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Experimental Investigation of Free-Convection Heat Transfer in Vertical Tube at Large Grashof Numbers
NASA Technical Reports Server (NTRS)
Eckert, E R G; Diaguila, A J
Report presents the results of an investigation conducted to study free-convection heat transfer in a stationary vertical tube closed at the bottom. The walls of the tube were heated, and heated air in the tube was continuously replaced by fresh cool air at the top. The tube was designed to provide a gravitational field with Grashof numbers of a magnitude comparable with those generated by the centrifugal field in rotating-blade coolant passages (10(8) to 10(13)). Local heat-transfer coefficients in the turbulent-flow range and the temperature field within the fluid were obtained.
Natural convection in a vertical plane channel: DNS results for high Grashof numbers
NASA Astrophysics Data System (ADS)
Kiš, P.; Herwig, H.
The turbulent natural convection of a gas ( Pr = 0.71) between two vertical infinite walls at different but constant temperatures is investigated by means of direct numerical simulation for a wide range of Grashof numbers (6.0 × 106 > Gr > 1.0 × 103). The maximum Grashof number is almost one order of magnitude higher than those of computations reported in the literature so far. Results for the turbulent transport equations are presented and compared to previous studies with special attention to the study of Verteegh and Nieuwstadt (Int J Heat Fluid Flow 19:135-149, 1998). All turbulence statistics are available on the TUHH homepage (http://www.tu-harburg.de/tt/dnsdatabase/dbindex.en.html). Accuracy considerations are based on the time averaged balance equations for kinetic and thermal energy. With the second law of thermodynamics Nusselt numbers can be determined by evaluating time averaged wall temperature gradients as well as by a volumetric time averaged integration. Comparing the results of both approaches leads to a direct measure of the physical consistency.
Large Eddy Simulation study of the development of finite-channel lock-release currents at high Grashof numbers
NASA Astrophysics Data System (ADS)
Ooi, Seng-Keat
Lock-exchange gravity current flows produced by the instantaneous release of a heavy fluid are investigated using 3-D well resolved Large Eddy Simulation simulations at Grashof numbers up to 8*10^9. It is found the 3-D simulations correctly predict a constant front velocity over the initial slumping phase and a front speed decrease proportional to t-1/3 (the time t is measured from the release) over the inviscid phase, in agreement with theory. The evolution of the current in the simulations is found to be similar to that observed experimentally by Hacker et al. (1996). The effect of the dynamic LES model on the solutions is discussed. The energy budget of the current is discussed and the contribution of the turbulent dissipation to the total dissipation is analyzed. The limitations of less expensive 2D simulations are discussed; in particular their failure to correctly predict the spatio-temporal distributions of the bed shear stresses which is important in determining the amount of sediment the gravity current can entrain in the case in advances of a loose bed.
Experimental investigation of free-convection heat transfer in vertical tube at large Grashof numbers / E. R. G. Eckert, A. J. Diaguila
NASA Technical Reports Server (NTRS)
Eckert, E R G; Diaguila, A J
Local free-convection heat-transfer coefficients and temperature fields in the turbulent flow range were obtained within a vertical, stationary tube closed at the boom, heated along its walls, and having a length-to-diameter ratio of 5. Convective heat-transfer coefficients were correlated by the general relations for free-convection heat transfer. These coefficients, converted to dimensionless Nusselt numbers were 35 percent below known relations for vertical flat plates. Air temperature measurements within the tube indicated a thin boundary layer along the heated wall surface and unstable conditions in the air flow.
NSDL National Science Digital Library
The purpose of this video tutorial is to review a couple ways in which we think about numbers. Thinking in terms of street numbers, money in bank accounts, and quantum particles (e.g. Bose-Einstein condensate) is contrasted with focusing on associating numbers with distinguishable manipulatives, as is more familiar in K-8 courses. This video concludes with a reminder that the symbol "infinity" is not, itself, a number.
NSDL National Science Digital Library
Jo Edkins
This engaging web site contains information and interactive applets related to various number systems: Egyptian, Babylonian, Chinese, Greek, Roman, Mayan, and Arabic. Users learn the history and structure of each system as well as how to count and write numbers. The site also allows users to explore finger systems, calculating machines, other number bases, and "interesting numbers." A series of pages on data and graphs includes information and activities on gathering, analyzing, graphing and sorting data. (Because the section on the Arabic number system is so extensive, it is cataloged separately as a related resource.)
Experimental study of low Prandtl number natural convection in an array of uniformly heated vertical cylinders
J. C. Dutton; J. R. Welty
An experimental program was conducted to study natural convection heat ; transfer in an array of uniformly heated vertical cylinders in mercury. The ; cylinders were arranged in an equilateral triangular pattern, and three bundle ; spacings, P\\/D = 1.5, 1.3, and 1.1, were studied. The heat transfer results are ; presented as local Nusselt number--modified Grashof number correlations. The
NSDL National Science Digital Library
M. Fisher
Let\\'s have some fun working on our math facts and putting numbers together to get new ones! Try out these games and see how you do-- First try to defeat this spaceship with your math fact skills: Spacey Math: A drill game where students are given a set of math facts to answer (can select addition, subtraction, multiplication, division). If you defeat the spaceship you can move on to helping save the poodles. They have to weigh in and they need to find out what numbers need to go on the other side of the scale to balance ...
NSDL National Science Digital Library
Hacker has given you a challenge. He'll run his number machine to create a number. Then you'll get three numbers between one and nine. The challenge is to make a number that is larger than the one on Hacker's machine. Be careful though--Hacker will give you numbers that can't be bigger than his!
NSDL National Science Digital Library
Clarity Innovations, Inc.
This iOS app helps students to visualize number sentences and create models for addition, subtractions, multiplication, and division. The number line can be adjusted to represent multiples of numbers from one to one hundred.
NSDL National Science Digital Library
Combine logic and numbers in this game for all ages. Players start with a 10x10 grid of the numbers 1 to 100. One person chooses a secret number and announces the range in which it falls. Other players ask yes or no questions to identify the number. They cross out the numbers on the board that are no longer possibilities. The player who identifies the secret number wins. Available as a downloadable pdf and in Spanish.
ERIC Educational Resources Information Center
Crawford, David
Presents three number games for mathematics classrooms designed to improve the learning of number concepts. Game topics include determining products, arranging mathematical signs, and factoring. (ASK)
NSDL National Science Digital Library
This interactive application helps students to learn visually about numbers from their possible arrangements and how those arrangements relate to division, multiplication, and factors. The web applet divides numbers and displays calculation to show the remainder as a number, fraction, or decimal value and allows demonstration of types of numbers such as prime, square, and triangular. The number explorer has automated tests for divisibility, factor pairs, or prime factors. Three different shapes can be used, the original fish swim around and obediently arrange themselves to show number properties. However balls or cards cards can be used instead, these animate faster and are better for displaying numbers.
NSDL National Science Digital Library
Mitchell Mark
This iOS app helps students make the transition from counting to number recognition by thinking of a number of objects in relation to five and ten. The app displays a set number of items from one to twenty in ten frames then flashes away after the preset number of seconds. The user must identify the number that was shown on the ten frames.
NSDL National Science Digital Library
In this online math game from Cyberchase, learners play against Hacker in a place value game. The goal is to make a number bigger than the one created by Hacker's number machine. Learners select the numbers in the order in which they want them to go into their machine. The challenge is to either make a number larger than the one on Hacker's machine or realize that it's impossible to make a number bigger than Hacker's, no matter what the combination.
NSDL National Science Digital Library
You will be working with numbers in all sorts of ways. First, you will play cop by picking numbers based on their divisibility. Then you will be adding and subtracting fractions in two fun and exciting games. First, as a cop, you will catch numbers that are divisible by which ever number you pick, avoinding crashing into non-divisible numbers. Number Cop-Divisibility Now, play Fishy Fractions! and help feed the seagull by practicing adding fractions. Make sure you read the instructions before getting started! Make sure to simplify your answers! After you ...
... numbered as well. Illustrations created by Simple Steps designer Michael Becker Universal Numbering System Adults In this ... indicates that it is a deciduous (primary or "baby") tooth. So, a child's first tooth on the ...
NSDL National Science Digital Library
This Science NetLinks interactive game helps students increase their logic and decision making skills by challenging a player to consider a series of mathematical processes to find a path from a starting number to a goal number in a math maze. The activity appears as a 5x5 matrix of numbers, each of which has an operation symbol next to it, indicating whether it will be added to, subtracted from, or multiplied by the previous number. Starting in the center with a given number, players choose an adjoining number to complete the next step and they proceed until successfully reaching the goal number or until they have run out of usable numbers on the game board. To add an additional challenge to the game, a player can limit each level to reaching the target in seven or fewer steps.
NSDL National Science Digital Library
This is a short study guide from the University of Maryland's Physics Education Research Group on introducing, interpreting, and using complex numbers. Mathematical equations are included to help students understand the nature of complex numbers.
NSDL National Science Digital Library
Ms. Simpson
Students will practice counting to 100, making numbers with base ten blocks and practicing ordinal numbers! Math is FUN! Lets have fun practicing counting to 100 ! Click when you are ready!Counting Now that you have practiced counting to 100, lets use the base ten blocks to make the number that is on the screen. Click when you are ready!Working with Base Ten Blocks We have now practiced counting and making numbers, lets ...
M. R. Schroeder
Number theory, an abstract branch of mathematics that deals with relationships between whole numbers, has provided highly useful answers to numerous real-world problems. The author briefly reviews earlier uses of number theory and then examines recent applications to music, cryptography, and error-correction codes
NSDL National Science Digital Library
The World of Numbers is "an amalgamation of randomly gathered numbers, curios, puzzles, palindromes, primes, gems, your much valued contributions and more general information." Choosing "number palindromes" from the drop-down menu will take you to a page with a list of links to webpages on palindromes -- numbers that read the same from left to right as from right to left. Also posted are more examples of square palindromes, circular primes, Palindromic Primes, Palindromic Tetrahedra, and much more. Visitors are invited to make their comments and contributions as well. Also provided are links to websites on integers and other special numbers, such as primes and zero.
NSDL National Science Digital Library
Dan Bunker
This open-ended interactive Flash applet helps students develop operation and number sense, facility with number facts, and understanding of equations. Users designate single-digit whole numbers or integers and operations on both sides of an equation and test for balance. Users can enter numbers by using the keyboard or arrow buttons or by dragging number tiles. Each element can be hidden and a seesaw may be toggled on/off. Teachers may use this applet to lead instruction, or students may use it independently to perform specific investigations or explore freely. Supplementary documents include Objectives, containing teaching suggestions, and a student recording sheet.
NSDL National Science Digital Library
With this interactive Flash applet, intended for use with a projector or interactive white board, teachers can help students understand place value and the structure of our number system. Shapes can be placed on the 100 chart; students use number patterns to determine which numbers are hidden under the shapes. By choosing Hide or Highlight and then selecting specific rows or columns to hide or highlight, the teacher can adjust the challenge level or bring attention to parts of the chart.
NSDL National Science Digital Library
Mrs. Pierce
The objective of this lesson is to gain a better understanding of complex numbers and their graphs Situation: The Swiss Mathemation, Jean Robert Argand developed a means to graphically represent complex numbers. This led to solving problems related to altenating electrical current, which provides current day luxuries. Could you do the same? Current Knowledge: Use your knowledge of complex number and the coordinate system and with your partner, ...
NSDL National Science Digital Library
American Association for the Advancement of Science
In this online puzzle game, learners need to choose a path from a starting number to a goal number. Along the path are simple operations (e.g. add 1, subtract 2, multiply by 2) to change the current number to a new number. This is a good challenge for young learners. When learners set up a free account at Kinetic City, they can answer bonus questions at the end of the activity as a quick assessment. As a larger assessment, learners can complete the Bug Blaster game after they've completed several activities.
NSDL National Science Digital Library
John Brignell, Professor Emeritus from the Department of Electronics & Computer Science at the University of Southampton, is the author of this informal website "devoted to the monitoring of the misleading numbers that rain down on us via the media." Brignell says he aims to "nail" a few of the "Single Issue Fanatics (SIFs), politicians, bureaucrats, quasi-scientists (junk, pseudo- or just bad)," who use misleading numbers to write catchy articles or who try to keep numbers away from public notice. Since April 2000, he has been posting a "number of the month" as well as a "number for the year," which offer his commentary on media usage of misleading numbers and explanations for why the numbers are misleading. He also posts book reviews and an extensive list of online resources on statistics and statistics education. The FAQ section includes answers to some interesting questions, such as "Is there such a thing as average global temperature?" and some more basic questions such as "What is the Normal Distribution and what is so normal about it?" The Bits and Pieces section includes a variety of short articles on statistics and his definitions for some terms he uses on the website. Visitors are also invited to join the discussion forum (complete with a few advertisements) and view comments by others who want to discuss "wrong numbers in science, politics and the media." A few comments sent to Brignell and his responses are also posted online. This site is also reviewed in the February 11, 2005_NSDL MET Report_.
NSDL National Science Digital Library
In this brief article the numerous uses of the number line are detailed: counting, measurement, addition, subtraction, decimals, and fractions. The article contains visual representations of the some of the concepts and links to related topics.
NSDL National Science Digital Library
Kuphaldt, Tony R.
Written by Tony R. Kuphaldt and Jason Starck, this chapter of All About Circuit's second volume on Alternating Current describes complex numbers: "In order to successfully analyze AC circuits, we need to work with mathematical objects and techniques capable of representing these multi-dimensional quantities. Here is where we need to abandon scalar numbers for something better suited: complex numbers." In addition to the introduction and credits to contributors, the chapter has seven sections: Vectors and AC waveforms, Simple vector addition, Complex vector addition, Polar and rectangular notation, Complex number arithmetic, More on AC "polarity," and Some examples with AC circuits. Each section has clear illustrations and a concise, bulleted review of what was covered at the end.
ERIC Educational Resources Information Center
Sezin, Fatin
It is instructive and interesting to find hidden numbers by using different positional numeration systems. Most of the present guessing techniques use the binary system expressed as less-than, greater-than or present-absent type information. This article describes how, by employing four cards having integers 1-64 written in different colours, one…
ERIC Educational Resources Information Center
Thelin, John R.
What topic would you choose if you had the luxury of writing forever? In this article, John Thelin provides his response: He would opt to write about the history of higher education in a way that relies on quantitative data. "Numbers, please!" is his research request in taking on a longitudinal study of colleges and universities over…
NSDL National Science Digital Library
Ms. Painter
Perform operations with whole numbers, simple fractions, and decimals. 1. Begin your work at the Comparing Fractions website. Complete 10 problems. 2. When you are finished Comparing Fractions, I\\'m sure you will hunger for more! Click on the website, Who Wants Pizza? These activities are sure to fill your brain with nutritious information. 3. Explore Egyptian ...
ERIC Educational Resources Information Center
Kathotia, Vinay
This article reports on work undertaken by schools as part of Qualifications and Curriculum Authority's (QCA's) "Engaging mathematics for all learners" project. The goal was to use in the classroom, materials and approaches from a Royal Institution (Ri) Year 10 master-class, "Number Sense", which was inspired by examples from Michael Blastland and…
NSDL National Science Digital Library
Mrs. Fincher
Let's get speedy with number use. Click on the game Going Bananas with Divsion which is in bold letters below. Using the mouse, click on Instructions and read them carefully. Then, click on Start Game . Then select 3-12 as your level to play. Use the mouse to select ...
NSDL National Science Digital Library
Judy Scotchmoor
In this lesson, learners are challenged to discover the relationship among six numbers. The objective of this activity is to engage learners in a problem-solving situation in which they practice aspects of the process of science. Learners can use an included Science Flowchart to chart their scientific experience. This lesson serves as a good introduction to the nature of scientific inquiry.
NSDL National Science Digital Library
This interactive applet helps students develop fluency with multiplication facts. Users chose a factor from among the digits 1-9, each of which is associated with a mnemonic graphic. The applet then displays three numbers and the user selects the one which is a multiple of the chosen factor. The player must respond correctly to ten examples to complete a round. A one-point penalty for selecting an incorrect product discourages guessing. The few words that are displayed are in Dutch.
NASA Technical Reports Server (NTRS)
2006-01-0129 January 2006 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows a spotted, high latitude plain, south of the Argyre basin. When the image was received from Mars by the MOC operations team, they noticed -- with a sense of humor -- the number '8' on this martian surface. The '8' is located at the center-right and is formed by the rims of two old impact craters that have been eroded and partly-filled and partly-buried beneath the surface. Location near: 68.6oS, 38.4oW Image width: 3 km (1.9 mi) Illumination from: upper left Season: Southern Summer
Some remarks concerning kissing numbers, blocking numbers and covering numbers
Chuanming Zong
This article shows an inequality concerning blocking numbers and Hadwiger's covering numbers and presents a strange phenomenon concerning kissing numbers and blocking numbers. As a simple corollary, we can improve the known upper bounds for Hadwiger's covering numbers ford-dimensional centrally symmetric convex bodies to 3d-1.
COMPLEX NUMBERS 1. Definition of complex numbers
La Rosa, Andres H.
COMPLEX NUMBERS 1. Definition of complex numbers Complex conjugate, Magnitude Operations Addition, multiplication, reciprocal number 2. Representation of complex numbers in polar complex variable #12;2.2.A Complex numbers #12;#12;3 #12;4 #12;In short, Anytime we write Ae j we
3. Complex Numbers 17 3 Complex Numbers
Givental, Alexander
3. Complex Numbers 17 3 Complex Numbers Law and Order Life is unfair: The quadratic equation x2 - 1 solutions to the equation. This is how complex numbers could have been invented. More formally, complex numbers a and b are called respectively the real part and imagi- nary part of the complex number z
Applications of Fibonacci Numbers
Benjamin, Arthur T.
Applications of Fibonacci Numbers Volume 9 KLUWERACADEMIC PUBLISHERS #12;Applications of Fibonacci Numbers I Volume 9 Proceedingsof The Tenth International Research Conference on Fibonacci Numbers the presence of both Fibonacci numbers and binomial coefficients demands a combinatorial explanation. Beginning
Floating Point Numbers Review of Numbers
Delgado-Frias, José G.
Floating Point Numbers #12;2 Review of Numbers Computers are made to deal with numbers What can we notation #12;3 Scientific Notation: Review 6.02 x 1023 radix (base)decimal point mantissa exponent Declare such variable in C as float #12;5 Floating Point (FP) Representation (1/2) Normal format: +1
Number Concepts with "Number Worlds": Thickening Understandings
ERIC Educational Resources Information Center
Liljedahl, Peter; Sinclair, Nathalie; Zazkis, Rina
This study focuses on the nature of preservice elementary school teachers' understandings of several concepts in elementary number theory that are evoked by a computer-based microworld called "Number Worlds". In particular, the focus is on the concepts of factor, multiple and prime number. The notion of "thickness" is examined with respect to…
Complex numbers Quaternions Imaginary numbers and Quaternions Katrin Leschke University of Leicester June 29, 2010 Katrin Leschke Imaginary numbers and Quaternions #12;Complex numbers Quaternions Imaginary numbers and Quaternions #12;Complex numbers Quaternions Vectors in 2dspace A vector in 2d
NSDL National Science Digital Library
In this lesson we are going to review even and odd numbers. Every number on the number line is either even or odd. If a number can be equally divided into 2 groups it is even. If it cannot be evenly divided it is odd. On the number line every other number is even and the rest are odd. Look at this ...
ERIC Educational Resources Information Center
Gurganus, Susan
"Number sense" is "an intuition about numbers that is drawn from all varied meanings of number" (NCTM, 1989, p. 39). Students with number sense understand that numbers are representative of objects, magnitudes, relationships, and other attributes; that numbers can be operated on, compared, and used for communication. It is fundamental knowledge…
Triangle Area Numbers and Solid Rectangular Numbers
Konstantine D. Zelator
In this work, we define a triangle area number to be the area number of a triangle whose sides have integer lengths, and whose area is a rational number. In Result 3, on page 17, we prove that every triangle area number is in fact an integer which is a multiple of 6. Certain divisibility and other conditions and formulas are also derived, which the three integer sidelengths must satisfy. On pages 20 and 21, we list all the triangle area numbers not exceeding 999.
NSDL National Science Digital Library
Mrs. Estes
Let\\'s learn about numbers! How many Fish? Count the Fish Let\\'s count! How many... Matching is fun! Match the number How well do I really know these numbers? Getting to know the numbers Counting the kids Kids on the bus We love Ants! Count the ants Flying into the univerise of numbers Rocket ...
Representing decimal numbers on the number line
NSDL National Science Digital Library
National Library of Virtual Manipulatives
The user can choose decimals with explore, practice, assess on the screen. Using explore, the student drags the point to the number line and the decimal value of that point is given. Using practice, the student drags the point to the location of the designated decimal number. Zooming in produces lines representing whole numbers, tenths, hundredths, and thousandths in succession. The zooming allows the student to choose the correct point, rather than the approximate location. The series of lines with successively smaller place values is a visual model for extending the base ten system to decimal numbers.
ERIC Educational Resources Information Center
Shi, Yixun
Starting with an interesting number game sometimes used by school teachers to demonstrate the factorization of integers, "sum-difference numbers" are defined. A positive integer n is a "sum-difference number" if there exist positive integers "x, y, w, z" such that n = xy = wz and x ? y = w + z. This paper characterizes all sum-difference numbers…
Spooky Sequences- Square Numbers
NSDL National Science Digital Library
Mark Cogan
This interactive Flash game helps students recognize and generate the sequence of square numbers, and also to discover the pattern of differences between them. The applet displays a sequence of six consecutive square numbers with one number missing. The player provides the missing number to "send the ghosts back to the haunted house." Each game consists of five sequences to complete.
ERIC Educational Resources Information Center
Wilkie, James E. B.; Bodenhausen, Galen V.
We examined the possibility that nonsocial, highly generic concepts are gendered. Specifically, we investigated the gender connotations of Arabic numerals. Across several experiments, we show that the number 1 and other odd numbers are associated with masculinity, whereas the number 2 and other even numbers are associated with femininity, in ways…
NSDL National Science Digital Library
Mrs. Williams
Numbers, Matching and Addition Let\\'s count How many chicks are there? Great! Now lets try Number Match Let\\'s try Seahorse Counting Now Concentrate on Concentration Number Match Addition Practice Quick Adding and Robot Addition Make the number with Base 10 ...
Liang, Y. Daniel
Case Study: Lotto Numbers The problem is to write a program that checks if all the input numbers cover 1 to 99. Each ticket for the Pick-10 lotto has 10 unique numbersCovered[98] is set to true (see Figure 6.2e). Figure 6.2 If number i appears in a Lotto ticket, isCovered[i-1
ERIC Educational Resources Information Center
Burkhart, Jerry
Prime numbers are often described as the "building blocks" of natural numbers. This article shows how the author and his students took this idea literally by using prime factorizations to build numbers with blocks. In this activity, students explore many concepts of number theory, including the relationship between greatest common factors and…
Shanguang Tan
A new kind of numbers called Hyper Space Complex Numbers and its algebras are defined and proved. It is with good properties as the classic Complex Numbers, such as expressed in coordinates, triangular and exponent forms and following the associative and commutative laws of addition and multiplication. So the classic Complex Number is developed from in complex plane with two dimensions to in complex space with N dimensions and the number system is enlarged also.
NSDL National Science Digital Library
Ms. Nielsen
Students will use rational numbers (i.e. multi-digit, decimals, and fractions) in order to complete a variety of division problems. State of Utah Core Curriculum: Standard 1 Objective 6 Demonstrate proficiency with the four operations, with positive rational numbers, and with addition and subtraction of integers. a. Multiply and divide a multi-digit number by a two-digit number, including decimals. b. Add, subtract, multiply, and divide fractions and mixed numbers. c. Add and subtract integers. Attachments Decimal ...
Parameterizing by the Number of Numbers
NASA Astrophysics Data System (ADS)
Fellows, Michael R.; Gaspers, Serge; Rosamond, Frances A.
The usefulness of parameterized algorithmics has often depended on what Niedermeier has called "the art of problem parameterization". In this paper we introduce and explore a novel but general form of parameterization: the number of numbers. Several classic numerical problems, such as Subset Sum, Partition, 3-Partition, Numerical 3-Dimensional Matching, and Numerical Matching with Target Sums, have multisets of integers as input. We initiate the study of parameterizing these problems by the number of distinct integers in the input. We rely on an FPT result for Integer Linear Programming Feasibility to show that all the above-mentioned problems are fixed-parameter tractable when parameterized in this way. In various applied settings, problem inputs often consist in part of multisets of integers or multisets of weighted objects (such as edges in a graph, or jobs to be scheduled). Such number-of-numbers parameterized problems often reduce to subproblems about transition systems of various kinds, parameterized by the size of the system description. We consider several core problems of this kind relevant to number-of-numbers parameterization. Our main hardness result considers the problem: given a non-deterministic Mealy machine M (a finite state automaton outputting a letter on each transition), an input word x, and a census requirement c for the output word specifying how many times each letter of the output alphabet should be written, decide whether there exists a computation of M reading x that outputs a word y that meets the requirement c. We show that this problem is hard for W[1]. If the question is whether there exists an input word x such that a computation of M on x outputs a word that meets c, the problem becomes fixed-parameter tractable.
Hypercomplex numbers Johanna Ramo
Wright, Francis
no meaning. What does minus three potatoes mean? The square root of a negative number was even worse ) + (ba + ab )i Irish mathematician William Hamilton noticed that the complex number a+bi can be written
NSDL National Science Digital Library
In this activity, learners will ask yes-no questions to identify a secret number (similar to Twenty Questions). Combine logic and numbers in this game for all ages. One person chooses a secret number and announces the range in which it falls, for instance: "I'm thinking of a number between 1 and 50." Other players ask yes or no questions to identify the number. The player who identifies the secret number wins. This game is easy to adapt to different ages: young children can ask and reason about "more than" and "less than" (Is it less than 7? Is there a 1 in the 10's place)? and older ones can ask about multiples, factors, or number relationships (Is it a multiple of 3? Is it a square number?). Available as a web page and downloadable pdf.
MedlinePLUS Videos and Cool Tools
HIV Wellness Numbers Updated:Mar 22,2012 Featured Video The Basics of HIV Management Length: 2:37 ... Learn more about your important heart-health numbers . HIV and Your Heart • Home • About HIV • HIV and ...
Mohd Abubakr
There has been always an ambiguity in division when zero is present in the denominator. So far this ambiguity has been neglected by assuming that division by zero as a non-allowed operation. In this paper, I have derived the new set of numbers by considering that a number divided by zero gives rise to "a beyond complex number". This is very similar to the way imaginary numbers are defined. It was only after considering i = sqrt(-1), we have been able to deduce all the laws for imaginary numbers. Similarly here, I have considered "a number when divided by zero gives rise to a beyond complex number". This is the introduction paper to this "beyond complex numbers" containing the algebra of it.
Harbour, Daniel, 1975-
The dissertation argues for the necessity of a morphosemantic theory of number, that is, a theory of number serviceable both to semantics and morphology. The basis for this position, and the empirical core of the dissertation, ...
NSDL National Science Digital Library
This problem offers a simple context to begin an exploration of the properties of numbers and to make conjectures about those properties. Learners explore the sums of consecutive numbers and whether all positive numbers from 1-30 can be written as the sum of two or more consecutive numbers. The Teachers' Notes page offers suggestions for implementation, key discussion questions, ideas for extension and support.
Rafael I. Rofa
Place value numbers, such as the binary or decimal numbers can be represented by the end vertices (leaf or pendant vertices) of rooted symmetrical trees. Numbers that consist of at most a fixed number of digits are represented by vertices that are equidistant from the root vertex and the corresponding number representations do not depend on the distance from the root vertex. In this paper, we introduce place value number systems which are representable by rooted symmetrical trees and in which the representation of a number depends on the distance of the corresponding vertex from the root vertex. Such dependence activates the role of zero in such a way as to render its function equivalent to that of any other single digit number. Thus, in addition to being a place value holder, the digit zero (just as any other single digit numeral) affects the value of a number regardless of its position. For example 012 is different, in the new systems, from 12. As such, these new number systems could be thought of as a natural development for the role of zero. We also illustrate how addition is performed in these newly constructed number systems. In addition to being mathematical structures which could be of mathematical interest, these new number systems could possibly have applications in computing and computing security.
