, 30, 651-660.
Crist, T. O., Veech, J. A., Gering, J. C., & Summerville, K. S. (2003). Partitioning species diversity across landscapes and regions: a hierarchical analysis of $$\alpha$$, $$\beta$$, and $$\gamma$$ diversity. The American Naturalist, 162, 734-743.
Fisher, R. A., Corbet, A. S., & Williams, C. B. (1943). The relation between the number of the species and the number of individuals in a random sample from animal population. Journal of Animal Ecology, 12, 42-58.
Green, J. L., & Plotkin, J. B. (2007). A statistical theory for sampling species abundances. Ecology Letters, 10, 1037-1045.
Grøtan, V., & Engen, S. (2008). Poilog: Poisson lognormal and bivariate Poisson lognormal distribution.
MacArthur, R. H. (1960). On the relative abundance of species. American Naturalist, 94, 25-36.
Motomura, I. (1932). On the statistical treatment of communities. Zoological Magazine, Tokyo, 44, 379-383.
Pardini, R., Faria, D., Accacio, G. M., Laps, R. R., Mariano-Neto, E., & Paciencia, M. L. B., et al. (2009). The challenge of maintaining Atlantic forest biodiversity: A multi-taxa conservation assessment of specialist and generalist species in an agro-forestry mosaic in southern Bahia. Biological Conservation, 142(6), 1178-1190.
Pardini, R., de Bueno, A. A., Gardner, T. A., Prado, P. I., & Metzger, J. P. (2010). Beyond the Fragmentation Threshold Hypothesis: Regime Shifts in Biodiversity Across Fragmented Landscapes. PLoS ONE, 5(10), 13666.
Ribeiro, D. B., Prado, P. I., Brown Jr, K. S., & Freitas, A. V. L. (2008). Additive partitioning of butterfly diversity in a fragmented landscape: importance of scale and implications for conservation. Diversity and Distributions, 14(6), 961-968. | CommonCrawl |
If the Wronskian is zero at some point, does this imply linear dependency of functions?
if for functions $f$ and $g$, the Wronskian $W(f,g)(x_0)$ is nonzero for some $x_0$ in [a,b] then f and g are linearly independent on [a,b].
If f and g are linearly dependent then the Wronskian is zero for all $x_0$ in [a,b].
My doubt is : If for some $x$ $W(f,g)(x)$ is zero, can we conclude that wronskian is identically zero as we know that wronskian is zero or never zero.
In one problem Wronskian $W$ was coming as $-x^2$ on $(\infty,-\infty)$. Since $W$ is $0$ for $x=0$ can we say wronskian is identically zero OR using point 1 we may conclude that we are getting more than one point where wronskian is not zero and hence functions are linearly independent.
"Identically zero" means "equal to zero for all values of $x$".
The function $-x^2$ is not identically zero, because there are values of $x$ (such as $1,2,3,\dots$) for which it's nonzero.
Since the Wronskian of linearly dependent functions is identically zero, the functions whose Wronskian is $-x^2$ are not linearly dependent.
As an aside: there is a scenario in which $W$ is either always zero or never zero: it happens when the two functions are solutions of the ODE of the form $y''+p(x)y'+q(x)y=0$. For such solutions, the Wronskian satisfies the identity $W(t)=W(s)\exp\left(-\int_s^t p(x)\,ds\right)$ which implies that if $W$ is zero at some point, it is zero everywhere.
Not the answer you're looking for? Browse other questions tagged linear-algebra ordinary-differential-equations or ask your own question.
Wronskian proof and linear dependency.
How to prove Linear Independence of piecewise functions?
Why does $W[y_1, y_2] = 0$ (wronskian) imply the following?
can linearly independent functions with zero wronskian be solutions to homogenous differential equation?
Are these functions linearly dependent?
Does vanishing of wronskian of solutions at point $\implies$ solutions are linearly dependent? | CommonCrawl |
Let, $x_1,x_2,x_3$ be age, length of employment, length of residence, and income.
My understanding is that the goal of transformation is to address the problem of normality. Looking at histograms of each variable we can see that they present very different distributions, which would lead me to believe that the transformations required are different on a variable by variable basis.
Lastly, how valid is it to transform variables using $\log(x_n + 1)$ where $x_n$ has $0$ values? Does this transform need to be consistent across all variables or is it used adhoc even for those variables which do not include $0$'s?
One transforms the dependent variable to achieve approximate symmetry and homoscedasticity of the residuals. Transformations of the independent variables have a different purpose: after all, in this regression all the independent values are taken as fixed, not random, so "normality" is inapplicable. The main objective in these transformations is to achieve linear relationships with the dependent variable (or, really, with its logit). (This objective over-rides auxiliary ones such as reducing excess leverage or achieving a simple interpretation of the coefficients.) These relationships are a property of the data and the phenomena that produced them, so you need the flexibility to choose appropriate re-expressions of each of the variables separately from the others. Specifically, not only is it not a problem to use a log, a root, and a reciprocal, it's rather common. The principle is that there is (usually) nothing special about how the data are originally expressed, so you should let the data suggest re-expressions that lead to effective, accurate, useful, and (if possible) theoretically justified models.
The histograms--which reflect the univariate distributions--often hint at an initial transformation, but are not dispositive. Accompany them with scatterplot matrices so you can examine the relationships among all the variables.
to the estimate. When $x \gt 0$, $z_x = 0$ so the second term drops out leaving just $\beta \log(x)$. When $x = 0$, "$\log(x)$" has been set to zero while $z_x = 1$, leaving just the value $\beta_0$. Thus, $\beta_0$ estimates the effect when $x = 0$ and otherwise $\beta$ is the coefficient of $\log(x)$.
Not the answer you're looking for? Browse other questions tagged r regression logistic data-transformation or ask your own question.
log transformation vs square root transformation, Can I do both?
How should I transform non-negative data including zeros?
What to do if residual plot looks good but qq-plot doesn't, after transforming the predictor and response variables?
How to back-transform negative Beta coefficients of linear regression after log transformation? | CommonCrawl |
Among the many equations that are used to determine the downforce applied by the strings to the bridge, foresaid equation encompasses a more general condition in which the angle of the string on two sides of the bridge can take different values. In the picture, the direction of the calculated force (corresponding to the central axis of the bridge) is shown. If a different direction is desired for the calculated force, use of vector calculation is required. It is also clear that in the case of two equal angles, the downforce will have its maximum value among the various states in which the overall angle ($\alpha + \beta$) is constant and also the transverse forces will cancel each other. | CommonCrawl |
Abstract: Neutron--induced nucleosynthesis plays an important role in astrophysical scenarios like in primordial nucleosynthesis in the early universe, in the s--process occurring in Red Giants, and in the $\alpha$--rich freeze--out and r--process taking place in supernovae of type II. A review of the three important aspects of neutron--induced nucleosynthesis is given: astrophysical background, experimental methods and theoretical models for determining reaction cross sections and reaction rates at thermonuclear energies. Three specific examples of neutron capture at thermal and thermonuclear energies are discussed in some detail. | CommonCrawl |
Is the sum of a Darboux function and a continuous function Darboux?
If $f$ is a Darboux function and $g$ is a continuous function, must $f+g$ be a Darboux function as well?
This is a very good question that leads into some fairly hard mathematics: the answer depends on what set theoretic assumptions you are prepared to make. If you assume the continuum hypothesis, there are what are called universally bad Darboux functions $f$ such that $f+g$ is not Darboux for any non-constant continuous $g$. See https://www.encyclopediaofmath.org/index.php/Darboux_property and the references it cites.
Not the answer you're looking for? Browse other questions tagged real-analysis or ask your own question.
Does the sum of two functions satisfying the intermediate value property also have this property?
Is there a different name for strongly Darboux functions?
Is intermediate value property equivalent to Darboux property?
Is every discontinuous everywhere Darboux function a constant image function?
Does $f(n\theta) \to 0$ for all $\theta>0$ and $f$ Darboux imply $f(x) \to 0$ as $x \to \infty$? | CommonCrawl |
Given the spectrum of analog signal $x_a(t)$ which is imaginary and band-limited, find the lowest sampling frequency to be able to reconstruct $x_a(t)$ from samples $x[n]$.
then the necessary minimum sampling rate which would avoid aliasing (spectral overlap) is given by $$ \Omega_s > ( \Omega_2 - \Omega_1 ) $$ Note that if the signal were real with a symmetric bandwidth then the minimum sampling rate would be twice that of the complex case. Also then the allowed range of valid sampling rates would be found differently.
Note that for a given sampling rate you will be getting $F_s$ complex samples per second which is equivalent to $2 \times F_s$ real samples per second. Hence the apparent advantage of complex sampling is actually not realized , as the total number of samples per second will be the same in both cases.
Not the answer you're looking for? Browse other questions tagged sampling homework nyquist or ask your own question. | CommonCrawl |
Lagrangian fibrations over quotient singularities.
On a conjecture of Matsushita (after van Geemen and Voisin).
Deformations of hyperkähler twistor spaces.
Abstract. We obtain novel results concerning the deformation theory of twistor spaces of irreducible holomorphic symplectic (ihs) manifolds. Specifically we show that the local deformations of such twistor spaces are unobstructed. The proof is based upon an extension theorem for families of ihs manifolds which compensates for the fact that, generally, fine moduli spaces of marked ihs manifolds do not exist.
On the local moduli of twistor spaces.
Abstract. I present and discuss new results concerning the deformation theory of compact complex manifolds that are non-isotrivially fibered in irreducible holomorphic symplectic manifolds. I exemplify these results with twistor spaces.
Abstract. I present some novel results concerning the deformation theory of twistor spaces of hyperkähler type. First and foremost, I show that the (local) deformations of such twistor spaces are unobstructed—a result which is new even in the K3 surface case. Time permitting, I touch upon the (global) structure of the moduli of hyperkähler twistor spaces.
Twistor spaces of K3 surfaces.
Abstract. Based on a joint project with Brecan, Schwald, and Greb I present some new results on twistor spaces of hyperkähler manifolds—with an emphasis on the K3 surface case. In particular, I show that the deformations of such twistor spaces are unobstructed.
Group actions on holomorphic Lagrangian fibrations.
Abstract. Let $n$ be a natural number, $G$ be a finite subgroup of the general linear group of degree $n$, and $B$ be an open neighborhood of the origin in $\mathbb C^n$ on which $G$ acts by matrix multiplication. Moreover, let $f \colon (X,\sigma) \to B$ be a holomorphic Lagrangian fibration and assume that we are given a holomorphic symplectic action of $G$ on $(X,\sigma)$ which makes the map $f$ equivariant. In my talk I ask: When the action of $G$ on $X$ is fixed point free, so that we can form the quotient $X/G$ as a complex manifold, what can we say about $G$? If $n=1$, for instance, the group $G$ is necessarily trivial. I will present partial results for $n>1$ and explain how these can be applied to study the singularities of base spaces of fibrations on irreducible holomorphic symplectic manifolds.
Deformations of twistor spaces of K3 surfaces.
Abstract. Twistor spaces of K3 surfaces are, noticeably non-Kähler, compact complex manifolds of dimension $3$ that come equipped with a holomorphic submersion to the complex-projective line. These spaces play a fundamental role in the moduli theory of K3 surfaces. In my talk I will explain this role and review the definition/construction of twistor spaces for general hyperkähler manifolds. Then, based on joint work in progress with Ana-Maria Brecan (Bayreuth), Martin Schwald, and Daniel Greb (both Essen), I present new results concerning the deformations of twistor spaces of K3 surfaces. Moreover, I will touch upon open problems and possible research directions.
Torelli theorems for K3 surfaces.
Extendability of parallel sections in vector bundles.
(Non-)existence of complex structures on S⁶: Etesi's work and ideas.
Finite quotients of three-dimensional complex tori.
Abstract. I will report on a joint project with Patrick Graf (Bayreuth). Using Graf's results about the algebraic approximation of Kähler threefolds of Kodaira dimension zero, we show that a three-dimensional compact, connected Kähler space $X$ with canonical singularities is the finite quotient of a complex torus if and only if the first and second Chern classes of $X$ vanish, in an appropriate sense. This brings together an old theorem of Yau (where $X$ is smooth) and a theorem of Shepherd-Barron and Wilson (where $X$ is projective).
Abstract. I will report on a current project with Patrick Graf (Bayreuth). Using Graf's recent results about the algebraic approximation of Kähler threefolds of Kodaira dimension zero, we show that a three-dimensional compact, connected Kähler space $X$ with isolated canonical singularities is the finite quotient of a complex torus if and only if the first and second Chern classes of $X$ vanish. This brings together an old theorem of Yau (where $X$ is smooth) and a theorem of Shepherd-Barron and Wilson (where $X$ is projective).
On singular symplectic complex spaces.
Period mappings for families of manifolds.
The local Torelli theorem for irreducible symplectic spaces. | CommonCrawl |
For $N$-point best-packing configurations $\omega_N$ on a compact metric space $(A, \rho)$, we obtain estimates for the mesh-separation ratio $\gamma(\rho_N , A)$, which is the quotient of the covering radius of $\omega_N$ relative to $A$ and the minimum pairwise distance between points in $\omega_N$ . For best-packing configurations $\omega_N$ that arise as limits of minimal Riesz $s$-energy configurations as $s \to \infty$, we prove that $\gamma(\omega_N , A) ≤ 1$ and this bound can be attained even for the sphere. In the particular case when $N = 5$ on $S^1$ with $\rho$ the Euclidean metric, we prove our main result that among the infinitely many 5-point best-packing configurations there is a unique configuration, namely a square-base pyramid $\omega^*_5$, that is the limit (as $s \to \infty$) of 5-point $s$-energy minimizing configurations. Moreover, $\gamma(\omega^*_5, S^2) = 1$. | CommonCrawl |
Truman has again been acknowledged by the Peace Corps as one of the top universities in the nation for producing Peace Corps volunteers.
With 22 alumni currently serving in the Peace Corps, Truman came in at No. 21 on that organization's list of medium-sized schools producing volunteers. This marks the second time in three years Truman has been included in the Peace Corps' top twenty-five rankings. Since the Peace Corps was founded in 1961, a total of 174 Truman alumni have served as volunteers.
For anyone interested in working with the Peace Corps, Betsy Blum, who served in Guinea, will be visiting Truman to host a public Peace Corps Information Session at 6 p.m. Feb. 11 in the Student Union Building Alumni Room.
The Peace Corps ranks its top volunteer-producing schools annually according to the size of the student body. The complete list of rankings can be found online at http://multimedia.peacecorps.gov/multimedia/pdf/stats/schools2010.pdf.
As the Peace Corps approaches its 50th anniversary, its service legacy continues to promote peace and friendship around the world with 7,671 volunteers serving in 76 host countries.
Peace Corps Volunteers must be U.S. citizens and at least 18 years of age. To learn more about the Peace Corps, go online to http://www.peacecorps.gov.
Dr. Troy D. Paino, Provost and Vice President for Academic Affairs, has been selected to serve as president of Truman State University.
The announcement was made Feb. 8 by Matthew W. Potter, Truman State University Board of Governors chair.
Paino will officially begin his duties as president May 10, 2010.
Paino has served as provost since 2008. In this leadership position he has served as a senior member of the president's cabinet and as the chief academic officer for the University. Additionally, Paino helped lead both the implementation of a comprehensive strategic plan to upgrade technology on campus and the establishment of the Truman Institute to develop programming aimed at generating revenue and building mutually beneficial relationships with business and community organizations. He also worked closely with faculty to establish new tenure and promotion policies and procedures and the Office of Student Research.
