text:
Generic name: theophylline [ thee-OF-i-lin ]
Brand name: Quibron-T
Quibron-T is used for:
Preventing and treating symptoms and blockage of airway due to asthma or other lung diseases (eg, emphysema, bronchitis). It may also be used for other conditions as determined by your doctor.
Quibron-T is a xanthine derivative. It works by relaxing the muscle around the airways in the lungs, which allows them to widen and makes breathing easier. It also improves contraction of the diaphragm (the major breathing muscle) and decreases the response of the airways to irritants.
Do NOT use Quibron-T if:
- you are allergic to any ingredient in Quibron-T, similar medicines (eg, aminophylline), or xanthines (eg, caffeine, chocolate)
- you are using large amounts of other products that contain xanthine (such as chocolate or caffeinated drinks)
- you are taking dipyridamole intravenously (IV), febuxostat, halothane, or St. John's wort
Contact your doctor or health care provider right away if any of these apply to you.
Before using Quibron-T:
Some medical conditions may interact with Quibron-T. Tell your doctor or pharmacist if you have any medical conditions, especially if any of the following apply to you:
- if you are pregnant, planning to become pregnant, or are breast-feeding
- if you are taking any prescription or nonprescription medicine, herbal preparation, or dietary supplement
- if you have allergies to medicines, foods, or other substances
- if you have a history of heart problems (eg, congestive heart failure, cor pulmonale), an irregular heartbeat, liver problems (eg, cirrhosis, hepatitis), viral infection, thyroid problems, increased acid levels in the body, brain or nerve problems, or seizures (eg, epilepsy)
- if you are in shock or have a fever, an ulcer, a severe infection, cystic fibrosis, or fluid in the lungs (pulmonary edema)
- if you smoke, are stopping or starting smoking, or are exposed to the smoke from cigarettes or marijuana
- if you are in the last 3 months of pregnancy
Some MEDICINES MAY INTERACT with Quibron-T. Tell your health care provider if you are taking any other medicines, especially any of the following:
- Aminoglutethimide, barbiturates (eg, phenobarbital), carbamazepine, hydantoins (eg, phenytoin), isoproterenol, moricizine, rifampin, St. John's wort, or sulfinpyrazone because they may decrease Quibron-T's effectiveness
- Allopurinol, beta-blockers (eg, propranolol), cimetidine, disulfiram, enoxacin, estrogen, febuxostat, fluvoxamine, interferon alpha, macrolide antibiotics (eg, clarithromycin, erythromycin), methotrexate, mexiletine, oral contraceptives (birth control pills), pentoxifylline, propafenone, quinolone antibiotics (eg, ciprofloxacin), tacrine, thiabendazole, ticlopidine, troleandomycin, verapamil, viloxazine, or zileuton because they may increase the risk of Quibron-T's side effects
- Ephedrine because the risk of side effects, such as nausea, nervousness, and trouble sleeping, may be increased
- Halothane because the risk of side effects such as irregular heartbeat may be increased
- Ketamine because the risk of seizures may be increased
- Adenosine, benzodiazepines (eg, diazepam, flurazepam, lorazepam, midazolam), dipyridamole IV, lithium, or nondepolarizing muscle relaxants (eg, pancuronium) because their effectiveness may be decreased by Quibron-T
This may not be a complete list of all interactions that may occur. Ask your health care provider if Quibron-T may interact with other medicines that you take. Check with your health care provider before you start, stop, or change the dose of any medicine.
How to use Quibron-T:
Use Quibron-T as directed by your doctor. Check the label on the medicine for exact dosing instructions.
- Some foods may change the effectiveness or increase the side effects of Quibron-T. Talk to your doctor about how you should take Quibron-T with regard to food. Do not suddenly change your diet or eating habits without first checking with your doctor.
- Take Quibron-T at evenly spaced times throughout the day. Taking Quibron-T at the same time each day will help you remember to take it. Contact your doctor with any questions or concerns about the best way to take Quibron-T.
- If you miss a dose of Quibron-T, skip the missed dose and go back to your regular dosing schedule. Do not take 2 doses at once.