Intuitive numbers guide decisions
Ellen Peters; Paul Slovic; Daniel Vastfjall; C. K. Mertz
Measuring reaction times to number comparisons is thought to reveal a processing stage in elementary numerical cognition linked to internal, imprecise representations of number magnitudes. These intuitive representations of the mental number line have been demonstrated across species and human development but have been little explored in decision making. This paper develops and tests hypotheses about the influence of such
ERIC Educational Resources Information Center
Allen, G. Donald
In human history, the origin of the numbers came from definite practical needs. Indeed, there is strong evidence that numbers were created before writing. The number "1", dating back at least 20,000 years, was found as a counting symbol on a bone. The famous statement by the German mathematician Leopold Kronecker (1823-1891), "God…
ERIC Educational Resources Information Center
Hanford, Terry; White, Kathleen
Although numbers such as average test scores or dropout rates can capture part of a school system's success or failure, school statistics seldom tell the whole story. School board members should realize that numbers might measure compliance or process, rather than improvement. Also, improvements in numbers might reflect changes in assessment…
NSDL National Science Digital Library
David Joiner
The process of creating numbers that simulate randomness on a computer is known as pseudorandom number generation. The "pseudo" in pseudo random refers to the fact that if you use a rule to generate a number, it is by definition not random, though it may appear so, and be close enough to random for all practical purposes.
NSDL National Science Digital Library
Give input to the Whole Number Cruncher and try to guess what it did from the output it generates. This activity only generates multiplication and addition functions to avoid outputting any negative numbers. Whole Number Cruncher is one of the Interactivate assessment explorers.
NSDL National Science Digital Library
The students will receive explicit instruction from the teacher on the definition of decomposing a number and how to represent a decomposition with manipulatives, drawings, and equations. The students will use linking cubes to reflect numbers from 11-19, and to show their understanding of how to decompose a number. Students will record decompositions as an equation.
Number Relationships in Preschool
ERIC Educational Resources Information Center
Jung, Myoungwhon
When a child understands number relationships, he or she comprehends the meaning of numbers by developing multiple, flexible ways of representing them. The importance of developing number relationships in the early years has been highlighted because it helps children build a good foundation for developing a more sophisticated understanding of…
NSDL National Science Digital Library
Illuminations NCTM
In this lesson, students make groups of zero to five objects, connect number names to the groups, compose and decompose numbers, and use numerals to record the size of a group. Visual, auditory, and kinesthetic activities are used to help students begin to acquire a sense of number.
Number Sense Made Simple Using Number Patterns
ERIC Educational Resources Information Center
Su, Hui Fang Huang; Marinas, Carol; Furner, Joseph
This article highlights investigating intriguing number patterns utilising an emerging technology called the Square Tool. Mathematics teachers of grades K-12 will find the Square Tool useful in making connections and bridging the gap from the concrete to the abstract. Pattern recognition helps students discover various mathematical concepts. With…
Convoluted convolved Fibonacci numbers
Pieter Moree
The convolved Fibonacci numbers F_j^(r) are defined by\\u000a (1-z-z^2)^{-r}=\\\\sum_{j>=0}F_{j+1}^(r)z^j. In this note some related numbers\\u000athat can be expressed in terms of convolved Fibonacci numbers are considered.\\u000aThese numbers appear in the numerical evaluation of a certain number\\u000atheoretical constant.\\u000a This note is a case study of the transform {1\\/n}\\\\sum_{d|n}mu(d)f(z^d)^{n\\/d},\\u000awith f any formal series and mu the Moebius function),
NSDL National Science Digital Library
This interactive Flash applet helps students explore place value and develop number sense within whole numbers, integers and decimals. It allows a child or teacher to select an interval in the given number line and show that interval divided into ten equal parts but on a larger scale, which can then be repeated. Users may choose the size of the interval between markers on the first number line and the starting number of that line, as well as whether to hide or show individual number lines and the numbers on them. This applet lends itself well for use on an interactive white board. A pdf guide to this collection of teaching applets is cataloged separately.
Abbas Edalat; Reinhold Heckmann
We introduce, in Part I, a number representation suitable for exact real number computation, consisting of an exponent and\\u000a a mantissa, which is an infinite stream of signed digits, based on the interval [?1,1]. Numerical operations are implemented\\u000a in terms of linear fractional transformations (LFT's). We derive lower and upper bounds for the number of argument digits that are needed
Interactive Fraction Number Lines
NSDL National Science Digital Library
Michael Green
In this lesson students make models of fractions, including a human number line. Using a number line, students develop conceptual understanding of fractions. Students use the number line to represent and compare fractions less than one. The activities are engaging and include full participation/engagement of all students. The fractions are limited to positive fractions less than one with a denominator of 2 or 4 including 0 and 1 whole.
NSDL National Science Digital Library
Ms. Parks
Let's learn how to count using these fun games. The first game allows us to count the amount of fish in the sea. Count the fish and choose the correct answer. Counting with fish. In this game, put numbers in order from 1-10. Practice putting numbers in order. Lets Count on a Cloud! Choose an object and then click on a number you want. It will count how ...
NSDL National Science Digital Library
This problem provides an opportunity to introduce the concept of representing operations on unknown numbers algebraically and leads to work on inverse operations. Students are asked to think of a number, follow a sequence of computational instructions and finally to enter the result into the "machine." Students explore how the "machine" works out the starting number. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support.
Complex Numbers and Trigonometry
NSDL National Science Digital Library
Alexanderson, Gerald L.
Complex numbers have applications in many applied sciences. This online text begins with an introduction to trigonometry, which serves as a starting point for additional discussion about complex numbers (also known as imaginary numbers). The drawings and figures are the only notable downside to this excellent resource, because many of them are somewhat crude; however, they are still fairly easy to follow. The book can be read online or downloaded for offline viewing.
NSDL National Science Digital Library
Teachers and students can use this interactive Java applet to model and carry out arithmetic operations on the number line. Users manipulate the size, position, and direction of color bars to represent addition, subtraction, multiplication and division with whole numbers, integers and fractions. Options include the ability to zoom in and out, change the colors of the bars, and adjust the step size of the bars and number line increments.
NASA Technical Reports Server (NTRS)
Baals, D. D. (editor)
Fundamental aerodynamic questions for which high Reynolds number experimental capability is required are discussed. The operational characteristics and design features of the National Transonic Facility are reviewed.
Honors problem 1: Complex numbers. Arithmetic of complex numbers
Leininger, Christopher J.
Honors problem 1: Complex numbers. Arithmetic of complex numbers Recall that the complex numbers identify the complex numbers with the set of linear polynomials with real coefficients). The numbers as a subset of the complex numbers by identifying the real number a with a+0i. The imaginary numbers
NSDL National Science Digital Library
This 4-minute video introduces the definition of a prime number and illustrates it through a discussion of factors and composite numbers. It makes use of the definition to explain why 1 is not a prime and ends with a question for the viewer to ponder.
Babinkostova, Liljana
Elliptic Curves Number Theory and Cryptography Second Edition © 2008 by Taylor & Francis Group, LLC Washington, Lawrence C. Elliptic curves : number theory and cryptography / Lawrence C. Washington. -- 2nd ed, elliptic curves started being used in cryptography and elliptic curve techniques were developed
NSDL National Science Digital Library
Ms. Johnson
Have fun with numbers! Visit Lemonade Larry to buy some fresh squeezed lemonade! Figure out the cost of each order. Spooky sequences!!! Figure out the missing number to send the ghosts back to the haunted house. Place value pirates. Please help match the pirate to the correct place value. Arrgh mates! ...
NSDL National Science Digital Library
In this activity students are asked to relate the numbers 1- 20 to rectangular shapes. Learners use unit squares or cubes to sort numbers by their 'shapes,' either squares, rectangles or sticks (rectangles of unit width). Ideas for implementation, extension and support are included.
ERIC Educational Resources Information Center
Onstad, Torgeir
After a brief historical account of Leonardo Pisano Fibonacci, some basic results concerning the Fibonacci numbers are developed and proved, and entertaining examples are described. Connections are made between the Fibonacci numbers and the Golden Ratio, biological nature, and other combinatorics examples. (MDH)
Unrecognizable Sets of Numbers
Marvin Minsky; Seymour Papert
When is a set A of positive integers, represented as binary numbers, "regular" in the sense that it is a set of sequences that can be recognized by a finite-state machine? Let ? A(n) be the number of members of A less than the integer n. It is shown that the asymptotic behavior of ? A(n) is subject to severe
Unrecognizable Sets of Numbers
Minsky, Marvin
When is a set A of positive integers, represented as binary numbers, "regular" in the sense that it is a set of sequences that can be recognized by a finite-state machine? Let pie A(n) be the number of members of A less ...
David P. Day; Wayne Goddard; Michael A. Henning; Henda C. Swart
For a graph G, a partiteness k 2 and a number of colours c, we dene the multipartite Ramsey number rc k(G) as the minimum value m such that, given any colouring using c colours of the edges of the complete balanced k-partite graph with m vertices in each partite set, there must exist a monochromatic copy of G. We
... Life Science > Genetics by the Numbers Inside Life Science View All Articles | Inside Life Science Home Page Genetics by the Numbers By Chelsea Toledo ... Genetics NIH's National DNA Day This Inside Life Science article also appears on LiveScience . Learn about related ...
Atanu Sengupta; Tapan Kumar Pal
This paper first presents a brief survey of the existing works on comparing and ranking any two interval numbers on the real line and then, on the basis of this, gives two approaches to compare any two interval numbers. The first one describes a value judgement index along with a discussion on its strength and weakness over the other approaches.
NSDL National Science Digital Library
Grinstead, Charles M.
Created by Charles M. Grinstead and J. Laurie Snell of Dartmouth College, this website is part of an online statistics textbook. Topics include: (1) Law of Large Numbers for Discrete Random Variables, (2) Chebyshev Inequality, (3) Law of Averages, (4) Law of Large Numbers for Continuous Random Variables, (5) Monte Carlo Method. There are several examples and exercises that accompany the material.
Avogadro's Number Ferromagnetically
ERIC Educational Resources Information Center
Houari, Ahmed
Avogadro's number, usually denoted by N[subscript A], plays a fundamental role in both physics and chemistry. It defines the extremely useful concept of the mole, which is the base unit of the amount of matter in the international system of units. The fundamental character of this number can also be illustrated by its appearance in the definitions…
NSDL National Science Digital Library
In this quick time video segment from Cyberchase, viewers learn about extending a vertical number line below zero as they watch the CyberSquad rescue the Cyberspace Council, which is being held captive by Hacker in a tall building. This video is also featured in the lesson plan: "Introducing Negative Numbers" (cataloged separately). Teaching Tips and a transcript are included.
Behmer, Spencer T.
Definitions · Numbered Space  a single space marked with a number and reserved for a single permit 24/7 · Unnumbered Space  a space which can be used by any customer allowed to park in that lot. High Low Average Question 4: If I buy a staff permit for an UNNUMBERED* space in a non-gated surface
Templates, Numbers & Watercolors.
ERIC Educational Resources Information Center
Clemesha, David J.
Describes how a second-grade class used large templates to draw and paint five-digit numbers. The lesson integrated artistic knowledge and vocabulary with their mathematics lesson in place value. Students learned how draftspeople use templates, and they studied number paintings by Charles Demuth and Jasper Johns. (KM)
NSDL National Science Digital Library
Visually explore counting and place value with different number bases, from base 2 to base 16, and up to the hundreds place using a clock like interface. The activity also allows you to look at the numbers on the clock in base 10 or in your other chosen base to explore the relationship between those values.
The monochromatic block number
Lorenzo Milazzo
In 1993 Voloshin introduced the concept of mixed hypergraph. A mixed hypergraph is characterised by the fact that it possesses anti-edges as well as edges. In a colouring of a mixed hypergraph, every anti-edge has at least two vertices of the same colour. In this paper a new parameter is introduced: the monochromatic block number mb. It is the number
NSDL National Science Digital Library
All those numbers in the newspaper: what do they mean? Challenge learners to find out as they develop their number sense. Distribute newspaper pages to learners so that each pair gets a section with numbers at the right level of difficulty: easy—weather or sports scores; medium—clothing ads or event listings with times and dates; hard—automobile ads, monetary exchange rates. Learners try to find the smallest and largest numbers on the page (including best deal/best rate) and explain to others what they found. Variation for younger learners: look for the largest or smallest number on a walk around the building or around the block. Available as a web page and downloadable pdf.
NSDL National Science Digital Library
James Barrett
This Flash applet generates number fact questions for the game of Bingo. Each of the six levels focuses on a different range of number facts (addition, subtraction, and multiplication), which are displayed one at a time in a variety of question formats. The applet is intended for use in a class/group setting with a projector or interactive whiteboard. Downloadable cards for each level are available from the menu page. At any time in a game the "number facts so far" feature will reveal all the questions presented in the current round to facilitate review or verification of a winning board.
NSDL National Science Digital Library
This activity for the interactive white board (free access with registration) allows a teacher to create an arithmetic sequence for students to watch being built as the sequence of numbers moves along a conveyor. Learners must determine the pattern being used so when the belt randomly stops, the missing number in the sequence can be dragged/ dropped into its place. The teacher sets the start number (0-19), the interval or common difference (1-10) and if the sequence will count up or down. This last option provides an opportunity to display patterns with integers.
Honors problem 1: Complex numbers. Arithmetic of complex numbers
Leininger, Christopher J.
Honors problem 1: Complex numbers. Arithmetic of complex numbers Recall that the complex numbers we can identify the complex numbers with the set of linear polynomials with real coefficients as a subset of the complex numbers by identifying the real number a with a + 0i. The imaginary numbers
Two Symmetric Properties of Mersenne Numbers and Fermat Numbers
Shi Yongjin
Mersenne numbers and Fermat numbers are two hot and difficult issues in number theory. This paper constructs a special group for every positive odd number other than 1, and discovers an algorithm for determining the multiplicative order of 2 modulo q for each positive odd number q. It is worth mentioning that this paper discovers two symmetric properties of Mersenne numbers and Fermat numbers.
D. R. Mack
Fibonacci numbers are explained, and some of the many manifestations of the Fibonacci series in nature are described. These range from the so-called golden spiral to the Penrose tiling patterns that describe the structure of quasicrystals
ERIC Educational Resources Information Center
Strawn, Candace A.
Describes LOGO's turtle graphics capabilities based on a sixth-grade classroom's activities with negative numbers and Logo programming. A sidebar explains LOGO and offers suggestions to teachers for using LOGO effectively. (LRW)
Habib, Ayman
UCGE Reports Number 20259 Department of Geomatics Engineering Alternative Methodologies for the Quality Control of LiDAR Systems (URL: http://www.geomatics IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE DEPARTMENT OF GEOMATICS
Calgary, University of
UCGE Reports Number 20114 Geomatics Engineering Department of Geomatics Engineering OF PHILOSOPHY DEPARTMENT OF GEOMATICS ENGINEERING CALGARY, ALBERTA DECEMBER, 1997 © Richard Walter Klukas 1997 of this dissertation, having a supervisor from Geomatics Engineering and a supervisor from Electrical Engineering
UCGE Reports Number 20342 Department of Geomatics Engineering Detecting Fraudulent Activities in Land Record Systems: An Application of Data Mining (URL: http://www.geomatics OF GEOMATICS ENGINEERING CALGARY, ALBERTA SEPTEMBER, 2011 © Thaer Shunnar 2011 #12;ii Abstract Tenure security
Calgary, University of
UCGE REPORTS Number 20310 Department of Geomatics Engineering Detection of High-Latitude Ionospheric Irregularities from GPS Radio Occultation (URL: http://www.geomatics FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE DEPARTMENT OF GEOMATICS ENGINEERING
NSDL National Science Digital Library
NCTM Illuminations
The resource consists of 3 unrelated problem-solving challenges that can build number sense. Activity 1: Students explore the concept of a million to determine if 1 million dollar bills can fit into a standard suitcase. Activity 2: Students use a paper disk to estimate and name exact fractions between 0 and 1. Activity 3: Students explore the effect of addition, subtraction, multiplication, and division on decimal numbers by playing an engaging game.
NSDL National Science Digital Library
This web page contains links to a video and several downloadable pdf files documenting the discussions of a third grade class investigating even and odd numbers. Included are a 10-minute Blue Stream video segment in which students discuss a classmate's suggestion that the number 6 could be even or odd, a document providing background information on the investigation that led to the discussion, a transcript of the video, and the teacher's journal entry reflecting on the discussion and its implications.
ERIC Educational Resources Information Center
Brown, Ezra; Brunson, Cornelius
Fibonacci's forgotten number is the sexagesimal number 1;22,7,42,33,4,40, which he described in 1225 as an approximation to the real root of x[superscript 3] + 2x[superscript 2] + 10x - 20. In decimal notation, this is 1.36880810785...and it is correct to nine decimal digits. Fibonacci did not reveal his method. How did he do it? There is also a…
High Lundquist Number Reconnection
NASA Astrophysics Data System (ADS)
Gardiner, T. A.
In recent years there has been a resurgence of interest in exploring the properties of resistive magnetic reconnection layers. This was spurred on by the observations that at high Lundquist number these systems depart from the traditional Sweet-Parker scaling, opening the possibility of so-called fast resistive magnetic reconnection. This proceedings presents my recent efforts at simulating resistive magnetic reconnection layers in high Lundquist number systems highlighting the numerical algorithms, simulation results and convergence behavior.
Dangerous Doubles (Doubling Numbers)
NSDL National Science Digital Library
Stephanie Sharrer
This lesson teaches students to use the strategy doubling numbers and doubles plus or minus one in order to use mental math to add one digit numbers. The students are engaged in learning through the read aloud of Double the Ducks by Stephen Murphy and then get to work with a partner to draw doubles and write equations that relate to their drawings. Students individually work on solving word problems using these strategies and manipulatives as necessary to solve.
Definitions Algebra of complex numbers
Lega, Joceline
Definitions Algebra of complex numbers Polar coordinates form of complex numbers Check your knowledge Review of Complex Numbers Definitions, Algebra of complex numbers, Polar coordinates Review of Complex Numbers #12;Definitions Algebra of complex numbers Polar coordinates form of complex numbers Check
Nelson, R.N. (ed.)
This publication lists all report number codes processed by the Office of Scientific and Technical Information. The report codes are substantially based on the American National Standards Institute, Standard Technical Report Number (STRN)-Format and Creation Z39.23-1983. The Standard Technical Report Number (STRN) provides one of the primary methods of identifying a specific technical report. The STRN consists of two parts: The report code and the sequential number. The report code identifies the issuing organization, a specific program, or a type of document. The sequential number, which is assigned in sequence by each report issuing entity, is not included in this publication. Part I of this compilation is alphabetized by report codes followed by issuing installations. Part II lists the issuing organization followed by the assigned report code(s). In both Parts I and II, the names of issuing organizations appear for the most part in the form used at the time the reports were issued. However, for some of the more prolific installations which have had name changes, all entries have been merged under the current name.
NSDL National Science Digital Library
Have you ever wondered about the mathematics behind the idea of "six degrees of separation?" The Erd's Number Project offers several fairly comprehensive lists of co-author relationships to elaborate (with a bit of humor) studies of the dynamics involved in "the collaboration graph," which the website says is "a 'real-life' fairly large graph for combinatorialists to study." The co-author relationship list begins with the Hungarian mathematician Paul Erd's and branches outward, so that anyone who co-authored with Erd's is assigned Erd's number 1 and anyone who co-authored with an Erd's number 1 is assigned the Erd's number 2, and so on. The website offers some suggestions for how the lists might be used, including finding your own Erd's number, testing algorithms, or just getting a sense of the different areas of mathematics represented by Erd's' co-authors. Visitors can also learn more about Erd's, read articles about collaboration in mathematics, or browse through the websites which are linked from the co-author data lists.
Cantlon, Jessica F; Platt, Michael L; Brannon, Elizabeth M
In a world without numbers, we would be unable to build a skyscraper, hold a national election, plan a wedding or pay for a chicken at the market. The numerical symbols used in all these behaviors build on the approximate number system (ANS) which represents the number of discrete objects or events as a continuous mental magnitude. Here, we first discuss evidence that the ANS bears a set of behavioral and brain signatures that are universally displayed across animal species, human cultures and development. We then turn to the question of whether the ANS constitutes a specialized cognitive and neural domain - a question central to understanding how this system works, the nature of its evolutionary and developmental trajectory and its physical instantiation in the brain. PMID:19131268
Third Grade Number Actiivities
NSDL National Science Digital Library
Nicola Godwin
This page provides examples of Third Grade Number (Operations and Algebraic Thinking, Number and Operations in Base Ten, and Number Operations-Fractions) activities aligned with the Common Core State Standards. A CCSS standard is stated and the possible activities are listed below and linked. All activities are suitable for use in Math Centers, small group or whole class settings and are designed to elicit a range of responses and provide opportunities for students to communicate their reasoning and mathematical thinking. Instructions for each task are typed in large print and written in child-friendly language to enable students to work on activities independently after a brief introduction to the task. All files listed are in PDF format.
Expansion of rational numbers in Mobius number systems Petr Kurka
Kurka, Petr
Expansion of rational numbers in M¨obius number systems Petr K°urka Center for Theoretical Study- tions. We say that a M¨obius number system is rational, if it represents rational numbers by periodic. In the present paper we study expansions of rational numbers in the integer M¨obius number systems, whose
Interaction between internal natural convection in an enclosure and an external natural convection boundary-layer flow
NASA Astrophysics Data System (ADS)
Sparrow, E. M.; Prakash, C.
An analysis is made of natural convection in a square enclosure, of which one vertical wall is cooled by an external natural convection boundary layer flow. The other vertical wall is maintained at a uniform temperature, while the horizontal walls are adiabatic. The resulting conjugate internal-external natural-convection problem was solved numerically for Grashof numbers between 1000 and 10,000,000 and for a Prandtl number of 0.7. Approximate solutions were also obtained using a model which avoids conjugate-type computations. For the overall heat transfer characteristics encompassing both the internal and external flows, the average Nusselt number displayed a power-law dependence on the Grashof number. The local heat flux variations along the convectively cooled wall were found to be appreciably smaller than those along the heated isothermal wall reflecting the counterflow nature of the heat exchange between the internal and external flows. In addition, the temperature variations along the convectively cooled wall increased with increasing Grashof number. The Grashof number also decisively affected the temperature distributions along the adiabatic walls. Streamline maps revealed little difference between the flow fields adjacent to the thermally active and thermally passive walls at low Grashof numbers, but marked differences were in evidence at high Grashof numbers. For the external natural convection, the local heat transfer coefficients were generally larger than those predicted by the local application of the classical isothermal-plate heat transfer coefficient formula.
Giuseppe Pirillo
Let ? be the golden ratio (?5 + 1)\\/2, fn the nth Fibonacci finite word and f the Fibonacci infinite word. Let r be a rational number greater than (2 + ?)\\/2 and u a nondashempty word. If ur is a factor of f, then there exists n ? 1 such that u is a conjugate of fn and, moreover,
NSDL National Science Digital Library
Why do quantitative biologists sometimes claim that mRNA copy numbers are Poisson distributed in simple models of gene transcription? The first video segment addresses this question under the simplifying assumption that mRNA degradation occurs after a well-defined, deterministic lifetime, and the second segment illustrates the same basic concept for the more realistic situation in which degradation is stochastic.
Khan, T.A.; Baum, J.W.; Beckman, M.C. [eds.] [eds.
This document contains information dealing with the lessons learned from the experience of nuclear plants. In this issue the authors tried to avoid the `tyranny` of numbers and concentrated on the main lessons learned. Topics include: filtration devices for air pollution abatement, crack repair and inspection, and remote handling equipment.
K. S. Babu; E. Kearns; U. Al-Binni; S. Banerjee; D. V. Baxter; Z. Berezhiani; M. Bergevin; S. Bhattacharya; S. Brice; R. Brock; T. W. Burgess; L. Castellanos; S. Chattopadhyay; M-C. Chen; E. Church; C. E. Coppola; D. F. Cowen; R. Cowsik; J. A. Crabtree; H. Davoudiasl; R. Dermisek; A. Dolgov; B. Dutta; G. Dvali; P. Ferguson; P. Fileviez Perez; T. Gabriel; A. Gal; F. Gallmeier; K. S. Ganezer; I. Gogoladze; E. S. Golubeva; V. B. Graves; G. Greene; T. Handler; B. Hartfiel; A. Hawari; L. Heilbronn; J. Hill; D. Jaffe; C. Johnson; C. K. Jung; Y. Kamyshkov; B. Kerbikov; B. Z. Kopeliovich; V. B. Kopeliovich; W. Korsch; T. Lachenmaier; P. Langacker; C-Y. Liu; W. J. Marciano; M. Mocko; R. N. Mohapatra; N. Mokhov; G. Muhrer; P. Mumm; P. Nath; Y. Obayashi; L. Okun; J. C. Pati; R. W. Pattie Jr.; D. G. Phillips II; C. Quigg; J. L. Raaf; S. Raby; E. Ramberg; A. Ray; A. Roy; A. Ruggles; U. Sarkar; A. Saunders; A. Serebrov; Q. Shafi; H. Shimizu; M. Shiozawa; R. Shrock; A. K. Sikdar; W. M. Snow; A. Soha; S. Spanier; G. C. Stavenga; S. Striganov; R. Svoboda; Z. Tang; Z. Tavartkiladze; L. Townsend; S. Tulin; A. Vainshtein; R. Van Kooten; C. E. M. Wagner; Z. Wang; B. Wehring; R. J. Wilson; M. Wise; M. Yokoyama; A. R. Young
This report, prepared for the Community Planning Study - Snowmass 2013 - summarizes the theoretical motivations and the experimental efforts to search for baryon number violation, focussing on nucleon decay and neutron-antineutron oscillations. Present and future nucleon decay search experiments using large underground detectors, as well as planned neutron-antineutron oscillation search experiments with free neutron beams are highlighted.
Number in Classifier Languages
ERIC Educational Resources Information Center
Nomoto, Hiroki
Classifier languages are often described as lacking genuine number morphology and treating all common nouns, including those conceptually count, as an unindividuated mass. This study argues that neither of these popular assumptions is true, and presents new generalizations and analyses gained by abandoning them. I claim that no difference exists…
NSDL National Science Digital Library
Ms. Allen
Play the counting games below. First, help Curious George juggle the fruit in the Curious George Juggling game. Next, count the fish in the Fish Counting game. Then, try to catch the correct number of fish in the net. Go Fishing! ...
NSDL National Science Digital Library
Laura Domalik
In this 5-minute video Laura Domalik defines number sense and provides instructional strategies for counting and vocabulary, including counting on, counting back, one more than (+1), one less than (-1), basic fact concepts of +1 and -1, and missing addends. She demonstrates a game called Garbage, which can be played alone or with a partner.
ERIC Educational Resources Information Center
Moomaw, Sally; Carr, Victoria; Boat, Mary; Barnett, David
A child's demonstration of his conceptual understanding of number bodes well for his future success in school mathematics. As youngsters' thinking becomes more logical, they apply one-to-one correspondence relationships to quantification. Yet, reliable assessment of young children's mathematical ability is difficult because of social and emotional…
ERIC Educational Resources Information Center
Trudgian, Timothy
One of the difficulties in any teaching of mathematics is to bridge the divide between the abstract and the intuitive. Throughout school one encounters increasingly abstract notions, which are more and more difficult to relate to everyday experiences. This article examines a familiar approach to thinking about negative numbers, that is an…
UCGE Reports Number 20318 Department of Geomatics Engineering Modelling Spatial Dependence in Multivariate Regression Models of Grizzly Bear Health in Alberta, Canada (URL: http://www.geomatics DEPARTMENT OF GEOMATICS ENGINEERING CALGARY, ALBERTA SEPTEMBER, 2010 © Tracy Timmins 2010 #12;ii Abstract
Calgary, University of
UCGE Reports Number 20271 Department of Geomatics Engineering Use of the Global Environmental Multiscale Model for Atmospheric Retrieval from Radio Occultation for Canadian Events (URL: http://www.geomatics DEPARTMENT OF GEOMATICS ENGINEERING CALGARY, ALBERTA JUNE, 2008 © Lance de Groot 2008 #12;ii Approval Page
UCGE Reports Number 20340 Department of Geomatics Engineering Remote sensing-based framework for forecasting forest fire danger conditions over boreal forest (URL: http://www.geomatics DEPARTMENT OF GEOMATICS ENGINEERING CALGARY, ALBERTA SEPTEMBER, 2011 © Musa. Shammi Akther 2011 #12;iii
UCGE Reports Number 20283 Department of Geomatics Engineering Developing Multimedia Land Record Systems (URL: http://www.geomatics.ucalgary.ca/research/publications) by Abdel Rahman Muhsen January 2009 OF MASTER OF SCIENCE DEPARTMENT OF GEOMATICS ENGINEERING CALGARY, ALBERTA JANUARY, 2009 © Abdel Rahman
Calgary, University of
UCGE Reports Number 20184 Department of Geomatics Engineering IF GPS Signal Simulator Development and Verification (URL: http://www.geomatics.ucalgary.ca/links/GradTheses.html) by Lei Dong December 2003 #12;THE DEPARTMENT OF GEOMATICS ENGINEERING CALGARY, ALBERTA November, 2003 © Lei Dong 2003 #12;ABSTRACT A software
Calgary, University of
UCGE Reports Number 20277 Department of Geomatics Engineering Ultra Wideband Augmented GPS (URL: http://www.geomatics.ucalgary.ca/research/publications) by David Sung-Tat Chiu December 2008 #12 OF GEOMATICS ENGINEERING CALGARY, ALBERTA DECEMBER, 2008 © David Sung-Tat Chiu 2008 ii #12;ABSTRACT UWB has
Calgary, University of
UCGE Reports Number 20234 Department of Geomatics Engineering Interference Effects on GPS Receivers in Weak Signal Environments (URL: http://www.geomatics.ucalgary.ca/links/GradTheses.html) by Nyunook Kim OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE DEPARTMENT OF GEOMATICS ENGINEERING CALGARY, ALBERTA January
UCGE Reports Number 20373 Department of Geomatics Engineering Peri- Urban Land Tenure in Ghana (Accra): Case Study of Bortianor (URL: http://www.geomatics.ucalgary.ca/graduatetheses) by Ephraim Newman FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTERS OF GEOMATICS ENGINEERING GEOMATICS ENGINEERING
UCGE Reports Number 20372 Department of Geomatics Engineering Land Registration Use: Sales in a State-Subsidised Housing Estate in South Africa (URL: http://www.geomatics IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF GEOMATICS
UCGE Reports Number 20272 Department of Geomatics Engineering Fiscal Cadastral Systems Reform A Case Study of the General Valuation Project 2000 in the City of Cape Town (URL: http://www.geomatics OF PHILOSOPHY DEPARTMENT OF GEOMATICS ENGINEERING CALGARY, ALBERTA JUNE, 2008 © Jennifer Whittal 2008 #12;iii
ERIC Educational Resources Information Center
Hahn, Nic
Remember paint by numbers? This revived trend was a perfect solution to teaching geometric shapes to the author's first-grade students. Geometric shapes are identified and used in early elementary art classrooms, but this lesson gives students a deeper understanding of shape, encourages problem-solving, and makes a strong correlation between math…
ERIC Educational Resources Information Center
Doyle, William R.