Prior to coming to Kirksville, Paino served as the dean of the college of liberal arts at Winona State University (Minn.) from 2004 to 2008. As the dean, Paino helped develop important University partnerships with the Great River Shakespeare Festival and Frozen River Film Festival. He also helped establish the Center for Engaged Research, Teaching & Scholarship, the American Democracy Project, and the Consortium for Liberal Arts & Sciences Promotion. He began his career at Winona State University in 1997 as an assistant professor of history. While on the faculty, he co-founded and directed the Law & Society Program from 1999 to 2004. He was promoted to the rank of professor in 2007.
Paino received his juris doctorate from Indiana University School of Law. Prior to arriving at Winona, he worked as a trial lawyer in Indianapolis. In addition to his academic and legal experience, Paino has served on several corporate boards and was a partner in a land development business.
Paino also has a Ph.D. and a Master of Arts degree in American Studies from Michigan State University and a Bachelor of Arts degree in history and philosophy from Evangel University in Springfield, Mo. His teaching and scholarly interests include 20th-century cultural and social history and American legal history. He has written journal articles, encyclopedia entries and book reviews on the history of American sport. His book, "The Social History of the United States: 1960s," was published in 2008.
Paino and his wife Kelly have two daughters, Sophia, age 12, and Chloe, age 10.
Paino currently serves on the Missouri Enterprise & Innovation Center board and will be inducted into Kirksville's Rotary club March 3. He has volunteered with the Big Brothers Big Sisters of Indianapolis and several arts and civic organizations in Minnesota.
In becoming the 16th president in Truman's history, Paino succeeds retiring Truman president Dr. Darrell W. Krueger.
For the fourth year in a row, the Missouri Court of Appeals, Western District, will convene court at Truman. At 9 a.m. Feb. 17, a three-judge panel consisting of Chief Judge Thomas H. Newton, Judge Joseph M. Ellis and Judge Cynthia L. Martin, will hear oral arguments in five cases in the Student Union Building Activities Room.
The cases are appeals from previously held trials in area circuit courts. The judges will hear attorneys argue whether the trials had errors, which should cause them to be retried, or the trial court's judgment reversed. The judges will read written arguments before the court session and may interrupt the attorneys' arguments with questions.
The three judges will take a break in between cases and remain after the session to discuss the court system and generally explain proceedings.
This will be the fifth session of the Western District at Truman and the 17th time that the court has convened in Kirksville. It convenes regularly in Kansas City. Its jurisdiction is appeals from trial courts in 45 counties, which includes all of northwest Missouri and most of central Missouri.
The Department of Music is hosting the 27th Annual Truman Piano Festival Feb. 19-20.
Serving as the guest artist in a solo piano recital at 8 p.m. Feb. 19 in the Ophelia Parrish Performance Hall will be Dr. Jeffrey Brown from Western Illinois University. Brown earned a Masters of Music and Doctor of Musical Arts in Piano Performance at Eastman School of Music. He also holds the Performer's Certificate from Eastman.
The recital will feature works by Bach/Busoni, Beethoven, Rachmaninoff and Brahms.
At 10 a.m. and 1 p.m. Feb. 20, Brown will present master classes in the Ophelia Parrish Performance Hall. Four Truman piano majors will perform in these classes. The recital and master classes are open to the public and are free of charge. For more information about the Truman Piano Festival, contact David McKamie, professor of music, at 785.4405.
Truman students Jaime Kelley (left) and Pat Zhang (right) help stock a food pantry at Victim Support Services during the MLK Challenge Jan. 18. One hundred students used the Martin Luther King Jr. Day break to donate "a day of service to remember a life of service." As part of the MLK Challenge, students volunteered at one of 10 project sites, including the Adair County Humane Society, Hospice of Northeast Missouri, Victim Support Services and Kirksville Part-Day Head Start among others. The day concluded with a Reflection Dinner on campus. The Multicultural Affairs Center, Student Senate, Missouri Campus Compact and the Center for Teaching and Learning all sponsored the MLK Challenge.
Truman students now have the opportunity to study abroad this summer in China at Shanghai University, May 20-June 29.
Prior knowledge of the Chinese language is not a requirement, as language courses for all levels will be offered, in addition to courses on literature, history, the economy and calligraphy. Students can earn six to seven Truman credit hours through the program.
During the trip, students will tour, among other attractions, the Chinese capitol city of Beijing, the Great Wall, the Forbidden City, the Summer Palace, the National Opera House, Tiananmen Square, the Chairman Mao Museum, and sites of the 2008 Olympic Games and the World Expo, which starts in May.
Participating students will gain knowledge of the language and culture in addition to experiencing personal contact with Shanghai University students and the Chinese people.
The cost for the four-week program is approximately $4,248 plus Truman tuition for six or seven credit hours. The price includes international transportation, insurance, Shanghai University tuition, textbooks and an on-campus dorm room. Transportation and lodging costs are also covered.
Students must have at least a 2.50 grade point average to participate. Contact Julie Minn at [email protected] for more information.
Darl Davis, director of the Regional Professional Development Center, (left) and Truman student Peter Bracha (right), hand Kits 4 Kids boxes to Convoy of Hope driver David Adams (center). Each kit includes a bottle of shampoo, a toothbrush, toothpaste, anti-bacterial soap, a comb and a hand towel. The Kits 4 Kids are being sent to Haitian children in the aftermath of the earthquake. The statewide goal, set forth by the Missouri Department of Education, was to assemble 100,000 kits in 10 days. More than 1,350 Kits 4 Kids were collected from schools in the area. Kits 4 Kids is sponsored by the Missouri Department of Education and Convoy of Hope, a nonprofit organization.
Truman State University Foundation scholarship applications for Truman students in the 2010-2011 academic year are now available. Applications are online and are due by midnight March 5. To learn more, go to http://www.truman.edu and click on Student Life/Money/Foundation Scholarships or go to https://secure.truman.edu/isupport-s/.
The Hispanic Scholarship Fund (HSF), the nation's leading organization supporting Hispanic higher education, is currently taking applications for the 2010 scholarship. The scholarship is available to permanent residents of the Greater Kansas City Metropolitan area defined as Clay, Jackson, Wyandotte, and Johnson counties. For more information, visit http://www.hispanicdevelopmentfund.org or call 816.701.8308. A limited number of applications are also available in the Financial Aid Office in McClain Hall 103. Applications are due March 1, 2010.
The Missouri Insurance Education Foundation will award scholarships to deserving students attending Missouri colleges or universities in a program that could lead to positions in the insurance industry in Missouri. The $2,500 C. Lawrence Leggett Scholarship is awarded to a junior or senior Missouri resident majoring in insurance or a related area of study in a Missouri college or university. In addition to the Leggett Scholarship, the foundation has made an additional scholarship available in the amount of $2,000. Application forms are available on their website at http://www.mief.org and due March 31.
An upgrade to the Banner system is scheduled to begin at 6 p.m. March 5.
It is anticipated that the upgrade will be completed by the end of the day March 8.
Banner and all Banner integrated services will be down during the upgrade, including all Banner links on TruView and mybill.truman.edu.
All users, including students, faculty and staff, will not have access to Banner during the upgrade period.
Beta Alpha Psi is sponsoring income tax assistance through the Voluntary Income Tax Assistance (VITA) program. IRS certified volunteers will be available during the times listed below to help students and members of the community file their income tax returns for FREE.
Participants need to bring Social Security cards for all involved, wage and earning statements, copies of last year's return (if available), bank routing numbers/direct deposit account numbers, total paid for day care provider and the day care provider's tax identifying number and if filling jointly, both spouses must be present.
For more information and a list of items to bring, visit http://bap.truman.edu or call 785.4268.
Hillel, the Student Affairs Office and Alpha Phi Omega will host a FREE dinner and a short presentation by an expert from the AntiDefamtion League, followed by a discussion about Internet humor and when humor becomes hate. A limited number of tickets are available.
Tickets are available in the CSI Office, Student Union Building.
Tickets are free with a Truman student ID.
General admission tickets will also be available for purchase online at http://sab.truman.edu/store.
E-mail [email protected] for more information.
by 5 p.m. Feb. 12.
The 2010 Student Research Conference is April 13. For more information, contact the Office of Student Research at [email protected] or 785.4455.
For more information, visit http://osr.truman.edu/truscholars/, e-mail [email protected] or call 785. 4455.
Truman's Mathematical Biology Program is currently accepting student applications for Summer 2010.
A $3,500 stipend plus room and board for the 10-week period are included.
For more information, e-mail [email protected] or stop by Violette Hall 2154. Application materials are available on the U drive at U\_MT Student File Area\mathbio\mathbio2010app.docx.
Volunteers are needed to read speeches from historic civil rights authors. Speeches can be selected from an established list or submitted for approval prior to the event. All speeches are to be from historic civil rights authors.
E-mail [email protected] for more information.
Due midnight March 5. Go to https://secure.truman.edu/isupport-s/ for a list of scholarships and to apply.
A total of 45 grants will be awarded nationwide, each worth $1,000.
Applicants need not be members of Phi Kappa Phi, can be any major, with at least a 3.5 GPA, at least 30 credit hours, but no more than 90 credit hours. Eligible Study Abroad Programs must begin between May 1, 2010 and June 31, 2011 Applications are due Feb. 24, 2010. Visit http://phikappaphi.org or e-mail [email protected] for more information.
Cost: Free with registration or $4 at the door.
At an Evening with Expo Experts you will receive lots of info on attending companies, how to approach an employer, what to say in an interview, how to polish your résumé and more. Also enjoy great food and activities like tie tying, professional makeup, and samples of professional dress.
RSVP on your online Expo registration form for this delicious and FREE brunch the morning before Career Expo. Most employers will be at the brunch and ready to speak with you about their company or organization.
Register for events at http://pdi.truman.edu and http://career.truman.edu.
Dress professionally in a matching suit.
Research employers and ask informed questions.
Prepare a résumé and have it reviewed at the Career Center.
Stand out by practicing your introduction.
Ask recruiters for business cards.
Write thank you notes to each employer.
All students are encouraged to file the 2010-2011 FAFSA located at http://www.fafsa.gov. It is important to apply before April 1 to be considered for all available funding. Questions may be directed to the Financial Aid Office, McClain Hall 103, 785.4130.
Test your knowledge of historical African-American figures, events and inventions.
Listen as the real Freedom Writers speak about their experiences and struggles throughout high school and how they overcame adversity to become successful.
The reception is open to all and includes special guest performances.
Ailey II is an exceptional dance performance company that merges the spirit and energy of the country's best young dance talent with the passion and creative vision of today's most outstanding choreographers.
Nominate student leaders for the month of February. Pick up nomination forms in the Center for Student Involvement in the Student Union Building or online at http://csi.truman.edu/gla/form.php.
Nomination deadline is 5 p.m. Feb. 10.
The Library Gallery is featuring an exhibit on several aspects of heart health including healthy relationships, exercise, nutrition, stress reduction, heart anatomy and physiology, smoking and the Winter Olympics 2010-U.S. Hopefuls.
For more information, contact Stacy Tucker-Potter in the Office of Advancement at 785.4167 or [email protected].
Help Truman boost international student recruitment by making a YouTube video that promotes the University to potential international students.
All videos must be submitted to [email protected] by Feb. 26.
E-mail Wilson Zhang at [email protected] for a list of rules and guidelines or with questions.
Including performances by Copacetic, Illusions Danz Team, Franklin Street Singers and the University Swingers. There will be free traditional Mardi Gras and Cajun cuisine for students as well as Mardi Gras trivia.
Taner Edis, associate professor of physics, published "Is The Universe Rational?" in Free Inquiry, 30:2 27-29 (2010).
Ronald A. Knight, professor emeritus of mathematics, had his paper, "Prolongational concepts for generalized flows," accepted for publication in Topology Proceedings. The paper is the third in a series of papers developing the notion of generalized dynamical systems as defined in Knight's paper "Initially deformed flows" which appeared in Volume 32 of Topology Proceddings in 2008.
Faculty and staff are invited to a Microsoft Access 2007 Presentation from 9 a.m.-3 p.m. Feb. 10 at the Kirksville TCRC, 315 S. Franklin. This one-day course teaches the basic functions and features of Access; how to design and create databases; how to work with tables, fields and records; and how to sort and filter data and create queries, forms and reports. This course is offered to faculty and staff for a reduced rate of $52 by the TCRC. For more information, call 785.2530 or e-mail [email protected].
The Weekly Lunch Series continues at 12:30 p.m. Feb. 10 in the Student Union Building Spanish Room with "Outcomes Based Local Assessment: Quantitative and Scientific Reasoning" by Karen Smith, associate professor of psychology, Phil Ryan, associate professor of mathematics, Glenn Wehner, professor of animal science, and Ian Lindevald, associate professor of physics. The group participated in a National Science Foundation grant and will discuss their findings and how their experiences might apply to assessments of other Truman learning outcomes.
The Spanish Club is hosting a presentation about Argentina at 7 p.m. Feb. 10 in Baldwin Hall 251. Katie Tolle, a third-year Spanish and English major, will present on her experiences studying abroad in Argentina in Fall 2009.
The Career Center is sponsoring "Careers in Government," a program for students interested in pursuing careers in government at 12 p.m. Feb. 11 at the Kirksville TCRC, 315 S. Franklin. Panelists are all Truman graduates representing various government agencies.
A Peace Corps Presentation will take place at 6 p.m. Feb. 11 in the Student Union Building Alumni Room. Those interested in opportunities with the Peace Corps can stop by. For more information, visit http://career.truman.edu.
The Pershing Society and University Swingers are hosting a three-day tango workshop. From 4-8 p.m. Feb. 11 is the Mate Mixer in the Student Union Building Spanish Room. Tango classes will be taking place from 4:30-8 p.m. Feb. 12 in Pershing Dance Studio. Classes continue from 10 a.m.-5:30 p.m. Feb. 13 in Pershing Dance Studio and the workshop wraps up with a dance from 8-11 p.m. Feb. 13 in Kirk Gym. Visit http://www.facebook.com/event.php?eid=281334092522&ref=mf for more information.
The next Safe Zone training for faculty and staff will take place at 11:30 a.m. Feb. 12 in the Student Union Building Conference Room 3000. Safe Zone trained members provide support, information and resources to gay, lesbian, bisexual and transgendered students, and most importantly create a safe space on campus. For more information, e-mail [email protected].
The Freedom Writers Series begins with film showings at 6 p.m. in Kirk Gym and 9 p.m. in the Student Union Building HUB on Feb. 13. At 7 p.m. Feb. 15 in Baldwin Auditorium, two of the original Freedom Writer students will present. To conclude the series, there will be a "Netiquette" dinner and discussion at 5:30 p.m. Feb. 16 in the Student Union Building Georgian Rooms. All events are free. Events are sponsored by Residence Life, New Students Program, Multicultural Affairs Center, Regional Professional Development Center, Center for Teaching and Learning, Student Senate, Center for Student Involvement, National Education Association and Student Affairs.
The Quincy Symphony Orchestra will present "From the Heart" at 3 p.m. Feb. 14 at Quincy Junior High School Morrison Theatre. Tickets are free for faculty, staff and students with a University ID. Visit http://www.qsoa.org for more information.
Cardinal Key is hosting Spring Rush. Rush applications are due to the Cardinal Key mailbox in the Center for Student Involvement by Feb. 17. Rush Week is Feb. 21-28. For more information, e-mail [email protected] or visit http://cardinalkey.truman.edu.
Bioethicist and Baptist pastor Dr. Terry Rosell will present a lecture on the sometimes unexpected tensions between organ donation and transplant and religious values systems in "What happens to Jesus if I donate my heart? A Narration of Religious-Cultural Influences on Organ Donation and Transplantation." The talk will take place at 6:30 p.m. Feb. 17 in the Student Union Building Activities Room. Rosell is the Sister Rosemary Flanigan Chair at the Center for Practical Bioethics in Kansas City.