Ask your health care provider any questions you may have about how to use Quibron-T.
Important safety information:
- Drinking alcohol may increase the risk of side effects of Quibron-T. Talk to your doctor before drinking alcohol while you are taking Quibron-T.
- Tell your doctor or dentist that you take Quibron-T before you receive any medical or dental care, emergency care, or surgery.
- Do not take more than the recommended dose or use more often than prescribed without checking with your doctor. If your symptoms become worse, contact your doctor.
- Carry an ID card at all times that says you take Quibron-T.
- Avoid large amounts of food or drink that have caffeine (eg, coffee, tea, cocoa, cola, chocolate).
- Notify your doctor if you develop a new illness, especially if it is accompanied by fever; if a chronic illness becomes worse; or if you start or stop smoking cigarettes or marijuana.
- Tell your doctor if another doctor prescribes a new medicine or tells you to stop using a medicine that you have already been taking. Tell your doctor if you start or stop any medicine, either prescription or over the counter.
- Quibron-T will not stop an asthma attack once one has started. Be sure to always carry appropriate rescue medicine (eg, bronchodilator inhaler) with you in case of an asthma attack.
- If you have more than one doctor, be sure to tell each of your doctors that you are taking Quibron-T.
- Diabetes patients - Quibron-T may affect your blood sugar. Check blood sugar levels closely. Ask your doctor before you change the dose of your diabetes medicine.
- Quibron-T may interfere with certain lab tests. Be sure your doctor and lab personnel know you are taking Quibron-T.
- Lab tests, including blood theophylline levels, may be performed while you use Quibron-T. These tests may be used to monitor your condition or check for side effects. Be sure to keep all doctor and lab appointments.
- Use Quibron-T with caution in the ELDERLY; they may be more sensitive to its effects.
- Caution is advised when using Quibron-T in CHILDREN, especially children younger than 1 year old; they may be more sensitive to its effects. Children may be more likely to experience mild, temporary behavior changes.
- PREGNANCY and BREAST-FEEDING: If you become pregnant, contact your doctor. You will need to discuss the benefits and risks of using Quibron-T while you are pregnant. Quibron-T is found in breast milk. If you are or will be breast-feeding while you use Quibron-T, check with your doctor. Discuss any possible risks to your baby.
Possible side effects of Quibron-T:
All medicines may cause side effects, but many people have no, or minor, side effects. Check with your doctor if any of these most COMMON side effects persist or become bothersome:
Seek medical attention right away if any of these SEVERE side effects occur:Irritability; mild, temporary caffeine-like effects (eg, headache, nausea, diarrhea, trouble sleeping); mild, temporary changes in behavior; restlessness; temporary increased urination.
Severe allergic reactions (rash; hives; itching; difficulty breathing; tightness in the chest; swelling of the mouth, face, lips, or tongue); confusion; dizziness; fast breathing; fast or irregular heartbeat; heart rhythm problems; seizures; severe or persistent nausea, diarrhea, or headache; sleeplessness; tremors; vomiting.
This is not a complete list of all side effects that may occur. If you have questions about side effects, contact your health care provider. Call your doctor for medical advice about side effects. To report side effects to the appropriate agency, please read the Guide to Reporting Problems to FDA.
If OVERDOSE is suspected:
Contact 1-800-222-1222 (the American Association of Poison Control Centers), your local poison control center, or emergency room immediately. Symptoms may include agitation; chest pain; confusion; decreased urination; fast or irregular heartbeat; headache; increased thirst; irritability; loss of appetite; muscle pain or tenderness; nausea; nervousness; persistent increased urination; restlessness; seizures; severe or persistent diarrhea; stomach pain; tremors or twitching; vomiting, especially of blood.
Proper storage of Quibron-T:Store Quibron-T at room temperature, between 59 and 86 degrees F (15 and 30 degrees C), in a tightly closed container. Store away from heat, moisture, and light. Do not store in the bathroom. Do not refrigerate. Keep Quibron-T out of the reach of children and away from pets.