Some say that the educators now have a gender-stratified system of higher education, with nearly 60 percent of all undergraduates being women and fewer men attending each year. The battle for gender equity for women in higher education has been a long and contentious one. In the decades since, increasing numbers of women have gone to college, to…
NSDL National Science Digital Library
Peter Boon
This applet allows students to freely build shapes by stacking cubes and "explore the relation between a building (house) consisting of cubes and the height numbers representing the height of the different parts of the building." This exercise helps students visualize and understand the concepts of volume and three-dimensional, measurable space.
Beyond complex numbers Johanna Ramo
Wright, Francis
Beyond complex numbers Johanna R¨am¨o July 22, 2010 These notes are written for the Goldsmiths- rational reals, negatives and finally to complex numbers. It has not always been easy to accept new numbers. Negative numbers were rejected for cen- turies, and complex numbers, the square roots of negative numbers
NSDL National Science Digital Library
In this 14-min video British teacher Rosalind Caren demonstrates group activities designed to develop number sense, fluency with addition and subtraction fact families, and reasoning skills. Caren exhibits effective questioning techniques and routines. Headteacher/math coordinator Kate Frood describes the guiding principles and expectations of teaching at the school. Following a class observation Frood provides constructive feedback to Caren and her teaching assistants.
NSDL National Science Digital Library
This 4-minute computer animation highlights three forms in nature that have connections with numbers and geometry. The Fibonacci sequence and the golden ratio are shown relating to the chambered nautilus shell and the sunflower seed pattern. The Delaunay triangulation and Voronoi tessellation are shown to simulate the capillary distribution on a dragonfly wing. Included are descriptions of the mathematics and stills from the production.
NSDL National Science Digital Library
The Maths Doctor website from Macmillan Publishers contains more than 250 lessons that are free for anyone. Each lesson includes a three to five minute video tutorial on the topic and a related worksheet for the student to complete. Each worksheet has a convenient QR code that a student can scan to access the video. The Number section contains numerous lessons ranging from Conversion of Units to Dividing Fractions to Subtracting Negative Integers.
John Stillwell
\\u000a Number theory is the second large field of mathematics that comes to us from the Pythagoreans via Euclid. The Pythagorean\\u000a theorem led mathematicians to the study of squares and sums of squares; Euclid drew attention to the primes by proving that there are infinitely many of them. Euclid's investigations were based on the so-called Euclidean algorithm, a method for finding
Total Number of Municipalities
Sibille, Etienne
Elected Officials Cities Contact Number Las Vegas, NV 702-229-6405 San Jose, CA 408-277-4000 Phoenix , AZ-427-4581 Tucson, AZ 520-791-4213 High African American Representation High Women Representation #12;Appendix 3 Washington 1 0 0.0% 14.8% 0.0 Dravosburg Boro Allegheny 1 0 0.0% 0.5% 0.0 Duquesne City Allegheny 1 0 0.0% 47
NASA Astrophysics Data System (ADS)
Allen, G. Donald
In human history, the origin of the numbers came from definite practical needs. Indeed, there is strong evidence that numbers were created before writing. The number "1", dating back at least 20,000 years, was found as a counting symbol on a bone. The famous statement by the German mathematician Leopold Kronecker (1823-1891), "God made the integers; all else is the work of man," has spawned a lively modern philosophical discussion, and this discussion begins by trying to get a philosophical handle on "1." This approach remains under heavy discussion, and is more-or-less unresolved (Frege in Die Grundlagen der Arithmetik (English: The foundations of arithmetic). Polhman, 1884). In this note, we consider the many facets of "one" in it many guises and applications. Nonetheless, "one" has multiple meanings, from the very practical to the abstract, from mathematics to science to basically everything. We examine here a mere slice of mathematical history with a focus on the most basic and applicable concept therein. It troubles many, particularly students, even today.
NSDL National Science Digital Library
Only in America, one might say, would artistic self-expression be so successfully mass produced, commodified, and regimented. Nevertheless, in a brave attempt at recuperation, the Smithsonian Institution's National Museum of American History offers this new Website on the popular 1950s' hobby of painting by number from the perspective of "the artists and entrepreneurs who created the popular paint kits, the cultural critics who reviled them, and the hobbyists who happily completed them and hung them in their homes." Taking a decidedly cultural studies approach, the Website stresses the pleasures derived from the activity as well as the modifications to the kits made by many participants. It also places the phenomenon in the context of the culture of the 1950s, particularly its expansion of leisure time. There are plenty of images here of the creation of the numbers kits as well as representations of the finished product. A bibliography and a bulletin board for posting reminiscences about painting by number are also provided. The authors claim the hobby, which pretty much died out in the 1960s, had the "peculiarly American virtue" of inviting people "who never held a brush before to enter a world of art and creativity." The editors invite our readers to be the judge of that.
Rocker, Graeme M; Verma, Jennifer Y; Demmons, Jillian; Mittmann, Nicole
The 'Number Needed to Treat' (NNT) is a useful measure for estimating the number of patients that would need to receive a therapeutic intervention to avoid one of the adverse events that the treatment is designed to prevent. We explored the possibility of an adaption of NNT to estimate the 'Number Needed to $ave' (NN$) as a new, conceptual systems metric to estimate potential cost-savings to the health system from implementation of a treatment, or in this case, a program. We used the outcomes of the INSPIRED COPD Outreach ProgramTM to calculate that 26 patients would need to complete the program to avoid healthcare expenditures of $100,000, based on hospital bed days avoided. The NN$ does not translate into 'cost savings' per se, but redirection of resource expenditures for other purposes. We propose that the NN$ metric, if further developed, could help to inform system-level resource allocation decisions in a manner similar to the way that the NNT metric helps to inform individual-level treatment decisions. PMID:25662619
Honors question 3: Complex numbers (revisited). Arithmetic of complex numbers
Leininger, Christopher J.
Honors question 3: Complex numbers (revisited). Arithmetic of complex numbers Recall that the complex numbers are formally defined as C = {a + bi} where a and b can be any real numbers and i is treated as a variable (so we can identify the complex numbers with the set of linear polynomials with real
q Numbers of quantum groups, Fibonacci numbers, and orthogonal polynomials
I. I. Kachurik
We obtain algebraic relations (identities) for q-numbers that do not contain q\\u000a ?-factors. We derive a formula that expresses any q-number [x] in terms of the q-number [2]. We establish the relationship between the q-numbers [n] and the Fibonacci numbers, Chebyshev polynomials, and other special functions. The sums of combinations of q-numbers, in particular, the sums of their powers, are
NSDL National Science Digital Library
Bill Kreahling, Bob Panoff, and the Shodor Education Foundation
This applet from the E-Examples of NCTM, which could be used as an interactive presentation tool, allows the student to link numerical patterns to a visual display as a number pattern is displayed on a calculator and on a hundred board simultaneously. The learner's task is to compare counting sequences on the calculator with the patterns they generate on the hundred board with the goal of helping students to see patterns and then make predictions. Instructions for using the applet are provided as well as background for the teacher.
NSDL National Science Digital Library
American Association for the Advancement of Science
Learners describe objects in a room using only numbers and shapes. They can measure the object (like a desk) and make a list of facts about it (e.g. 21 inches tall, 42 inches wide, 3 different colors). Then other learners try to identify the objects described. When learners set up a free account at Kinetic City, they can answer bonus questions at the end of the activity as a quick assessment. As a larger assessment, learners can complete the Bug Blaster game after they've completed several activities.
NASA Astrophysics Data System (ADS)
Holik, Federico
Since its origins, quantum mechanics has presented problems with the concept of individuality. It is argued that quantum particles do not have individuality, and so, one can speak about "entities without identity". On the contrary, we claim that the problem of quantum non individuality goes deeper, and that one of its most important features is the fact that there are quantum systems for which particle number is not well defined. In this work, we continue this discussion in relation to the problem about the one and the many.
Finite Neutrosophic Complex Numbers
W. B. Vasantha Kandasamy; Florentin Smarandache
In this book for the first time the authors introduce the notion of real neutrosophic complex numbers. Further the new notion of finite complex modulo integers is defined. For every $C(Z_n)$ the complex modulo integer $i_F$ is such that $2F_i = n - 1$. Several algebraic structures on $C(Z_n)$ are introduced and studied. Further the notion of complex neutrosophic modulo integers is introduced. Vector spaces and linear algebras are constructed using these neutrosophic complex modulo integers.
NSDL National Science Digital Library
This is an activity about assessing magnetic activity on the Sun as astronomers do. Learners will select and compare five visible light solar images and identify and label each individual sunspot group. Then, learners will count all possible sunspots from each group and use both counts in a standard equation to calculate the Relative Sunspot Number for each respective solar image. This activity requires access to the internet to obtain images from the SOHO image archive. This is Activity 8 of the Space Weather Forecast curriculum.
Complex Numbers First: Define i
Sands, Jonathan W.
Complex Numbers First: Define i Solve the quadratic: Ryan Tarring Max Van Over Mike Diamond Mentor therefore, #12;The set of complex numbers is when we add real numbers to real multiples of this imaginary unit Complex numbers are written in the form: a +bi for real numbers a&b if b is not equal to 0 #12
Crossing Numbers and Parameterized Complexity
Michael J. Pelsmajer; Marcus Schaefer
The odd crossing number of G is the smallest number of pairs of edges that cross an odd number of times in any drawing of G. We show that there always is a drawing realizing the odd crossing number of G that uses at most 9k crossings, where k is the odd crossing number of G. As a consequence of
Neutrino number of the universe
Kolb, E.W.
The influence of grand unified theories on the lepton number of the universe is reviewed. A scenario is presented for the generation of a large (>> 1) lepton number and a small (<< 1) baryon number. 15 references.
Series of Reciprocal Triangular Numbers
ERIC Educational Resources Information Center
Bruckman, Paul; Dence, Joseph B.; Dence, Thomas P.; Young, Justin
Reciprocal triangular numbers have appeared in series since the very first infinite series were summed. Here we attack a number of subseries of the reciprocal triangular numbers by methodically expressing them as integrals.
Modular redundant number systems
With the increased use of public key cryptography, faster modular multiplication has become an important cryptographic issue. Almost all public key cryptography, including most elliptic curve systems, use modular multiplication. Modular multiplication, particularly for the large public key modulii, is very slow. Increasing the speed of modular multiplication is almost synonymous with increasing the speed of public key cryptography. There are two parts to modular multiplication: multiplication and modular reduction. Though there are fast methods for multiplying and fast methods for doing modular reduction, they do not mix well. Most fast techniques require integers to be in a special form. These special forms are not related and converting from one form to another is more costly than using the standard techniques. To this date it has been better to use the fast modular reduction technique coupled with standard multiplication. Standard modular reduction is much more costly than standard multiplication. Fast modular reduction (Montgomery`s method) reduces the reduction cost to approximately that of a standard multiply. Of the fast multiplication techniques, the redundant number system technique (RNS) is one of the most popular. It is simple, converting a large convolution (multiply) into many smaller independent ones. Not only do redundant number systems increase speed, but the independent parts allow for parallelization. RNS form implies working modulo another constant. Depending on the relationship between these two constants; reduction OR division may be possible, but not both. This paper describes a new technique using ideas from both Montgomery`s method and RNS. It avoids the formula problem and allows fast reduction and multiplication. Since RNS form is used throughout, it also allows the entire process to be parallelized.
Abstract. Geometry and Complex Numbers GEOMETRY AND COMPLEX NUMBERS
Lee, Carl
Abstract. Geometry and Complex Numbers GEOMETRY AND COMPLEX NUMBERS JERZY DYDAK Contents 1. Introduction 2 2. Solving equations 10 3. Geometric proofs 20 Key words and phrases. Complex numbers. 1 #12-Euclidean, Projective, and Discrete' by Michael Henle (2nd edition, Prentice Hall). (2) `Complex numbers and geometry
Number Games, Magnitude Representation, and Basic Number Skills in Preschoolers
ERIC Educational Resources Information Center
Whyte, Jemma Catherine; Bull, Rebecca
The effect of 3 intervention board games (linear number, linear color, and nonlinear number) on young children's (mean age = 3.8 years) counting abilities, number naming, magnitude comprehension, accuracy in number-to-position estimation tasks, and best-fit numerical magnitude representations was examined. Pre- and posttest performance was…
Pauli Pascal Pyramids, Pauli Fibonacci Numbers, and Pauli Jacobsthal Numbers
Martin Erik Horn
The three anti-commutative two-dimensional Pauli Pascal triangles can be generalized into multi-dimensional Pauli Pascal hyperpyramids. Fibonacci and Jacobsthal numbers are then generalized into Pauli Fibonacci numbers, Pauli Jacobsthal numbers, and Pauli Fibonacci numbers of higher order. And the question is: are Pauli rabbits killer rabbits?
Generalized Lucas Numbers and Relations with Generalized Fibonacci Numbers
Kaygisiz, Kenan
In this paper, we present a new generalization of the Lucas numbers by matrix representation using Genaralized Lucas Polynomials. We give some properties of this new generalization and some relations between the generalized order-k Lucas numbers and generalized order-k Fibonacci numbers. In addition, we obtain Binet formula and combinatorial representation for generalized order-k Lucas numbers by using properties of generalized Fibonacci numbers.
Section 5.6 Complex Numbers1 Section 5.Section 5.Section 5.Section 5.6666 Complex NumbersComplex NumbersComplex NumbersComplex Numbers
Farlow, Jerry
Section 5.6 Complex Numbers1 Section 5.Section 5.Section 5.Section 5.6666 Complex NumbersComplex NumbersComplex NumbersComplex Numbers Purpose of SectionPurpose of SectionPurpose of SectionPurpose of Section To introduce the field ( ), ,+ ×» of complex numbers and their Cartesian
HOPF ALGEBRAS AND TRANSCENDENTAL NUMBERS Michel Waldschmidt Universit´e P. et M. Curie (Paris VI clear, but we point out that it already plays a role in transcendental number theory: St´ephane Fischler-Lindemann). If is a non-zero algebraic number, then e is a transcendental number. Equivalently, if is a non
Stirling Numbers for Complex Arguments
L. Bruce Richmond; Donatella Merlini
We define the Stirling numbers for complex values and obtain extensions of certain identities involving these numbers. We also show that the generalization is a natural one for proving unimodality and monotonicity results for these numbers. The definition is based on the Cauchy integral formula and can be used for many other combinatorial numbers. PII. S0895480195284329 1. Introduction. In this
Divisibility - Prime and Composite Numbers
NSDL National Science Digital Library
Mrs. Harris
Learn how to tell if a number is divisible by 2, 3, 5, 6, 9, or 10. Learn about prime and composite numbers This is a PowerPoint teaching Divisibility rules PowerPoint on Divisibility Have fun practicing divisibility! Divisibility Rules Practice Prime Factorization with this Factor Tree. Factor Tree You can be a Prime Number Cop while you play this game. Catch those prime numbers! Number Cop ...
Lepton family number violation
Herczeg, P.
At present there is evidence from neutrino oscillation searches that the neutrinos are in fact massive particles and that they mix. If confirmed, this would imply that the conservation of LFN is not exact. Lepton family number violation (LFNV) has been searched for with impressive sensitivities in many processes involving charged leptons. The present experimental limits on some of them (those which the author shall consider here) are shown in Table 1. These stringent limits are not inconsistent with the neutrino oscillation results since, given the experimental bounds on the masses of the known neutrinos and the neutrino mass squared differences required by the oscillation results, the effects of LFNV from neutrino mixing would be too small to be seen elsewhere (see Section 2). The purpose of experiments searching for LFNV involving the charged leptons is to probe the existence of other sources of LFNV. Such sources are present in many extensions of the SM. In this lecture the author shall discuss some of the possibilities, focusing on processes that require muon beams. Other LFNV processes, such as the decays of the kaons and of the {tau}, provide complementary information. In the next Section he shall consider some sources of LFNV that do not require an extension of the gauge group of the SM (the added leptons or Higgs bosons may of course originate from models with extended gauge groups). In Section 3 he discusses LFNV in left-right symmetric models. In Section 4 he considers LFNV in supersymmetric models, first in R-parity conserving supersymmetric grand unified models, and then in the minimal supersymmetric standard model with R-parity violation. The last section is a brief summary of the author`s conclusions.
Topological completions of the field of rational numbers which consist of Liouville numbers and rational numbers
J. E. Marcos
Some subfields of the field of real numbers which consist exclusively of rational numbers and Liouville numbers are given. Each of these fields is a completion of the rational number field endowed with a field topology finer than the usual topology.
The concrete theory of numbers: initial numbers and wonderful properties of numbers repunit
Boris V. Tarasov
In this work initial numbers and repunit numbers have been studied. All numbers have been considered in a decimal notation. The problem of simplicity of initial numbers has been studied. Interesting properties of numbers repunit are proved: $gcd(R_a, R_b) = R_{gcd(a,b)}$; $R_{ab}/(R_aR_b)$ is an integer only if $gcd(a,b) = 1$, where $a\\geq1$, $b\\geq1$ are integers. Dividers of numbers repunit, are researched by a degree of prime number.
Truly Hypercomplex Numbers: Unification of Numbers and Vectors
Redouane Bouhennache
Since the beginning of the quest of hypercomplex numbers in the late eighteenth century, many hypercomplex number systems have been proposed but none of them succeeded in extending the concept of complex numbers to higher dimensions. This paper provides a definitive solution to this problem by defining the truly hypercomplex numbers of dimension N greater than or equal to 3. The secret lies in the definition of the multiplicative law and its properties. This law is based on spherical and hyperspherical coordinates. These numbers which I call spherical and hyperspherical hypercomplex numbers define Abelian groups over addition and multiplication. Nevertheless, the multiplicative law generally does not distribute over addition, thus the set of these numbers equipped with addition and multiplication does not form a mathematical field. However, such numbers are expected to have a tremendous utility in mathematics and in science in general.
15. Stress Sheet, Truss number 2, span number 6, Superior ...
Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey
15. Stress Sheet, Truss number 2, span number 6, Superior Avenue viaduct. Drawing courtesy Engineering Dept., City of Cleveland. - Superior Avenue Viaduct, Cleveland East & West side, Cuyahoga Valley Vicinity, Cleveland, Cuyahoga County, OH
The Case of Blake: Number-Word and Number Development.
ERIC Educational Resources Information Center
Benson, Alexis P.; Baroody, Arthur J.
Noting that current research on childrens mathematical development does not adequately detail how toddlers represent small numbers and the role that number words play in the development of number understanding, this study used a combination of methods to examine mathematical development in one toddler. Underlying the study was an Integrated Model…
The bondage numbers of graphs with small crossing numbers
Jia Huang; Jun-ming Xu
The bondage number b(G) of a nonempty graph G is the cardinality of a smallest edge set whose removal from G results in a graph with domination number greater than the domination number (G) of G. Kang and Yuan proved b(G) 8 for every connected planar graph G. Fischermann, Rautenbach and Volkmann obtained some further results for connected planar graphs.
Concatenated Fibonacci and Lucas numbers do not form normal numbers
Mendonça, J Ricardo G
We show that the infinite decimal numbers $\\mathcal{F} = 0.F_{1}F_{2}F_{3}...$ and $\\mathcal{L} = 0.L_{1}L_{2}L_{3}...$ obtained by concatenating respectively the Fibonacci and the Lucas numbers for their fractional parts are not normal numbers to base 10.
Graphs, partitions and Fibonacci numbers
Arnold Knopfmacher; Robert F. Tichy; Stephan Wagner; Volker Ziegler
Abstract The Fibonacci number of a graph is the number of independent vertex subsets. In this paper, we investigate trees with large Fibonacci number. In particular, we show that all trees with n edges and Fibonacci number,> 2,\\/4 for constants A,B as n ! 1. This is proved by using a natural correspondence between partitions of integers and star-like trees.
Random Numbers and Quantum Computers
ERIC Educational Resources Information Center
McCartney, Mark; Glass, David
The topic of random numbers is investigated in such a way as to illustrate links between mathematics, physics and computer science. First, the generation of random numbers by a classical computer using the linear congruential generator and logistic map is considered. It is noted that these procedures yield only pseudo-random numbers since…
ERIC Educational Resources Information Center
Jue, Brian
Separate a three-digit number into its component digits. After raising each digit to the third power and computing the sum of the cubes, determine how often the original number reappears. Modular arithmetic is used to reduce the number of potential solutions to a more manageable quantity. (Contains 4 tables.)
Numbers and Math. Beginnings Workshop.
ERIC Educational Resources Information Center
Gross, Fred E.; Elkind, CavidEpstein, Ann S.; Copley, Juanita V.; Haugen, Ginny; Haugen, Kirsten
Presents five articles addressing numbers and math instruction for young children: "Math Talk with Young Children: One Parent's Experience" (Fred E. Gross); "How Children Build Their Understanding of Numbers" (David Elkind); "Early Math: It's More than Numbers" (Ann S. Epstein); "Assessing Mathematical Learning: Observing and Listening to…
Transcendental L2 -Betti numbers
Sunder, V S
Transcendental L2 -Betti numbers Atiyah's question Thomas Schick G¨ottingen OA Chennai 2010 Thomas Schick (G¨ottingen) Transcendental L2 -Betti numbers Atiyah's question OA Chennai 2010 1 / 24 #12). Thomas Schick (G¨ottingen) Transcendental L2 -Betti numbers Atiyah's question OA Chennai 2010 2 / 24 #12
The Algebra of Complex Numbers.
ERIC Educational Resources Information Center
LePage, Wilbur R.
This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…
Simple Remarks on Carmichael Numbers
NASA Astrophysics Data System (ADS)
Uchiyama, Shigenori
An odd composite number n for which an-1 ? 1 (mod n) for all integers a coprime to n is called a Carmichael number. This paper shows that some class of Carmichael numbers which have relatively large prime factors can be recognized in deterministic polynomial time under the assumption of the Extended Riemann Hypothesis (ERH). Also some related problems are discussed.
ERIC Educational Resources Information Center
Fletcher, Rodney
This article presents a guided investigation into the spacial relationships between the centres of the squares in a Fibonacci tiling. It is essentially a lesson in number pattern, but includes work with surds, coordinate geometry, and some elementary use of complex numbers. The investigation could be presented to students in a number of ways…
Office Use Only Application Number
University of Technology, Sydney
1. PERSONAL DETAILS Your name as shown on your passport Title (Mr,Ms, etc) Family Name(s) Given Name(s) Day Month Year Date of Birth Male Sex Female Citizenship Country of Birth Passport Number Postal Local Number Country Fax Area Local Number Email Passport Photograph Please attach a passport sized
On Blocking Numbers of Surfaces
Wing Kai Ho
The blocking number of a manifold is the minimal number of points needed to block out lights between any two given points in the manifold. It has been conjectured that if the blocking number of a manifold is finite, then the manifold must be flat. In this paper we prove that this is true for 2-dimensional manifolds with non-trivial fundamental
Data Compression with Prime Numbers
Gordon Chalmers
A compression algorithm is presented that uses the set of prime numbers. Sequences of numbers are correlated with the prime numbers, and labeled with the integers. The algorithm can be iterated on data sets, generating factors of doubles on the compression.
Higher-order Carmichael numbers
NASA Astrophysics Data System (ADS)
Howe, Everett W.
We define a Carmichael number of order m to be a composite integer n such that nth-power raising defines an endomorphism of every Z/nZ-algebra that can be generated as a Z/nZ-module by m elements. We give a simple criterion to determine whether a number is a Carmichael number of order m, and we give a heuristic argument (based on an argument of Erdos for the usual Carmichael numbers) that indicates that for every m there should be infinitely many Carmichael numbers of order m. The argument suggests a method for finding examples of higher-order Carmichael numbers; we use the method to provide examples of Carmichael numbers of order 2.
Schulte, Mike
IDENTIFICATION NUMBER REQUIREMENTS SOCIAL SECURITY NUMBER (SSN) OR INDIVIDUAL TAXPAYER Identification Number Needed Post Doctoral Fellow Employee-in-Training X10NN Post Doctoral Trainee Employee-in-Training X30NN Graduate Intern/Trainee Employee-in-Training X75NN Fellow Student Assistant Y21NN Scholar
Approximate Number Sense, Symbolic Number Processing, or Number-Space Mappings: What Underlies Mathematics Achievement?
ERIC Educational Resources Information Center
Sasanguie, Delphine; Gobel, Silke M.; Moll, Kristina; Smets, Karolien; Reynvoet, Bert
In this study, the performance of typically developing 6- to 8-year-old children on an approximate number discrimination task, a symbolic comparison task, and a symbolic and nonsymbolic number line estimation task was examined. For the first time, children's performances on these basic cognitive number processing tasks were explicitly contrasted…
Children's mappings between number words and the approximate number system.
Odic, Darko; Le Corre, Mathieu; Halberda, Justin
Humans can represent number either exactly - using their knowledge of exact numbers as supported by language, or approximately - using their approximate number system (ANS). Adults can map between these two systems - they can both translate from an approximate sense of the number of items in a brief visual display to a discrete number word estimate (i.e., ANS-to-Word), and can generate an approximation, for example by rapidly tapping, when provided with an exact verbal number (i.e., Word-to-ANS). Here we ask how these mappings are initially formed and whether one mapping direction may become functional before the other during development. In two experiments, we gave 2-5year old children both an ANS-to-Word task, where they had to give a verbal number response to an approximate presentation (i.e., after seeing rapidly flashed dots, or watching rapid hand taps), and a Word-to-ANS task, where they had to generate an approximate response to a verbal number request (i.e., rapidly tapping after hearing a number word). Replicating previous results, children did not successfully generate numerically appropriate verbal responses in the ANS-to-Word task until after 4years of age - well after they had acquired the Cardinality Principle of verbal counting. In contrast, children successfully generated numerically appropriate tapping sequences in the Word-to-ANS task before 4years of age - well before many understood the Cardinality Principle. We further found that the accuracy of the mapping between the ANS and number words, as captured by error rates, continues to develop after this initial formation of the interface. These results suggest that the mapping between the ANS and verbal number representations is not functionally bidirectional in early development, and that the mapping direction from number representations to the ANS is established before the reverse. PMID:25721021
Blocking numbers and fixing numbers of convex bodies
Long Yu
In the present paper we study the blocking number of a convex body. We determine the blocking number of the crosspolytope in E3. We also estimate that the blocking number of the lp unit ball in E3 is at most 6, for ln3ln2p+?. For a d-dimensional cylinder H whose base is a (d?1)-dimensional convex body K, we obtain a lower
Numbers and time doubly dissociate.