Students In Free Enterprise (SIFE) will host an international business discussion at 6 p.m. Feb. 22 in the Student Union Building Georgian Room. Students will be served dinner and participate in round table discussions over topics such as doing business internationally. All majors are welcome. Register at http://pdi.truman.edu by Feb. 15.
An information meeting for India Study Abroad will take place at 4 p.m. Feb. 23 in Violette Hall 1010 and Feb. 24 in Violette Hall 1146. For more information, e-mail [email protected]. | CommonCrawl |
Abstract: We develop the theory of n-stacks (or more generally Segal n-stacks which are $\infty$-stacks such that the morphisms are invertible above degree n). This is done by systematically using the theory of closed model categories (cmc). Our main results are: a definition of n-stacks in terms of limits, which should be perfectly general for stacks of any type of objects; several other characterizations of n-stacks in terms of ``effectivity of descent data''; construction of the stack associated to an n-prestack; a strictification result saying that any ``weak'' n-stack is equivalent to a (strict) n-stack; and a descent result saying that the (n+1)-prestack of n-stacks (on a site) is an (n+1)-stack. As for other examples, we start from a ``left Quillen presheaf'' of cmc's and introduce the associated Segal 1-prestack. For this situation, we prove a general descent result, giving sufficient conditions for this prestack to be a stack. This applies to the case of complexes, saying how complexes of sheaves of $\Oo$-modules can be glued together via quasi-isomorphisms. This was the problem that originally motivated us. | CommonCrawl |
We prove that the modified Korteweg–de Vries (mKdV) equation is unconditionally well-posed in $H^s(\mathbb R)$ for $s > 1/3$. Our method of proof combines the improvement of the energy method introduced recently by the first and third authors with the construction of a modified energy. Our approach also yields a priori estimates for the solutions of mKdV in $H^s(\mathbb R)$, for $s > 0$, and enables us to construct weak solutions at this level of regularity. | CommonCrawl |
Since I am still waiting for my immune system to win its week-long fight with some viruses (go cytokines go!), I figured I would deviate from the planning and write something related to, not ecology directly, but how to mislead people with statistics. And it involves the logistic curve, so it is basically population dynamics anyways.
The new "Rule of 21" at NIH states, basically, that the investing more than two R01 grants into any scientists is fine, but more than that sees a decrease in productivity. Unsurprisingly, this was met with outrage by some (which is understandable, even though I agree with the rule), and in the case of the link just before, trying to argument against the rule with bad statistics. And I do not like bad statistics.
The figure on the left shows the relative citation rate (vertical axis) versus the relative funding in R01 equivalent units (on the horizontal axis). These are the empirical data. Shane Crotty (author of the blog post linked earlier) added a linear regression, forced to go through the origin, to show that returns keep on increasing.
But let's start by listing what is right with this linear regression. Both axes are expressed as relative units, so by definition, a PI with the equivalent of a single R01 ($x=7$) will be cited with the equivalent of one R01 ($y=1$). But through any single point, there is approximately an infinite a number of function that can pass, so this is not really informative.
The second point that is assumed to be that a PI with no R01 ($x=0$) will have a relative citation score of 0 ($y=0$. This is called forcing the regression through the origin. Ecologists have argued that even when you have pre-existing knowledge that this should be the case, it is not always advised to force your regression this way. Do we have pre-existing knowledge here? A quick examination of the figure shows that the relative citation rate reaches 0 at about half a R01 equivalent. But we cannot rule out the fact that 0 R01 equivalent would result in 0 citations, so I can live with this hypothesis.
But there is something more problematic in here: using a linear regression at all. This assumes that the rate of increase in citation score is positive, and constant with regard to the equivalent amount of R01; specifically, $y = x/7$. And now is the time to remember that for any problem, there is a trivially wrong null hypothesis that will let you tell the story you want. The lemma, of course, is that this trivially wrong null hypothesis is often a linear regression forced through the origin, but I digress. The bottom line is, this figure is using a blatantly wrong baseline estimation to tell a story (let people get as many R01 as they can).
The question is to determine if there is a point of inflection around x=14, which is equivalent to 2 R01. A point of inflection, in plain language, is a value for which the function grows slower after than it did before. In terms of citations per R01 invested, this is the number of R01 above which less citations are generated (and therefore the cap for maximal return on investment). If the relationship between y and x is , one way to find a point of inflection is to find the value of x for which . means the second derivative, which represents the rate of change of the rate of change: assuming you are walking, is your position, is your speed, and is your acceleration.
Now, instead of setting up a strawman baseline (a linear regression going through 0), we can actually look at the data. And they scream "logistic!". A logistic function has the shape , where L is the value at the plateau (the maximum citation score that you can achieve), k is the steepness (the maximum "acceleration" of the citation score when you gain an additional R01), and x0 is the value of the midpoint. Because logistic functions are beautiful, the x0 parameter is (using this expression of the logistic) the solution to , and is therefore the answer we are looking for.
As I worked with bacterial growth data during my PhD, I am somewhat expert at guesstimating values for these curves. Based on the data, I would start with $6 \leq L \leq 8$, and any positive value for $k$ (about 0.5?). Plugging these values and the logistic function (as well as the data extracted from the figure) in a genetic optimization routine (which is frankly overkill, but I had this code ready to run), I get $x_0 \approx 12.4$. Plotting the value of the second derivative, we get the result on the right. The point of inflection (i) exists and (ii) is reached around approximately two equivalent R01.
The original figure is a teachable moment.
Converting intuition into a numerical framework can work, as long as this is done in a way that is relatable to the data. If not, it becomes easy to mislead or deceive people with what looks like a quantitative argument, but is in fact a misapplication of the methods. This also emphasize how important the visual inspection of the data is before the start of the analysis. There is no way to justify fitting a linear regression through these data.
Previous post: When exactly is it citizen science?
Next post: We can't see the forest for the bird. | CommonCrawl |
I'm a master's degree student at the University of Turin (Italy).
Also check out my blog at lqmath.wordpress.com !
11 If every subsequence of $(x_n)$ has a subsequence converging weakly to $x$ then $x_n$ converges weakly to $x$.
7 Examples of $(\mathcal K^\bot)^\bot=\mathcal K$ failing.
7 Extending an equality from a dense subspace - possible mistake in a proof. | CommonCrawl |
Abstract: Let $X$ be a partial flag variety, stratified by orbits of the Borel. We give a criterion for the category of modular perverse sheaves to be equivalent to modules over a Koszul ring. This implies that modular category $\mathcal O$ is governed by a Koszul-algebra in small examples. | CommonCrawl |
Abstract. We study transport in quantum systems consisting of a finite array of N identical single-channel scatterers. A general expression of the S matrix in terms of the individual-element data obtained recently for potential scattering is rederived in this wider context. It shows in particular how the band spectrum of the infinite periodic system arises in the limit $N\to\infty$. We illustrate the result on two kinds of examples. The first are serial graphs obtained by chaining loops or T-junctions. A detailed discussion is presented for a finite-periodic "comb"; we show how the resonance poles can be computed within the Krein formula approach. Another example concerns geometric scatterers where the individual element consists of a surface with a pair of leads; we show that apart of the resonances coming from the decoupled-surface eigenvalues such scatterers exhibit the high-energy behavior typical for the delta' interaction for the physically interesting couplings. | CommonCrawl |
is a torsion-free ring which has residue fields in any characteristics. It is a noetherian principal ideal domain. The abelian group generates the category of abelian groups, since every abelian group can be written by generators and relations and this corresponds to a surjection of some power of onto the group (and the relations generate the kernel). Every abelian group is a -module just by the operation ( times).
is a finite (hence noetherian) torsion ring, and we have maps given by reduction modulo . One can also write down (non-canonically) an isomorphism of groups , the group of -th roots of unity, by mapping a generator to a primitive -th root of unity. Under this isomorphism, the map "reduction mod " corresponds to taking the -th power of a -th root of unity to obtain a -th root of unity.
is a field of characteristics 0 with ring of integers , i.e. it is the field of fractions of . As an abelian group, is divisible, so it is an injective object in the category of abelian groups. -modules are the same as -vector spaces.
is a ring in which every element is torsion, since , with many summands, equals , so is in . As a quotient of a divisible group, is divisible. It is a cogenerator of the category of abelian groups, i.e. every abelian group maps injectively in a sufficiently large power of (this gives us the fact, that the category of abelian groups has enough injectives).
is the completion of at the prime , i.e. at the -adic valuation (hence has a nontrivial topology). One can also define equivalently and the corresponding limit topology is the same as the completion topology. It contains . It is also torsion-free of characteristics 0 and has residue field (did I mention that is prime? is always prime).
is the field of fractions of , and one can also write .
is the profinite completion of the integers . It is torsion-free.
. It has a natural topology making it a topological ring, which is different from the subspace topology. Oh, by the way, this ring is called the finite Adèles. The product is called the Adèles (of ).
, a polynomial ring in countably infinite many variables, has every finitely generated ring as quotient ring. This generalizes to higher cardinalities. @Jan: thanks for this addition to the list.
Do you know more interesting rings derived from these? Did I miss interesting properties?
Any ring is a quotient of a polynomial ring over $\mathbb Z$ in infinitely many variables. | CommonCrawl |
Binomial $(n, p)$ probabilities involve powers and factorials, both of which are difficult to compute when $n$ is large. This section is about simplifying the computation of the entire distribution. The result also helps us understand the shape of binomial histograms.
Fix $n$ and $p$, and let $P(k)$ be the binomial $(n, p)$ probability of $k$. That is, let $P(k)$ be the chance of getting $k$ successes in $n$ independent trials with probability $p$ of success on each trial.
How is this more illuminating than plugging into the binomial formula? To see this, fix $k \ge 1$ and calculate the ratio $R(k)$.
Now observe that comparing $R(k)$ to 1 tells us whether the histogram is going up, staying level, or going down at $k$.
tells us the the ratios are a decreasing function of $k$. In the formula, $n$ and $p$ are the parameters of the distribution and hence constant. It is $k$ that varies, and $k$ appears in the denominator.
This implies that once $R(k) < 1$ for some $k$, it will remain less than 1 for all larger $k$. In other words, once the histogram starts going down, it will keep going down. It cannot come back up again.
That is why binomial histograms are either non-increasing or non-decreasing, or they go up and come down. But they can't look like waves on the seashore. They can't go up, come down, and go up again.
Let's visualize this for a $n = 23$ and $p = 0.7$, two parameters that have no significance other than being our choice to use in this example.
# to find all the ratios at once.
What Python is helpfully telling us is that the invisible bar at 1 is 53.666… times larger than the even more invisible bar at 0. The ratios decrease after that but they are still bigger than 1 through $k = 16$. The histogram rises till it reaches its peak at $k = 16$. You can see that $R(16) = 1.1666 > 1$. Then the ratios drop below one, so the histogram starts going down.
A mode of a discrete distribution is a possible value that has the highest probability. There may be more than one such value, so there may be more than one mode.
For all $k$ such that $R(k) \ge 1$, we will say that the binomial histogram is rising at $k$. Which values of $k$ have this property? To answer this, we have to solve an inequality.
We have shown that for all $k$ in the range 0 through the integer part of $(n+1)p$, the histogram rises; for larger $k$, it falls.
Therefore the peak of the histogram is at the integer part of $(n+1)p$. That's a mode of the binomial.
The mode of the binomial $(n, p)$ distribution is the integer part of $(n+1)p$. If $(n+1)p$ is an integer, then $(n+1)p - 1$ is also a mode.
To see that this is consistent with what we observed in our numerical example above, let's calculate $(n+1)p$ in that case.
The integer part of $(n+1)p$ is 16, which is the mode that we observed.
But in fact, $np$ is a more natural quantity to calculate. For example, if you are counting the number of heads in 100 tosses of a coin, then the distribution is binomial $(100, 1/2)$ and you naturally expect $np = 50$ heads. You don't want to be worrying about $101 \times (1/2)$.
In fact you don't have to worry when $n$ is large, because then $np$ and $(n+1)p$ are pretty close. In a later section we will examine a situation in which you can use $np$ to get an approximation to the shape of the binomial distribution when $n$ is large. | CommonCrawl |
We present a novel class of oscillatory integrators for the Klein-Gordon-Zakharov system which are uniformly accurate with respect to the plasma frequency c. Convergence holds from the slowly-varying low-plasma up to the highly oscillatory high-plasma frequency regimes without any step size restriction and, especially, uniformly in c. The introduced schemes are moreover asymptotic consistent and approximates the solutions of the corresponding Zakharov limit system in the high-plasma frequency limit (c $\rightarrow$ $\infty$). We in particular present the construction of the first- and second-order uniformly accurate oscillatory integrators and establish rigorous, uniform error estimates. Numerical experiments underline our theoretical convergence results. | CommonCrawl |
1970: In Archive for Rational Mechanics and Analysis, 37,181--191, 1970.
Abstract: We consider the pressure and the correlation functions of a one dimensional lattice gas in which the mutual interaction decreases as $r \exp(-n^t)$, ($r,t>0$), when the nterparticle distance $n\to\infty$. We prove that such a system cannot show phase transitions of order $k\ge1$ in the sense that the pressure and the corelation functions are infinitely differentiable with respect to any relevant parameter (such as th temperature or the chemical potential). | CommonCrawl |
Mass Ave - a long road that goes to $+\infty$ (Atlantic ocean) in the East and $-\infty(0.6-0.8i)$ in the West has decided to reduce its carbon footprint. So they have built a Victorian house in the middle of the road. It's actually a great idea. Drivers may get discouraged and take a different route which will lower the CO2 emissions near the Harvard Law School which is a good thing, as consensus of scientists thinks. Amen.
These guys across the street have a much more straightforward approach to moving than your humble correspondent.
The Ukrainian House (see the picture), the Baker House, and the carriage house will be moved from the Harvard Law School area - where they want to build the Northwest Corner - to another street one block to the North - where they needed to demolish a part of the North Hall dormitories. The houses will be transferred on the wheels.
It's impressive but it's nothing like the Church of the Annunciation of the Virgin Mary (built 1517-1532) in Most, a Czech city, that was transported by 841.1 meters within 28 days by Czechoslovak engineers from Škoda Pilsen and Průmstav Pardubice, heroes of socialism, in 1975.
The speed was about 1-3 centimeters a minute and the whole operation gave communist Czechoslovakia a lot of new dirty brown coal to burn. The coal contains a lot of uranium so when you burn it, you release more radioactivity than any nuclear power plant except for Chernobyl ever can.
The building was mentioned in Guinness book of records as the heaviest building ever moved on wheels.
thanks this was a really interesting article! it was interesting to me while ive been looking for long distance movers in Victoria. thanks for the post!
Is Witten working on loop quantum gravity?
CO2 emissions: China has surpassed U.S.
Is cosmology behind the second law? | CommonCrawl |
So far we have put emphasis on the importance of finding a basis $B_V$ of a finite-dimensional vector space $V$ for which the matrix of a linear operator $T$ with respect to $B_v$, $\mathcal M (T, B_V)$ is upper triangular (or diagonal). One of the reasons why we want to find such a basis is because the eigenvalues of $T$ can easily be obtained as noted in the following proposition.
Proposition 1: Let $V$ be a finite-dimensional vector space. If $T \in \mathcal L (V)$ and $\mathcal M (T, B_V)$ is an upper triangular matrix with respect to some basis $B_V$ of $V$, then the eigenvalues of $T$ are the entries on the main diagonal of $\mathcal M (T, B_V)$. | CommonCrawl |
implying $\alpha=\beta=\gamma,\;$ as the sides of an equilateral triangle.
are aslo the side lengths of a triangle.
for $a,b,c\;$ from a triangle.