General information:
- If you have any questions about Quibron-T, please talk with your doctor, pharmacist, or other health care provider.
- Quibron-T is to be used only by the patient for whom it is prescribed. Do not share it with other people.
- If your symptoms do not improve or if they become worse, check with your doctor.
- Check with your pharmacist about how to dispose of unused medicine.
This information is a summary only. It does not contain all information about Quibron-T. If you have questions about the medicine you are taking or would like more information, check with your doctor, pharmacist, or other health care provider.
Further information
Always consult your healthcare provider to ensure the information displayed on this page applies to your personal circumstances.


text:
Need lower attrition? Balance price and value Analyzing customers' habits can be the key to long-term retention, says Devcon's Brandon Savage
By Rich Miller
Updated Tue May 7, 2013
YARMOUTH, Maine—When it comes to alarm services, customers can choose packages ranging from a Pinto to a Ferrari. If you're lucky, they'll pony up for a Ferrari. But will they get their money's worth by putting it through its paces?
The answer can reveal a lot about patterns of usage, which in turn can serve as a barometer for how much alarm customers should be charged—and the chances of keeping them for the long haul.
"Usage is a proxy for value, and by monitoring it we can start to match price to the value that the customer is experiencing," said Brandon Savage, senior vice president of customer experience for Devcon Security. "We can use that [information] to help reduce attrition."
Savage delivered his message during "Matching Price with Value: Moving Attrition to Retention," a recent webinar hosted by the Central Station Alarm Association. Analyzing the habits of customers can lead to more effective pricing and increased RMR, but he said the point is lost on many alarm companies.
Responding to a question about whether $35 a month is too much to charge for monitoring services, he rolled out the auto analogy.
"For digital monitoring or for two-way monitoring with fully interactive services?" he asked, referencing Pinto vs. Ferrari. "Thirty-five dollars may be on the high side for digital monitoring, but it may be on the low side for fully interactive. The real question is, is the customer who is driving the Ferrari using that premium service, or are they just letting it sit in the driveway?"
To find out, Savage said alarm companies can use an RFM (recency, frequency and monetary value) analysis. By plotting on a graph how recently and how often customers are using their systems, companies can determine how to better serve them and which products to offer.
"The customer who is more recent will be of more value to you," he said. "One with less recency is on the bottom side of the curve and you need to be doing outreach to get them to use their system more."
Savage used a blue line on a graph to represent high-use customers, a green line for low-use customers and a red line for the fees being charged. He said the attrition rate for high-use customers is typically lower than for low-use customers.
"The blue line shows customers who are experiencing more value than what they're paying for. Upsell them on more services to boost RMR," he said. "The green line, below the red, shows customers who aren't using their systems [as frequently]. We can reach out and try to get them more training. If we can't do that, perhaps we can reach out and lower their prices—reduce them from a platinum package to a gold package. If we don't, we could lose them and the RMR that goes with them."
Pertinent information isn't limited to the arming and disarming of systems; it can include the use of thermostats, locks and notifications during a certain period of time. Savage said analyzing the data from such interactive services is "very much in its infancy" in the alarm industry, presenting challenges to making well-informed decisions.
"It's certainly not easy," he said. "In my opinion, AlarmNet and Alarm.com are still struggling with finding out how to share this data in the most useful format, particularly [with] small dealers who don't have a business intelligence group. Talking to reps helps, but there is not a single answer. … I'd like to put more pressure on vendors to understand that they have to share data to make it useful."

subset: commoncrawl


text:
- Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).
One of the earliest mathematical writings is the Babylonian tablet BC 7289, which gives a sexagesimal numerical approximation of , the length of the diagonal in a unit square. Being able to compute the sides of a triangle (and hence, being able to compute square roots) is extremely important, for instance, in carpentry and construction.[2]
Numerical analysis continues this long tradition of practical mathematical calculations. Much like the Babylonian approximation of , modern numerical analysis does not seek exact answers, because exact answers are often impossible to obtain in practice. Instead, much of numerical analysis is concerned with obtaining approximate solutions while maintaining reasonable bounds on errors.