Cappelletti, Marinella; Freeman, Elliot D; Cipolotti, Lisa
The magnitude dimensions of number, time and space have been suggested to share some common magnitude processing, which may imply symmetric interaction among dimensions. Here we challenge these suggestions by presenting a double dissociation between two neuropsychological patients with left (JT) and right (CB) parietal lesions and selective impairment of number and time processing respectively. Both patients showed an influence of task-irrelevant number stimuli on time but not space processing. In JT otherwise preserved time processing was severely impaired in the mere presence of task-irrelevant numbers, which themselves could not be processed accurately. In CB, impaired temporal estimation was influenced by preserved number processing: small numbers made (already grossly underestimated) time intervals appear even shorter relative to large numbers. However, numerical estimation was not influenced by time in healthy controls and in both patients. This new double dissociation between number and time processing and the asymmetric interaction of number on time: (1) provides further support to the hypothesis of a partly shared magnitude system among dimensions, instead of the proposal of a single, fully shared system or of independent magnitude systems which would not explain dissociations or interactions among dimensions; (2) may be explained in terms of a stable hierarchy of dimensions, with numbers being the strongest. PMID:21807010
Dynamic Virtual Credit Card Numbers
NASA Astrophysics Data System (ADS)
Molloy, Ian; Li, Jiangtao; Li, Ninghui
Theft of stored credit card information is an increasing threat to e-commerce. We propose a dynamic virtual credit card number scheme that reduces the damage caused by stolen credit card numbers. A user can use an existing credit card account to generate multiple virtual credit card numbers that are either usable for a single transaction or are tied with a particular merchant. We call the scheme dynamic because the virtual credit card numbers can be generated without online contact with the credit card issuers. These numbers can be processed without changing any of the infrastructure currently in place; the only changes will be at the end points, namely, the card users and the card issuers. We analyze the security requirements for dynamic virtual credit card numbers, discuss the design space, propose a scheme using HMAC, and prove its security under the assumption the underlying function is a PRF.
Huang, Yi Ting; Spelke, Elizabeth; Snedeker, Jesse
Number words are generally used to refer to the exact cardinal value of a set, but cognitive scientists disagree about their meanings. Although most psychological analyses presuppose that numbers have exact semantics (two means EXACTLY TWO), many linguistic accounts propose that numbers have lower-bounded semantics (AT LEAST TWO), and that speakers restrict their reference through a pragmatic inference (scalar implicature). We address this debate through studies of children who are in the process of acquiring the meanings of numbers. Adults and 2- and 3-year-olds were tested in a novel paradigm that teases apart semantic and pragmatic aspects of interpretation (the covered box task). Our findings establish that when scalar implicatures are cancelled in the critical trials of this task, both adults and children consistently give exact interpretations for number words. These results, in concert with recent work on real-time processing, provide the first unambiguous evidence that number words have exact semantics. PMID:25285053
Multiplying Fractions and Mixed Numbers
NSDL National Science Digital Library
This lesson is designed to reinforce skills associated with multiplying fractions and mixed numbers and allow students to visualize the effects of multiplying by a fraction or mixed number. Students review the concepts of fractions and mixed numbers and how to multiply them, and use an interactive applet to visualize what happens to a whole number when it is multiplied by a fraction or mixed number. Students then answer questions from the Multiplying Fractions Worksheet (Flesch-Kincaid reading level = 5.3) to encourage them to look closely at the patterns created. As independent practice, students complete the Multiplying Mixed Numbers Worksheet (Flesch-Kincaid reading level = 5.7). A teacher/student discussion outline and instructions for leading guided practice are included.
Chaotic Nonlinear Prime Number Function
NASA Astrophysics Data System (ADS)
Mateos, Luis A.
Dynamical systems in nature, such as heartbeat patterns, DNA sequence pattern, prime number distribution, etc., exhibit nonlinear (chaotic) space-time fluctuations and exact quantification of the fluctuation pattern for predictability purposes has not yet been achieved [1]. In this paper a chaotic-nonlinear prime number function P(s) is developed, from which prime numbers are generated and decoded while composite numbers are encoded over time following the Euler product methodology, which works on sequences progressively culled from multiples of the preceding primes. By relating this P(s) to a virtually closed 2D number line manifold, it is possible to represent the evolving in time of nonlinear (chaotic) systems to a final value where the system becomes stable, becomes linear. This nonlinear prime number function is proposed as a chaotic model system able to describe chaotic systems.
Catalan Numbers, the Hankel Transform, and Fibonacci Numbers
Aleksandar Cvetkovic; Predrag Rajkovic; Milos Ivkovic
We prove that the Hankel transformation of a sequence whose elements are the sums of two adjacent Catalan numbers is a subsequence of the Fibonacci numbers. This is done by finding the explicit form for the coefficients in the three-term recurrence relation that the corresponding orthogonal polynomials satisfy.
Towards implementation of a binary number system for complex numbers
Tariq Jamil; N. Holmes; D. Blest
These days computer operations involving complex numbers are most commonly performed by dealing with the real and imaginary parts separately and then accumulating their individual results to get the final result of the operation. This divide-and-conquer technique forsakes the advantages of using complex numbers in computer arithmetic and there exists a need, at least for some problems, to treat a
Higher-order Fibonacci numbers
Milan Randi?; Daniel A. Morales; Oswaldo Araujo
We consider a generalization of Fibonacci numbers that was motivated by the relationship of the HosoyaZ topological index to the Fibonacci numbers. In the case of the linear chain structures the new higher order Fibonacci numbershFn are directly related to the higher order Hosoya-typeZ numbers. We investigate the limitsFn\\/Fn-1 and the corresponding equations, the roots of which allow one to
Familial sinistrals avoid exact numbers.
Sauerland, Uli; Gotzner, Nicole
We report data from an internet questionnaire of sixty number trivia. Participants were asked for the number of cups in their house, the number of cities they know and 58 other quantities. We compare the answers of familial sinistrals--individuals who are left-handed themselves or have a left-handed close blood-relative--with those of pure familial dextrals--right-handed individuals who reported only having right-handed close blood-relatives. We show that familial sinistrals use rounder numbers than pure familial dextrals in the survey responses. Round numbers in the decimal system are those that are multiples of powers of 10 or of half or a quarter of a power of 10. Roundness is a gradient concept, e.g. 100 is rounder than 50 or 200. We show that very round number like 100 and 1000 are used with 25% greater likelihood by familial sinistrals than by pure familial dextrals, while pure familial dextrals are more likely to use less round numbers such as 25, 60, and 200. We then use Sigurd's (1988, Language in Society) index of the roundness of a number and report that familial sinistrals' responses are significantly rounder on average than those of pure familial dextrals. To explain the difference, we propose that the cognitive effort of using exact numbers is greater for the familial sinistral group because their language and number systems tend to be more distributed over both hemispheres of the brain. Our data support the view that exact and approximate quantities are processed by two separate cognitive systems. Specifically, our behavioral data corroborates the view that the evolutionarily older, approximate number system is present in both hemispheres of the brain, while the exact number system tends to be localized in only one hemisphere. PMID:23544052
On Blocking Numbers of Surfaces
Wing Kai Ho
The blocking number of a manifold is the minimal number of points needed to\\u000ablock out lights between any two given points in the manifold. It has been\\u000aconjectured that if the blocking number of a manifold is finite, then the\\u000amanifold must be flat. In this paper we prove that this is true for\\u000a2-dimensional manifolds with non-trivial fundamental
NSDL National Science Digital Library
Students use these virtual fraction bars to model fractional addition, subtraction, multiplication (of fractions by whole numbers), and division on a number line. Students can create bars in positive or negative fractional lengths; align, stack, or remove bars; and change the number line marks in increments between 1/2 and 1/15. Applet instructions and teaching ideas are included in the links at the top of the page.
Schladow, S. Geoffrey
DIAGNOSIS NUMBER OF CASES CARDIOVASCULAR Cardiovascular disease .........................................................36 Crop Disorder.....................................................12 Digestive Disease/Plant/worms...........................14 Liver disease ......................................................14 Liver tumor
Compendium of Experimental Cetane Numbers
Yanowitz, J.; Ratcliff, M. A.; McCormick, R. L.; Taylor, J. D.; Murphy, M. J.
This report is an updated version of the 2004 Compendium of Experimental Cetane Number Data and presents a compilation of measured cetane numbers for pure chemical compounds. It includes all available single compound cetane number data found in the scientific literature up until March 2014 as well as a number of unpublished values, most measured over the past decade at the National Renewable Energy Laboratory. This Compendium contains cetane values for 389 pure compounds, including 189 hydrocarbons and 201 oxygenates. More than 250 individual measurements are new to this version of the Compendium. For many compounds, numerous measurements are included, often collected by different researchers using different methods. Cetane number is a relative ranking of a fuel's autoignition characteristics for use in compression ignition engines; it is based on the amount of time between fuel injection and ignition, also known as ignition delay. The cetane number is typically measured either in a single-cylinder engine or a constant volume combustion chamber. Values in the previous Compendium derived from octane numbers have been removed, and replaced with a brief analysis of the correlation between cetane numbers and octane numbers. The discussion on the accuracy and precision of the most commonly used methods for measuring cetane has been expanded and the data has been annotated extensively to provide additional information that will help the reader judge the relative reliability of individual results.
Inclusion of heat transfer computations for particle laden flows
NASA Astrophysics Data System (ADS)
Feng, Zhi-Gang; Michaelides, Efstathios E.
A newly developed direct numerical simulation method has been used to study the dynamics of nonisothermal cylindrical particles in particulate flows. The momentum and energy transfer equations are solved to compute the effects of heat transfer in the sedimentation of particles. Among the effects examined is the drag force on nonisothermal particles, which we found strongly depends on the Reynolds and Grashof numbers. It was observed that heat advection between hotter particles and fluid causes the drag coefficient of particles to significantly increase at relatively low Reynolds numbers. For Grashof number of 100, the drag enhancement effect diminishes when the Reynolds number exceeds 50. On the contrary, heat advection with colder particles reduces the drag coefficient for low and medium Reynolds number (Re<50) for Grashof number of -100. We used this numerical method to study the problem of a pair of hot particles settling in a container at different Grashof numbers. In isothermal cases, such a pair of particles would undergo the well-known drafting-kissing-tumbling (DKT) motion. However, it was observed that the buoyancy currents induced by the hotter particles reverse the DKT motion of the particles or suppress it altogether. Finally, the sedimentation of a circular cluster of 172 particles in an enclosure at two different Grashof numbers was studied and the main features of the results are presented.
Rational Numbers and Proportional Reasoning
NSDL National Science Digital Library
Carol R. Findell
In this workshop session, elementary and middle school teachers look at ways to interpret, model and work with rational numbers and to explore the basics of proportional reasoning. These ideas are investigated through interactive applets, problem sets, and a video of teachers solving one of the problems. This is session 8 of Learning Math: Number and Operations, a free online course.
Toddlers' Spontaneous Attention to Number
ERIC Educational Resources Information Center
Baroody, Arthur J.; Li, Xia; Lai, Meng-lung
Hannula and Lehtinen (2001, 2005) defined spontaneous focusing on numerosity (SFON) as the tendency to notice the relatively abstract attribute of number despite the presence of other attributes. According to nativists, an innate concept of one to three directs young children's attention to these "intuitive numbers" in everyday situations--even…
Investigating the Randomness of Numbers
ERIC Educational Resources Information Center
Pendleton, Kenn L.
The use of random numbers is pervasive in today's world. Random numbers have practical applications in such far-flung arenas as computer simulations, cryptography, gambling, the legal system, statistical sampling, and even the war on terrorism. Evaluating the randomness of extremely large samples is a complex, intricate process. However, the…
Davies, Christopher
) Rounding to a specified number of significant figures The first significant figure of a decimal quantity to a specified number of significant figures, we use the same principle as in (a), but starting from the first significant figure, then working to the right. EXAMPLES 1. 362.5863 = 362.59 to 5 significant figures; 362
NSDL National Science Digital Library
The students perform the Sieve of Eratosthenes in class to find the prime number between 1 and 100. They also look for patterns such as where the multiples of 2 or 5 appear in the sieve. At home or in a computer lab they then research the Fibonacci Sequence and other number systems.
Know Your Blood Sugar Numbers If you have diabetes, keeping your blood sugar (glucose) numbers in your target range can help you feel ... Prevention There are two ways to measure blood sugar. 1 The A1C is a lab test that ...
Number Talks Build Numerical Reasoning
ERIC Educational Resources Information Center
Parrish, Sherry D.
"Classroom number talks," five- to fifteen-minute conversations around purposefully crafted computation problems, are a productive tool that can be incorporated into classroom instruction to combine the essential processes and habits of mind of doing math. During number talks, students are asked to communicate their thinking when presenting and…
Spontaneous Number Representation in Mosquitofish
ERIC Educational Resources Information Center
Dadda, Marco; Piffer, Laura; Agrillo, Christian; Bisazza, Angelo
While there is convincing evidence that preverbal human infants and non-human primates can spontaneously represent number, considerable debate surrounds the possibility that such capacity is also present in other animals. Fish show a remarkable ability to discriminate between different numbers of social companions. Previous work has demonstrated…
Color by Numbers: Image Representation
NSDL National Science Digital Library
Computers store drawings, photographs, and other pictures using only numbers. Through this activity, learners decode numbers to create pictures using the same process that computers use. They can then create and code their own pictures for other learners to decode. This lesson includes three activities (1 introductory and 2 worksheet) and background information.
On amicable numbers Carl Pomerance
Pomerance, Carl
On amicable numbers Carl Pomerance To Professor Helmut Maier on his sixtieth birthday Abstract Let, these upper bounds have progressed as follows: Carl Pomerance Dartmouth College, Hanover, NH 03755, USA firstname.lastname@example.com Mathematics Subject Classification: 11A25, 11N25 Key Words: amicable number 1 #12;2 Carl Pomerance x
On Counting the Rational Numbers
ERIC Educational Resources Information Center
Almada, Carlos
In this study, we show how to construct a function from the set N of natural numbers that explicitly counts the set Q[superscript +] of all positive rational numbers using a very intuitive approach. The function has the appeal of Cantor's function and it has the advantage that any high school student can understand the main idea at a glance…
Measuring Distance of Fuzzy Numbers by Trapezoidal Fuzzy Numbers
NASA Astrophysics Data System (ADS)
Hajjari, Tayebeh
Fuzzy numbers and more generally linguistic values are approximate assessments, given by experts and accepted by decision-makers when obtaining value that is more accurate is impossible or unnecessary. Distance between two fuzzy numbers plays an important role in linguistic decision-making. It is reasonable to define a fuzzy distance between fuzzy objects. To achieve this aim, the researcher presents a new distance measure for fuzzy numbers by means of improved centroid distance method. The metric properties are also studied. The advantage is the calculation of the proposed method is far simple than previous approaches.
Learning Math: Number and Operations
NSDL National Science Digital Library
In this video- and web-based course K-8 teachers examine the three main categories in the Number and Operations strand of Principles and Standards of School Mathematics (NCTM): understanding numbers, representations, relationships, and number systems; the meanings of operations and relationships among those operations; and reasonable estimation and fluent computation. The course covers the real number system, place value, the behavior of zero and infinity, meanings and models of basic operations, percentages, modeling operations with fractions, and basic number theory topics (factors, multiples, divisibility tests). The course consists of 10 approximately 2.5 hour sessions, each with video programming, problem-solving activities, and interactive activities and demonstrations on the web. Participants can work through the sessions on their own, in a study group, or as part of a facilitated, face-to-face, graduate-level course for credit.
Talmi, Igal [Weizmann Institute of Science, Rehovot (Israel)
The discovery of magic numbers led to the shell model. They indicated closure of major shells and are robust: proton magic numbers are rather independent of the occupation of neutron orbits and vice versa. Recently the magic property became less stringent and we hear a lot about the discovery of new magic numbers. These, however, indicate sub-shell closures and strongly depend on occupation numbers and hence, may be called quasi-magic numbers. Some of these have been known for many years and the mechanism for their appearance as well as disappearance, was well understood within the simple shell model. The situation will be illustrated by a few examples which demonstrate the simple features of the shell model. Will this simplicity emerge from the complex computations of nuclear many-body theory?.
Hurwitz numbers and BKP hierarchy
S. M. Natanzon; A. Yu. Orlov
We consider special series in ratios of the Schur functions which are defined by integers $\\textsc{f}\\ge 0$ and $\\textsc{e} \\le 2$, and also by the set of $3k$ parameters $n_i,q_i,t_i,\\,i=1,..., k$. These series may be presented in form of matrix integrals. In case $k=0$ these series generates Hurwitz numbers for the $d$-fold branched covering of connected surfaces with a given Euler characteristic $\\textsc{e}$ and arbitrary profiles at $\\textsc{f}$ ramification points. If $k>0$ they generate weighted sums of the Hurwitz numbers with additional ramification points which are distributed between color groups indexed by $i=1,...,k$, the weights being written in terms of parameters $n_i,q_i,t_i$. By specifying the parameters we get sums of all Hurwitz numbers with $\\textsc{f}$ arbitrary fixed profiles and the additional profiles provided the following condition: both, the sum of profile lengths and the number of ramification points in each color group are given numbers. In case $\\textsc{e}=\\textsc{f}=1,2$ the series may be identified with BKP tau functions of Kac and van de Leur of a special type called hypergeometric tau functions. Sums of Hurwitz numbers for $d$-fold branched coverings of ${\\mathbb{RP}}^2$ are related to the one-component BKP hierarchy. We also present links between sums of Hurwitz numbers and one-matrix model of the fat graphs.
Reynolds number influences in aeronautics
NASA Technical Reports Server (NTRS)
Bushnell, Dennis M.; Yip, Long P.; Yao, Chung-Sheng; Lin, John C.; Lawing, Pierce L.; Batina, John T.; Hardin, Jay C.; Horvath, Thomas J.; Fenbert, James W.; Domack, Christopher S.
Reynolds number, a measure of the ratio of inertia to viscous forces, is a fundamental similarity parameter for fluid flows and therefore, would be expected to have a major influence in aerodynamics and aeronautics. Reynolds number influences are generally large, but monatomic, for attached laminar (continuum) flow; however, laminar flows are easily separated, inducing even stronger, non-monatomic, Reynolds number sensitivities. Probably the strongest Reynolds number influences occur in connection with transitional flow behavior. Transition can take place over a tremendous Reynolds number range, from the order of 20 x 10(exp 3) for 2-D free shear layers up to the order of 100 x 10(exp 6) for hypersonic boundary layers. This variability in transition behavior is especially important for complex configurations where various vehicle and flow field elements can undergo transition at various Reynolds numbers, causing often surprising changes in aerodynamics characteristics over wide ranges in Reynolds number. This is further compounded by the vast parameterization associated with transition, in that any parameter which influences mean viscous flow development (e.g., pressure gradient, flow curvature, wall temperature, Mach number, sweep, roughness, flow chemistry, shock interactions, etc.), and incident disturbance fields (acoustics, vorticity, particulates, temperature spottiness, even electro static discharges) can alter transition locations to first order. The usual method of dealing with the transition problem is to trip the flow in the generally lower Reynolds number wind tunnel to simulate the flight turbulent behavior. However, this is not wholly satisfactory as it results in incorrectly scaled viscous region thicknesses and cannot be utilized at all for applications such as turbine blades and helicopter rotors, nacelles, leading edge and nose regions, and High Altitude Long Endurance and hypersonic airbreathers where the transitional flow is an innately critical portion of the problem.
Transient natural convection heat and mass transfer in crystal growth
NASA Technical Reports Server (NTRS)
Han, Samuel S.
A numerical analysis of transient combined heat and mass transfer across a rectangular cavity is performed by a numerical method based on the SIMPLE algorithm. The physical parameters are selected to represent a range of possible crystal growth in solutions. Numerical results are compared with available experimental data to confirm the accuracy of the results. Good qualitative agreements are obtained for the average mass transfer rate across the cavity. Also, qualitative agreements are observed for the global development of thermal and solute fields. It is found that the thermal and solute fields become highly oscillatory when the thermal and solute Grashof numbers are large. Oscillations are probably caused by a number of different instability mechanisms. By reducing the gravity some of these instabilities were made to disappear at the lower Grashof numbers. Transient temperature and solute distribution near the crystal growing surface are highly non-uniform at the higher Grashof numbers. These non-uniformities are less severe in the reduced gravity environments but still exist. The effects of convection on the rate of average mass transfer are more than one order of magnitude higher than those of conduction in the range of Grashof numbers studied. Dependency of mass transfer rate on the Grashof number indicates that the convection effects many not be negligible even in the microgravity environments for the range of parameters investigated.
BKP and projective Hurwitz numbers
Sergei Natanzon; Alexander Orlov
We consider $d$-fold branched coverings of the projective plane $\\mathbb{RP}^2$ and show that the hypergeometric tau function of the BKP hierarchy of Kac and van de Leur is the generating function for the weighted sums of the related Hurwitz numbers. In particular we get the $\\mathbb{RP}^2$ analogue of the $\\mathbb{CP}^1$ generating functions proposed by Okounkov. Hurwitz numbers weighted by the Hall-Littlewood and by the Macdonald polynomials are the other examples. We also consider integrals of tau functions which generate projective Hurwitz numbers.
Numbered nasal discs for waterfowl
Bartonek, J.C.; Dane, C.W.
Numbered nasal discs were successfully used in studies requiring large numbers of individually marked waterfowl. The procedure for constructing these discs is outlined. Blue-winged teal (Anas discors) with 5/8-inch discs, and canvasback (Aythya valisineria) and redhead (A. americana) with 3/4-inch discs can be individually identified up to 50 and 80 yards, respectively, with a gunstock-mounted, 20-power spotting scope. The particular value of these markers is their durability, the number of combinations possible, and the apparent absence of behavioral or mortality influence among such species as the blue-winged teal.
Incomplete Fibonacci and Lucas numbers
Piero Filipponi
A particular use of well-known combinatorial expressions for Fibonacci and Lucas numbers gives rise to two interesting classes\\u000a of integers (namely, the numbersF\\u000a n(k) andL\\u000a n(k)) governed by the integral parametersn andk. After establishing the main properties of these numbers and their interrelationship, we study some congruence properties\\u000a ofL\\u000a n(k), one of which leads to a supposedly new characterisation of
NSDL National Science Digital Library
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Below are pictures of the first three triangular numbers: In general, the $n^{\\text{th}}$ triangular number is the total number of dots in $n$ columns ...
On rings of structural numbers
Powell, Wayne Bruce
ON RINGS OF STRUCTURAL NUMBERS A Thesis by WAYNE BRUCE POWELL Submitted to the Graduate College of Texas A&M University in partial fulfil1ment of the requirement for the degree of MASTER OF SCIENCE December 1973 Major Subject: h1athematics... ON RINGS OF STRUCTURAL NUMBERS A Thesis by WAYNE BRUCE POWELL Approved as to style and content by: C airman Committee Head of Oepar t l. , k / Me er )I Member Oecember 1973 ABSTRACT On Rings of Structural Numbers. (December 1973) Wayne Bruce...
Veiga, Pedro Manuel Barbosa
Drop/Add Card SIS Call Number (5 digits) Course Prefix (2-4 letters) Course Number (4 digits):_________________________________________________________________________ SIS Call Number (5 digits) Course Prefix (2-4 letters) Course Number (4 digits) Section Number (3
Fibonacci Numbers and the Spreadsheet.
ERIC Educational Resources Information Center
Verderber, Nadine L.
Described is a classroom activity incorporating a computer spreadsheet to study number patterns generated by the Fibonacci sequence. Included are examples and suggestions for the use of the spreadsheet in other recursive relationships. (JJK)
Tam, Daniel See Wai, 1980-
The work described in this thesis centers on inertialess motion at low Reynolds numbers at the crossroad between biofluids and microfluids. Here we address questions regarding locomotion of micro-swimmers, transport of ...
NSDL National Science Digital Library
This whole-class lesson will reinforce the concept of comparing two 3-digit numbers as well as provide practice for students to become comparing experts. Students will use playing cards to practice their skills.
NSDL National Science Digital Library
Nicola Godwin
This page provides examples of 4th Grade Number (Operations and Algebraic Thinking, Number and Operations in Base Ten, and Number Operations-Fractions) activities aligned with the Common Core State Standards. A CCSS standard is stated and the possible activities are listed below and linked. All activities are suitable for use in Math Centers, small group or whole class settings and are designed to elicit a range of responses and provide opportunities for students to communicate their reasoning and mathematical thinking. Instructions for each task are typed in large print and written in child-friendly language to enable students to work on activities independently after a brief introduction to the task. All files for the 4th Grade Number Activities listed are in PDF format.
NSDL National Science Digital Library
Nicola Godwin
This page provides examples of 5th Grade Number (Operations and Algebraic Thinking, Number and Operations in Base Ten, and Number Operations-Fractions) activities aligned with the Common Core State Standards. A CCSS standard is stated and the possible activities are listed below and linked. All activities are suitable for use in Math Centers, small group or whole class settings and are designed to elicit a range of responses and provide opportunities for students to communicate their reasoning and mathematical thinking. Instructions for each task are typed in large print and written in child-friendly language to enable students to work on activities independently after a brief introduction to the task. All files for the 5th Grade Number Activities listed are in PDF format.
Atomic Structure - A Numbers Game
ERIC Educational Resources Information Center
George, W. O.; Vincent, A.
Emphasizes the simplicity and elegance of early discoveries related to the hydrogen spectrum and provides an elementary experimental basis of quantum theory based on a "numbers game" which can be played by students. (Author/GS)
OFFICE USE ONLY Reference number
Dixon, Peter
-exempt 501(c)(3) organization and your donation is tax deductible to the extent allowed by law. Thank youAlumni Fund Donation Form. OFFICE USE ONLY Reference number: Thank you for supporting Sheffield
NSDL National Science Digital Library
Grace M. Burton / Illuminations NCTM
"Students will: Construct groups of 0 to 10 objects Identify and write the numerals 0 to 10 Record the number of objects in groups of size 0 to 10" (from NCTM Illuminations) Lesson one of a six lesson unit.
The Plane of Complex Numbers In this chapter we'll introduce the complex numbers as a plane of numbers.
Wortman, Kevin
The Plane of Complex Numbers In this chapter we'll introduce the complex numbers as a plane of numbers. Each complex number will be identified by a number on a "real axis" and a number on an "imaginary axis". This description of the complex numbers is analogous to the description of R2 using cartesian
Neural Addition and Fibonacci Numbers
Valeriu Beiu
This paper presents an intriguing relation between neural networks having as weights the Fibonacci numbers and the Addition of (two) binary numbers. The practical application of interest is that such 'Fibonacci' networks are VLSI-optimal with respect\\u000a to the area of the circuit. We shortly present the state-of-the-art, and detail a class of multilayer solutions for Addition. For this class we
Entropy estimation and Fibonacci numbers
NASA Astrophysics Data System (ADS)
Timofeev, Evgeniy A.; Kaltchenko, Alexei
We introduce a new metric on a space of right-sided infinite sequences drawn from a finite alphabet. Emerging from a problem of entropy estimation of a discrete stationary ergodic process, the metric is important on its own part and exhibits some interesting properties. Notably, the number of distinct metric values for a set of sequences of length m is equal to Fm+3 - 1, where Fm is a Fibonacci number.
Number Sense Games and Activities
NSDL National Science Digital Library
Mrs. Barker
Students will select online games related to number sense and play them individually or with a partner Odd or Even Can you tell the difference between odd or even? Choose one of these games for some practice! Don\\'t be afraid. The ghosts in this game only haunt those who don\\'t know odd or even numbers. Surely that\\'s not YOU! Even Ghostblasters Odd Ghostblasters Odd/Even Building Game Counting Patterns I know you can count ...
Baryon number violating nuclear decay
C S Warke
The expressions for baryon number violating nuclear partial decay widths are derived from the interactions as predicted by\\u000a grand unified theories. Theory predicts that the baryon number violating proton decay inside the nucleus is hindered relative\\u000a to the free proton decay rate. In the case of closed shell nuclei, the meson spin-isospin dependence of the partial width\\u000a is the same
Why are airport runways numbered?
NSDL National Science Digital Library
This Figure This! activity provides students an opportunity to apply their knowledge of angles and compass directions to solve a problem in the context of airport runways. The introduction calls students' attention to the numbers assigned to both ends of runways. Students are asked to find a missing runway number. The activity includes links to a solution hint, the solution, related math questions, and additional resources.
Bass Numbers and Semidualizing Complexes
Sean Sather-Wagstaff
Let R be a commutative local noetherian ring. We prove that the existence of a chain of semidualizing R-complexes of length (d+1) yields a degree-d polynomial lower bound for the Bass numbers of R. We also show how information about certain Bass numbers of R provide restrictions on the lengths of chains of semidualizing R-complexes. To make this article somewhat
Overpseudoprimes, and Mersenne and Fermat numbers as primover numbers
Shevelev, Vladimir; Velásquez-Soto, Juan Miguel; Castillo, John H
We introduce a new class of pseudoprimes-so called "overpseudoprimes to base $b$", which is a subclass of strong pseudoprimes to base $b$. Denoting via $|b|_n$ the multiplicative order of $b$ modulo $n$, we show that a composite $n$ is overpseudoprime if and only if $|b|_d$ is invariant for all divisors $d>1$ of $n$. In particular, we prove that all composite Mersenne numbers $2^{p}-1$, where $p$ is prime, are overpseudoprime to base 2 and squares of Wieferich primes are overpseudoprimes to base 2. Finally, we show that some kinds of well known numbers are overpseudoprime to a base $b$.