Hence, $\alpha+\beta\gt\gamma.\;$ Similarly, $\alpha+\gamma\gt\beta\;$ and $\beta+\gamma\gt\alpha,\;$ implying that $\alpha,\;$ $\beta,\;$ $\gamma\;$ are the sides of a triangle.
The problem has been kindly posted by Dorin Marghidanu at the CutTheKnotMath facebook page. Leo Giugiuc's solution (Proof 1) followed almost immediately thereafter. Proof 2 is by Rishi Nirvikalpa; Proof 3 is by Dorin Marghidanu; Proof 4 by Ravi Prakash; Proof 5 is by Marian Dinca.
Daniel Hardisky has independently observed that, due to the Law of Sines, $\beta=\gamma,\;$ such that the resulting triangle is isosceles. | CommonCrawl |
Abstract: Advancements in high temperature superconducting technology have opened a path toward high-field, compact fusion devices. This new parameter space introduces both opportunities and challenges for diagnosis of the plasma. This paper presents a physics review of a neutron diagnostic suite for a SPARC-like tokamak [Greenwald et al 2018 doi:10.7910/DVN/OYYBNU]. A notional neutronics model was constructed using plasma parameters from a conceptual device, called the MQ1 (Mission $Q \geq 1$) tokamak. The suite includes time-resolved micro-fission chamber (MFC) neutron flux monitors, energy-resolved radial and tangential magnetic proton recoil (MPR) neutron spectrometers, and a neutron camera system (radial and off-vertical) for spatially-resolved measurements of neutron emissivity. Geometries of the tokamak, neutron source, and diagnostics were modeled in the Monte Carlo N-Particle transport code MCNP6 to simulate expected signal and background levels of particle fluxes and energy spectra. From these, measurements of fusion power, neutron flux and fluence are feasible by the MFCs, and the number of independent measurements required for 95% confidence of a fusion gain $Q \geq 1$ is assessed. The MPR spectrometer is found to consistently overpredict the ion temperature and also have a 1000$\times$ improved detection of alpha knock-on neutrons compared to previous experiments. The deuterium-tritium fuel density ratio, however, is measurable in this setup only for trace levels of tritium, with an upper limit of $n_T/n_D \approx 6\%$, motivating further diagnostic exploration. Finally, modeling suggests that in order to adequately measure the self-heating profile, the neutron camera system will require energy and pulse-shape discrimination to suppress otherwise overwhelming fluxes of low energy neutrons and gamma radiation. | CommonCrawl |
by Sreyan Chatterjee, Gausia Shaikh and Bhargavi Zaveri.
The legal framework for insolvency resolution in India underwent a structural change when the Insolvency and Bankruptcy Code, 2016 (IBC) was passed in May 2016. Once the provisions relating to corporate insolvency were notified (November 2016), the first cases of insolvency started being admitted in the National Company Law Tribunal (NCLT), the quasi-judicial tribunal vested with adjudication powers under the IBC. The final orders on these cases became the first public records of India's new insolvency framework. In a recent working paper titled Watching India's insolvency reforms: a new dataset of insolvency cases, we introduce a new dataset of all final orders passed by the NCLT and the appellate forum, the National Company Law Appellate Tribunal (NCLAT) under the IBC. In the paper, we also illustratively apply the data to answer questions about the economic impact of the IBC and the functioning of the judiciary under it. This blogpost presents some summary statistics on the IBC and our preliminary findings relating to the working of the IBC.
We use information collected from the final orders published by the NCLT in the first six months of operationalisation of the IBC, that is, from 1st December, 2016 until 15th May, 2017 (hereafter, "sample period"). There are 23 fields of information for each case in the data-set. This includes parameters such as, who are the initial users of the insolvency process under the IBC, what kind of evidence are they using to support their claims before the NCLT, the average time taken by the NCLT to dispose off cases, the outcome of the proceedings, reason for dimissal of a case and the variation in admission and dismissal across the nine benches of the NCLT.
Does the law improve the balance between rights of the creditors and the firm debtor during insolvency?
The Indian legal regime preceding the IBC conferred weak rights on creditors, especially unsecured creditors. It created scope for the judiciary to intervene in the commerical matters of debt re-structuring. The law itself and the courts and tribunals enforcing it, also exhibited a rehabilitation and pro-debtor bias (Ravi 2015). While the sample period represents the earliest days of operationalisation of the IBC and the current data-set is small to conclusively answer this question, this early data indicates that there has been a shift in the enforcement of creditors' rights under the IBC. Table 1 shows who used the IBC during the first six months of its operationalisation.
Table 1: Who used the IBC?
Of the 110 cases that were disposed off during the sample period, 75 percent of the cases were triggered by creditors. Of these, 75 percent were filed by unsecured operational creditors. This indicates that operational creditors, who hitherto had weak enforcement rights, have taken recourse to the IBC to enforce their claims. There may be multiple reasons for the relatively low number of financial creditors taking recourse to the IBC during the first six months. Anecdotal evidence suggests that firm debtors default to financial creditors the last. Financial creditors may largely be secured creditors who may choose to enforce their claim by realising their security. There was lack of regulatory certainty on provisioning norms for banks and the apprehension of scrutiny by the anti-corruption investigative agencies among bank management. However, in the absence of data on default or the enforcement of security by financial creditors in India, the reason for the divergence in creditor behavior in triggering the IBC is unclear.
Another feature of interest is the behaviour of the debtor. There is a commonly voiced apprehension that the debtor will avoid resorting to insolvency because the IBC moves away from the debtor-in-possession model to a framework where the debtor's board is suspended and the affairs of the debtor are run by an independent insolvency professional. However, contrary to this apprehension, around 24 percent of the petitions in this early six month period have been filed by debtors.
Of the 110 cases that were filed, 50% of them have been admitted by the NCLT and are now undergoing a mutually negotiated debt restructuring process. This shows that unlike the previous regime where the judicial bodies exhibited a pro-debtor bias, there is no explicit admission or dismissal bias for insolvency cases under the IBC.
Within the caveat that these are early days and we still have to observe how these cases get resolved, the observed data suggests that creditors are able to use the new insolvency and bankruptcy regime with increasing confidence compared to the previous regime.
Does the law empower various types of creditors when the firm defaults?
Table 2 shows the kind of operational creditors who took resort to the IBC during the sample period. While majority of the operational creditors are suppliers to the debtor, we find that even holders of decrees are taking recourse to the IBC.
Table 3 shows the outcomes of the insolvency cases filed by different kinds of creditors during the sample period. While 43 percent of the cases filed by the financial creditors were dismissed, the percentage of dismissal for operational creditors is slightly higher at 58 percent.
A reading of Tables 2 and 3 would indicate that even during the earliest days of its operationalisation, a wide variety of creditors have shown the ability to trigger insolvency proceedings under the IBC. This is in contrast to the previous regime where only a certain subset of creditors were able to trigger insolvency proceedings against firm debtors, and other creditors had to file cases in civil courts.
Does the law empower only large sized debt holders?
Table 4 shows the size of debt claims that have been used to trigger the IBC during the sample period. The table also presents the distribution across the different quartiles, by showing threshold values at three different cut-off points: for the 25th percentile point, the 50th percentile and the 75th percentile point. The 25th percentile point is the value below which 25 percent of the cases will fall, the 50th percentile point is the point below which 50 percent of the cases will fall and so on. Further, this has been done by the different types of stakeholders: financial creditors, operational creditors and the debtor.
million (or Rs.856.5 crores) which was only 8 times larger. This shows that operational creditors, who had considerably weaker rights under the previous regime, had considerably large debt repayments due from firm debtors. Thus, while the IBC is being triggered by creditors on a wide range of size of defaults, most of the cases observed so far (more than 75 percent of the cases) tend to be triggered using debt defaults that are approximately 10 to 100 times larger than the threshold of Rs.100,000 set in the law.
We find that the published data is ambiguous about behavioural or structural changes in the judiciary to fit within the role defined for it, in the IBC. The information display systems of the NCLT do not give an overview of the entire cycle of a case, and bits and pieces of information are available in the final orders. For instance, while each order specifies the date on which it was passed, several orders do not capture other information critical for assessing the time taken for the disposal of insolvency petitions, such as: the date on which the insolvency petition was filed, the date on which it first came up for hearing. 16 of the 110 orders studied did not reflect the amount of debt or default that was the subject matter of the case. Admittedly, there are more laborous methods to discern the entire life cycle and facts of a given case, such as examining the case records maintained by the registry at the each bench of the NCLT. However, for reasons explained in our paper, we find that these methods will also not help in ascertaining the performance of the NCLT as a whole. This constrains the ability of both the court administration as well as independent researchers to readily assess the performance of the NCLT.
With the limited data that is available from the published orders, we have attempted to answer two important questions about the functioning of the NCLT under the IBC.
Does the NCLT function within the timelines set in the law?
The IBC requires the NCLT to dispose off an insolvency petition within 14 calendar days from the date on which it is filed before it. Our dataset captures the following dates in the life-cycle of an insolvency petition: date on which the case is filed (T0), date on which it first comes up for hearing (T1) and the date on which it is disposed off (T2). The amount of time that elapses between T0 and T1 could be attributed to the internal processes of the NCLT in scheduling hearings for a case. Our assessment shows that the NCLT exceeds the timeline of 14 days prescribed by statute. Table 5 summarises our findings.
Table 5 shows that the average time taken from the date of filing the insolvency petition to the date on which it first comes up for hearing, is 18 days. The average time between the date on which it first came up for hearing and the date on which it is finally disposed off, is 16 days. Finally, the average time taken for disposal is 24 days (T0 to T2). This is significantly more than the timeline of 14 days prescribed under the IBC. Currently, the data does not allow us to analyse the reasons for this delay.
Is the role played by the NCLT as visualised within the IBC?
While the law enumerates specific grounds for dismissing an insolvency case and is largely biased towards allowing an insolvency to be triggered if the debtor has committed a default in repayment of an undisputed debt, the NCLT has dismissed petitions on extraneous considerations as well. Table 6 shows the various grounds on which insolvency petitions were dismissed during the sample period.
A review of a sample of dismissals classified as "Others" in Table 6 shows that the NCLT considers factors not explicitly spelt out in the IBC for dismissing the insolvency petition. For instance, in an insolvency petition filed before the Mumbai bench, the Tribunal recognized that all the ingredients required under the IBC were present to admit the petition. However, the NCLT extended the scope of its inquiry to the balance sheet of the debtor and held that since the debtor had sufficient assets on its balance sheet, it would be unfair and inconvenient for the debtor if the petition were admitted. The NCLT ignored the creditor's argument that the provisions of the IBC do not allow the Tribunal to embark upon a balance sheet analysis.
This indicates that the NCLT seems to be viewing the admission of an insolvency case as an excessively harsh outcome for a debtor. If this trend continues, it may degenerate into a debtor-favouring bias going ahead. Thus, the data shows that the working of the NCLT is not always in line with the letter and spirit of the IBC.
We find that there is no standardised format of recording case information. Consequently, several final orders lack in basic information such as the kind of creditor who filed the petition, the claim amount and the date on which the insolvency case was instituted. Our finding on information gaps in the orders of the NCLT is in line with the findings of other research done with respect to the orders passed by the Debt Recovery Tribunals in India (Regy and Roy 2017).
There are three adverse consequences of such information gaps in the NCLT orders. First, the absence of basic information about the case hinders the ability of the NCLT to monitor the efficiency of its own benches. It also constrains researchers from assessing the quality of the procedural requirements and outcomes of the law. Second, this will hinder the ability to identify systemic lapses in the functioning of tribunals and in designing appropriate interventions. Third, inadequate or incomplete data has implications for the overall accountability and transparency of these tribunals to the public, and in the long run, will erode the credibility of the NCLT as an institution.
The empirical analysis in our paper, though preliminary, indicates that the IBC is likely to have a structural change in the behaviour of economic agents, as well as in the areas where the NCLT functions as the adjudicator under the IBC. Our exercise of building a dynamic dataset that is geared towards impact assessment, also brings out the gaps in data that courts publish. Our findings on the data gaps, elaborated in greater detail in the paper, will provide a framework for re-thinking the data management and publication systems of tribunals in India.
The ultimate goal of this dataset is to provide a foundation to answer questions on the impact of the IBC and the overall functioning of the Indian bankruptcy regime. The dataset is dynamic and will be updated on a regular basis. As the insolvency cases increase, the dataset will too increase in scope and size. As more data gets published, relevant fields, such as recovery rates and expenses associated with the recovery process, can potentially be integrated into the dataset. This will fuel deeper research on insolvency and credit markets in India. Such data-backed research will support policy interventions in this space in the years to come.
The Indian insolvency regime in practice -- an analysis of insolvency and debt recovery proceedings, Aparna Ravi. Economic & Political Weekly, Volume 1, No. 51, December 2015.
Understanding Judicial Delays in Debt Tribunals, Shubho Roy and Prasanth Regy. NIPFP Working Paper 195, May 2017.
We thank Susan Thomas for useful discussions and insights on empirics.
The authors are researchers at the Indira Gandhi Institute of Development Research.
Flat buyers under IBC: Creditors or consumers?
The Indian bankruptcy regime is developing very fast. There is a risk that the law may soon diverge from the original policy intent. One such example is the recent regulation by IBBI creating a third category of creditors - other than financial or operational creditor. Commentators have suggested that flat buyers would fall under this third category. This comes in the backdrop of recent decisions of NCLT and NCLAT that have left flat buyers jittery about their future once the real estate company enters corporate insolvency resolution process (CIRP).
prompted IBBI to create a third category of creditors. This third creditor can neither trigger the CIRP, nor be on the Committee of Creditors (CoC). Second, BLRC had categorically stated that not all assets present within the insolvent company shall form part of the liquidation. Whether the corresponding provisions of IBC will protect flat buyers of insolvent real estate companies remains to be seen.
There are multiple ways in which creditors could be classified: financial versus operational, secured versus unsecured etc. The BLRC had to decide how to classify creditors in different contexts. One such context was CIRP - who will trigger it? Who will be on the CoC? Faced with these questions, the BLRC report noted that both the debtor and the creditors should have the power to trigger CIRP. However, a creditor could trigger the CIRP only on clear evidence of default. Since the process of establishing default would have to be different for financial and operational creditors, the BLRC had to classify creditors into these two categories. In this policy scheme, no third category of creditors was envisaged.
The Committee deliberated on who should be on the creditors committee, given the power of the creditors committee to ultimately keep the entity as a going concern or liquidate it. The Committee reasoned that members of the creditors committee have to be creditors both with the capability to assess viability, as well as to be willing to modify terms of existing liabilities in negotiations. Typically, operational creditors are neither able to decide on matters regarding the insolvency of the entity, nor willing to take the risk of postponing payments for better future prospects for the entity. The Committee concluded that, for the process to be rapid and efficient, the Code will provide that the creditors committee should be restricted to only the financial creditors.
In spite of the clear policy rationale for having only two types of creditors (financial and operational) for the CIRP process, the ambiguous language of IBC has now caused confusion.
First, most Indian statutes have only one section for definitions. In contrast, IBC has three sections with the title "Definitions" - section 3, 5 and 79. While section 3 is for the entire Code, section 5 is only for Part II (corporate insolvency) and section 79 is only for Part III (personal insolvency). The word "creditor" is defined in section 3(10) to include "any person to whom a debt is owed and includes a financial creditor, an operational creditor, a secured creditor, an unsecured creditor and a decreeholder". This inclusive definition suggests that under IBC there could be creditors other than "financial creditor" and "operational creditor". This doubt is further entrenched because various sections within Part II (corporate insolvency) use "creditor" as well as "financial creditor" and "operational creditor". This drafting gives the impression that the legislature has used the word "creditor" to include more than just financial and operational creditor in CIRP.
Second, Indian statutes usually use a negative definition while making binary classifications. For instance, under FEMA there are only two kinds of transactions: "capital account transaction" and "current account transactions". To achieve this, the law provides a principle-based definition of "capital account transaction". Then it defines "current account transactions" simply as "a transaction other than a capital account transaction". Similarly, IBC could have also defined "financial debt" and then defined "operational debt" as any debt other than "financial debt". That would have ensured that there is no third category of debts (and creditors). Unfortunately, IBC provides principle-based definition for both "financial debt" and "operational debt", thus creating scope for a third category of debts.
These legislative ambiguities seem to have prompted IBBI to create a third category of creditors, contrary to the orginal policy intent.
Some commentators have opined that certain flat buyers would fall under this third category of creditors. Simultaneously, IBBI has categorically denied media reports suggesting that flat buyers will now be part of CoC. On the other hand, NCLT has ruled that flat buyers are not "operational creditors" either. In view of these differing view points, it would be useful to first understand the basics of a simple flat purchase transaction.
Most buyers pay the real estate developer in advance for delivery of the property at a future date. The problem begins when the developer defaults in delivering the property on time. Buyers resort to various legal actions either to get possession of the property or to get their money back. Clearly, in these cases the buyers are not creditors of the real estate company. They are merely consumers of its services. Just like a pre-paid mobile customer is a consumer of the telco.
In one exceptional case - Nikhil Mehta v. AMR Infrastructure - NCLAT held the concerned flat buyers to be "financial creditors". But this was because of an exceptional clause in their agreement. The developer had contractually agreed to pay a monthly amount to the buyers till the property was delivered to them. In view of this unique clause, NCLAT held that these flat buyers were "financial creditors" of the developer company. This is not a principle of general applicability. Therefore, it can be concluded that all flat buyers are consumers but not necessarily financial creditors.
If flat buyers are consumers of the real estate company, what happens to them if a bank triggers CIRP against the real estate company? This is an important question with practical implications. Although the BLRC did not discuss this issue specifically, it had explicitly recommended that "not all assets that are present within the entity, from the start of the IRP, can be considered for liquidation." Accordingly, section 36 of the IBC excludes "assets held in trust for any third party" from being included in the liquidation estate.
It could be legitimately argued that the funds and properties held by the insolvent real estate company in trust for the third party consumers (flat buyers) should get the protection under section 36. In that case, these funds and properties cannot be taken away by the creditors (like banks) of the real estate company. However, section 18 of the IBC suggests that the interim resolution professional cannot take control and custody of these assets. In view of this contradiction, it needs to be seen how the jurisprudence on "assets held in trust" develops to provide effective remedy to aggrieved flat buyers under IBC.
When IBC was enacted, policymakers realised that unforeseen challenges are likely to crop up during its implementation. That is why section 242 of IBC empowers the Central Government to remove difficulties faced during implementation. However, if necessary, the government can always streamline the law by suitably amending it. In view of the above complications arising out of the insolvencies in the real estate sector, policymakers need to consider if IBC is currently equipped to handle the challenges ahead or would an amendment be necessary to equip it suitably.
Pratik Datta is a researcher.
Should we recapitalise the banks? by Ajay Shah in Business Standard, August 20, 2017.
Three young chess players who could be the next world beaters by Devangshu Datta in Business Standard, August 19, 2017.
Has resistance to economic reforms waned in India? by Tadit Kundu in Mint, August 17, 2017.
The costly failure of the South Asian judiciary in Mint, August 17, 2017.
Silly responses to financial internationalisation: Bank Negara hits out at SGX and ICE in The Star, August 10, 2017.
Part 1: NPA crisis: The rise and fall of Bhushan Steel into the great Indian debt trap, August 8, 2017. Part 2: NPA crisis: Why banks keep lending big bucks, try to hide the distress signals, August 9, 2017. Part 3: NPA crisis: Banking on a new law for answers, August 10, 2017.
An unsettling precedent under IBC by Gausia Shaikh & Bhargavi Zaveri in Business Standard, August 8, 2017.
New technology accelerates the rise of English in India: Duolingo looks to learn more Indian languages by Shashwati Shankar in The Economic Times, August 7, 2017.
Government may give Bhim App users cashback bonanza on Independence Day by Digbijay Mishra in The Economic Times, August 7, 2017. Also see: Subsidies are the last refuge of a failed policy maker, April 16, 2016.
Discrimination, norms, family issues or safety? Why Indian women are quitting jobs by Namita Bhandare in The Hindustan Times, August 5, 2017.
EH Carr's sense of history by Tim Black in Spiked, July 2017.
by Vrinda Bhandari and Renuka Sane and Bhargavi Zaveri.
The public discourse on Aadhaar has largely focused on concerns about the privacy issues associated with the collection of personal information, and the constitutionality of the Aadhaar (Targeted Delivery of Financial and Other Subsidies, Benefits and Services) Act, 2016 ("the Act"). Regardless of the outcome of the case at the Supreme Court, most residents will likely have to interact with the UIDAI, which is the body empowered to roll out an enrollment and authentication program for beneficiaries of welfare programs.
The UIDAI is an Agent established by the Principal (Parliament), with three powers. The law allows the State to compel an individual seeking a state-sponsored subsidy to undergo the enrollment and authentication processes designed by the UIDAI (although Aadhaar has now been made mandatory for certain non-welfare schemes as well, which goes beyond the conception in the law). The UIDAI is empowered to license and regulate Registrars and enrolling agencies to collect the demographic and biometric information of individuals, and enroll them under the Act. Finally, the UIDAI has quasi-judicial powers, such as the power to suspend the licenses of such enrolling agencies and Registrars.
Since the 1980s, governments have established specialised organisations which perform certain functions. These Agents have diverse mandates such as regulating a specific sector (SEBI and TRAI); administration of social welfare schemes (the erstwhile Benefits Agency in the UK); and running prisons (such as the HM Prison Service (HMPS) in the UK or the Dienst Justitiële Inrichtingen - National Agency for Correctional Institutions (DJI) in the Netherlands).
Unfettered discretion: When agencies have the power to write subordinate legislation (i.e. regulations), this power is often not accompanied by checks and balances. In liberal democracies, there are elaborate checks and balances that are placed upon Parliamentary law. These checks and balances can, and often are, diluted in the context of the "regulatory state". For example, in all these years of SEBI's establishment, only one of its quasi-legislative instruments has been challenged. Compare and contrast this to the constitutional challenge that virtually every significant parliamentary law faces in India. Similarly, in the last 30 years, no order issued by RBI has been challenged by the person penalised. This leads to the possibility of abuse of power (Cochrane, 2015).
For FY 2012, a pre-determined strategic goal of the SSA was to deliver "quality disability decisions and services".
The SSA's performance report also shows the funds allocated to each objective and a statement of reasons where the performance metric is not met.
Requiring an annual report in a prescribed form describing UIDAI's past activities, accounts, and future programmes of work, to be laid before each House of Parliament [Section 27 of the Act]. However, no such manner and form for the publication of the report has been laid down in the Aadhaar Regulations, nor does such a Report seem to be available in the public domain.
The conduct of an agency is largely shaped by the law governing it. For instance, Burman and Zaveri (2016) find that there is a correlation between the laws which mandate transparency of a regulator and the responsiveness of such regulators to citizens' preferences. Similarly, the detailed performance reporting by the SSA is underpinned by a law called the Government Performance and Results Act, 1993, a law that set up a performance-oriented framework of reporting for the US federal agencies to show the progress they make towards achieving their goals.
In the absence of such statutorily mandated accountability standards, measuring the performance of the UIDAI is difficult. Stories of security breaches and authentication failures for availing benefits abound. For instance, Scroll.in queried the UIDAI about the authentication requests received between September 2010 (when the first Aadhaar number was issued) till October 2016, and how many failed or succeeded. The query was aimed at assessing the efficacy of biometric authentication. The UIDAI replied that it had not maintained any records between September 2010 and September 2012 and that it did not maintain authentication data state-wise. More importantly, the UIDAI revealed that data about the success or failure of the over 331 crore authentication requests was "not readily available", nor was the breakup of the negative reply to the requesting authority on each of the five modes of authentication "readily available".
Similarly, cases of fake Aadhaar cards have also been reported. Pertinently, in response to an RTI filed by PTI, seeking details related to all cases of duplicate and fake Aadhaar cards and the action taken on them, the UIDAI refused the request on the grounds that the disclosure might affect national security, or lead to incitement of an offence. The UIDAI also informed PTI that its CIDR facilities, information assets, logistics and infrastructure and dependencies, are all classified as "protected system" under the IT Act, and are thus, exempt from RTI. It further stated that the format in which it held the information contained identity details, which may be prone to identity theft, if divulged. The practical reality thus is that cases of unauthorised leaks/disclosures of identity information are being dealt with on a case to case basis, with zero clarity in the law on who is to be held accountable for such lapses in the future.
The report of the Bankruptcy Law Reforms Committee (2015), drew on the regulatory governance framework recommended by the FSLRC and recommended four elements for achieving accountability of the Insolvency and Bankruptcy Board of India, India's new insolvency regulator. While some of these elements were codified in the Insolvency and Bankruptcy Code, others are sought to be implemented in the course of setting up the Insolvency and Bankruptcy Board of India. Recent events at TRAI are pushing the organisation towards sound processes.
Cochrane, J. (2015), The rule of law in the Regulatory State.
Heidenheimer, A.J., Heclo, H. and Teich Adams, C. (1990), Comparative Public Policy: The Politics of Social Choice in America, Europe, and Japan, (3rd edition) New York: St. Martins.
Maggetti, Martino (2010). Legitimacy and Accountability of Independent Regulatory Agencies: A Critical Review, Living Reviews in Democracy Vol 2.
Pollitt, Christopher, Colin Tablot, Janice Caufield, and Amanda Smullen (2004), Agencies: how governments do things through semi-autonomous organizations, New York: Palgrave Macmillan.
Young Han Chun, Hal G. Rainey (2005), Goal Ambiguity in U.S. Federal Agencies, J. Public Adm. Res. Theory 2005, 15 (1): 1-30.
Burman, Anirudh and Zaveri, Bhargavi (2016), Regulatory responsiveness in India: A normative and empirical framework for assessment, IGIDR Working Paper WP-2016-025, October 2016.
Vrinda Bhandari is a practicing advocate in Delhi. Renuka Sane is a researcher at the National Institute of Public Finance and Policy, Delhi. Bhargavi Zaveri is a researcher at the IGIDR Finance Research Group, Mumbai.
The broad set of Indian listed companies have a high trailing P/E ratio. This suggests that the market believes there will be high earnings growth in the future.
Some finance practitioners back out an earnings time series as Nifty market capitalisation divided by Nifty P/E. This `Implied Nifty Earnings' series shows strong growth over long time horizons.
In this article, we show that this quick-and-dirty method has an upward bias in the estimation of aggregate earnings growth. In truth, earnings growth by Indian firms has been stalled for a decade.
The graph above shows the long time-series of the trailing P/E ratio of the CMIE Cospi index, which measures the broad market valuation. This shows that we are near some of the highest valuations in history.
These high P/E ratios would generally suggest that the stock market expects that a period of great earning growth is around the corner. It's important to look back at the recent history of earnings growth in order to evaluate this optimism.
As Nifty market capitalisation is measured in rupees, and the P/E ratio is dimensionless, the division yields an earnings value in rupees.
This shows pretty good growth in the earnings of the Nifty companies. In the latest few years, the growth is slow, but when compared with a decade ago, the earnings expansion is remarkable. Overall, it's a gain of 18$\times$ in 18 years, which is quite a performance. It is consistent with the common view that India is a high earnings-growth economy.
The set of firms that make up Nifty changes through time. From 1996 to 2017, there were 118 firms which have been a member of Nifty atleast once.
The Nifty components at time $t_1$ are often different from those prevalent at time $t_2$. Some firms are added and some are removed. We tend to think that these are a few random fluctuations which would tend to cancel out. However, the changes in the set are non-random, and they do not cancel out.
The management of Nifty uses a rule set that roughly summarises to this: (a) A pool of eligible firms is formed where the firms have adequate stock market liquidity based on the Impact Cost measure, and (b) If an eligible firm is over 2$\times$ larger (by market capitalisation) than the smallest incumbent, then a set change is effected where the smallest incumbent is removed and the large new liquid firm is brought in. The earnings of the new entrant will generally be higher than the earnings of the smallest incumbent who is removed, as the market value of the new entrant is over 2$\times$ higher.
Here is one example, from the April-May-June 2016 quarter. In this quarter, three firms were removed (Vedanta, Cairn India, Punjab National Bank) and three firms were added (Aurobindo Pharma, Bharti Infratel and Eicher Motors) to Nifty. The remaining 47 firms were unchanged. Let's pull together the information about earnings across these changes.
The best estimator of earnings growth is that which is made using the identical set of firms observed at two points in time. In the above example, there are 47 firms in Nifty who were present at both points in time. Their aggregate earnings declined from Rs.735B to Rs.635B, a decline of 14%.
Three firms were present in Q1 2016 -- Vedanta, Cairn, PNB -- and when their earnings data is used, the aggregate earnings of the 50 firms in Nifty at that point in time works out to Rs.717B. These were replaced by Aurobindo Pharma, Bharti Infratel, Eicher Motors in Q2 2016, and when their earnings data is used, the aggregate earnings of the 50 firms in Nifty at that point in time works out to Rs.657B. The earnings growth obtained by comparing these two inconsistent sets was -8%, which is a more optimistic picture when compared with the decline of 14% for the consistent set.
There is a big discrepancy, of 6 percentage points across one quarter, and the direction of the bias in in favour of greater optimism.
The wrong method (merely comparing the profits across inconsistent sets across time) does not just introduce random noise, it is biased. It systematically overstates earnings growth of the Nifty set.
What actually happened to earnings growth of Indian firms?
Oil companies have extreme earnings fluctuations based on fluctuations of global crude oil prices. Their profits do not describe what is going on in India. Finance companies have problems in earnings data, such as the concealment of bad assets by banks. Hence, we look at non-oil non-finance companies only. Aggregation of accounting data for this set of firms is an excellent source of insight into India's business cycle fluctuations.
At every two consecutive quarters, we construct a set of listed firms which are observed in both quarters. We sum up the earnings of this set at each of the two quarters. These two summed earnings are comparable across time, as they pertain to the identical set of firms.
This yields a nominal percentage growth of aggregate earnings from one quarter to the next.
We start an index at 100 and cumulate it up through time using each of these carefully constructed estimates of earnings growth.
This tells a story where the average earnings index grew from 126 in 2000 to 996 in 2010, but declined to 783.98 in the Oct-Dec 2016 quarter. Nominal earnings has stagnated in the last decade.
The compound average growth rate of earnings of all listed firms is similar to that of non-finance non-oil firms. Both estimates are roughly 8 percentage points per year below the quick and dirty method.
The quick and dirty method suggests 18$\times$ earnings growth in 18 years. The correct method shows 8$\times$ earnings growth in the same period, and stagnation in the last decade.
The stock market believes that a great wave of earnings growth is around the corner, and India is generally considered a market with high earnings growth. However, earnings growth has been elusive for the last decade. More generally, in the past, the Indian stock market has done well on differentiating between firms -- in voting with a high P/E ratio for firms that will do well in the future -- but has fared poorly at macroeconomic thinking.
This R program when run using data from CMIE Prowess DX (Mar-2017 vintage) replicates Figure 3 above.
I thank Nilesh Shah and Mahesh Vyas for valuable discussions. Pramod Sinha wrote the code and it was audited by Dhananjay Ghei and Shekhar Hari Kumar.