Transport numbers in transdermal iontophoresis.
Mudry, Blaise; Guy, Richard H; Delgado-Charro, M Begońa
Parameters determining ionic transport numbers in transdermal iontophoresis have been characterized. The transport number of an ion (its ability to carry charge) is key to its iontophoretic delivery or extraction across the skin. Using small inorganic ions, the roles of molar fraction and mobility of the co- and counterions present have been demonstrated. A direct, constant current was applied across mammalian skin in vitro. Cations were anodally delivered from either simple M(+)Cl(-) solutions (single-ion case, M(+) = sodium, lithium, ammonium, potassium), or binary and quaternary mixtures thereof. Transport numbers were deduced from ion fluxes. In the single-ion case, maximum cationic fluxes directly related to the corresponding ionic aqueous mobilities were found. Addition of co-ions decreased the transport numbers of all cations relative to the single-ion case, the degree of effect depending upon the molar fraction and mobility of the species involved. With chloride as the principal counterion competing to carry current across the skin (the in vivo situation), a maximum limit on the single or collective cation transport number was 0.6-0.8. Overall, these results demonstrate how current flowing across the skin during transdermal iontophoresis is distributed between competing ions, and establish simple rules with which to optimize transdermal iontophoretic transport. PMID:16443654
Searching for the highest number.
Howe, Piers D L; Little, Daniel R
When viewing a collection of products how does a consumer decide which one to buy? To do this task, the consumer not only needs to evaluate the desirability of the products, taking into account factors such as quality and price, but also needs to search through the products to find the most desirable one. We studied the search process using an abstraction of a common consumer choice task. In our task, observers searched an array of numbers for the highest. Crucially, the observers did not know in advance what this number would be, which made it difficult to know when the search should be terminated. In this way, our search task mimicked a problem often faced by consumers in a supermarket setting where they also may not know in advance what the most desirable product will be. We compared several computational models. We found that our data was best described by a process that assumes that observers terminate their search when they find a number that exceeds an internal threshold. Depending on the observer and the circumstances, this threshold appeared either to be fixed or to decrease over the course of the trial. This threshold can explain why in some situations the observers terminate the search without inspecting all the numbers in the display, whereas in other situations observers act in a seemingly irrational manner, continuing the search even after inspecting all the numbers. PMID:25427843
Complex Numbers and Physical Reality
V. V. Lyahov; V. M. Nechshadim
Some aspects of the development of physics and the mathematics set one think about relation between complex numbers and reality around us. If number to spot as the relation of two quantities, from the fact of existence of complex numbers and accepted definition of number it is necessary necessity complex value to assign to all physical quantities. The basic property of quantity to be it is more or less, therefore field of complex quantities, if it exists, it is necessary is ranked. The hypothesis was proposed that lexicographic ordering may be applied to the complex physical quantities. A set of the ranked complex numbers is quite natural to arrange on a straight line that represents in this case a non-Archimedean complex numerical axis. All physical quantities are located on the relevant non-Archimedean complex numerical axes, forming a new reality - "complex-valued" world. Thus, we get the conclusion that the resulting non-Archimedean complex numerical axis may serve as an example of the ideal mathematical object - hyperreal numerical axis. So, differentiation and integration on the non-Archimedean complex numerical axis can be realized using methods of nonstandard analysis. Certain properties of a new "complex-valued" reality, its connection with our "real" world and possibility of experimental detection of complex physical quantities are discussed.
8 Generalized Carmichael Numbers ON GENERALIZED CARMICHAEL NUMBERS
Halbeisen, Lorenz
exist which are squares. 1 Introduction: Historical Background On October 18th, 1640, Pierre de Fermat wrote in a letter to Bernard Frenicle de Bessy that if p is a prime number, then p divides ap,1 , 1 for all integers a not divisible by p, a result now known as Fermat's Little Theorem". An equivalent
Number Meaning and Number Grammar in English and Spanish
ERIC Educational Resources Information Center
Bock, Kathryn; Carreiras, Manuel; Meseguer, Enrique
Grammatical agreement makes different demands on speakers of different languages. Being widespread in the languages of the world, the features of agreement systems offer valuable tests of how language affects deep-seated domains of human cognition and categorization. Number agreement is one such domain, with intriguing evidence that typological…
Negative Numbers and Antimatter Particles
NASA Astrophysics Data System (ADS)
Tsan, Ung Chan
Dirac's equation states that an electron implies the existence of an antielectron with the same mass (more generally same arithmetic properties) and opposite charge (more generally opposite algebraic properties). Subsequent observation of antielectron validated this concept. This statement can be extended to all matter particles; observation of antiproton, antineutron, antideuton … is in complete agreement with this view. Recently antihypertriton was observed and 38 atoms of antihydrogen were trapped. This opens the path for use in precise testing of nature's fundamental symmetries. The symmetric properties of a matter particle and its mirror antimatter particle seem to be well established. Interactions operate on matter particles and antimatter particles as well. Conservation of matter parallels addition operating on positive and negative numbers. Without antimatter particles, interactions of the Standard Model (electromagnetism, strong interaction and weak interaction) cannot have the structure of group. Antimatter particles are characterized by negative baryonic number A or/and negative leptonic number L. Materialization and annihilation obey conservation of A and L (associated to all known interactions), explaining why from pure energy (A = 0, L = 0) one can only obtain a pair of matter particle antimatter particle — electron antielectron, proton and antiproton — via materialization where the mass of a pair of particle antiparticle gives back to pure energy with annihilation. These two mechanisms cannot change the difference in the number of matter particles and antimatter particles. Thus from pure energy only a perfectly symmetric (in number) universe could be generated as proposed by Dirac but observation showed that our universe is not symmetric, it is a matter universe which is nevertheless neutral. Fall of reflection symmetries shattered the prejudice that there is no way to define in an absolute way right and left or matter and antimatter. Experimental observation of CP violation aroused a great hope for explaining why our universe is not exactly matter antimatter symmetric. Sakharov stated that without the violation of baryonic number, it is not possible to obtain from pure energy a universe made of only matter. The fact that our universe is asymmetric (in number) but perfectly neutral, points toward the existence of a hypothetic interaction violating A and L but conserving all charges. This Matter Creation (MC) interaction creating either a pair of matter particles or antimatter particles (instead of a pair of particle antiparticle) would have a charge BAL = (A-L) and a neutral messenger Z*. Even if CP is conserved, MC would allow the creation of a number of matter particles not exactly equal to the number of antimatter particles. Our universe would then correspond to the remaining excess when all matter antimatter pairs have disappeared. Observation of matter nonconservation processes would be of great interest to falsify this speculation. In a plan with A and L as axes, pure energy is represented by the origin (A = 0, L = 0). A symmetric universe is also represented by (A = 0, L = 0) meaning that there are exactly the same number of baryons and antibaryons, and the same number of leptons and antileptons. Our present matter universe is instead represented by a point of the diagonal with A = L = present A value. This value is tiny relative to the number of gammas resulting from the annihilation of matter-antimatter particles.
Experimental Determination of Ramsey Numbers
NASA Astrophysics Data System (ADS)
Bian, Zhengbing; Chudak, Fabian; Macready, William G.; Clark, Lane; Gaitan, Frank
Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to their explosive rate of growth. Recently, an algorithm that can be implemented using adiabatic quantum evolution has been proposed that calculates the two-color Ramsey numbers R(m,n). Here we present results of an experimental implementation of this algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(m,2) for 4?m?8. The R(8,2) computation used 84 qubits of which 28 were computational qubits. This computation is the largest experimental implementation of a scientifically meaningful adiabatic evolution algorithm that has been done to date.
Learning math: Number and operations
NSDL National Science Digital Library
Carol R. Findell
This online workshop for elementary and middle school teachers covers the real number system, place value, the behavior of zero and infinity, the meanings and models of basic operations, percentages, and modeling operations with fractions, often with the aid of concrete, physical models that enhance understanding. It also examines basic number theory topics, such as factors and multiples, as well as divisibility tests. Each of its ten sessions contains video programming, problem-solving activities provided online and in a print guide, and interactive activities and demonstrations on the Web.
Count the Dots: Binary Numbers
NSDL National Science Digital Library
National Center for Women and Information Technology
Data in computers is stored and transmitted as a series of zeros and ones. Learners explore how to represent numbers using just these two symbols, through a binary system of cards. When the card's dots are showing, its value is 1 and the dots are counted. When the card's dots are not showing, its value is 0 and the dots are not counted. Learners model binary counting to discover patterns and represent numbers. This activity includes three worksheet activities (1 introductory and 2 extensions) for learners to complete and background information for the instructor.
Euler's number, a first introduction
NSDL National Science Digital Library
In the first video segment, we introduce Euler's number by considering the problem of interest compounded continuously. After we obtain the power-series representation for exp(x), we explore its properties, in the next four video segments, to convince ourselves that exp(x) is literally an exponential function, meaning a number, approximately 2.71828, taken to the power x. In the final two segments, we present the natural logarithm and demonstrate that it is the anti-derivative of 1/x.
13 January 1996 Beastly Numbers
California at Berkeley, University of
13 January 1996 Page 1 Beastly Numbers Prof. W. Kahan Departments of Mathematics, and of Elect. Eng. & Computer Science #1776 University of California Berkeley CA 94720Â1776 Abstract: It seems unlikely that two computers, designed by different people 1800 miles apart, would be upset in the same way by the same two
13 January 1996 Beastly Numbers
California at Berkeley, University of
13 January 1996 Page 1 Beastly Numbers Prof. W. Kahan Departments of Mathematics, and of Elect. Eng. & Computer Science #1776 University of California Berkeley CA 94720-1776 Abstract: It seems unlikely that two computers, designed by different people 1800 miles apart, would be upset in the same way by the same two
Herculano-Houzel, Suzana; Avelino-de-Souza, Kamilla; Neves, Kleber; Porfírio, Jairo; Messeder, Débora; Mattos Feijó, Larissa; Maldonado, José; Manger, Paul R.
What explains the superior cognitive abilities of the human brain compared to other, larger brains? Here we investigate the possibility that the human brain has a larger number of neurons than even larger brains by determining the cellular composition of the brain of the African elephant. We find that the African elephant brain, which is about three times larger than the human brain, contains 257 billion (109) neurons, three times more than the average human brain; however, 97.5% of the neurons in the elephant brain (251 billion) are found in the cerebellum. This makes the elephant an outlier in regard to the number of cerebellar neurons compared to other mammals, which might be related to sensorimotor specializations. In contrast, the elephant cerebral cortex, which has twice the mass of the human cerebral cortex, holds only 5.6 billion neurons, about one third of the number of neurons found in the human cerebral cortex. This finding supports the hypothesis that the larger absolute number of neurons in the human cerebral cortex (but not in the whole brain) is correlated with the superior cognitive abilities of humans compared to elephants and other large-brained mammals. PMID:24971054
ERIC Educational Resources Information Center
Materiales, 1997
These three journals of contemporary cultural, historical, and social interest contain activities designed to enhance the awareness of students of Spanish as a foreign language regarding the entire panorama of daily life in Spain. Number 21 focuses on the role of modern Spanish women; their career status; female authors; and the changing place of…
ALUMNI NEWSLETTER Number 10 (2007)
ALUMNI NEWSLETTER Number 10 (2007) Message from the Head Paul L. Smith Earth and Ocean Sciences Head Dear Alumni and Friends This has been a year of great achievement, increasing opportunity funding for student support and increased space to house more students. The space problem is particularly
EMERGENCY PHONE NUMBERS Medical Emergency
Chou, James
an emergency: Remain calm. Report all injuries first. Try to call from a desk phone, not a cell phone. Describe the type of emergency (fire, medical, utility disruption, public safety, etc). Give the phoneEMERGENCY PHONE NUMBERS Medical Emergency 911 Harvard University Police Department (617) 495
Number Crunching: A Sheep's Tale
ERIC Educational Resources Information Center
Sam, Chris Lam
In this article, the author talks about an allegorical tale which he has written as a message for teachers of mathematics. The story is about Gordon, who led a flock of small sheep. Gordon was a mathematics genius; however, his flock criticized his teaching of numbers and his boring lectures. His furry-god-farmer advised him to share his…
High Reynolds number research - 1980
NASA Technical Reports Server (NTRS)
Mckinney, L. W. (editor); Baals, D. D. (editor)
The fundamental aerodynamic questions for which high Reynolds number experimental capability is required were examined. Potential experiments which maximize the research returns from the use of the National Transonic Facility (NTF) were outlined. Calibration plans were reviewed and the following topics were discussed: fluid dynamics; high lit; configuration aerodynamics; aeroelasticity and unsteady aerodynamics; wind tunnel/flight correlation; space vehicles; and theoretical aerodynamics
SUBJECT: Effective Date: Policy Number
Glebov, Leon
of the policy and who are not members of the university community (i.e., faculty member, staff memberSUBJECT: Effective Date: 12-15-10 Policy Number: 3-103.1 Fishing on UCF Properties Supersedes: Page/ACCOUNTABILITY: This policy applies to anyone on University of Central Florida campuses. POLICY STATEMENT: The University
Residual number processing in dyscalculia?
Cappelletti, Marinella; Price, Cathy J.
Developmental dyscalculia – a congenital learning disability in understanding numerical concepts – is typically associated with parietal lobe abnormality. However, people with dyscalculia often retain some residual numerical abilities, reported in studies that otherwise focused on abnormalities in the dyscalculic brain. Here we took a different perspective by focusing on brain regions that support residual number processing in dyscalculia. All participants accurately performed semantic and categorical colour-decision tasks with numerical and non-numerical stimuli, with adults with dyscalculia performing slower than controls in the number semantic tasks only. Structural imaging showed less grey-matter volume in the right parietal cortex in people with dyscalculia relative to controls. Functional MRI showed that accurate number semantic judgements were maintained by parietal and inferior frontal activations that were common to adults with dyscalculia and controls, with higher activation for participants with dyscalculia than controls in the right superior frontal cortex and the left inferior frontal sulcus. Enhanced activation in these frontal areas was driven by people with dyscalculia who made faster rather than slower numerical decisions; however, activation could not be accounted for by response times per se, because it was greater for fast relative to slow dyscalculics but not greater for fast controls relative to slow dyscalculics. In conclusion, our results reveal two frontal brain regions that support efficient number processing in dyscalculia. PMID:24266008
Fibonacci numbers and trigonometric identities
N. Garnier; O. Ramare
Webb & Parberry proved in 1969 a startling trigonometric iden- tity involving Fibonacci numbers. This identity has remained isolated up to now, despite the amount of work on related polynomials. We provide a wide generalization of this identity together with what we believe (and hope!) to be its proper understanding.
Europe Note Europe note number
MĂĽller, Jens-Dominik
1 Europe Note Europe note number: E/2012/05 Date 23 April 2012 Distribution Vice HE International Unit European Activity Survey of UK HEIs - Wales Introduction 1. This E-note reports the survey was collected from November 2011 to December 2011 using an online survey tool. Separate E-notes
Europe Note Europe note number
MĂĽller, Jens-Dominik
Europe Note Europe note number: E/2012/04 Date 23 April 2012 Distribution Vice of the 2011 UK HE International Unit European Activity Survey of UK HEIs - Scotland Introduction 1. This E-note using an online survey tool. Separate E-notes have been developed with results for the UK as a whole
Europe Note Europe note number
MĂĽller, Jens-Dominik
1 Europe Note Europe note number: E/2012/02 Date 23 April 2012 Distribution Vice HE International Unit European Activity Survey of UK HEIs - UK Introduction 1. This E-note informs UK to December 2011 using an online survey tool. Separate E-notes have been developed with results for England
Europe Note Europe note number
MĂĽller, Jens-Dominik
1 Europe Note Europe note number: E/2012/03 Date 15 April 2012 Distribution Vice 1. This E-note reports on the outcomes for England and Northern Ireland of the UK HE International was collected from November 2011 to December 2011 using an online survey tool. Separate E-notes have been
Davies, Christopher
is z. 6 ? z Surface P Ignoring atmospheric pressure, the pressure, p, at P is measured as the thrust"JUST THE MATHS" UNIT NUMBER 13.16 INTEGRATION APPLICATIONS 16 (Centres of pressure) by A.J.Hobson 13.16.1 The pressure at a point in a liquid 13.16.2 The pressure on an immersed plate 13
Oxidation Numbers and Their Limitations.
ERIC Educational Resources Information Center
Woolf, A. A.
Reviews a method for determining oxidation numbers in covalent compounds and balancing mixed organic-inorganic or purely organic systems. Points out ambiguities presented when adjacent atoms have small or zero electronegativity differences. Presents other limitations that arise when using electronegativity values. (CW)
Gummy vs. Gum (Number Pattern)
NSDL National Science Digital Library
Beacon Learning Center
"In this lesson, students use gummy bears and sticks of gum to discover a number pattern and write an equation that describes it. This lesson should be conducted after students have worked with patterns and one- and two-step equations." from the Beacon Learning Center.
Mitosis and Meiosis Chromosome number
Dellaire, Graham
Lecture 5 Mitosis and Meiosis #12;Chromosome number Early improvements in our ability to look look at normal chromosomes as they go through mitosis and meiosis #12; Mitosis The biologic function until the daughter cell in its turn reaches the S phase of the new cell cycle #12; Meiosis Biological
The Mathematics of Identification Numbers.
ERIC Educational Resources Information Center
Gallian, Joseph A.
Discussed are the mathematical methods for detecting a variety of common error patterns within the bar-coded identification numbers utilized in conjunction with scanning devices. Schemes for the use of check digits are examined that ensure conditions for detecting errors of specific types, including single digit error, transposition error, twin…
Davies, Christopher
"JUST THE MATHS" UNIT NUMBER 2.2 SERIES 2 (Binomial series) by A.J.Hobson 2.2.1 Pascal's Triangle 2.2.1 PASCAL'S TRIANGLE Initially, we consider some simple illustrations obtainable from very elementary expansions follow the diagramatic pattern called PASCAL'S TRIANGLE: 1 1 1 2 1 1 3 3 1 1 4 6 4 1
ERIC Educational Resources Information Center
Surrena, Michelle
In order to inspire her students to work in mixed media, the author chose to highlight the art of Jasper Johns and Robert Indiana, both of whom used numbers and letters as a main focus in their art. In this article, the author describes a mixed-media printmaking project. (Contains 2 online resources.)
Topology of Numbers Allen Hatcher
Hatcher, Allen
of the connection with the Pythagorean Theorem. Our goal will be a formula that gives them all. The ancient GreeksTopology of Numbers Allen Hatcher Chapter 0. Preview Pythagorean Triples. Rational Points on Other Quadratic Curves. Rational Points on a Sphere. Pythagorean Triples and Quadratic Forms. Pythagorean Triples
The elephant brain in numbers.
Herculano-Houzel, Suzana; Avelino-de-Souza, Kamilla; Neves, Kleber; Porfírio, Jairo; Messeder, Débora; Mattos Feijó, Larissa; Maldonado, José; Manger, Paul R
What explains the superior cognitive abilities of the human brain compared to other, larger brains? Here we investigate the possibility that the human brain has a larger number of neurons than even larger brains by determining the cellular composition of the brain of the African elephant. We find that the African elephant brain, which is about three times larger than the human brain, contains 257 billion (10(9)) neurons, three times more than the average human brain; however, 97.5% of the neurons in the elephant brain (251 billion) are found in the cerebellum. This makes the elephant an outlier in regard to the number of cerebellar neurons compared to other mammals, which might be related to sensorimotor specializations. In contrast, the elephant cerebral cortex, which has twice the mass of the human cerebral cortex, holds only 5.6 billion neurons, about one third of the number of neurons found in the human cerebral cortex. This finding supports the hypothesis that the larger absolute number of neurons in the human cerebral cortex (but not in the whole brain) is correlated with the superior cognitive abilities of humans compared to elephants and other large-brained mammals. PMID:24971054
Arrighi, Roberto; Togoli, Irene; Burr, David C.
Much evidence has accumulated to suggest that many animals, including young human infants, possess an abstract sense of approximate quantity, a number sense. Most research has concentrated on apparent numerosity of spatial arrays of dots or other objects, but a truly abstract sense of number should be capable of encoding the numerosity of any set of discrete elements, however displayed and in whatever sensory modality. Here, we use the psychophysical technique of adaptation to study the sense of number for serially presented items. We show that numerosity of both auditory and visual sequences is greatly affected by prior adaptation to slow or rapid sequences of events. The adaptation to visual stimuli was spatially selective (in external, not retinal coordinates), pointing to a sensory rather than cognitive process. However, adaptation generalized across modalities, from auditory to visual and vice versa. Adaptation also generalized across formats: adapting to sequential streams of flashes affected the perceived numerosity of spatial arrays. All these results point to a perceptual system that transcends vision and audition to encode an abstract sense of number in space and in time. PMID:25377454
International Standard Serial Number (ISSN)
International Standard Serial Number (ISSN) Presented by: Marcia Salmon Graduate Journal world-wide #12;ISSN Portal The ISSN register may be accessed through the ISSN Portal (http://portal://www.collectionscanada.gc.ca/isn/ 041011-2000-e.html ISSN Portal http://portal.issn.org #12;
ERIC Educational Resources Information Center
Materiales, 1995
Four booklets present articles on Spanish language and culture aimed at teachers of Spanish in the United States for student use in their classes. Number 17, "Los Jovenes Espanoles" (Spanish Youth), includes articles on Spanish youth sports, music, gangs, thoughts, and t-shirt slogans: (1) "Young Spanish Athletes"; (2) "Youth Music"; (3) "Urban…
Solar System Number-Crunching.
ERIC Educational Resources Information Center
Albrecht, Bob; Firedrake, George
Defines terrestrial and Jovian planets and provides directions to obtain planetary data from the National Space Science Data Center Web sites. Provides "number-crunching" activities for the terrestrial planets using Texas Instruments TI-83 graphing calculators: computing volumetric mean radius and volume, density, ellipticity, speed, surface…
ERIC Educational Resources Information Center
Barker, Lindsay
How this teacher develops composition of ten with second graders was dramatically reshaped by the 2006 release of NCTM's "Curriculum Focal Points." The release of "Curriculum Focal Points"--particularly the suggestion that number sense and computation be focal areas in the second-grade mathematics curriculum--resulted in positive changes in this…
Note on the Theory of Perfect Numbers
N. A. Carella
A perfect number is a number whose divisors add up to twice the number itself. The existence of odd perfect numbers is a millennia-old unsolved problem. This note proposes a proof of the nonexistence of odd perfect numbers. More generally, the same analysis seems to generalize to a proof of the nonexistence of odd multiperfect numbers.
Student Learning Centre Review of Number
directions, { ... , -4 , -3 , -2 , -1 , 0 , 1, 2 , 3 , 4 , 5, ...} is the set of integers. Rational numbers are all the numbers on the real number line that are not rational, e.g. 2, -10, ,5 /2 Every real number) integers (d) negative real numbers (e) rational (f) irrational (g) prime (h) composite 2. Use a number line
Real numbers. Constants, variables, and mathematical modeling.
Alekseenko, Alexander
with their multiplicative inverses we get Rational numbers, or numbers of the form m n , where m and n are integer numbers. It can be verified that all addition and multiplication properties make sense for the rational numbers and multiplicative inverses to m n ? The Irrational numbers is the next stage after the Rational numbers
Wisconsin at Madison, University of
Identification Number Needed Post Doctoral Fellow Employee-in-Training X10NN Post Doctoral Trainee Employee-in-Training X30NN Graduate Intern/Trainee Employee-in-Training X75NN Fellow Student Assistant Y21NN Scholar Academic Staff Limited Various Research Associate Employee-in-Training X01NN J-1Student, J-1 Non-Student, F
Remarks On General Fibonacci Numbers
Masum Billal
We dedicate this paper to investigate the most generalized form of Fibonacci Sequence, one of the most studied sections of the mathematical literature. One can notice that, we have discussed even a more general form of the conventional one. Although it seems the topic in the first section has already been covered before, but we present a different proof here. Later I found out that, the auxiliary theorem used in the first section was proven and even generalized further by F. T. Howard. Thanks to Curtis Cooper for pointing out the fact that this has already been studied and providing me with references. the At first, we prove that, only the common general Fibonacci Sequence can be a divisible sequence under some restrictions. In the latter part, we find some properties of the sequence, prove that there are infinite alternating bisquable Fibonacci sequence(defined later) and provide a lower bound on the number of divisors of Fibonacci numbers.
NASA Astrophysics Data System (ADS)
Nakayama, Kazunori; Takahashi, Fuminobu; Yanagida, Tsutomu T.
We propose that the stability of dark matter is ensured by a discrete subgroup of the U(1)B-L gauge symmetry, Z(B-L). We introduce a set of chiral fermions charged under the U(1)B-L in addition to the right-handed neutrinos, and require the anomaly-cancellation conditions associated with the U(1)B-L gauge symmetry. We find that the possible number of fermions and their charges are tightly constrained, and that non-trivial solutions appear when at least five additional chiral fermions are introduced. The Fermat theorem in the number theory plays an important role in this argument. Focusing on one of the solutions, we show that there is indeed a good candidate for dark matter, whose stability is guaranteed by Z(B-L).
Cosmic Rays and Sunspot Numbers
NSDL National Science Digital Library
Susan Higley
In this activity students analyze and compare two or more graphs to determine if there is a correlation between sunspot number and the variation of cosmic ray flux. They discover that cosmic rays are very energetic particles, mostly protons and electrons, that enter the solar system from the depths of interstellar space and that although the Earth's magnetic field partially shields us from these particles, so too does the much more extended solar wind with its own magnetic field. This is a three-part lesson in which students will construct line graphs displaying the cosmic ray flux and sunspot numbers for a period of time, and then determine if there is a correlation. In order to compare these two sets of data, students will need to scale the data in order to visualize the results. Teacher and student notes for the graphing calculator are included.
Women in Politics: Beyond Numbers
NSDL National Science Digital Library
Developed by the International Institute for Democracy and Electoral Assistance (IDEA), Women in Politics: Beyond Numbers is an initiative devoted to researching, evaluating, and promoting the role and impact of women in the advancement of sustainable democracy and electoral processes worldwide. This Website functions as an international resource providing information about IDEA's research projects and publications related to women's political involvement. The site features an extensive report, "Women in Parliament: Beyond Numbers," that examines such issues as obstacles to women's political participation and the impact of women in international politics, as well as compares the involvement of women within various electoral systems. The site also includes links to relevant resources and maintains several interactive forums for discussing IDEA's projects to enhance women's political participation.
Algorithms in algebraic number theory
Hendrik W. Lenstra Jr.
In this paper we discuss the basic problems of algorithmic algebraic number\\u000atheory. The emphasis is on aspects that are of interest from a purely\\u000amathematical point of view, and practical issues are largely disregarded. We\\u000adescribe what has been done and, more importantly, what remains to be done in\\u000athe area. We hope to show that the study of
Ultrafilters and combinatorial number theory
Neil Hindman; Los Amgeles
Our concern is with two areas of mathematics and a, possibly surprising, intimate connection between them. One is the branch\\u000a of combinatorial number theory which deals with the ability, given a finite partition of ?, to find sums or products of certain\\u000a descriptions lying in one cell of that partition. The other is the branch of set theoretic topology dealing
Signed domination numbers of graphs
Jaeun Lee; Xin-zhong Lu
Let G be a flnite connected simple graph with vertex set V (G) and edge set E(G). A function f : V (G) ! fˇ1;1g is a signed dominating function if for every vertex v 2 V (G), the closed neighborhood of v contains more vertices with function values 1 than with ˇ1. The signed domination number ?s(G) of G
Fibonacci numbers and orthogonal polynomials
Christian Berg
We prove that the sequence $(1\\/F_{n+2})_{n\\\\ge 0}$ of reciprocals of the Fibonacci numbers is a moment sequence of a certain discrete probability, and we identify the orthogonal polynomials as little $q$-Jacobi polynomials with $q=(1-\\\\sqrt{5})\\/(1+\\\\sqrt{5})$. We prove that the corresponding kernel polynomials have integer coefficients, and from this we deduce that the inverse of the corresponding Hankel matrices $(1\\/F_{i+j+2})$ have integer
Diophantine approximations with Fibonacci numbers
Zhuravleva, Victoria
Let $F_{n}$ be the $n$-th Fibonacci number. Put $\\varphi=\\frac{1+\\sqrt5}{2}$. We prove that the following inequalities hold for any real $\\alpha$: 1) $\\inf_{n \\in \\mathbb N} ||F_n\\alpha||\\le\\frac{\\varphi-1}{\\varphi+2}$, 2) $\\liminf_{n\\to \\infty}||F_n\\alpha||\\le 1/5$, 3) $\\liminf_{n \\to \\infty}||\\varphi^n \\alpha||\\le 1/5$. These results are the best possible.