Elements of the recovery by Ajay Shah in Business Standard, August 6, 2017.
A judgment for the ages by Chinmayi Arun in The Hindu, August 3, 2017.
Needed, a financial redressal agency editorial in The Economic Times, August 2, 2017. Also see.
India's complicated infrastructure story by Ashwini Mehra in Mint, August 2, 2017.
The Past Week Proves That Trump Is Destroying Our Democracy by Yascha Mounk in The New York Times, August 1, 2017.
Equity Derivatives versus Cash Equities in India by Jayanth Varma in Prof. Jayanth R. Varma's Financial Markets Blog, July 31, 2017. Also see: Strategic thinking in financial markets policy, July 24, 2017.
Artificial Intelligence Is Stuck. Here's How to Move It Forward. by Gary Marcus in The New York Times, July 29, 2017. Also see: Project Tanzanite: Obtaining fundamental progress in the macroeconomics of developing countries, October 24, 2011.
Trump is something the nation did not know it needed by George F. Will in The Washington Post, July 28, 2017.
Why the Scariest Nuclear Threat May Be Coming from Inside the White House by Michael Lewis in Vanityfair, July 26, 2017.
Agrarian crisis: the challenge of a small farmer economy by Sudipto Mundle in Mint, July 21, 2017.
Emerging infectious diseases, One Health and India by Shahid Jameel in The Hindu, July 15, 2017.
Bitcoins are business as usual in Bengaluru by Aditi Phadnis in Business Standard, July 15, 2017.
History of Aadhaar: How Nandan's core team came together by Shankkar Aiyar in Yourstory, July 13, 2017.
How Do We Contend With Trump's Defiance of 'Norms'? by Emily Bazelon in The New York Times, July 11, 2017.
The Danger of Deconsolidation: The Democratic Disconnect by Roberto Stefan Foa and Yascha Mounk in Journal of democracy, July, 2016.
The empty brain by Robert Epstein in Aeon, May 18, 2016.
In his recent speech at RBI's Annual Statistics Day Conference, RBI Deputy Governor Viral Acharya called for the creation of a Public Credit Registry (PCR). A PCR is a comprehensive database of all borrowings in the country. The Deputy Governor suggested that submission of information to this registry should be compulsory, and that it should be managed by the RBI. He added that the RBI intended to establish a task force for setting up the PCR.
In this article, we argue that there is no market failure that justifies the establishment of a PCR, and that there is no evidence that a PCR is required for an efficient credit market. Given that India has a surfeit of credit information entities, the creation of a new PCR in the RBI is unlikely to help.
The public economics approach is that markets work reasonably well in most situations. State intervention should be avoided if possible. Public choice theory suggests that a bureaucracy will try to expand its own budget and functions. A proposal by an agency that tries to enlarge itself should be treated with scepticism.
In this light, does India require a PCR run by the RBI? World Bank data shows that most countries around the world do not have PCRs. Countries such as the US, UK, Canada, Australia, New Zealand, Netherlands, Sweden, Norway, Japan, South Korea, all have highly developed credit markets without having PCRs. In these countries, private sector credit bureaus fulfil this function. The international examples the Deputy Governor cited in his speech (Thomson Reuters Dealstreet, and Dun & Bradstreet) are both private entities. The major Consumer Reporting Agencies in the US, as well as the Credit Reference Agencies in the UK, are all private entities functioning in competitive markets.
These examples suggest that the credit information industry need not suffer from market failures, as long as appropriate statutory frameworks are in place to deal with issues such as the privacy, safety, and sharing of information. The absence of PCRs in most well-functioning credit markets indicate that PCRs are not required for competitive credit markets.
India already has a large number of entities involved in providing credit information. There are four Credit Information Companies (CICs), all regulated by the RBI. It is mandatory for institutional lenders to provide credit information to these companies. The RBI has extensive powers over CICs: even their membership fees and annual fees are decided by the RBI. Apart from this, the RBI has previously created the Central Repository of Information on Large Credits (CRILC). The Central Registry of Securitisation, Asset Reconstruction, and Security Interest (CERSAI) was created by the government to record the creation of security interests over property. The MCA21 database of the Ministry of Corporate Affairs is used to record charges on the assets of companies.
The Insolvency and Bankruptcy Code (IBC) has introduced yet another type of entity to this space: Information Utilities (IUs). The design of IUs has been thought through by the Bankruptcy Law Reforms Committee and by the Working Group on Information Utilities. The Insolvency and Bankruptcy Board of India (IBBI) has recently issued regulations that enable the registration and operation of IUs, though no IUs have started operations as of yet.
To justify a PCR, the RBI needs to explain not just what market failures it seeks to solve, but also why all these other entities were (or, in the case of IUs, will be) ineffective in solving those market failures, and why PCRs will succeed.
To make a case for having a PCR in India, the RBI needs to articulate what market failures the PCR will solve. We have seen above that market failures are not necessarily a feature of the credit information industry, and that PCRs are not necessary to achieve competitive credit markets.
In India, a number of entities exist that are related to providing credit information. They include four CICs, CRILC, CERSAI, other databases in the RBI and the Ministry of Corporate Affairs, and the upcoming IUs. Given the existence of all these entities, the RBI also needs to argue why the existing entities are not sufficient, and why yet another government agency needs to be set up. In the absence of such articulation, it is not clear that further state intervention in the form of PCRs is warranted.
Shah, Ajay, Solving market failures through information interventions, Ajay Shah's blog, April 2015.
Government of India, The Insolvency and Bankruptcy Code, 2016.
Insolvency and Bankruptcy Board of India, Insolvency and Bankruptcy Board of India (Information Utilities) Regulations, 2017.
Prasanth Regy is a researcher at the National Institute of Public Finance and Policy, New Delhi.
The author would like to thank Anirudh Burman, Pratik Datta, and an anonymous referee, for helpful comments. | CommonCrawl |
Abstract: It is known that quantum effects leads to an exponentially rapid destruction of the stochastic phase trajectory of a nonlinear oscillator excited by a regular force exerted on it by an external source. In the present paper, the exponentially growing quantum corrections are completely summed. As a result, the semiclassical series for the quantum-mechanical expectation values is rearranged in such a way that it no longer contains the exponentially growing terms. The main term of the obtained series leads in the case of stochastic motion to the same dependence of the mean action of the oscillator on the time as in the classical case, and the first correction has the order $\hbar^2$. At the same time, the mean powers of the action contain already in the leading approximation corrections of order $\hbar$ that grow as powers with the time, though they do not change the asymptotic behavior as $t\rightarrow\infty$. The obtained results are not sensitive to the choice of the initial state of the oscillator. | CommonCrawl |
6 How to avoid primarily opinion-based holds?
4 Are there double standards for pushy questions, exemplified by two recent ones on nuke power?
41 I'm afraid of chemicals. How do I handle my required uni biology class?
33 Why did no student correctly find a pair of $2\times 2$ matrices with the same determinant and trace that are not similar?
32 Is it okay to include a simplified and easy version of a result already proved? | CommonCrawl |
How did someone discover N, order of G for SECP256k1?
Could someone please explain, in simple and easy terms, how the creators did (or should have) derived the N, order of G for SECP256k1?
I understand that (N-1) is the total number of valid points on the curve, but how was that determined without going through and trying to count them?
I have seen similar questions, but the answers are either using terminologies I don't understand and or don't contain a "simple" and "easy" explanation.
Actually no. $N$ is the number of points on the curve, $N-1$ is the number of non-trivial points, where the point at infinity $\mathcal O$ is the trivial point (because it is essentially the $0$ for curves).
First, let's assume we already know the order of the curve, ie the number of points on it. Let's call this number $n$. It turns out that for secp256k1 $n$ is a prime. Now we know by Lagrange's Theorem the order of any subgroup (like the subgroup generated by $G$) of secp256k1 must divide $n$, so either have $1$ or $n$ elements. But the only element that generates a subgroup with one element is $\mathcal O$ (because $\mathcal O+\mathcal O=\mathcal O$) and thus $G$ must have order $n$.
But how do we find the order of the curve? It turns out that mathematicians have already solved this problem and found an algorithm to efficiently count the number of points on a curve without actually visiting every single one, it's called Schoof's algorithm. Now the details of this algorithm are very complex and thus I won't go into them here. If you really want to know, you can read the linked article and the references given at the bottom of the page.
Not the answer you're looking for? Browse other questions tagged public-key elliptic-curves algorithm-design or ask your own question.
Sextic twist optimization of BN pairing - cubic root extraction required?
Why does knowing the number of points on a curve help solve ECCDLP?
Is there any pattern in points on EC?
What are the steps for finding points on finite field elliptic curves?
What is the difference between a dual cipher and a tweak? | CommonCrawl |
Recall that in 2-dimensional space, an equation containing the variables $x$ and $y$ represents a curve. We will now extend this to look at equations involving three variables, commonly $x$, $y$, and $z$ (though sometimes $x_1$, $x_2$, and $x_3$) which happen to form surfaces in 3-dimensional space.
We will first outline some examples of equations and their corresponding surfaces in 3-dimensions. | CommonCrawl |
Gelfreich V. G., Lerman L. M.
We study the splitting of a separatrix in a generic unfolding of a degenerate equilibrium in a Hamiltonian system with two degrees of freedom. We assume that the unperturbed fixed point has two purely imaginary eigenvalues and a non-semisimple double zero one. It is well known that a one-parameter unfolding of the corresponding Hamiltonian can be described by an integrable normal form. The normal form has a normally elliptic invariant manifold of dimension two. On this manifold, the truncated normal form has a separatrix loop. This loop shrinks to a point when the unfolding parameter vanishes. Unlike the normal form, in the original system the stable and unstable separatrices of the equilibrium do not coincide in general. The splitting of this loop is exponentially small compared to the small parameter. This phenomenon implies nonexistence of single-round homoclinic orbits and divergence of series in normal form theory. We derive an asymptotic expression for the separatrix splitting. We also discuss relations with the behavior of analytic continuation of the system in a complex neighborhood of the equilibrium.
Gelfreich V. G., Turaev D. V.
We show that a generic area-preserving two-dimensional map with an elliptic periodic point is $C^\omega$-universal, i.e., its renormalized iterates are dense in the set of all real-analytic symplectic maps of a two-dimensional disk. The results naturally extend onto Hamiltonian and volume-preserving flows.
Gelfreich V. G., Gelfreikh N. G.
We study normal forms for families of area-preserving maps which have a fixed point with neutral multipliers $\pm 1$ at $\varepsilon = 0$. Our study covers both the orientation-preserving and orientation-reversing cases. In these cases Birkhoff normal forms do not provide a substantial simplification of the system. In the paper we prove that the Takens normal form vector field can be substantially simplified. We also show that if certain non-degeneracy conditions are satisfied no further simplification is generically possible since the constructed normal forms are unique. In particular, we provide a full system of formal invariants with respect to formal coordinate changes.
The paper is devoted to the problem of analytical classification of conformal maps of the form $f : z \mapsto z + z^2 +\ldots$ in a neighborhood of the degenerate fixed point $z=0$. It is shown that the analytical invariants, constructed in the works of Voronin and Ecalle, may be considered as a measure of splitting for stable and unstable (semi-) invariant foliations associated with the fixed point. This splitting is exponentially small with respect to the distance to the fixed point. | CommonCrawl |
Photonics North 2019 is an IEEE sponsored conference. After many requests from past Photonics North participants, the conference has once again secured technical sponsorship from the IEEE Photonics Society. As a result, Photonics North also gained access to publish with the IEEE. The Photonics North committee will do its utmost to maintain the conference quality and have the one-page conference abstracts published through IEEE Xplore as well as other Abstracting and Indexing (A&I) databases.
The one-page abstract complied with IEEE format is all you have to submit. The conference does not plan to publish a full-length paper-based proceedings. This would allow the authors to submit a full-length paper elsewhere and with any journal before or after the conference. Please note that only those papers accepted by the conference review committee will be included in the conference proceedings. For both oral and poster presentations, papers must be presented by at least one of the authors of the paper. Those papers whose author failed to register and present at the conference will be removed from publication with the IEEE.
Abstracts submitted are reviewed by experts selected by the conference committee for their demonstrated knowledge of particular topics. Authors will be notified of the review results by email.
If your paper is accepted, it will be assigned to either a lecture session or a poster session. Prepare your presentation accordingly, following the guidelines below. The author request for an oral or poster presentation is taken into consideration but the final decision to place a paper in lecture or poster session rests with the evaluation committee.
Abstracts may be no longer than 1 page, including all text, figures, and references. Please note that after the submission deadline the list and the order of the authors cannot be modified, and must remain unchanged in the final version of the manuscript.
Photonics North requires that each accepted paper be presented by one of the authors' in-person at the conference site according to the schedule published. Presentation by anyone else than one of the co-authors (proxies, video or remote cast) is not allowed, unless explicitly approved before the conference by the technical co-chairs. One of the authors must register for the conference and must register before the author registration deadline. Failure to do so will result in automatic withdrawal of the paper from BOTH the conference program and proceedings archived on IEEE Xplore.
For posters, one author must be present at the poster during the entire duration of the session.
Papers must be submitted in Adobe's Portable Document Format (PDF) and must strictly adhere to the IEEE Requirements for PDF Documents v3.2.
Text should preferably appear in two columns, each 86 mm (3.39") wide with 6 mm (0.24") spacing between columns.
To achieve the best viewing experience for the review process and conference proceedings, we strongly encourage authors to use Times-Roman or Computer Modern fonts. If a font face is used that is not recognized by the submission system, your document will not be reproduced correctly.
The paper title must appear in boldface letters. Do not use LaTeX math notation ($x_y$) in the title.
The title must be representable in the Unicode character set. Lastly, try to avoid uncommon acronyms in the title.
The authors' name(s) and affiliation(s) appear below the title in capital and lower case letters. Photonics North does not perform blind reviews, so be sure to include the author list in your submitted paper. Papers with multiple authors and affiliations may require two or more lines for this information. The order of the authors on the document should exactly match in number and order the authors typed into the online submission form.
Text file containing paper-abstract in text format (for copying and pasting into webpage form).
Questions concerning the paper-submission process should be addressed to [email protected]. Please include your paper number(s) and title(s) on all correspondence. | CommonCrawl |
Commonly used password hashing algorithms work like this today: Salt the password and feed it into a KDF. For example, using PBKDF2-HMAC-SHA1, the password hashing process is DK = PBKDF2(HMAC, Password, Salt, ...). Because HMAC is a 2-round hashing with padded keys, and SHA1 a series of permutations, shifts, rotations and bitwise operations, fundamentally, the whole process is some basic operations organized in a certain way. It's not obvious, fundamentally, how difficult they really are to compute. That's probably why one-way functions are still a belief and we have seen some historically important cryptographic hash functions became insecure and deprecated.
I was wondering if it's possible to leverage NP complete problems to hash passwords in a brand new way, hoping to give it a more solid theoretical foundation. The key idea is, suppose P != NP (if P == NP then no OWF so current schemes break as well), being an NPC problem means the answer is easy to verify but hard to compute. This property fits well with the requirements of password hashing. If we view the password as the answer to an NPC problem, then we can store the NPC problem as the hash of the password to counter offline attacks: It's easy to verify the password, but hard to crack.
Suppose the binary string is 000. Then only 1 of 8 clause is false (the first one). If we discard the first clause and AND the remaining 7 clauses, then 000 is a solution of the resulting formula. So if we store the formula, then we can verify 000.
The problem is, for a 3-bit string, if you see 7 different clauses there, then you instantly know which one is missing, and that would reveal the bits.
So later I decided to discard 3 of them, only keeping the 4 marked by 001, 010, 100 and 111. This sometimes introduces collisions but makes solving the problem less trivial. The collisions don't always happen, but whether they would surely disappear when the input has more bits is not known yet.
Edit. In the general case where the binary string can be any of (000, 001, ..., 111), there are still 8 clauses where 7 are true and 1 is false. Pick the 4 clauses that give truth value (001, 010, 100, 111). This is reflected in the prototype implementation below.
Edit. As the answer shown by @D.W. below, this method of choosing clauses may still result in too many clauses on a given set of variables which makes it possible to quickly narrow down their values. There are alternate methods of choosing the clauses among the total 7 * C(n, 3) clauses. For example: Pick a different number of clauses from a given set of variables, and do that only for adjacent variables ( (x_0, x_1, x_2), (x_1, x_2, x_3), (x_2, x_3, x_4), ... ) and thus form a cycle instead of a clique. This method is likely not working as well because intuitively you can try assignments using induction to test whether all clauses can be satisfied. So to make it simple explaining the overall structure let's simply use the current method.
The number of clauses for an n-bit string is 4 * C(n, 3) = 4 * n * (n - 1) * (n - 2) / 6 = O(n^3), which means the size of hash is polynomial of the size of password.
There's a prototype implementation in Python here. It generates a 3-SAT problem instance from a user input binary string.
Does the above construction (as implemented in the prototype) work as secure password hashing, or at least look promising, can be revised, etc.? If not, where it fails?
Because we have 7 * C(n, 3) clauses to choose from, is it possible to find another way to construct a secure 3-SAT instance suitable for use as password hash, possibly with the help of randomization?
Are there any similar work trying to leverage NP completeness to design proven secure password hashing schemes, and already got some results (either positive or negative)? Some intros and links would be very welcome.
Edit. I'd accept the answer below by @D.W., who was the first to reply and gave great insights about the problem structure as well as useful resources. The naive clause selection scheme introduced here (as implemented in the Python prototype) didn't seem to work because it's possible to quickly narrow down variable assignments in small groups. However, the problem remains open because I haven't seen a formal proof showing such NPC-to-PasswordHashing reductions won't work at all. Even for this specific 3-SAT reduction problem, there might be different ways of choosing clauses that I don't want to enumerate here. So any updates and discussions are still very welcome.
Unfortunately, this doesn't seem to work (see below for details), and it seems hard to find a way to make this kind of idea yield a provably secure scheme.
You're not the first to think of the idea of trying to base cryptography on NP-complete problems. The problem is that NP-hardness only ensures worst-case hardness, but cryptography requires average-case hardness. There have been multiple attempts to base cryptography on NP-complete problems (e.g., knapsack cryptosystems), but they have not fared well. Typically what happens is that people discover algorithms that are often effective on average (or with non-trivial probability), even though in the worst case they are exponential; this is enough to break the crypto, even though it doesn't contradict the NP-hardness.
The point of relying on a NP-hard problem is presumably to ensure some kind of provable security for your scheme (e.g., if P $\ne$ NP then your cryptosystem is secure), but because of the difference between worst-case vs average-case hardness, that kind of result doesn't actually follow, and it's not clear how to build a cryptosystem where we do obtain such a result.
I suggest reading more about the subject. You can find some useful starting points at The significance of NP-Hard Problems in Cryptography, Average-case complexity open problems other than one-way functions, Status of Impagliazzo's Worlds?, Worst case to average case reductions.
That said, it appears your scheme will be easy to break no matter how you instantitate those details. Intuitively, 3SAT instances with so many clauses are usually easy. More specifically, I will describe an attack that solves the type of 3SAT instances generated by your scheme. First, let's try to recover $x_0,x_1,x_2,x_3,x_4$. Focus on just the clauses that mention only those variables (and not any other). There should be 40 such clauses, because there are 10 ways to choose a subset of 3 of the variables. There are $2^5$ possible assignments to those 5 variables, so try them all and discard any assignment that is violated by any of the 40 clauses. I predict that this will leave you with only about one assignment that is consistent with all clauses.
This can be repeated for each group of 5 variables, uniquely recovering the unique satisfying assignment for each. If there is any ambiguity, the candidate assignments can be checked against other clauses.
In this way, we see that there is an efficient algorithm that will typically solve the class of 3SAT instances generated by your procedure. It won't solve all 3SAT instances, but the instances you generate have a special structure, and it does solve instances with that special structure effectively. This illustrates the point well: some instances of 3SAT are easier than others, and the hardness of 3SAT (in worst-case complexity) says little or nothing about the hardness of the special instances you generate or the hardness of an average 3SAT instance.
Not the answer you're looking for? Browse other questions tagged np-hardness cr.crypto-security np-complete security or ask your own question. | CommonCrawl |
We study eigenvalues of 3D Schrödinger operators modified by a stochastic term $V_N$, oscillating at typical frequency $N \gg 1$. Such operators are a rough model for the propagation of waves inside a disordered medium. Using a perturbation argument, we show that eigenvalues converge almost surely as $N \rightarrow \infty$. The rate of convergence is investigated: we identify two regimes, deterministic and stochastic, depending on high-frequency interference and on the typical amplitude of the low-frequencies of $V_N$ -- created by large deviations effects. | CommonCrawl |
1(a) Define surveying. Classify surveying on the basis of the purposes of the survey.
1(b) Differentiate between Whole circle bearing (WCB) and Reduced bearing system. If $\theta$ is the WCB, what would be the reduced bearing in all four quadrants?
1(d) Define contour and contour interval. State any four characteristics of contours.
1(e) Explain the temporary adjustments of a theodolite.
1(f) A tacheometer has a diaphragm with three cross hairs spaced at a distance of 1.20mm. The focal length of the object glass is 24cm and the distance of the object glass from the trunnion axis is 10cm. Calculate the tacheometric constants.
2(a) A survey was conducted round a lake and the bearings as shown aside were obtained. Determine which of the stations are affected by local attraction and give the values of the corrected bearings.
2(b) Compare: Surveyors Compass and Prismatic Compass.
2(c) A road embankment 30m wide at top with side slope of 2 to 1 have ground levels at 100 meters interval along line PQ as under: P(153.0), 151.8, 151.2, 150.6, (149.2)Q. The formation level at P is 161.4m with a uniformly falling gradient of 1 in 50 from P to Q. Find volume of earthwork by prismoidal formula. Assume the ground to be level in c/s.
2 1.645 ? 0.500 ?
4 ? 1.965 ? ?
5 2.050 1.825 0.400 ?
8 ? 2.100 ? ?
3(b) Explain reciprocal levelling with its procedure and purpose.
4(a) List the accessories required for Plane Table Survey. Describe the intersection method of plane table survey with its advantage.
(ii) Measurement of horizontal angle by method of Repetition.
4(c) A 20m chain was found to be 4 cm too long after chaining 1420m. It was 8 cm too long at the end of day's work after chaining a total distance of 2400 m. If the chain was correct before commencement of the work, find the true distance.
irregular boundary line. Calculate the area using Simpson's Rule.
5(c) Write down the procedure of Indirect Ranging with a suitable sketch.
6(a) Initially, a staff was held vertically at a distance of 46.2m and 117.6m from the centre of a theodolite fitted with stadia hairs and the staff intercepts with the telescope horizontal were 0.45m and 1.15m respectively. The instrument was then set over a station P having RL as 150m, the height of instrument axis being 1.38m. The stadia hair readings on a staff held vertically at a station Q with instrument at P were 1.200, 1.930 and 2.650 m respectively, while the vertical angle(depression) was - 9$^o$30'. Find RL of Q & dist. PQ.
6(b) In a 2 plane method exercise, points P and Q are two instrument stations and point R is the point whose elevation is to be known. The values of included angles $\theta$p & $\theta$q are 64$^o$30' & 58$^o$15' respectively. The values of vertical angle $\alpha$p & $\alpha$q are 20$^o$43'20" & 19$^o$44'55" respectively. The height of instrument at P and Q are 1.450 and 1.550 m respectively while the backsights taken on benchmark (RL= 100.125 m) from P & Q are 1.625 and 1.125 m respectively. Distance PQ is 180m. Determine the ground elevations of both the instrument station and elevation of point R.
6(c) Explain tie line, check line, base line and main survey line with neat sketch. | CommonCrawl |
This notebook demonstrates quantum teleportation. We first use Qiskit's built-in simulator to test our quantum circuit, and then try it out on a real quantum computer.
This story will involve three individuals. Let's call them Abraham, Alice and Bob.
1: Abraham generates a quantum state $|\psi\rangle = \alpha|0\rangle + \beta|1\rangle$.
2: Abraham "gives" this quantum state to Alice - effectively, what this means is that Alice can now act on this quantum state. However, Abraham gives the state to Alice with the caveat that she doesn't know the coefficients $\alpha$ and $\beta$.
3: Alice now wants to pass on this quantum state to Bob, who is very far away. Alice and Bob can talk over the phone.
So how does Alice pass on the information to Bob without knowing the coefficients? She uses quantum teleportation.
1: Before they parted ways, Alice and Bob created an entangled Bell pair. Each one of them held on to one of the two qubits in the Bell pair when they parted ways.
In quantum circuit language, the way to create a Bell pair between two qubits is to first transfer one of them to the Bell basis ($|+\rangle$ and $|-\rangle$) by using a Hadamard gate, and then to apply a CNOT gate onto the other qubit controlled by the one in the Bell basis. Let's say Alice owns $q_1$ and Bob owns $q_2$ after they part ways.
2: Once Abraham gives Alice control of $|\psi\rangle$, Alice applies a CNOT gate on $q_1$, controlled by $|\psi\rangle$.
3: Next, Alice applies a Hadamard gate to $|\psi\rangle$, and applies a measurement to both qubits that she owns.
And voila! At the end of this protocol, the qubit that Abraham gave Alice has now teleported to Bob. You are encouraged to write out the states that result from this protocol and verify that it works.
In this notebook, we will pretend to be Abraham by giving Alice a secret state $|\psi\rangle$. This state will be generated by applying a series of unitary gates on a qubit that is initialized to the ground state, $|0\rangle$. Go ahead and fill in the secret unitary that will be applied to $|0\rangle$ before passing on the qubit to Alice.
If the quantum teleportation circuit works, then at the output of the protocol discussed above will be the same state passed on to Alice by Abraham. Then, we can undo the applied secret_unitary (by applying its conjugate transpose), to yield the $|0\rangle$ that we started with.
We will then do repeated measurements of Bob's qubit to see how many times it gives 0 and how many times it gives 1.
In the ideal case, and assuming our teleportation protocol works, we will always measure 0 from Bob's qubit because we started off with $|0\rangle$.
In a real quantum computer, errors in the gates will cause a small fraction of the results to be 1. We'll see how it looks.
# Next, apply the teleportation protocol.
since for a unitary u, u^dagger u = I.
Note that the results on the x-axis in the histogram above are ordered as $c_2c_1c_0$. We can see that only results where $c_2 = 0$ appear, indicating that the teleporation protocol has worked.
As we see here, there are a few results that contain the case when $c_2 = 1$ in a real quantum computer. These arise due to errors in the gates that were applied. Another source of error is the way we're checking for teleportation - we need the series of operators on $q_2$ to be exactly the inverse unitary of those that we applied to $q_0$ at the beginning.
In contrast, our simulator in the earlier part of the notebook had zero errors in its gates, and allowed error-free teleportation. | CommonCrawl |
The result is remarkable avoidance of self-intersection, regardless of how convoluted is the original curve, and ultimate convergence to a "round point." See, e.g., this YouTube Video.
Q. Has this flow been studied along vectors at some fixed angle to the normal? E.g., at $90^\circ$ counterclockwise of the normal, tangent to the curve?
Presumably, for any angle $\alpha > 0$ counterclockwise of the normal, the curve might self-intersect during its evolution. But perhaps it still converges to a limit shape?
Browse other questions tagged reference-request dg.differential-geometry mg.metric-geometry curves-and-surfaces flows or ask your own question. | CommonCrawl |
So what is Sage? Sage is comprehensive mathematics software that you can use from your computer, or even certain mobile devices.
The first thing we'll want to do is get people started up on Sage. Nothing could be easier.
Type "2+2" in the box.
If you ever have trouble during the talk, you can always go and type commands here to your heart's content!
However, this can only handle one-off computations. There are two options for doing lots of them online.
Many of you may already be set up on the local Gordon server; it's easy to get a new account if you don't already have an account. See http://sagemath.org/doc/prep/Logging-On.html for some nice screenshots. I'll be using this for most of this talk.
A somewhat more powerful, but also more intimidating, process is to create an account at https://cloud.sagemath.com/, which essentially provides a complete computer system online for you, including native Sage worksheets.
Type in $2+2$ and evaluate it!
This last thing is done by clicking in the 'cell' like the one below, typing 2+2, and then either clicking "Evaluate" (or the "Run" button) or pressing Shift and Enter simultaneously (Shift-Enter).
If you really want to, you can even "Edit a copy" of this worksheet, located at http://sage.math.gordon.edu/home/pub/86/; once you've logged in, click "Edit a copy", or follow the instructions at http://doc.sagemath.org/html/en/prep/Logging-On.html.
Once you've done this, the main goal for today is to give you an introduction to how to use Sage, whether or not you are required to use it in a class.
Sage is the ONLY comprehensive program, free or not, which is freely available from any internet-accessible computer with a reasonably modern web browser. There is nothing to download, no Java applet which needs to load, nothing like that. It's all modern Web 2.0 technology like Google Docs/Drive.
As you can see, when you click on a "cell", there is a little 'evaluate' link right below it on the left. You may click on this to ask Sage to do something, or you can press Shift and Enter at the same time. In the case above, I have asked it to define a function of a variable $x$. Notice that exponentiation is denoted with the carat (Shift-6) and multiplication with the asterisk (Shift-8). Other than this, Sage 'knows' about most math expressions via something called a preparser, but you must do these correctly (especially multiplication!).
Notice that if I check the "Typeset" button at the top, it is nicely typeset, using MathJax, the standard for web mathematics. Surrounding something with "pretty_print()" also will do this.
And now it is a simple matter to do some calculus homework checking. What was the integral of the square root of $x^2+5x+1$ again?
Notice I included the variable; otherwise, how does Sage know I didn't mean an integral with respect to some other variable?
But if you do declare it (the syntax is always the same), neat things can happen!
And of course other calculus stuff works, too.
Before we see what else Sage can do, I should point out that you should feel free to just type whatever you can and see what works.
If you don't remember a name of a command, but suspect it starts with a certain letter or combination of letters, you can type them and then [tab]. This tab-completion is very handy.
If you find the name but don't remember the syntax or what it does, you can type the command and ?, then evaluate or tab and it will give you that information.
If you already have an object defined (like the function $f$ above), you can type a period/dot after its name, and then [tab]. This will give you everything you can do to this object.
Before we move on to linear algebra, I wanted to show you some eye candy. Just in case you thought Sage wasn't up to applications.
Now, those of you in the know noticed that the specific commands I used seem to indicate doing things like matrix inversion and other matrix operations - that is to say, it involves linear algebra! So let's see what Sage can do with linear algebra.
So Sage can pretty easily create matrices and vectors and do things with them. One interesting point here is that vectors are not regarded as $1\times n$ or $n\times 1$ matrices, but as their own entities. Even w*w makes sense, and gives the dot product (the only reasonable interpretation of the product of two vectors).
It also tells me if there is not a solution, which certainly can happen!
Notice that most commands are accessed by dot/period and function_name(). This allows Sage to only try to do math on things that deserve it; for instance, you don't want the determinant of a polynomial to be possible! What would that even mean?
Or to the end of your spring course!
Differential equations can be nicely modeled too. Here is a slope field, just for you!
If you know how to ask a little more of Sage, you can define your own interactive demos. This is not too hard, but does require you to be able to follow the examples given in interact? fairly closely.