Large Number Discrimination by Mosquitofish
Agrillo, Christian; Piffer, Laura; Bisazza, Angelo
Background Recent studies have demonstrated that fish display rudimentary numerical abilities similar to those observed in mammals and birds. The mechanisms underlying the discrimination of small quantities (<4) were recently investigated while, to date, no study has examined the discrimination of large numerosities in fish. Methodology/Principal Findings Subjects were trained to discriminate between two sets of small geometric figures using social reinforcement. In the first experiment mosquitofish were required to discriminate 4 from 8 objects with or without experimental control of the continuous variables that co-vary with number (area, space, density, total luminance). Results showed that fish can use the sole numerical information to compare quantities but that they preferentially use cumulative surface area as a proxy of the number when this information is available. A second experiment investigated the influence of the total number of elements to discriminate large quantities. Fish proved to be able to discriminate up to 100 vs. 200 objects, without showing any significant decrease in accuracy compared with the 4 vs. 8 discrimination. The third experiment investigated the influence of the ratio between the numerosities. Performance was found to decrease when decreasing the numerical distance. Fish were able to discriminate numbers when ratios were 1?2 or 2?3 but not when the ratio was 3?4. The performance of a sample of undergraduate students, tested non-verbally using the same sets of stimuli, largely overlapped that of fish. Conclusions/Significance Fish are able to use pure numerical information when discriminating between quantities larger than 4 units. As observed in human and non-human primates, the numerical system of fish appears to have virtually no upper limit while the numerical ratio has a clear effect on performance. These similarities further reinforce the view of a common origin of non-verbal numerical systems in all vertebrates. PMID:21203508
W. B. Langdon
Limited numerical precision of nVidia GeForce 8800 GTX and other GPUs requires careful implementation of PRNGs. The Park-Miller PRNG is programmed using G80's native Value4f floating point in RapidMind C++. Speed up is more than 40. Code is available via ftp ftp:\\/\\/cs.ucl.ac.uk\\/genetic\\/gp-code\\/random-numbers\\/gpu park-miller.tar.gz
Properties of proper rational numbers
Konstantine Zelator
This short article is aimed at educators and teachers of mathematics.Its goal is simple and direct:to explore some of the basic/elementary properties of proper rational numbers.A proper rational number is a rational which is not an integer. A proper rational r can be written in standard form: r=c/b,where c and b are relatively prime integers; and with b greater than or equal to 2. There are seven theorems, one proposition, and one lemma; Lemma1, in this paper. Lemma1 is a very well known result, commonly known as Euclid's lemma.It is used repeatedly throughout this paper, and its proof can be found in reference[1]. Theorem4(i) gives precise conditions for the sum of two proper rationals to be an integer.Theorem5(a) gives exact conditions for the product to be an integer. Theorem7 states that there exist no two proper rationals both of whose sum and product are integers.This follows from Theorem6 which states that if two rational numbers have a sum being an integer; and a product being an integer;then these two rationals must both be in fact integers.
Recalibration of Zurich Sunspot Number
NASA Astrophysics Data System (ADS)
Svalgaard, Leif; Bertello, L.
Three independent datasets support the finding that a discontinuous change of 20% was introduced in the Zurich Sunspot Number, Rz, when Max Waldmeier took over the production of Rz in 1946. The range of the diurnal variation of the geomagnetic field (the East-component) is controlled by the EUV-induced conductivity of the day-side ionosphere and indicates a 23% increase of Rz from 1946 on. The Greenwich Sunspot Areas (and the Group Sunspot Number derived from the Greenwich data since 1874) indicate a 17.5% increase of Rz. A CaII K-line index derived from recently digitized Mount Wilson Observatory spectroheliograms (since 1915) indicates a 21% increase in Rz. Friedli [2005] notes that "The new observer-team in Zurich was thus relatively inexperienced and Waldmeier himself feared that his scale factor could vary". We suggest that his fear was not unfounded and that the Zurich Sunspot Number be increased by 20% before 1946 to match the modern record.
Hydromagnetic Flow Past an Exponentially Accelerated Isothermal Vertical Plate with Uniform Mass Diffusion in the Presence of Chemical Reaction of first Order
NASA Astrophysics Data System (ADS)
Muthucumaraswamy, R.; Valliammal, V.
An exact solution of an unsteady flow past an exponentially accelerated infinite isothermal vertical plate with uniform mass diffusion in the presence of a transverse magnetic field has been studied. The plate temperature is raised to Tw and the species concentration level near the plate is also made to rise C?w . The dimensionless governing equations are solved using the Laplace-transform technique. The velocity, temperature and concentration profiles are studied for different physical parameters such as the magnetic field parameter, chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number, time and a. It is observed that the velocity decreases with increasing the magnetic field parameter.
Complex Numbers A complex number is a number of the form a + bi, where a and b are real numbers and i =
Ikenaga, Bruce
3-30-2008 Complex Numbers A complex number is a number of the form a + bi, where a and b are real numbers and i = -1 (so i2 = -1). For example, here are some complex numbers: 2 + 3i, -77.5i, 13 7, -54, 1 + i 2 . Notice that real numbers are special kinds of complex numbers -- namely, those that don
A Pseudo-Random Number Generator Based on Normal Numbers
Bailey, David H.
In a recent paper, Richard Crandall and the present author established that each of a certain class of explicitly given real constants, uncountably infinite in number, is b-normal, for an integer that appears in the formula defining the constant. A b-normal constant is one where every string of m digits appears in the base-b expansion of the constant with limiting frequency b{sup -m}. This paper shows how this result can be used to fashion an efficient and effective pseudo-random number generator, which generates successive strings of binary digits from one of the constants in this class. The resulting generator, which tests slightly faster than a conventional linear congruential generator, avoids difficulties with large power-of-two data access strides that may occur when using conventional generators. It is also well suited for parallel processing--each processor can quickly and independently compute its starting value, with the collective sequence generated by all processors being the same as that generated by a single processor.
NASA Astrophysics Data System (ADS)
Blanco-Pillado, Jose J.; Olum, Ken D.; Shlaer, Benjamin
Using recent simulation results, we provide the mass and speed spectrum of cosmic string loops. This is the quantity of primary interest for many phenomenological signatures of cosmic strings, and it can be accurately predicted using recently acquired detailed knowledge of the loop production function. We emphasize that gravitational smoothing of long strings plays a negligible role in determining the total number of existing loops. We derive a bound on the string tension imposed by recent constraints on the stochastic gravitational wave background from pulsar timing arrays, finding G? ?2.8×10-9. We also provide a derivation of the Boltzmann equation for cosmic string loops in the language of differential forms.
8.NS Identifying Rational Numbers
NSDL National Science Digital Library
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Decide whether each of the following numbers is rational or irrational. If it is rational, explain how you know. $0.33\\overline{3}$ $\\sqrt{4}$ $\\sqrt{2...
Numbers in English and Chinese language use
ZHANG Wu-ping
The cultural connotations of numbers in English and Chinese languages are demonstrated to discuss the grammatical functions of the numbers and their rhetoric usages. For a foreign language learner, it is essential that they know not only the denotation of the numbers, but also the connotation of the numbers. Numbers frequently play an important role in daily communication.
Numbers, Counting, and Infinity in Middle Schools.
ERIC Educational Resources Information Center
Meconi, L. J.
Discusses the use of middle-school students' natural understanding of large numbers to introduce the concept of infinity. Presents activities that investigate infinite sets by demonstrating a one-to-one correspondence between the counting numbers and the given set. Examples include prime numbers, Fibonacci numbers, fractions, even and odd numbers,…
Expansion of algebraic numbers Complexity of words
Waldschmidt, Michel
Expansion of algebraic numbers Complexity of words Words and transcendence Continued fractions Survey of some recent results on the complexity of expansions of algebraic numbers Michel Waldschmidt Expansion of algebraic numbers Complexity of words Words and transcendence Continued fractions Diophantine
Braess's Paradox, Fibonacci Numbers, and Exponential Inapproximability
Lin, Henry
Braess's Paradox, Fibonacci Numbers, and Exponential Inapproximability Henry Lin # , Tim of twocommodity networks, related to the Fibonacci numbers, in which both of these quantities grow commodity networks is arguably quite unexpected, given the negligible dependence on the number
The number of neutrino species
NASA Astrophysics Data System (ADS)
Denegri, D.; Sadoulet, B.; Spiro, M.
The authors review the methods used before the operation of the high energy Stanford and CERN e+e- colliders to determine the number of neutrino species N?, or an upper limit on this number, within the framework of the Standard Model of light stable neutrinos interacting according to the SU(2)×U(1) universal couplings. The astrophysical limit based on the neutrino burst from supernova 1987A is discussed first, followed by a discussion of the cosmological constraint based on the observed He/H abundance ratio. Finally, the particle physics methods based on single-photon production in e+e- collisions, on the production of monojets in ppŻ collisions, and on the determination of N? from the ratio of the W-->l?Ż to Z0-->llŻ partial cross sections in ppŻ collisions are discussed. The various sources of uncertainty and the experimental backgrounds are presented, as well as an idea of what may be expected on this subject in the future. There is a remarkable agreement between the various methods, with central values for N? between 2 and 3 and with upper limits N?<6. Combining all determinations, the authors obtain a central value N?=2.1+0.6-0.4 for mtop=50 GeV/c2 and N?=2.0+0.6-0.4 if mtop>=mW. The results are perfectly compatible with the a priori knowledge that at least three families of neutrinos should exist. The observed consistency between this a priori knowledge, the laboratory determinations of N?, and determinations from SN 1987A and cosmology represent an astounding success for the Standard Model and for the current descriptions of stellar collapse and the Big-Bang primordial nucleosynthesis. These results, however, severely limit the number of additional families. Although the consistency is significantly worse, four families still provide a reasonable fit. In the framework of the Standard Model, a fifth light neutrino is, however, unlikely. A noted added in proof summarizes the results recently obtained at the Fermilab pŻp and the Stanford and CERN e+e- colliders which confirm these conclusions.
Agrillo, Christian; Dadda, Marco; Serena, Giovanna; Bisazza, Angelo
Background Research on human infants, mammals, birds and fish has demonstrated that rudimentary numerical abilities pre-date the evolution of human language. Yet there is controversy as to whether animals represent numbers mentally or rather base their judgments on non-numerical perceptual variables that co-vary with numerosity. To date, mental representation of number has been convincingly documented only for a few mammals. Methodology/Principal Findings Here we used a training procedure to investigate whether mosquitofish could learn to discriminate between two and three objects even when denied access to non-numerical information. In the first experiment, fish were trained to discriminate between two sets of geometric figures. These varied in shape, size, brightness and distance, but no control for non-numerical variables was made. Subjects were then re-tested while controlling for one non-numerical variable at a time. Total luminance of the stimuli and the sum of perimeter of figures appeared irrelevant, but performance dropped to chance level when stimuli were matched for the cumulative surface area or for the overall space occupied by the arrays, indicating that these latter cues had been spontaneously used by the fish during the learning process. In a second experiment, where the task consisted of discriminating 2 vs 3 elements with all non-numerical variables simultaneously controlled for, all subjects proved able to learn the discrimination, and interestingly they did not make more errors than the fish in Experiment 1 that could access non-numerical information in order to accomplish the task. Conclusions/Significance Mosquitofish can learn to discriminate small quantities, even when non-numerical indicators of quantity are unavailable, hence providing the first evidence that fish, like primates, can use numbers. As in humans and non-human primates, genuine counting appears to be a 'last resort' strategy in fish, when no other perceptual mechanism may suggest the quantity of the elements. However, our data suggest that, at least in fish, the priority of perceptual over numerical information is not related to a greater cognitive load imposed by direct numerical computation. PMID:19274079
Eric Lauga
In many biological systems, microorganisms swim through complex polymeric fluids, and usually deform the medium at a rate faster than the inverse fluid relaxation time. We address the basic properties of such life at high Deborah number analytically by considering the small-amplitude swimming of a body in an arbitrary complex fluid. Using asymptotic analysis and differential geometry, we show that for a given swimming gait, the time-averaged leading-order swimming kinematics of the body can be expressed as an integral equation on the solution to a series of simpler Newtonian problems. We then use our results to demonstrate that Purcell's scallop theorem, which states that time-reversible body motion cannot be used for locomotion in a Newtonian fluid, breaks down in polymeric fluid environments.
Indexing the approximate number system.
Inglis, Matthew; Gilmore, Camilla
Much recent research attention has focused on understanding individual differences in the approximate number system, a cognitive system believed to underlie human mathematical competence. To date researchers have used four main indices of ANS acuity, and have typically assumed that they measure similar properties. Here we report a study which questions this assumption. We demonstrate that the numerical ratio effect has poor test-retest reliability and that it does not relate to either Weber fractions or accuracy on nonsymbolic comparison tasks. Furthermore, we show that Weber fractions follow a strongly skewed distribution and that they have lower test-retest reliability than a simple accuracy measure. We conclude by arguing that in the future researchers interested in indexing individual differences in ANS acuity should use accuracy figures, not Weber fractions or numerical ratio effects. PMID:24361686
Links to Information on Number Systems
NSDL National Science Digital Library
Math Forum
Site provides links to Web sites covering topics about different numbering systems. The site includes links to Arabic, Chinese, Mayan, Roman, Greek, Egyptian, and Babylonian numbering system resources.
Number line bounce (grades 6-8)
NSDL National Science Digital Library
Utah State University. National Library of Virtual Manipulatives for Interactive Mathematics
This online number line game for summing numbers challenges the student to find a sequence of operations with four numbers that results in a given target number. The numbers are illustrated as bouncing balls on a number line. Each bounce can be in either a positive or negative direction. The student can use a guess-and-check approach to solving the problem or a more sophisticated strategy. After finding a correct sequence and reaching the target number on the number line, the student forms the number sentence that illustrates the sequence of operations used to arrive at the target number. Instructions for using the manipulative, a description of this summing activity, and a link to the National Council of Teachers of Mathematics (NCTM) standard for number and operations are included. Copyright 2005 Eisenhower National Clearinghouse
Fun With Complex Numbers Algebra 5/Trig
Lega, Joceline
Fun With Complex Numbers Algebra 5/Trig Spring 2010 Instructions: There are none! This contains questions by these subsections. 1 Background Recall that the complex number system C is the set of all complex numbers in section 1.5 of your textbook. You should be accustomed to thinking of the real numbers
The Kolmogorov Complexity of Liouville Numbers \\Lambda
The Kolmogorov Complexity of Liouville Numbers \\Lambda Ludwig Staiger Institut für Informatik The complexity of real numbers 8 3.1 Random reals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 The Kolmogorov complexity of Liouville numbers . . . . . . . . 9 3.3 The Hausdorff dimension of Liouville numbers
Contextual Effects on Number-Time Interaction
ERIC Educational Resources Information Center
Lu, Aitao; Hodges, Bert; Zhang, Jijia; Zhang, John X.
Time perception has long been known to be affected by numerical representations. Recent studies further demonstrate that when participants estimate the duration of Arabic numbers, number magnitude, though task-irrelevant, biases duration judgment to produce underestimation for smaller numbers and overestimation for larger numbers. Such effects…
Fascinating Fibonaccis: Mystery and Magic in Numbers.
ERIC Educational Resources Information Center
Garland, Trudi Hammel
This document presents activities and information related to Fibonacci numbers, which are based upon the Golden Ratio, in areas of the arts, sciences, and mathematics. The work is organized into eight chapters: (1) "Origins and Definitions"; (2) "Fibonacci Numbers in Nature"; (3) "Fibonacci Numbers in Art and Architecture"; (4) "Fibonacci Numbers…
The Decimal Number System and Young Children
ERIC Educational Resources Information Center
Harrison, John
In this article, the author believes that a visual image of the number system is helpful to everyone, especially children, in understanding what is, after all, an abstract idea. The simplest model is the number line, a row of equally spaced numbers, starting at zero. This illustrates the continuous progression of the natural numbers, moving to the…
McClendon, David M.
which solves the equation 2x = 3. 1.3. Rational numbers. To fix this, we consider the rational numbers divisors, and q = 0. What is great about the rational numbers is that you get all the pros of the integers and you can also divide one rational number by another (as long as the divisor is not zero) and get
On the Betti Numbers of Chessboard Complexes
Joel Friedman; Phil Hanlony
In this paper we study the Betti numbers of a type of simplicial complex known as a chessboard complex. We obtain a formula for their Betti numbers as a sum of terms involving partitions. This formula allows us to determine which is the first nonvanishing Betti number (aside from the 0-th Betti number). We can therefore settle certain cases of
Logic Design Chapter 1: Binary Numbers
Wu, Xiaolin
with decimal numbers consisting of digits of 10 possible values, 0, 1, ..., 9 Decimal vs. Binary Numbers · Decimal number system As a digit has 10 possible values (human hands!), decimal numbers are said of four bits: nibble · A group of eight bits: byte Conversion between Decimal and Binary · Converting
McCabe, Cynthia
CONSTRUCTING ALGEBRAIC LINKS FOR LOW EDGE NUMBERS CYNTHIA L. MCCABE Dept. of firstname.lastname@example.com ABSTRACT A method is given for economically constructing any algebraic knot or link K. This construction: knot, link, edge number, stick number, algebraic link, arborescent link 1. Introduction The edge number
Copy number variations among silkworms
Background Copy number variations (CNVs), which are important source for genetic and phenotypic variation, have been shown to be associated with disease as well as important QTLs, especially in domesticated animals. However, little is known about the CNVs in silkworm. Results In this study, we have constructed the first CNVs map based on genome-wide analysis of CNVs in domesticated silkworm. Using next-generation sequencing as well as quantitative PCR (qPCR), we identified ~319 CNVs in total and almost half of them (~ 49%) were distributed on uncharacterized chromosome. The CNVs covered 10.8 Mb, which is about 2.3% of the entire silkworm genome. Furthermore, approximately 61% of CNVs directly overlapped with SDs in silkworm. The genes in CNVs are mainly related to reproduction, immunity, detoxification and signal recognition, which is consistent with the observations in mammals. Conclusions An initial CNVs map for silkworm has been described in this study. And this map provides new information for genetic variations in silkworm. Furthermore, the silkworm CNVs may play important roles in reproduction, immunity, detoxification and signal recognition. This study provided insight into the evolution of the silkworm genome and an invaluable resource for insect genomics research. PMID:24684762
Verification Challenges at Low Numbers
Benz, Jacob M.; Booker, Paul M.; McDonald, Benjamin S.
Many papers have dealt with the political difficulties and ramifications of deep nuclear arms reductions, and the issues of "Going to Zero". Political issues include extended deterrence, conventional weapons, ballistic missile defense, and regional and geo-political security issues. At each step on the road to low numbers, the verification required to ensure compliance of all parties will increase significantly. Looking post New START, the next step will likely include warhead limits in the neighborhood of 1000 . Further reductions will include stepping stones at1000 warheads, 100's of warheads, and then 10's of warheads before final elimination could be considered of the last few remaining warheads and weapons. This paper will focus on these three threshold reduction levels, 1000, 100's, 10's. For each, the issues and challenges will be discussed, potential solutions will be identified, and the verification technologies and chain of custody measures that address these solutions will be surveyed. It is important to note that many of the issues that need to be addressed have no current solution. In these cases, the paper will explore new or novel technologies that could be applied. These technologies will draw from the research and development that is ongoing throughout the national laboratory complex, and will look at technologies utilized in other areas of industry for their application to arms control verification.
Number systems, ?-splines and refinement
NASA Astrophysics Data System (ADS)
Zube, Severinas
This paper is concerned with the smooth refinable function on a plane relative with complex scaling factor . Characteristic functions of certain self-affine tiles related to a given scaling factor are the simplest examples of such refinable function. We study the smooth refinable functions obtained by a convolution power of such charactericstic functions. Dahlke, Dahmen, and Latour obtained some explicit estimates for the smoothness of the resulting convolution products. In the case ?=1+i, we prove better results. We introduce ?-splines in two variables which are the linear combination of shifted basic functions. We derive basic properties of ?-splines and proceed with a detailed presentation of refinement methods. We illustrate the application of ?-splines to subdivision with several examples. It turns out that ?-splines produce well-known subdivision algorithms which are based on box splines: Doo-Sabin, Catmull-Clark, Loop, Midedge and some -subdivision schemes with good continuity. The main geometric ingredient in the definition of ?-splines is the fundamental domain (a fractal set or a self-affine tile). The properties of the fractal obtained in number theory are important and necessary in order to determine two basic properties of ?-splines: partition of unity and the refinement equation.
On Liouville Numbers Yet Another Application of Functional Analysis to Number Theory
of Transcendental Numbers On Liouville Numbers p.4/42 #12;Transcendental Numbers Gottfried Leibniz Leonhard Euler "omnem rationem transcendunt" (Gottfried Leibniz, 1682 - ? - 1704) On Liouville Numbers p.5/42 #12
h-analogue of Fibonacci Numbers
H. B. Benaoum
In this paper, we introduce the h-analogue of Fibonacci numbers for non-commutative h-plane. For h h'= 1 and h = 0, these are just the usual Fibonacci numbers as it should be. We also derive a collection of identities for these numbers. Furthermore, h-Binet's formula for the h-Fibonacci numbers is found and the generating function that generates these numbers is obtained.
Generating functions, Fibonacci numbers and rational knots
A. Stoimenow
We describe rational knots with any of the possible combinations of the properties (a)chirality, (non-)positivity, (non-)fiberedness, and unknotting number one (or higher), and determine exactly their number for a given number of crossings in terms of their generating functions. We show in particular how Fibonacci numbers occur in the enumeration of fibered achiral and unknotting number one rational knots. Then
Prime number generation and factor elimination
Vineet Kumar
We have presented a multivariate polynomial function termed as factor elimination function,by which, we can generate prime numbers. This function's mapping behavior can explain the irregularities in the occurrence of prime numbers on the number line. Generally the different categories of prime numbers found till date, satisfy the form of this function. We present some absolute and probabilistic conditions for the primality of the number generated by this method. This function is capable of leading to highly efficient algorithms for generating prime numbers.
NASA Astrophysics Data System (ADS)
Elmasry, Amr; Jensen, Claus; Katajainen, Jyrki
We introduce a new number system that supports increments with a constant number of digit changes. We also give a simple method that extends any number system supporting increments to support decrements using the same number of digit changes. In the new number system the weight of the ith digit is 2 i - 1, and hence we can implement a priority queue as a forest of heap-ordered complete binary trees. The resulting data structure guarantees O(1) worst-case cost per insert and O(lg{n}) worst-case cost per delete, where n is the number of elements stored.
Towards the geometry of double Hurwitz numbers
Vakil, Ravi
. In this paper, we determine the structure of double Hurwitz numbers using tec* *h- niques from geometry that the points mapping to 0 and 1 are labelled. Thus the double Hurwitz numbers under this convention are j
Appendix 36 Number of KEFs by Biome
Appendix 36 Number of KEFs by Biome Table 1. The number of Key Ecological Functions performed by the biomes pertinent to Sub basin planning Select Key Ecological Functions Eastside (Interior) Grasslands
Number Theory in the High School Classroom.
ERIC Educational Resources Information Center
Dence, Thomas
Demonstrates some of the usefulness of number theory to students on the high school setting in four areas: Fibonacci numbers, Diophantine equations, continued fractions, and algorithms for computing pi. (ASK)
A determinant of generalized Fibonacci numbers
Krattenthaler, Christian
We evaluate a determinant of generalized Fibonacci numbers, thus providing a common generalization of several determinant evaluation results that have previously appeared in the literature, all of them extending Cassini's identity for Fibonacci numbers.
ChemTeacher Resource: Oxidation Number Exercise
NSDL National Science Digital Library
This is an exercise in determining the oxidation numbers in ions and compounds. Calculate the oxidation numbers of all the elements using the standard assignment rules, then mouse over the formula to reveal the answers.
Whence the complex numbers? Hans Halvorson
Halvorson, Hans
not fully understand why the complex numbers C play such a central role in our best theories of physical content with cataloging reasons why the real numbers R will not suffice. One of the reasons that R
On Ramachandra's Contributions to Transcendental Number Theory
Paris-Sud XI, Université de
On Ramachandra's Contributions to Transcendental Number Theory Michel WALDSCHMIDT Universit P. et M(C) for the complex topology? The other contributions of Ramachandra to transcendental number theory are dealt
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 2011 CFR
...with voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with berth...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2014 CFR
...ACCOMPLISHMENT OF VESSEL REPAIRS UNDER NATIONAL SHIPPING AUTHORITY MASTER LUMP SUM REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP Contract number shall be inserted in every job order and supplemental job...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2012 CFR
...ACCOMPLISHMENT OF VESSEL REPAIRS UNDER NATIONAL SHIPPING AUTHORITY MASTER LUMP SUM REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP Contract number shall be inserted in every job order and supplemental job...
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 2010 CFR
...with voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with berth...
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 2014 CFR
...with voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with berth...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2013 CFR
...ACCOMPLISHMENT OF VESSEL REPAIRS UNDER NATIONAL SHIPPING AUTHORITY MASTER LUMP SUM REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP Contract number shall be inserted in every job order and supplemental job...
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 2012 CFR
...with voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with berth...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2010 CFR
...ACCOMPLISHMENT OF VESSEL REPAIRS UNDER NATIONAL SHIPPING AUTHORITY MASTER LUMP SUM REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP Contract number shall be inserted in every job order and supplemental job...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2011 CFR
...ACCOMPLISHMENT OF VESSEL REPAIRS UNDER NATIONAL SHIPPING AUTHORITY MASTER LUMP SUM REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP Contract number shall be inserted in every job order and supplemental job...
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 2013 CFR
...with voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with berth...
Rockin' Round the Number Line: Lesson Two
NSDL National Science Digital Library
Andreas Howell
After completing the formative assessments for proficiency with place value, the concept of "half-way", and estimation using a real world context, students will complete the lesson which uses their prior knowledge to support them in drawing conclusions about number patterns used in estimation and rounding numbers. Students will identify which "ten" or "hundred" the whole number falls closest to based on whether the number falls before or after a "half-way" number. Finally students will conclude that there are number patterns that guide estimation when one does not have a specific context that determines a need. Specifically we can use "half-way" numbers that are multiples of 5 to guide whether we "round up" or "round down" when estimating stand alone numbers.
The Blocking Numbers of Convex Bodies
L. Dalla; David G. Larman; Peter Mani-levitska; Chuanming Zong
. Besides determining the exact blocking numbers of cubes and balls, a conditional lower bound for the blocking numbers of\\u000a convex bodies is achieved. In addition, several open problems are proposed.
Developing Young Children's Multidigit Number Sense.
ERIC Educational Resources Information Center
Diezmann, Carmel M.; English, Lyn D.
This article describes a series of enrichment experiences designed to develop young (ages 5 to 8) gifted children's understanding of large numbers, central to their investigation of space travel. It describes activities designed to teach reading of large numbers and exploring numbers to a thousand and then a million. (Contains ten references.) (DB)
Reading the World through Very Large Numbers
ERIC Educational Resources Information Center
Greer, Brian; Mukhopadhyay, Swapna
One original, and continuing, source of interest in large numbers is observation of the natural world, such as trying to count the stars on a clear night or contemplation of the number of grains of sand on the seashore. Indeed, a search of the internet quickly reveals many discussions of the relative numbers of stars and grains of sand. Big…
Number-Theoretic Functions via Convolution Rings.
ERIC Educational Resources Information Center
Berberian, S. K.
Demonstrates the number theory property that the number of divisors of an integer n times the number of positive integers k, less than or equal to and relatively prime to n, equals the sum of the divisors of n using theory developed about multiplicative functions, the units of a convolution ring, and the Mobius Function. (MDH)
Turing's normal numbers: towards randomness Veronica Becher
presumably in 1938 Alan Turing gave an algorithm that produces real numbers normal to every integer base- putable normal numbers, and this result should be attributed to Alan Turing. His manuscript entitled "ATuring's normal numbers: towards randomness Ver´onica Becher Universidad de Buenos Aires & CONICET
Oswin Aichholzer; Thomas Hackl; Birgit Vogtenhuber; Clemens Huemer; Ferran Hurtado; Hannes Krasser
We investigate the number of plane geometric, i.e., straight-line, graphs, a set S of n points in the plane admits. We show that the number of plane graphs and connected plane graphs as well as the number of cycle- free plane graphs is minimized when S is in convex position. Moreover, these results hold for all these graphs with an
Digraph girth via chromatic number Peter Keevash
Keevash, Peter
Digraph girth via chromatic number Peter Keevash Zhentao Li Bojan Mohar Bruce Reed § Abstract Let D be a digraph. The chromatic number (D) of D is the smallest number of colours needed to colour of a shortest directed cycle, or if D is acyclic. Let G(k, n) be the maximum possible girth of a digraph on n
Number Pieces, by the Math Learning Center
NSDL National Science Digital Library
This free iOS app uses virtual base-10 blocks to help students develop their understanding of place value and computation strategies with multi-digit numbers. Students use the number pieces to represent multi-digit numbers, regroup, add, subtract, multiply, and divide.