Of course there is a lot more to math than just this! In fact, Sage's greatest strong suit is in things like high-precision numerical computing, number theory and abstract algebra, because that is the roots of its founders. But the examples I've shown you are all the basic ones in freshman and sophomore courses.
Interlude: What kind of program is Sage? What language does it use?
It is based on the Python language we use for our intro course at Gordon.
So all the same stuff that works there, works here!
Sage also contains the best of open-source mathematical programs. As an example, the program R is actually a component of Sage, which we can use directly from the notebook.
There is one last thing I haven't shown too much of, namely plotting. But we should certainly return to that as our final set of examples before I set us all loose.
You'll notice the "figsize=5"; that's just there because the projector I use probably won't project this worksheet at full size so we make graphics a bit smaller.
Browse the published worksheets at this server!
Sage is also so much more than this. As one example, for those familiar with LaTeX, you can combine the power of Sage and LaTeX in SageTeX! I use this to prepare many of my lecture notes and handouts for students.
Remember, for once-off computations you have some nice options with the Sage cell servers; for more in-depth ones, use the notebook server or the SageMath Cloud. Let's check that out for a little bit.
Do you have any questions about other things you might want to try?
Sage is always looking for help!
I can mentor nearly anyone who has had the intro programming course in Python at Gordon through a first contribution to Sage. See me for more details. | CommonCrawl |
first the Bell-LaPadula Model cannot capture changes over time. second, more serious problem arises when one considers that subjects in the Chinese Wall model may choose which CDs(company dataset) to access; in other words, initially a subject is free to access all objects. the Bell-LaPadula Model cannot emulate the Chinese Wall model.
Ravi S. Sandhu has given a part of a positive answer in his 1992 paper entitled Lattice-Based Enforcement of Chinese Walls (preprint). The idea is to build a lattice from the $n$ Conflict Of Interest (COI) classes defined in the Chinese Wall: elements are tuples of the form $[l_1, \ldots, l_n]$ where $l_i$ is either $\bot$ when no document from class $i$ has been accessed yet or a document's identifier from the class $i$.
To capture the dynamic character of the Chinese Wall policy model, the users' labels have to be updated when he/she reads a document pertaining to a COI class. In this sense, the translation is closer to high-water mark than to pure Bell-LaPadula.
Not the answer you're looking for? Browse other questions tagged information-theory security access-control or ask your own question. | CommonCrawl |
I'm a mathematician doing some work which is related to $\mathcal N=2$ supersymmetric quantum field theory in $d=4$ and am a little confused about the physical notion of moduli space in this context. I apologize in advance if this question is too basic, or too vague, or just kind of stupid. References to appropriate literature would be most welcome.
the moduli space of complexified Kähler structures (A-model) or the moduli space of complex structures (B-model).
Question. What is the relationship between these various moduli spaces? Are they the same in some appropriate sense? If they are different which is the one with a "Coulomb branch"?
The impression I get is that the appropriate moduli space has some singular points, at which the corresponding physical theory is special (e.g, conformal?).
Question. What sort of nice things happen with physical theories corresponding to singular points of the moduli space? Are these the theories we're actually interested in and the generic points correspond to more calculable approximations of these theories?
This is going to be a severely incomplete answer, more importantly, I am also new to the subject, so this is a personal understanding, not a definitive answer, I apologize for that. A couple of good references on 4d N=2 theories that I am aware of are [1,2].
Q1) Moduli spaces of type 2 and 3 can be cast in the same light, type 1 is somewhat different. Coulomb branch belongs to type 1.
in cases where we can assign some cohomology groups to the theories, the groups don't generically change under movement along the moduli spaces, but they can change at singular points.
Certainly, the singular points are more colorful than a generic point, what we are more interested in can, I think, vary from problem to problem.
Comments about moduli spaces of type 2 and 3 in your list: Any field theory is defined with a set of "static" data, the idea is that given a fixed "type" of theory there's a space of static data such that each point of that space defines a theory of the same type.
The summary here is that, given a symmetry algebra, there may be a family of theories with that symmetry algebra, the family is parametrized by a moduli space. Singular points are special, they can have enlarged symmetry.
*I would love to be corrected for anything I might have said wrong. | CommonCrawl |
A mathematical model of motion of solid particles withselective permeability and a mixture of moving gases is developedwith the use of averaging principles of mechanics of multiphase media.The derived system of quasi-linear partial differential equations isstudied for a particular one-dimensional isothermal case.
Interaction of a shock wave with a system of motionlessor relaxing particles is numerically simulated. Regimes of the gas flowaround these particles are described, and the influence of the initialparameters of the examined phenomenon on the flow pattern is analyzed.The drag coefficient of particles is calculated as a function of theMach number behind the shock wave at a fixed Reynolds number. Thedynamics of heat exchange for particles of different sizes(10$\mu$m--1mm) is determined, and the laws of thermal relaxationafter passing of a shock wave over the system of particles are found.The times of thermal and velocity relaxation of particles are estimatedas functions of the Reynolds number, and the predicted relaxation timeis compared with the corresponding empirical dependences.
Currently available methods of computing thelaminar--turbulent transition (LTT), including methods used ingas-dynamic software packages, are analyzed from the viewpoint of LTTsimulation accuracy.
A three-dimensional supersonic turbulent flow withsymmetric normal injection of circular jets from the channel walls isnumerically simulated. The initial Favre-averaged Navier-Stokesequations closed by the $k$--$\omega$ turbulence model are solved by analgorithm based on an ENO scheme. The mechanism of the formation ofvortical structures due to the interaction of the jet with the freestream is studied for jet to crossflow total pressure ratios rangingfrom 3 to 50. It is known from experiments reported in the literaturethat, for $n\ge 10$, mixing of the jet with the high-velocity flowleads to the formation of a pair of vortices and of an additionalseparation zone near the wall behind the jet. It is demonstrated thatthe present numerical results are consistent with such findings andthat the pressure distribution on the wall ahead of the jet in theplane of symmetry is also in reasonable agreement with availableexperimental data.
This paper presents a numerical simulation of the flowresulting from transverse jet injection into a supersonic flow througha slot nozzle, at different pressures in the injected jet and mainflow. Calculations on grids with different resolutions use theSpalart--Allmaras turbulence model, the $k$--$\varepsilon$ model,the $k$--$\omega$ model and the SST model. Based on a comparison ofthe calculated and experimental data on pressure distribution on thewall, the length of the recirculation area and depth of penetration ofthe jet in the supersonic flow, conclusions are made about the accuracyof the calculation results of the different turbulence models and theapplicability of these models for solving similar problems.
A functional mathematical model of a hydrogen-driven combustion chamber for a scramjet is described. The model is constructed with the use of one-dimensional steady gas-dynamic equations and parametrization of the channel configuration and the governing parameters (fuel injection into the flow, fuel burnout along the channel, dissipation of kinetic energy, removal of some part of energy generated by gases for modeling cooling of channel walls by the fuel) with allowance for real thermophysical properties of the gases. Through parametric calculations, it is found that fuel injection in three cross sections of the channel consisting of segments with weak and strong expansion ensures a supersonic velocity of combustion products in the range of free-stream Mach numbers $\mboxM_\infty = 6\mbox--12$. It is demonstrated that the angle between the velocity vectors of the gaseous hydrogen flow and the main gas flow can be fairly large in the case of distributed injection of the fuel. This allows effective control of the mixing process. It is proposed to use the exergy of combustion products as a criterion of the efficiency of heat supply in the combustion chamber. Based on the calculated values of exergy, the critical free-stream Mach number that still allows scramjet operation is estimated.
The operation of an electromagnetic multirail launcher of solids powered from a pulsed magnetohydrodynamic (MHD) generator is studied. The plasma flow in the channel of the pulsed MHD generator and the possibility of launching solids in a rapid-fire mode of launcher operation are considered. It is shown that this mode of launcher operation can be implemented by matching the plasma flow dynamics in the channel of the pulsed \hboxMHD generator and the launching conditions. It is also shown that powerful pulsed MHD generators can be used as a source of electrical energy for rapid-fire electromagnetic rail launchers operating in a burst mode.
Theproblemofflowsinitiatedbyvertical lifting of a rectangular beam partially submerged in shallow water filling a rectangular prismatic channel with a horizontal bottom is studied in the long-wavelength approximation. The width of the beam is equal to the channel width, and its upper and lower planes are parallel to the channel bottom. In the first stage of the flow, the lower surface of the low beam is completely submerged in the liquid, which is lifted after it by hydrostatic pressure. Conditions for the well-posedness of this problem are obtained, and solutions describing the liquid flow in the region adjacent to the bottom surface of the beam and in outer regions with a free upper boundary are constructed for different laws of lifting of the beam.
A method of designing a supersonic axisymmetric tunnel air inlet based on the problem of an inverted flow in an annular nozzle with isentropic expansion is considered. The nozzle contour is constructed by the method of characteristics. Parameters of one inlet for viscous and inviscid gas flows are calculated.
The reflection and refraction of acoustic waves at different angles of incidence on the interface between a vapor--gas--droplet system and air are studied. From an analysis of analytical solutions, it has been found that in the case of incidence on the interface from the side of the vapor--gas--droplet medium, there is a critical angle of incidence at which the wave is completely reflected from the boundary, i.e., total internal reflection takes place. It is shown that for a certain angle of incidence on the interface both from the air side and from the mixture side and for a certain volume fraction of water in the disperse system, complete transmission of the acoustic wave through the medium is observed.
This paper is a review of studies carried out on the basis of two-dimensional boundary-value problems of filtration theory. The role of critical regimes determining the specifics of filtration flows with moving boundaries is noted.
A mathematical model for hydraulic fracturing is proposed. The model is based on the presentation of the fractured portion of the stratum adjacent to the well as a heterogeneous fractured porous medium. Assumptions usually used in the theory of elastic flow are applied. Formulas for determining the size of the hydraulic fracturing zone and the degree of fracture opening under conditions of relative equilibrium are derived.
Gas filtration from an underground reservoir through a layer of a porous medium due to an instantaneous increase in the gas pressure in the reservoir is studied. The problem is considered in a one-dimensional formulation in the general case where the temperatures of the gas and the porous medium are different and unstable, and in the case of a high specific heat of the solid phase and a high interfacial heat-transfer rate. The dynamics of the gas flow at the inlet and outlet of the underground reservoir is analyzed, the time of unloading of the system is estimated as a function of the permeability of the porous medium. It is shown that, depending on the properties of the porous layer, two characteristic gas flow regimes are possible: a fast discharge regime and a slow regime which is determined mainly by barodiffusion.
This paper describes an experimental study of heat transfer in a channel behind a backward-facing step in the presence of a disturbance in front of it in the form of a single rib in the range of the Reynolds numbers $\Re = 5000\mbox--15\,000$. The influence of the rib position and height on heat transfer intensity behind the backward-facing step is investigated. It is shown that reattachment of the flow disturbed by the obstacle intensifies the heat transfer on the surface behind the backward-facing step.
An analysis of a second-grade fluid in a semi-porous channel in the presence of a chemical reaction is carried out to study the effects of mass transfer and magnetohydrodynamics. The upper wall of the channel is porous, while the lower wall is impermeable. The basic governing flow equations are transformed into a set of nonlinear ordinary differential equations by means of a similarity transformation. An approximate analytical solution of nonlinear differential equations is constructed by using the homotopy analysis method. The features of the flow and concentration fields are analyzed for various problem parameters. Numerical values of the skin friction coefficient and the rate of mass transfer at the wall are found.
The influence of two nanomodifiers with different compositions during their homogenization in the AL7 aluminum melt and moulding on the properties of the modified aluminum alloy is studied. Experiments are performed with the use of a centrifugal conductive magnetohydrodynamic pump. The melt is poured into a graphite mould with three cylindrical channels 38 mm in diameter and 160 mm long, which are designed for a metal mass of 500g. Two compositions are used as modifying agents: nano-scale particles of the aluminum nitride powder 40--100nm in size and metallized carbon nanotubes smaller than 25 nm, which are clad with aluminum to improve wetting of their surface. The analysis of the structure of the experimental and reference samples shows that the use of modifiers leads to refinement of the grain structure of the cast metal. According to the Hall--Petch theory, this effect may result in improvement of mechanical characteristics of the cast metal.
The microscopic behavior of nanofluids in the Poiseuille flow in a nanochannel is examined by means of molecular dynamics simulation through visual observations and statistic analysis. For nanofluid flows inside the nanochannel, a clustering effect is observed during the time evolution of the system. The cluster moves along the centerline of the nanochannel due to the maximum velocity in the middle part of the Poiseuille flow. The attractive force is believed to be the primary culprit behind the agglomeration of nanoparticles.
The dependence of a scalar measure of the structural changes occurring in a material under plastic deformation on a plastic strain measure and the dependence of a free energy measure on a structural change measure are constructed using experimental data that allow the expended plastic work to be divided into a latent part and a thermal part. The obtained dependences, kinematic relations, a constitutive equation, and a heat-conduction equation that satisfy the principles of thermodynamics and objectivity are used to construct a model of thermo-elastic--inelastic processes in the presence of finite deformations and structural changes in the material. The model is tested on the problem of temperature changes in the process of adiabatic elastic--plastic compression, which has experimental support.
A program of experiments to identify the type of elastic anisotropy of material is proposed. The position of the principal axes of material anisotropy is determined by measuring the strains resulting from compression of a cubic sample along three of its faces. For the subsequent identification of the type of anisotropy, samples oriented along definite principal axes are used.
We consider the linear unsteady motion of an IL-76TD aircraft on ice. Water is treated as an ideal incompressible liquid, and the liquid motion is considered potential. Ice cover is modeled by an initially unstressed uniform isotropic elastic plate, and the load exerted by the aircraft on the ice cover with consideration of the wing lift is modeled by regions of distributed pressure of variable intensity, arranged under the aircraft landing gear. The effect of the thickness and elastic modulus of the ice plate, takeoff and landing regimes on stress-strain state of the ice cover used as a runway.
The processes of high-velocity oblique collision of metal plates which lead to the formation of their joints (seizure) are considered. It is found that the cleaning of the plate surface necessary for seizure results from a jet flow (particle stream), whose source is at least one of the welded materials or an interlayer of ductile material located in the initial region of collision. It is shown that additional cleaning may occur due to the emergence of rotating microregions in intense gradient flows localized in the joint area; seizure on cleaned surfaces is due to reduction of the surface energy of the system. | CommonCrawl |
which will in general be a $g \times g$ matrix.
Let us imagine a surface where all the period integrals are proportional to each other by some constant of proportionality, so in effect there is only one independent period, and all the information about the surface captured by the other cycles is obtained by simply multiplying by the appropriate constant. Is there a way to write down an "effective genus-$1$ curve" for this higher genus surface?
If someone hands me a period matrix, is there a way to reconstruct the curve it came from?
Any related comments/helpful links will be much appreciated.
Eremenko already commented about Q1 (but see comments below). To clarify further about Q2: Any period matrix can be shown to be symmetric with positive definite imaginary part, although in general, not all matrices of this type come from Riemann surfaces. However, if you happen know the matrix comes from a Riemann surface, then the surface can be reconstructed from it, in theory, by Torelli's theorem. You would need to look at the proofs, of which there are several, to do this explicitly.
Not the answer you're looking for? Browse other questions tagged periods higher-genus-curves or ask your own question.
Does there exist a non-isotrivial fibration of genus two over P^1 with only 3 singular fibres of general type surfaces?
Igusa invariants of genus 2 curves as Siegel modular functions?
What is the probability that a randomly chosen number from set of c.e.number is period(number)?
Is the isogeny class 1109.a of abelian surfaces in the LMFDB complete? | CommonCrawl |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.