Insights into Our Understandings of Large Numbers
ERIC Educational Resources Information Center
Kastberg, Signe E.; Walker, Vicki
This article explores prospective teachers' understandings of one million to gain insights into the development of adult understanding of large numbers. Themes in the prospective teachers' work included number associated with a quantity of objects, number as an abstraction, and additive and multiplicative approaches. The authors suggest that the…
RNG: A Practitioner's Overview Random Number Generation
Mascagni, Michael
RNG: A Practitioner's Overview Random Number Generation A Practitioner's Overview Prof. Michael, DOE/ASCI, NATO, and NSF #12;RNG: A Practitioner's Overview Outline of the Talk Types of random numbers of quasirandom number generation Randomization and Derandomization Conclusions #12;RNG: A Practitioner's Overview
182 MATHEMATICS MAGAZINE The Fibonacci Numbers--
Benjamin, Arthur T.
182 MATHEMATICS MAGAZINE The Fibonacci Numbers-- Exposed More Discretely ARTHUR T. BENJAMIN Harvey generalize Fibonacci and Lucas numbers: Given nonnegative integers a and b, the generalized Fibonacci: The Art of Combinatorial Proof, published by the MAA. #12;VOL. 76, NO. 3, JUNE 2003 183 Fibonacci numbers
Resolving Number Ambiguities during Language Comprehension
ERIC Educational Resources Information Center
Bader, Markus; Haussler, Jana
This paper investigates how readers process number ambiguous noun phrases in subject position. A speeded-grammaticality judgment experiment and two self-paced reading experiments were conducted involving number ambiguous subjects in German verb-end clauses. Number preferences for individual nouns were estimated by means of two questionnaire…
The competition numbers of complete tripartite graphs
The competition numbers of complete tripartite graphs SUH-RYUNG KIM Department of Mathematics For a graph G, it is known to be a hard problem to compute the competition number k(G) of the graph G in general. In this paper, we give an explicit formula for the competition numbers of complete tripartite
Lozano-Robledo, Alvaro
THE CONGRUENT NUMBER PROBLEM KEITH CONRAD 1. Introduction A right triangle is called rational when its legs and hypotenuse are all rational numbers. Examples of rational right triangles include) rational numbers can occur as the area of a rational right triangle. For instance, no rational right
Vector Rational Number Reconstruction Curtis Bright
Storjohann, Arne
Vector Rational Number Reconstruction Curtis Bright firstname.lastname@example.com Arne Storjohann astorjoh and |ni| N for a given magnitude bound N. Applying elementwise rational number reconstruction requires. INTRODUCTION A rational number reconstruction of an integer a Z with respect to a positive modulus M Z>0
On Unit Sum Numbers of Rational Groups
Brendan Goldsmith; C. Meehan; S. L. Wallutis
The unit sum numbers of rational groups are investigated: the importance of the prime 2 being an automorphism of the rational group is discussed and other results are achieved by considering the number and distribution of rational primes which are, or are not, automorphisms of the group. Proof is given of the existence of rational groups with unit sum numbers
Lozano-Robledo, Alvaro
THE CONGRUENT NUMBER PROBLEM KEITH CONRAD 1. Introduction A right triangle is called rational when its legs and hypotenuse are all rational numbers. Examples of rational right triangles include) ratio- nal numbers can occur as the area of a rational right triangle. For instance, no rational right
Vector Rational Number Reconstruction Curtis Bright
Storjohann, Arne
Vector Rational Number Reconstruction By Curtis Bright A research paper presented to the University Bright 2009 #12;Vector Rational Number Reconstruction August 26, 2009 Abstract The final step of some algebraic algorithms is to reconstruct the common denominator d of a collection of rational numbers (ni/d)1
KIAS SEOUL, February 2004 Transcendental Number Theory
Waldschmidt, Michel
KIAS SEOUL, February 2004 Transcendental Number Theory: the State of the Art Michel Waldschmidt of transcendental numbers. http://www.math.jussieu.fr/miw/ 2 #12;Early History ( 1934) J. Liouville(1844) Â First examples of transcendental numbers. n1 10-n! is transcendental Idea of the proof. If is an algebraic
Calculating Mach Numbers Using Ratios and Fractions
NSDL National Science Digital Library
A mach number represents how many times the speed of sound a vehicle is traveling. NASA uses mach numbers to describe the speed of their planes. This video shows you how algebra can be used to determine the mach number of a NASA plane.
The Decimal Representation of Real Numbers
ERIC Educational Resources Information Center
Kalapodi, A.
The representation of natural numbers in decimal form is an unequivocal procedure while for the representation of real numbers some ambiguities concerning the existence of infinitely many digits equal to 9 still emerge. One of the most frequently confronted misunderstandings is whether 0.999...equals 1 or not, and if not what number does this…
Approximation of complex algebraic numbers by algebraic numbers of bounded degree
Evertse, Jan-Hendrik
Approximation of complex algebraic numbers by algebraic numbers of bounded degree YANN BUGEAUD (Strasbourg) & JAN-HENDRIK EVERTSE (Leiden) Abstract. To measure how well a given complex number can be ap numbers , but up to now not for complex, non-real algebraic numbers . In this paper we compute wn(), w n
Approximation of complex algebraic numbers by algebraic numbers of bounded degree
Evertse, Jan-Hendrik
Approximation of complex algebraic numbers by algebraic numbers of bounded degree YANN BUGEAUD (Strasbourg) & JANHENDRIK EVERTSE (Leiden) Abstract. To measure how well a given complex number # can be ap for real al gebraic numbers #, but up to now not for complex, nonreal algebraic numbers #. In this paper
International Students And Social Security Numbers International Students And Social Security Numbers
International Students And Social Security Numbers International Students And Social Security for your Social Security number. Some colleges and schools use Social Security numbers as stu- dent identification numbers. If you do not have a Social Security number, the college or school should be able to give
Children's Number Sequences: An Explanation of Steffe's Constructs and an Extrapolation to Rational Numbers of Arithmetic.
ERIC Educational Resources Information Center
Olive, John
Children's number sequence progress through several developmental changes that are brought about through adaptations in the children's counting activities. Introduces key psychological aspects of number sequences, pre-numerical counting schemes, an initial number sequence, a tacitly-nested number sequence, explicitly-nested number sequence, and…
48 CFR 52.204-6 - Data Universal Numbering System (DUNS) Number.
Code of Federal Regulations, 2011 CFR
...offeror may obtain a DUNS number— (i) Via the Internet...v) Company telephone number. (vi) Date the company was started. (vii) Number of employees at your location...and address (reporting relationship within your...
48 CFR 52.204-6 - Data Universal Numbering System (DUNS) Number.
Code of Federal Regulations, 2010 CFR
...offeror may obtain a DUNS number— (i) Via the Internet...v) Company telephone number. (vi) Date the company was started. (vii) Number of employees at your location...and address (reporting relationship within your...
On the binary expansions of algebraic numbers
Bailey, David H.; Borwein, Jonathan M.; Crandall, Richard E.; Pomerance, Carl
Employing concepts from additive number theory, together with results on binary evaluations and partial series, we establish bounds on the density of 1's in the binary expansions of real algebraic numbers. A central result is that if a real y has algebraic degree D > 1, then the number {number_sign}(|y|, N) of 1-bits in the expansion of |y| through bit position N satisfies {number_sign}(|y|, N) > CN{sup 1/D} for a positive number C (depending on y) and sufficiently large N. This in itself establishes the transcendency of a class of reals {summation}{sub n{ge}0} 1/2{sup f(n)} where the integer-valued function f grows sufficiently fast; say, faster than any fixed power of n. By these methods we re-establish the transcendency of the Kempner--Mahler number {summation}{sub n{ge}0}1/2{sup 2{sup n}}, yet we can also handle numbers with a substantially denser occurrence of 1's. Though the number z = {summation}{sub n{ge}0}1/2{sup n{sup 2}} has too high a 1's density for application of our central result, we are able to invoke some rather intricate number-theoretical analysis and extended computations to reveal aspects of the binary structure of z{sup 2}.
Relativistic theory of tidal Love numbers
Taylor Binnington; Eric Poisson
In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.
Fibonacci Numbers and the Golden Section
NSDL National Science Digital Library
Knott, Ron.
In 1202, the mathematician Fibonacci investigated the problem of how fast rabbits could breed under ideal circumstances. This problem and many more are detailed at the Fibonacci Numbers and the Golden Section Website, made available by Dr. Ron Knott of the University of Surrey (UK). A new addition to the site is a link to a reference page of over 100 formulas and equations demonstrating the properties of Fibonacci, Phi, and Lucus numbers series. The site's many links are categorized in the following sections: Fibonacci Numbers and Golden sections in Nature; The Intriguing Mathematical World of Fibonacci and Phi; The Puzzling World of Fibonacci Numbers; The Golden String; Fibonacci: the Man and His Times; and More Applications of Fibonacci Numbers and Phi. This site, through its extensive listings of links, contains a plethora of mathematical theories, equations, and proofs based on Fibonacci numbers.
High speed optical quantum random number generation.
Fürst, Martin; Weier, Henning; Nauerth, Sebastian; Marangon, Davide G; Kurtsiefer, Christian; Weinfurter, Harald
We present a fully integrated, ready-for-use quantum random number generator (QRNG) whose stochastic model is based on the randomness of detecting single photons in attenuated light. We show that often annoying deadtime effects associated with photomultiplier tubes (PMT) can be utilized to avoid postprocessing for bias or correlations. The random numbers directly delivered to a PC, generated at a rate of up to 50 Mbit/s, clearly pass all tests relevant for (physical) random number generators. PMID:20588431
HotBits: Genuine Random Numbers
NSDL National Science Digital Library
Walker, John
HotBits is a genuine random number generator powered by radioactive decay. Simply click the "Request HotBits" link, and specify how many bytes you would like (up to 2048) and in what form you prefer them. Hexadecimal returns numbers and letters, while C language returns integers. Then click the "Get HotBits" button, and your random numbers will appear on the screen.
Circulant Digraphs Integral over Number Fields
Li, Fei
A number field K is a finite extension of rational number field Q. A circulant digraph integral over K means that all its eigenvalues are algebraic integers of K. In this paper we give the sufficient and necessary condition for circulant digraphs which are integral over a number field K. And we solve the Conjecture3.3 in [XM] and find it is affirmative.
Paths and stability number in digraphs
Fox, Jacob
The Gallai-Milgram theorem says that the vertex set of any digraph with stability number k can be partitioned into k directed paths. In 1990, Hahn and Jackson conjectured that this theorem is best possible in the following strong sense. For each positive integer k, there is a digraph D with stability number k such that deleting the vertices of any k-1 directed paths in D leaves a digraph with stability number k. In this note, we prove this conjecture.
Using the Number Line to Compare
NSDL National Science Digital Library
In this lesson, students determine differences using the number line to compare lengths. Because this model is based on linear measurement, it is a distinctly different representation from the models presented in the previous two lessons. At the end of this lesson, children are encouraged to predict differences and answer puzzles involving subtraction. Students will: use the number line model to find differences by comparing lengths solve and create puzzles using the number line
Rockin' Round the Number Line: Lesson One
NSDL National Science Digital Library
Kimberly RobersonHoy
After completing the formative assessment for proficiency with place value, students will complete the lesson which uses their knowledge of place value to identify where a certain number falls on a number line. Student will then identify which "ten" or "hundred" the whole number falls closest to. Finally students will conclude that when given a real world problem the context of the problem or "need" demonstrated in the problem will help them to decide which "ten" or "hundred" to round to.
Demonstrations of the Enormity of Avogadro's Number.
ERIC Educational Resources Information Center
Diemente, Damon
Describes three calculations used to make students aware of the size of Avogadro's number: (1) the new size of a 6-inch diameter ball with volume increased by a factor of Avogadro's number; (2) the number of moles of sand grains in the Sahara Desert; and (3) the dimensions and length of a mole of hydrogen atoms shaped into a cube, a square, and a…
Grant Title: CHILDHOOD OBESITY PREVENTION Funding Opportunity Number: USDA-NIFA-AFRI-004156. CFDA Number(s): 10.310.
Farritor, Shane
Grant Title: CHILDHOOD OBESITY PREVENTION Funding Opportunity Number: USDA-NIFA-AFRI-004156. CFDA, including food environment, that influence childhood obesity and use this information to develop obesity among children, the number one nutrition-related problem in the US. Food is an integral part
7.NS Operations on the number line
NSDL National Science Digital Library
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: A number line is shown below. The numbers $0$ and $1$ are marked on the line, as are two other numbers $a$ and $b$. Which of the following numbers is n...
CRC octane-number-requirement survey, 1990
Not Available
An annual statistical survey of octane number requirements of current model vehicles is conducted by the Coordinating Research Council, Inc. Test data have been obtained by seventeen companies on 356 1990 vehicles including passenger cars and light-duty trucks and vans, of which 169 were equipped with knock sensors. Octane number requirements were determined by testing at maximum-throttle conditions, as well as at part-throttle, with three unleaded fuel series of varying sensitivities. Requirements are expressed as the (R+M)/2 octane number, Research octane number, and Motor octane number of the reference fuel producing knock which was recurrent and repeatable at the lowest audible level. Estimated octane number requirements for the total vehicles are weighted in proportion to the 1990 vehicle model production and/or sales figures. The octane number requirements of 1990 models with average sensitivity unleaded fuels were 85.4 (R+M)/2 octane numbers at the 50 percent satisfaction level, and 89.2 (R+M)/2 octane numbers at the 90 percent satisfaction level.
CRC octane number requirement survey for 1989
Not Available
An annual statistical survey of octane number requirements of current model vehicles is conducted by the Coordinating Research Council, Inc. Test data have been obtained by eighteen companies on 391 1989 vehicles including passenger cars and light-duty trucks and vans, of which 179 were equipped with knock sensors. Maximum octane number requirements were determined by testing at maximum-throttle conditions, as well as at part-throttle, with three unleaded fuel series of varying sensitivities. Requirements are expressed as the (R+M)/2 octane number, Research octane number, and Motor octane number of the reference fuel producing knock which was recurrent and repeatable at the lowest audible level. Estimated octane number requirements for the total vehicles are weighted in proportion to the 1989 vehicle model production and/or sales figures. The maximum octane number requirements of 1989 models with average sensitivity unleaded fuels were 85.1 (R+M)/2 octane numbers at the 50 percent satisfaction level, and 89.2 (R+M)/2 octane numbers at the 90 percent satisfaction level. Comparison with previous Surveys are made in this report.
CRC octane number requirement survey 1992
Not Available
An annual statistical survey of octane number requirements of current model vehicles is conducted by the Coordinating Research Council, Inc. Test data have been obtained by ten companies on 184 1992 vehicles including passenger cars and light-duty trucks and vans, of which 88 were equipped with knock sensors. Octane number requirements were determined by testing at maximum-throttle conditions, as well as at part-throttle, with four unleaded fuel series of varying sensitivities, one containing 15 percent methyl tertiary butyl ether. Requirements are expressed as the (R+M)/2 octane number, Research octane number, and Motor octane number of the reference fuel producing knock which was recurrent and repeatable at the lowest audible level. Estimated octane number requirements for the total vehicles are weighted in proportion to the 1992 vehicle model production and/or sales figures. The octane number requirements of 1992 models with average sensitivity unleaded fuels were 85.1 (R+M)/2 octane numbers at the 50 percent satisfaction level, and 92.0 (R+M)/2 octane numbers at the 90 percent satisfaction level. In order to make a more powerful test of statistical significance of the FBRUM fuel series, the 1991 ONRS was pooled with the 1992 ONRS and compared with the pooled data for the FBRU fuel series. There was no significant difference between the two fuel series up to about 90 percent satisfaction. Beyond 90 percent satisfaction, the variability in the data is high.
Complex Rational Numbers in Quantum Mechanics
Paul Benioff
A binary representation of complex rational numbers and their arithmetic is described that is not based on qubits. It takes account of the fact that $0s$ in a qubit string do not contribute to the value of a number. They serve only as place holders. The representation is based on the distribution of four types of systems, corresponding to $+1,-1,+i,-i,$ along an integer lattice. Complex rational numbers correspond to arbitrary products of four types of creation operators acting on the vacuum state. An occupation number representation is given for both bosons and fermions.
Using Call Numbers to Find Books 8/23/2012 Using Call Numbers to Find Books
Su, Xiao
Using Call Numbers to Find Books 8/23/2012 Using Call Numbers to Find Books 1. Using Call Numbers to Find Books 2. A call number is like a book's address. It tells you where the book is located of Congress Classification System and the Dewey Decimal System. 5. We'll start by looking for a book
GEOMETRY AND COMPLEX NUMBERS (February 4, 2004) 7 6. Basic proofs for complex numbers
Lee, Carl
GEOMETRY AND COMPLEX NUMBERS (February 4, 2004) 7 6. Basic proofs for complex numbers Problem 6;GEOMETRY AND COMPLEX NUMBERS (February 4, 2004) 9 Problem 6.3. Prove that tan(arg(z)) = Im(z)/Re(z). #12;10 JERZY DYDAK Problem 6.4. Prove that z · Żz = |z|2 . #12;GEOMETRY AND COMPLEX NUMBERS (February 4, 2004
On the domination number and the 2-packing number of Fibonacci cubes and Lucas cubes
Paris-Sud XI, Université de
On the domination number and the 2-packing number of Fibonacci cubes and Lucas cubes Aline Castro, respectively. The domination number of Fibonacci cubes and Lucas cubes is studied. In particular it is proved of these graphs in Section 2. In Section 3 we study the domination number of Fibonacci cubes as initiated in [12
Fibonacci Numbers. You may have heard about the Fibonacci sequence of numbers. It
Brand, Neal
Fibonacci Numbers. You may have heard about the Fibonacci sequence of numbers. It starts previous numbers. This gives an easy way to write out the Fibonacci sequence as far as you wish. Suppose with the numbers 1; 1; 2; 3; 5; 8; 13; 21; 34; 55; 89; \\Delta \\Delta \\Delta Even if you haven't seen them before
Predicting landfalling hurricane numbers from basin hurricane numbers: basic statistical analysis
Laepple, T; Penzer, J; Bellone, E; Nzerem, K; Laepple, Thomas; Jewson, Stephen; Penzer, Jeremy; Bellone, Enrica; Nzerem, Kechi
One possible method for predicting landfalling hurricane numbers is to first predict the number of hurricanes in the basin and then convert that prediction to a prediction of landfalling hurricane numbers using an estimated proportion. Should this work better than just predicting landfalling hurricane numbers directly? We perform a basic statistical analysis of this question in the context of a simple abstract model.
Name: U of M ID number: Social Security number: Date of birth
Amin, S. Massoud
Name: U of M ID number: Social Security number: Date of birth: Phone (home): Phone (other is private. Except for social security number, which is voluntary, all information requested on this form-Manitoba reciprocity fee status will be granted. Failure to provide your social security number will have no effect
Deriving the number of jobs in proximity services from the number of inhabitants in French rural
Paris-Sud XI, Université de
Deriving the number of jobs in proximity services from the number of inhabitants in French rural a minimum requirement approach to derive the number of jobs of proximity services per inhabitant observe that the minimum number of service jobs per inhabitant (interpreted as jobs of proximity services
Number Worlds: Visual and Experimental Access to Elementary Number Theory Concepts
ERIC Educational Resources Information Center
Sinclair, Nathalie; Zazkis, Rina; Liljedahl, Peter
Recent research demonstrates that many issues related to the structure of natural numbers and the relationship among numbers are not well grasped by students. In this article, we describe a computer-based learning environment called "Number Worlds" that was designed to support the exploration of elementary number theory concepts by making the…
Mental Number Line, Number Line Estimation, and Mathematical Achievement: Their Interrelations in Grades 5 and 6
ERIC Educational Resources Information Center
Schneider, Michael; Grabner, Roland H.; Paetsch, Jennifer
As indicated by the distance effect and the spatial-numerical association of response codes (SNARC) effect, natural numbers are mentally represented on a number line. Purportedly, this number line underlies children's number sense, which supports the acquisition of more advanced mathematical competencies. In 3 studies with a total of 429 fifth and…
Natural convection in unsteady Couette motion
A. K. Singh
Unsteady free convective flow of an incompressible viscous fluid between two vertical parallel plates is considered for impulsive start of one of the plates. Expressions for velocity and temperature fields and their related quantities are obtained by the Laplace transform technique. The effect of Grashof number is to increase the velocity of both air and water and to decrease the
Estimation of convective mass transfer in solar distillation systems
Sanjay Kumar; G. N. Tiwari
In this article a thermal model has been developed to determine the convective mass transfer for different Grashof Number range in solar distillatiOn process. The model is based on simple regression analysis. Based on the experimental data obtained from the rigorous outdoor experimentation on passive and active distillation systems for summer climatic conditions, the values of C and n have
Long-Wave Instability of Advective Flows in Inclined Layer with Solid Heat Conductive Boundaries
R. V. Sagitov; A. N. Sharifulin
We investigate the stability of the steady convective flow in a plane tilted layer with ideal thermal conductivity of solid boundaries in the presence of uniform longitudinal temperature gradient. Analytically found the stability boundary with respect to the long-wave perturbations, find the critical Grashof number for the most dangerous among them of even spiral perturbation.
Effects of pitch on auditory number comparisons.
Campbell, Jamie I D; Scheepers, Florence
Three experiments investigated interactions between auditory pitch and the numerical quantities represented by spoken English number words. In Experiment 1, participants heard a pair of sequential auditory numbers in the range zero to ten. They pressed a left-side or right-side key to indicate if the second number was lower or higher in numerical value. The vocal pitches of the two numbers either ascended or descended so that pitch change was congruent or incongruent with number change. The error rate was higher when pitch and number were incongruent relative to congruent trials. The distance effect on RT (i.e., slower responses for numerically near than far number pairs) occurred with pitch ascending but not descending. In Experiment 2, to determine if these effects depended on the left/right spatial mapping of responses, participants responded "yes" if the second number was higher and "no" if it was lower. Again, participants made more number comparison errors when number and pitch were incongruent, but there was no distance × pitch order effect. To pursue the latter, in Experiment 3, participants were tested with response buttons assigned left-smaller and right-larger ("normal" spatial mapping) or the reverse mapping. Participants who received normal mapping first presented a distance effect with pitch ascending but not descending as in Experiment 1, whereas participants who received reverse mapping first presented a distance effect with pitch descending but not ascending. We propose that the number and pitch dimensions of stimuli both activated spatial representations and that strategy shifts from quantity comparison to order processing were induced by spatial incongruities. PMID:24832608
Degree-associated reconstruction number of graphs
Michael D. Barrus; Douglas B. West
A card of a graph G is a subgraph formed by deleting one vertex. The Reconstruc- tion Conjecture states that each graph with at least three vertices is determined by its multiset of cards. A dacard specifies the degree of the deleted vertex along with the card. The degree-associated reconstruction number drn(G) is the minimum number of dacards that determine
Royer, Dana
HANDBOOK FOR PARENTS 2013Â2014 #12;ii USEFUL TELEPHONE NUMBERS The telephone number. We have prepared this handbook because we thought it would be helpful for you, as parents're not sure whom to call, feel free to contact the Office of Alumni and Parent Relations at 860
Predicting the required number of training samples
NASA Technical Reports Server (NTRS)
Kalayeh, H. M.; Landgrebe, D. A.
A criterion which measures the quality of the estimate of the covariance matrix of a multivariate normal distribution is developed. Based on this criterion, the necessary number of training samples is predicted. Experimental results which are used as a guide for determining the number of training samples are included.
New String Theories And Their Generation Number
Arel Genish; Doron Gepner
New heterotic string theories in four dimensions are constructed by tensoring a nonstandard SCFT along with some minimal SCFT's. All such theories are identified and their particle generation number is found. We prove that from the infinite number of new heterotic string theories only the {6} theory predicts three generations as seen in nature which makes it an interesting candidate for further study.
The covering number in learning theory
Ding-xuan Zhou
The covering number of a ball of a reproducing kernel Hilbert space as a subset of the continuous function space plays an important role in Learning Theory.We give estimates for this covering number by means of the regularity of the Mercer kernel K: For convolution type kernels Kđx; t ŢĽ kđxtŢ on ˝0; 1? n; we provide estimates depending on
Study odd numbers with traditional functions
Elias Rios
In this paper we will focus on the study of relationships that can exist between odd numbers and different traditional functions like the gamma function, Riemann zeta function or function of von Mangoldt. Number theory applies to this study. It will also analyze the convergence of the series obtained as a result of that relationship.
Equal Opportunities Monitoring Job reference number
, sexual orientation, gender reassignment, marital or civil partnership status, religion, religious beliefEqual Opportunities Monitoring Name: Job reference number: (if applicable) Post applied for: Pay Number: (for internal candidates only): The Authority is committed to provide equal opportunity to any
40 CFR 86.1204 - Section numbering.
Code of Federal Regulations, 2011 CFR
... Evaporative Emission Test Procedures for New Gasoline-Fueled, Natural Gas-Fueled, Liquefied Petroleum Gas-Fueled and Methanol-Fueled Heavy-Duty Vehicles § 86.1204 Section numbering. The section numbering system set forth in § 86.104...
Keypad Geometry and Divisibility of Numbers
ERIC Educational Resources Information Center
Van Dyke, Frances; Keynes, Michael
In this article, the authors show how students can form familiar geometric figures on the calculator keypad and generate numbers that are all divisible by a common number. Students are intrigued by the results and want to know "why it works". The activities can be presented and students given an extended amount of time to think about them. As…
Astronomy Basics Large and Small Numbers
Walter, Frederick M.
and 10 have exponents of 0 because 100=1. #12;Significant Figures 1.234 x 106 = 12.34 x 105 = 0.1234 x is preferred). The significant figures are the number of digits in the mantissa. This number (1.234 x 106 ) has 4 significant figures. For most purposes in this course, 2 or 3 significant figures suffice. #12
Brandeis University Psychology current number of majors
Fraden, Seth
, perception, memory and emotion; and the effects of brain damage. the psychology department at Brandeis offersBrandeis University Psychology fast facts current number of majors and minors: 282 NumberBoUt the Program the Department of Psychology helps students establish a strong scientific and research foundation
Signed domination numbers of directed graphs
Bohdan Zelinka
The concept of signed domination number of an undirected graph (introduced by J. E. Dunbar, S. T. Hedetniemi, M. A. Henning and P. J. Slater) is transferred to directed graphs. Exact values are found for particular types of tournaments. It is proved that for digraphs with a directed Hamiltonian cycle the signed domination number may be arbitrarily small.
Validation of Dunbar's number in Twitter conversations
Bruno Goncalves; Nicola Perra; Alessandro Vespignani
Modern society's increasing dependency on online tools for both work and recreation opens up unique opportunities for the study of social interactions. A large survey of online exchanges or conversations on Twitter, collected across six months involving 1.7 million individuals is presented here. We test the theoretical cognitive limit on the number of stable social relationships known as Dunbar's number.
Nonclassicality in phase-number uncertainty relations
Matia-Hernando, Paloma; Luis, Alfredo [Departamento de Optica, Facultad de Ciencias Fisicas, Universidad Complutense, 28040 Madrid (Spain)
We show that there are nonclassical states with lesser joint fluctuations of phase and number than any classical state. This is rather paradoxical since one would expect classical coherent states to be always of minimum uncertainty. The same result is obtained when we replace phase by a phase-dependent field quadrature. Number and phase uncertainties are assessed using variance and Holevo relation.
Nephron Number in Patients with Primary Hypertension
Gunhild Keller; Gisela Zimmer; Gerhard Mall; Eberhard Ritz; Kerstin Amann
background A diminished number of nephrons has been proposed as one of the factors contribut- ing to the development of primary hypertension. methods To test this hypothesis, we used a three-dimensional stereologic method to compare the number and volume of glomeruli in 10 middle-aged white patients (age range, 35 to 59 years) with a history of primary hypertension or left
Infinite Sums of M-Bonacci Numbers
ERIC Educational Resources Information Center
A-iru, Muniru A.
In this note, we construct infinite series using M-bonacci numbers in a manner similar to that used in previous studies and investigate the convergence of the series to an integer. Our results generalize the ones obtained for Fibonacci numbers.
A Partition Formula for Fibonacci Numbers
Philipp Fahr; Claus Michael Ringerl
We present a partition formula for the even index Fibonacci numbers. The formula is motivated by the appearance of these Fibonacci numbers in the representation theory of the socalled 3-Kronecker quiver, i.e., the oriented graph with two vertices and three arrows in the same direction.
Hardware realization of a Fermat number transform
J. McClellan
The hardware design and implementation of a Fermat number transform (FNT) is described. The arithmetic logic design is treated in detail and a new data representation for integers modulo a Fermat number is derived. In addition, the FNT is compared with the fast Fourier transform (FFT) on the basis of hardware required for a pipeline convolver.
The factorization of the ninth Fermat number
H. W. Lenstra; M. S. Manasse; J. M. Pollard
In this paper we exhibit the full prime factorization of the ninth Fermat number Fg = 2512 + 1 . It is the product of three prime factors that have 7, 49, and 99 decimal digits. We found the two largest prime factors by means of the number field sieve, which is a factoring algorithm that depends on arithmetic in
Our Numbers Are up! (Is That Good?)
ERIC Educational Resources Information Center
Speyer, Mark
There has been an increase on the number of applicants and the average SAT scores of the admitted students to colleges and universities in the United States. The total number of applicants may increase for purely external reasons, such as more students graduating from high school or more students reading good things about a particular college, but…
Families of Linear Recurrences for Catalan Numbers
ERIC Educational Resources Information Center
Gauthier, N.
Four different families of linear recurrences are derived for Catalan numbers. The derivations rest on John Riordan's 1973 generalization of Catalan numbers to a set of polynomials. Elementary differential and integral calculus techniques are used and the results should be of interest to teachers and students of introductory courses in calculus…
ERIC Educational Resources Information Center
Goldenhersh, Barbara, Ed.
This document consists of three issues of the journal "Seedbed," an outcome of the Teachers' Center Project at Southern Illinois University at Edwardsville (SIUE). Issue Number 29 contains 67 articles on teachers' ideas that they thought worth sharing with other teachers. Issue Number 30 consists of a single paper, "Children and Mathematics in the…
Writing about Numbers We Should Know
NSDL National Science Digital Library
Neil Lutsky
This opening assignment for an introductory quantitative reasoning course asks students to write about "Numbers We Should Know." Its goal is to help students begin to think quantitatively, evaluate the sources of quantitative information critically, and write using numbers precisely and thoughtfully.
Good Morning, Numbers Day: Motivating for Mathematics
ERIC Educational Resources Information Center
Ramentol, Salvador Vidal
The aversion that many girls and boys experience towards mathematics has been one of the author's major concerns since he started teaching. In this article, he describes a project called "Numbers Day" that was designed to improve students' attitudes toward mathematics. There are many features of Numbers Day that teachers might incorporate into…
Ford, Kevin
inequality (y) Li(y) holds. #12;PRIME NUMBER RACE AND ZEROS OF L-FUNCTIONS 3 7. "Racing problems". The "primeCHEBYSHEV'S CONJECTURE AND THE PRIME NUMBER RACE Kevin Ford , Sergei Konyagin July, 2002 1, there are interesting inequities in the functions (x, k, l) for fixed k. Of particular interest is the behavior
Blanchette, Robert A.
SOCIAL SECURITY NUMBER AND NAME VERIFICATION Academic Year 2012Â2013 *FA552-A* Please recycle. SECTION A. Student information DIRECTIONS--You must verify your name and Social Security number a legible copy of your Social Security card with this completed document and return it to One Stop Student
Amin, S. Massoud
SOCIAL SECURITY NUMBER AND NAME VERIFICATION Academic Year 2013Â2014 *FA552-A* Please recycle. DIRECTIONS--You must verify your name and Social Security number for processing of your 2013Â2014 Free Application for Federal Student Aid (FAFSA) to continue. Please attach a legible copy of your Social Security
Amin, S. Massoud
SOCIAL SECURITY NUMBER AND NAME VERIFICATION Academic Year 2014Â2015 *FA552-A* Please recycle. DIRECTIONS--You must verify your name and Social Security number for processing of your 2014Â2015 Free Application for Federal Student Aid (FAFSA) to continue. Please attach a legible copy of your Social Security
Human odontoblast cell numbers after dental injury
P. E Murray; P. J Lumley; J.-C Franquin; M Remusat; A. J Smith
Objectives: The purpose of this study was to measure the changes in odontoblast cell numbers in response to cavity restoration variables and patient factors, and the effect these factors have on dental repair by tertiary dentinogenesis. The number of vital odontoblasts is a critical factor for pulpal repair following restorative surgery, and yet little information is available on these cell
From Whole Numbers to Invert and Multiply
ERIC Educational Resources Information Center
Cavey, Laurie O.; Kinzel, Margaret T.
Teachers report that engaging students in solving contextual problems is an important part of supporting student understanding of algorithms for fraction division. Meaning for whole-number operations is a crucial part of making sense of contextual problems involving rational numbers. The authors present a developed instructional sequence to…
The Second Strong Law of Small Numbers.
ERIC Educational Resources Information Center
Guy, Richard K.
Presented are 44 examples in which students are invited to guess what pattern of numbers is emerging and to decide whether the pattern will persist. Topics of examples include Pascal's triangle, integers, vertices, Fibonacci numbers, power series, partition functions, and Euler's theorem. The answers to all problems are included. (KR)
Predict octane number for gasoline blends
A. H. Zahed; S. A. Mullah; M. D. Bashir
A model with five independent variables is used to predict the octane number of gasoline blends with more accuracy than any previous model. Often, it is useful to know the resulting octane number before the gasoline is blended. Clearly, such a model is useful because good predictive models have been few and far between. With high-powered and faster personal computers,
Octane number prediction for gasoline blends
Nikos Pasadakis; Vassilis Gaganis; Charalambos Foteinopoulos
Artificial Neural Network (ANN) models have been developed to determine the Research Octane Number (RON) of gasoline blends produced in a Greek refinery. The developed ANN models use as input variables the volumetric content of seven most commonly used fractions in the gasoline production and their respective RON numbers. The model parameters (ANN weights) are presented such that the model
enter part number BNC / RP-BNC
Berns, Hans-Gerd
enter part number Products 7/16 1.0/2.3 1.6/5.6 AFI AMC BNC / RP-BNC C FAKRA SMB FME HN MCX Mini ------- Product Search ------- Inventory Search Search Results for: 31-10152-RFX Results: 1 - 1 of 1 Part Number. All rights reserved. Copyright | Terms & Conditions | RF E-Mail Client | Contact Us | Amphenol
Class numbers of complex quadratic fields
Ezra Brown
Congruence conditions on the class numbers of complex quadratic fields have recently been studied by various investigators, including Barrucand and Cohn, Hasse, and the author. In this paper, we study the class number of Q([radical sign] - pq), where p [reverse not equivalent] q (mod 4) are distinct primes.
On the Concept Image of Complex Numbers
ERIC Educational Resources Information Center
Nordlander, Maria Cortas; Nordlander, Edvard
A study of how Swedish students understand the concept of complex numbers was performed. A questionnaire was issued reflecting the student view of own perception. Obtained answers show a variety of concept images describing how students adopt the concept of complex numbers. These concept images are classified into four categories in order to…
Algorithmic Number Theory-The Complexity Contribution
Leonard M. Adleman
Though algorithmic number theory is one of man's oldest intellectual pursuits, its current vitality is perhaps unrivalled in history. This is due in part to the injection of new ideas from computational complexity. In this paper, a brief history of the symbiotic relationship between number theory and complexity theory will be presented. In addition, some of the technical aspects underlying
New Numbers in Mathematics in South Africa
ERIC Educational Resources Information Center
Engelbrecht, Johann; Harding, Ansie
This article is a follow-up of a study conducted in 2000 by the same authors on trends in numbers of mathematics majors at South African universities. Data from 12 universities for the 2000-2007 period is investigated. The previously observed trend of general and dramatic decrease in numbers of mathematics majors appears to have been reversed and…
The Game Chromatic Number of Random Graphs
Sudakov, Benjamin
The Game Chromatic Number of Random Graphs Tom Bohman,1, * Alan Frieze,1, Benny Sudakov2,3, 1 23 December 2005; accepted 8 August 2006 Published online 17 April 2007 in Wiley InterScience (www wins iff at the end of the game all the vertices of G are colored. The game chromatic number g
Company number 5857955 Wellcome Trust Finance plc
Rambaut, Andrew
holders and that the Company achieves sufficient return on its assets to be profitable, before anyCompany number 5857955 Wellcome Trust Finance plc Annual Report and Financial Statements Year ended 30 September 2013 #12;Company number 5857955 Wellcome Trust Finance plc Contents Page Directors
-P and T number -Residence Permit
- P and T number - Residence Permit - Banking Information - Insurance - Other... #12;P and T number service options when opening bank account #12;Swedish Migration Board - Migrationsverket 2012 or online. When you apply for an extension by post, you must use the form Application for residence permit
Understanding a Child's Development of Number Sense
NSDL National Science Digital Library
Marilyn Burns
The brief video clips on this webpage illustrate the range of number sense exhibited by students in grades Pre K-2. In interviews, Cena and Jonathan, both age 7, and Rudy, age 9, demonstrate different levels of understanding number and place value concepts. The page includes discussion questions for each set of videos as well as concluding reflection questions.
Dividing Fraction by a Whole Number
NSDL National Science Digital Library
Mrs. West
Everything you need to know about Dividing Fractions by a Whole Number. Learn the steps for dividing fractions by whole numbers in How to do it. Start out slow and divide with Fractions fun with soccer. Speed up the fun with Fraction Hoops. ...
Fostering At-Risk Preschoolers' Number Sense
ERIC Educational Resources Information Center
Baroody, Arthur; Eiland, Michael; Thompson, Bradley
Research Findings: A 9-month study served to evaluate the effectiveness of a pre-kindergarten number sense curriculum. Phase 1 of the intervention involved manipulative-, game-based number sense instruction; Phase 2, computer-aided mental-arithmetic training with the simplest sums. Eighty 4- and 5-year-olds at risk for school failure were randomly…
Clinicopathological assessment of the nephron number
Tsuboi, Nobuo; Kanzaki, Go; Koike, Kentaro; Kawamura, Tetsuya; Ogura, Makoto; Yokoo, Takashi
Recent studies have demonstrated much larger variability in the total number of nephrons in normal populations than previously suspected. In addition, it has been suggested that individuals with a low nephron number may have an increased lifetime risk of hypertension or renal insufficiency, emphasizing the importance of evaluating the nephron number in each individual. In view of the fact that all previous reports of the nephron number were based on analyses of autopsy kidneys, the identification of surrogate markers detectable in living subjects is needed in order to enhance understanding of the clinical significance of this parameter. In this review, we summarize the clinicopathological factors and findings indicating a reduction in the nephron number, focusing particularly on those found at the time of a preserved renal function. PMID:25852857
Relativistic theory of surficial Love numbers
Philippe Landry; Eric Poisson
A relativistic theory of surficial Love numbers, which characterize the surface deformation of a body subjected to tidal forces, was initiated by Damour and Nagar. We revisit this effort in order to extend it, clarify some of its aspects, and simplify its computational implementation. First, we refine the definition of surficial Love numbers proposed by Damour and Nagar, and formulate it directly in terms of the deformed curvature of the body's surface, a meaningful geometrical quantity. Second, we develop a unified theory of surficial Love numbers that applies equally well to material bodies and black holes. Third, we derive a compactness-dependent relation between the surficial and (electric-type) gravitational Love numbers of a perfect-fluid body, and show that it reduces to the familiar Newtonian relation when the compactness is small. And fourth, we simplify the tasks associated with the practical computation of the surficial and gravitational Love numbers for a material body.
On the number of Latin squares
McKay, Brendan D
We (1) determine the number of Latin rectangles with 11 columns and each possible number of rows, including the Latin squares of order~11, (2) answer some questions of Alter by showing that the number of reduced Latin squares of order $n$ is divisible by $f!$ where $f$ is a particular integer close to $\\frac12n$, (3) provide a formula for the number of Latin squares in terms of permanents of $(+1,-1)$-matrices, (4) find the extremal values for the number of 1-factorisations of $k$-regular bipartite graphs on $2n$ vertices whenever $1\\leq k\\leq n\\leq11$, (5) show that the proportion of Latin squares with a non-trivial symmetry group tends quickly to zero as the order increases.
Photon-number tomography and fidelity
O. V. Man'ko
The scheme of photon-number tomography is discussed in the framework of star-product quantization. The connection of dual quantization scheme and observables is reviewed. The quantizer and dequantizer operators and kernels of star product of tomograms in photon-number tomography scheme and its dual one are presented in explicit form. The fidelity and state purity are discussed in photon{number tomographic scheme, and the expressions for fidelity and purity are obtained in the form of integral of the product of two photon-number tomograms with integral kernel which is presented in explicit form. The properties of quantumness are discussed in terms of inequalities on state photon{number tomograms.
LEAN: laser-etched aqua number
NASA Astrophysics Data System (ADS)
Schell, Karel J.
A security device on a banknote has to be recognized immediately by the general public and has to enable the general public to establish the genuineness of the banknote. This is the so-called first line of defense. Recently the development of the ability to establish the genuiness has gained momentum and is called 'self authenticating.' Comparing the banknote number with a 'watermark number' can do authenticating. The watermark number is engraved by a laser beam in the paper and is -- as the printed number -- different for each note. Recent progress in the material processing by laser enables the engraving of the individual watermark number for each banknote in line with the production process.
Relativistic theory of surficial Love numbers
NASA Astrophysics Data System (ADS)
Landry, Philippe; Poisson, Eric
A relativistic theory of surficial Love numbers, which characterize the surface deformation of a body subjected to tidal forces, was initiated by Damour and Nagar. We revisit this effort in order to extend it, clarify some of its aspects, and simplify its computational implementation. First, we refine the definition of surficial Love numbers proposed by Damour and Nagar and formulate it directly in terms of the deformed curvature of the body's surface, a meaningful geometrical quantity. Second, we develop a unified theory of surficial Love numbers that applies equally well to material bodies and black holes. Third, we derive a compactness-dependent relation between the surficial and (electric-type) gravitational Love numbers of a perfect-fluid body and show that it reduces to the familiar Newtonian relation when the compactness is small. And fourth, we simplify the tasks associated with the practical computation of the surficial and gravitational Love numbers for a material body.
Low Reynolds number airfoil survey, volume 1
NASA Technical Reports Server (NTRS)
Carmichael, B. H.
The differences in flow behavior two dimensional airfoils in the critical chordlength Reynolds number compared with lower and higher Reynolds number are discussed. The large laminar separation bubble is discussed in view of its important influence on critical Reynolds number airfoil behavior. The shortcomings of application of theoretical boundary layer computations which are successful at higher Reynolds numbers to the critical regime are discussed. The large variation in experimental aerodynamic characteristic measurement due to small changes in ambient turbulence, vibration, and sound level is illustrated. The difficulties in obtaining accurate detailed measurements in free flight and dramatic performance improvements at critical Reynolds number, achieved with various types of boundary layer tripping devices are discussed.
Bit recycling for scaling random number generators
Mennucci, Andrea C G
Many Random Number Generators (RNG) are available nowadays; they are divided in two categories, hardware RNG, that provide "true" random numbers, and algorithmic RNG, that generate pseudo random numbers (PRNG). Both types usually generate random numbers (X_n) as independent uniform samples in a range 0...2^b-1, with b = 8, 16, 32 or b = 64. In applications, it is instead sometimes desirable to draw random numbers as independent uniform samples (Y_n) in a range 1, . . . M, where moreover M may change between drawings. Transforming the sequence (X_n) to (Y_n) is sometimes known as scaling. We discuss different methods for scaling the RNG, both in term of mathematical efficiency and of computational speed.
Compendium of Experimental Cetane Number Data
Murphy, M. J.; Taylor, J. D.; McCormick, R. L.
In this report, we present a compilation of reported cetane numbers for pure chemical compounds. The compiled database contains cetane values for 299 pure compounds, including 156 hydrocarbons and 143 oxygenates. Cetane number is a relative ranking of fuels based on the amount of time between fuel injection and ignition. The cetane number is typically measured either in a combustion bomb or in a single-cylinder research engine. This report includes cetane values from several different measurement techniques - each of which has associated uncertainties. Additionally, many of the reported values are determined by measuring blending cetane numbers, which introduces significant error. In many cases, the measurement technique is not reported nor is there any discussion about the purity of the compounds. Nonetheless, the data in this report represent the best pure compound cetane number values available from the literature as of August 2004.
Links with small lattice stick numbers
NASA Astrophysics Data System (ADS)
Hong, Kyungpyo; No, Sungjong; Oh, Seungsang
Knots and links have been considered to be useful models for structural analysis of molecular chains such as DNA and proteins. One quantity that we are interested in for molecular links is the minimum number of monomers necessary for realizing them. In this paper we consider every link in the cubic lattice. The lattice stick number sL(L) of a link L is defined to be the minimum number of sticks required to construct a polygonal representation of the link in the cubic lattice. Huh and Oh found all knots whose lattice stick numbers are at most 14. They proved that only the trefoil knot 31 and the figure-eight knot 41 have lattice stick numbers of 12 and 14, respectively. In this paper we find all links with more than one component whose lattice stick numbers are at most 14. Indeed we prove combinatorically that s_L(2^2_1)=8, s_L(2^2_1 \\sharp 2^2_1)=s_L(6^3_2)=s_L(6^3_3)=12, s_L(4^2_1)=13, s_L(5^2_1)=14 and any other non-split links have stick numbers of at least 15.
Generating functions for weighted Hurwitz numbers
Mathieu Guay-Paquet; J. Harnad
Double Hurwitz numbers enumerating weighted $n$-sheeted branched coverings of the Riemann sphere or, equivalently, weighted paths in the Cayley graph of $S_n$ generated by transpositions are determined by an associated weight generating function. A uniquely determined $1$-parameter family of 2D Toda $\\tau$-functions of hypergeometric type is shown to consist of generating functions for such weighted Hurwitz numbers. Four classical cases are detailed, in which the weighting is uniform: Okounkov's double Hurwitz numbers, for which the ramification is simple at all but two specified branch points; the case of Belyi curves, with three branch points, two with specified profiles; the general case, with a specified number of branch points, two with fixed profiles, the rest constrained only by the genus; and the signed enumeration case, with sign determined by the parity of the number of branch points. Using the exponentiated quantum dilogarithm function as weight generator, three new types of weighted enumerations are introduced. These determine {\\em quantum} Hurwitz numbers depending on a deformation parameter $q$. By suitable interpretation of $q$, the statistical mechanics of quantum weighted branched covers may be related to that of Bosonic gases. The standard double Hurwitz numbers are recovered in the classical limit.
Theory of analogous force on number sets
NASA Astrophysics Data System (ADS)
Canessa, Enrique
A general statistical thermodynamic theory that considers given sequences of x-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability distributions px for natural numbers, we claim that they lead to a better understanding of probabilistic laws associated with number theory. Sequences of numbers are treated as the size measure of finite sets. By considering px to describe complex phenomena, the theory leads to derive a distinct analogous force fx on number sets proportional to (? px/? x) T at an analogous system temperature T. In particular, this leads to an understanding of the uneven distribution of integers of random sets in terms of analogous scale invariance and a screened inverse square force acting on the significant digits. The theory also allows to establish recursion relations to predict sequences of Fibonacci numbers and to give an answer to the interesting theoretical question of the appearance of the Benford's law in Fibonacci numbers. A possible relevance to prime numbers is also analyzed.
An Introduction to the Theory of Numbers
NSDL National Science Digital Library
Moser, Leo
Written by Leo Moser and presented by the Trillia Group, this virtual text introduces visitors to the theory of numbers. After agreeing to the terms and conditions of use, users will be able to download the full document as an 87-page pdf file in either large or regular print. The chapters include: "Compositions and Partitions," "Irrational Numbers," "Diophantine Equations," and "Geometry of Numbers." The terms limit this free download to students in mathematic self-study or for instructors to consider this text for use in their classrooms.
MSSM with gauged baryon and lepton numbers
Fornal, Bartosz
A simple extension of the minimal supersymmetric standard model in which baryon and lepton numbers are local gauge symmetries spontaneously broken at the supersymmetry scale is reported. This theory provides a natural explanation for proton stability. Despite violating R-parity, it contains a dark matter candidate carrying baryon number that can be searched for in direct detection experiments. The model accommodates a light active neutrino spectrum and predicts one heavy and two light sterile neutrinos. It also allows for lepton number violating processes testable at the Large Hadron Collider.
MSSM with gauged baryon and lepton numbers
Bartosz Fornal
A simple extension of the minimal supersymmetric standard model in which baryon and lepton numbers are local gauge symmetries spontaneously broken at the supersymmetry scale is reported. This theory provides a natural explanation for proton stability. Despite violating R-parity, it contains a dark matter candidate carrying baryon number that can be searched for in direct detection experiments. The model accommodates a light active neutrino spectrum and predicts one heavy and two light sterile neutrinos. It also allows for lepton number violating processes testable at the Large Hadron Collider.
Effective sunspot number (SSNi) comparison study
NASA Astrophysics Data System (ADS)
Hart, Mary L.
This report documents the results of a USAFETAC study done to determine whether or not reliable global effective sunspot numbers for the Air Force Global Weather Central's (AFGWC's) Ionospheric Conductivity and Electron density (ICED) Model could be calculated based on the present number (11) of digital ionosonde sites. The study found that increasing the number of sites would have a limited effect on ICED output, and that it was feasible to run the ICED model using the present 11-station network, subject to certain limitations.
Standard random number generation for MBASIC
NASA Technical Reports Server (NTRS)
Tausworthe, R. C.
A machine-independent algorithm is presented and analyzed for generating pseudorandom numbers suitable for the standard MBASIC system. The algorithm used is the polynomial congruential or linear recurrence modulo 2 method. Numbers, formed as nonoverlapping adjacent 28-bit words taken from the bit stream produced by the formula a sub m + 532 = a sub m + 37 + a sub m (modulo 2), do not repeat within the projected age of the solar system, show no ensemble correlation, exhibit uniform distribution of adjacent numbers up to 19 dimensions, and do not deviate from random runs-up and runs-down behavior.
On the highest chromosome number in mammals.
Schmid, M; Fernández-Badillo, A; Feichtinger, W; Steinlein, C; Roman, J I
The mitotic and meiotic chromosomes of the semiaquatic rodent Ichthyomys pittieri (Rodentia, Cricetinae) from Venezuela were analyzed by means of conventional staining and several banding techniques. The diploid chromosome number of this rare species is 2n = 92, which is the highest value known for mammals. It is assumed that this exceptionally high chromosome number is the result of repeated centric fissions. The karyotype of I. pittieri was compared with that of Anotomys leander, for which a diploid number of 2n = 92 has also been reported. The karyological relationships existing within the Neotropical Cricetidae are summarized. PMID:3073914
47 CFR 52.111 - Toll free number assignment.
Code of Federal Regulations, 2011 CFR
... 2011-10-01 2011-10-01 false Toll free number assignment. 52.111 Section 52.111...CARRIER SERVICES (CONTINUED) NUMBERING Toll Free Numbers § 52.111 Toll free number assignment. Toll free numbers...
47 CFR 52.111 - Toll free number assignment.
Code of Federal Regulations, 2014 CFR
... 2014-10-01 2014-10-01 false Toll free number assignment. 52.111 Section 52.111...CARRIER SERVICES (CONTINUED) NUMBERING Toll Free Numbers § 52.111 Toll free number assignment. Toll free numbers...
47 CFR 52.111 - Toll free number assignment.
Code of Federal Regulations, 2010 CFR
... 2010-10-01 2010-10-01 false Toll free number assignment. 52.111 Section 52.111...CARRIER SERVICES (CONTINUED) NUMBERING Toll Free Numbers § 52.111 Toll free number assignment. Toll free numbers...
47 CFR 52.111 - Toll free number assignment.
Code of Federal Regulations, 2013 CFR
... 2013-10-01 2013-10-01 false Toll free number assignment. 52.111 Section 52.111...CARRIER SERVICES (CONTINUED) NUMBERING Toll Free Numbers § 52.111 Toll free number assignment. Toll free numbers...
47 CFR 52.111 - Toll free number assignment.
Code of Federal Regulations, 2012 CFR
... 2012-10-01 2012-10-01 false Toll free number assignment. 52.111 Section 52.111...CARRIER SERVICES (CONTINUED) NUMBERING Toll Free Numbers § 52.111 Toll free number assignment. Toll free numbers...
21 CFR 207.35 - Notification of registrant; drug establishment registration number and drug listing number.
Code of Federal Regulations, 2010 CFR
21 Food and Drugs 4 2010-04-01 2010-04-01 false Notification of registrant; drug establishment registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION,...
21 CFR 207.35 - Notification of registrant; drug establishment registration number and drug listing number.
Code of Federal Regulations, 2011 CFR
21 Food and Drugs 4 2011-04-01 2011-04-01 false Notification of registrant; drug establishment registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION,...
21 CFR 207.35 - Notification of registrant; drug establishment registration number and drug listing number.
Code of Federal Regulations, 2014 CFR
21 Food and Drugs 4 2014-04-01 2014-04-01 false Notification of registrant; drug establishment registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION,...
21 CFR 207.35 - Notification of registrant; drug establishment registration number and drug listing number.
Code of Federal Regulations, 2013 CFR
21 Food and Drugs 4 2013-04-01 2013-04-01 false Notification of registrant; drug establishment registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION,...
21 CFR 207.35 - Notification of registrant; drug establishment registration number and drug listing number.
Code of Federal Regulations, 2012 CFR
21 Food and Drugs 4 2012-04-01 2012-04-01 false Notification of registrant; drug establishment registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION,...
Crossing number, pair-crossing number, and Petr Kolman, Ji r Matou sek
Matousek, Jiri
Crossing number, pair-crossing number, and expansion Petr Kolman, Ji#20; r#19; #16; Matou#20; sek and Matou#20;sek [5] shows that in general, given a drawing, it need not be possible to eliminate multiple
27 CFR 20.179 - Package identification number or serial number.
Code of Federal Regulations, 2011 CFR
...2011-04-01 false Package identification number...Dealers § 20.179 Package identification number... A dealer who fills packages with specially denatured spirits shall mark each package with a package...
27 CFR 20.179 - Package identification number or serial number.
Code of Federal Regulations, 2010 CFR
...2010-04-01 false Package identification number...Dealers § 20.179 Package identification number... A dealer who fills packages with specially denatured spirits shall mark each package with a package...
27 CFR 20.179 - Package identification number or serial number.
Code of Federal Regulations, 2014 CFR
...2014-04-01 false Package identification number...Dealers § 20.179 Package identification number... A dealer who fills packages with specially denatured spirits shall mark each package with a package...
27 CFR 20.179 - Package identification number or serial number.
Code of Federal Regulations, 2012 CFR
...2012-04-01 false Package identification number...Dealers § 20.179 Package identification number... A dealer who fills packages with specially denatured spirits shall mark each package with a package...
27 CFR 20.179 - Package identification number or serial number.
Code of Federal Regulations, 2013 CFR
...2013-04-01 false Package identification number...Dealers § 20.179 Package identification number... A dealer who fills packages with specially denatured spirits shall mark each package with a package...
Mining for Numbers. A Heuristic Approach to Some Prime Number Work
ERIC Educational Resources Information Center
Tapson, Frank
Whole numbers written in spiral or triangular patterns with spaces occupied by prime numbers blocked in produces interesting visual patterns. Described is a game based on these patterns that may be played at many different levels. (JP)
CIMAS Post Doctoral Associate Position number 048650
Position Number: 048650 Paygrade: 7 Department/Hospital COOP INST FOR MARINE AND ATMOS STUDIES Pay Band Min in publishing results in the peer-reviewed literature. The successful candidate must demonstrate interest
Getting Help: Know the Numbers (For Parents)
... Lessons? Visit KidsHealth in the Classroom What Other Parents Are Reading Measles: What to Know Vaccines: FAQs ... to Expect Getting Help: Know the Numbers KidsHealth > Parents > First Aid & Safety > Emergencies > Getting Help: Know the ...
Department of Defense Worldwide Numbers for TBI
... quarter. Information posted here is collected from electronic medical records in cooperation with the Armed Forces Health Surveillance ... are added each calendar quarter. To reflect updated medical record information, all TBI numbers, 2000 to most recent ...
An Application of Number Theory to Cryptology.
ERIC Educational Resources Information Center
Snow, Joanne R.
Discussed is an application of number theory to cryptology that can be used with secondary school students. Background on the topics is given first, followed by an explanation for use of the topic. (MNS)
Carol A. Lucas
This article briefly explains the cooperative learning technique of jigsaw. It then details the use of a jigsaw lesson for explaining complex numbers to intermediate algebra students. The article includes copies of the handouts given to the expert groups.
9 CFR 351.6 - Official number.
Code of Federal Regulations, 2010 CFR
...CERTIFICATION CERTIFICATION OF TECHNICAL ANIMAL FATS FOR EXPORT Procedure for Obtaining Service...will assign a certified technical animal fat plant number to each plant granted service...to identify all certified technical animal fat prepared or stored by the...
REJUVENATION RESEARCH Volume 8, Number 2, 2005
Rose, Michael R.
REJUVENATION RESEARCH Volume 8, Number 2, 2005 © Mary Ann Liebert, Inc. Testing Whether Male Age in Drosophila, medflies, wasps, yeast, nematodes, and humans.113 There is no widely accepted explanation