Numerical analysis naturally finds applications in all fields of engineering and the physical sciences, but in the 21st century, the life sciences and even the arts have adopted elements of scientific computations. Ordinary differential equations appear in the movement of heavenly bodies (planets, stars and galaxies); optimization occurs in portfolio management; numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology.
Before the advent of modern computers numerical methods often depended on hand interpolation in large printed tables. Since the mid 20th century, computers calculate the required functions instead. The interpolation algorithms nevertheless may be used as part of the software for solving differential equations.
General introduction
The overall goal of the field of numerical analysis is the design and analysis of techniques to give approximate but accurate solutions to hard problems, the variety of which is suggested by the following.
- Advanced numerical methods are essential in making numerical weather prediction feasible.
- Computing the trajectory of a spacecraft requires the accurate numerical solution of a system of ordinary differential equations.
- Car companies can improve the crash safety of their vehicles by using computer simulations of car crashes. Such simulations essentially consist of solving partial differential equations numerically.
- Hedge funds (private investment funds) use tools from all fields of numerical analysis to calculate the value of stocks and derivatives more precisely than other market participants.
- Airlines use sophisticated optimization algorithms to decide ticket prices, airplane and crew assignments and fuel needs. This field is also called operations research.
- Insurance companies use numerical programs for actuarial analysis.
The rest of this section outlines several important themes of numerical analysis.
The field of numerical analysis predates the invention of modern computers by many centuries. Linear interpolation was already in use more than 2000 years ago. Many great mathematicians of the past were preoccupied by numerical analysis, as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial, Gaussian elimination, or Euler's method.
To facilitate computations by hand, large books were produced with formulas and tables of data such as interpolation points and function coefficients. Using these tables, often calculated out to 16 decimal places or more for some functions, one could look up values to plug into the formulas given and achieve very good numerical estimates of some functions. The canonical work in the field is the NIST publication edited by Abramowitz and Stegun, a 1000-plus page book of a very large number of commonly used formulas and functions and their values at many points. The function values are no longer very useful when a computer is available, but the large listing of formulas can still be very handy.
The mechanical calculator was also developed as a tool for hand computation. These calculators evolved into electronic computers in the 1940s, and it was then found that these computers were also useful for administrative purposes. But the invention of the computer also influenced the field of numerical analysis, since now longer and more complicated calculations could be done.
Direct and iterative methods
Direct vs iterative methods
Consider the problem of solving
- 3x3 + 4 = 28
for the unknown quantity x.
Direct method 3x3 + 4 = 28. Subtract 4 3x3 = 24. Divide by 3 x3 = 8. Take cube roots x = 2. For the iterative method, apply the bisection method to f(x) = 3x3 − 24. The initial values are a = 0, b = 3, f(a) = −24, f(b) = 57.
Iterative method a b mid f(mid) 0 3 1.5 −13.875 1.5 3 2.25 10.17... 1.5 2.25 1.875 −4.22... 1.875 2.25 2.0625 2.32... We conclude from this table that the solution is between 1.875 and 2.0625. The algorithm might return any number in that range with an error less than 0.2.
Discretization and numerical integration
In a two hour race, we have measured the speed of the car at three instants and recorded them in the following table.
Time 0:20 1:00 1:40 km/h 140 150 180 A discretization would be to say that the speed of the car was constant from 0:00 to 0:40, then from 0:40 to 1:20 and finally from 1:20 to 2:00. For instance, the total distance traveled in the first 40 minutes is approximately (2/3h × 140 km/h) = 93.3 km. This would allow us to estimate the total distance traveled as 93.3 km + 100 km + 120 km = 313.3 km, which is an example of numerical integration (see below) using a Riemann sum, because displacement is the integral of velocity.
Ill posed problem: Take the function f(x) = 1/(x − 1). Note that f(1.1) = 10 and f(1.001) = 1000: a change in x of less than 0.1 turns into a change in f(x) of nearly 1000. Evaluating f(x) near x = 1 is an ill-conditioned problem.
Well-posed problem: By contrast, the function is continuous and so evaluating it is well-posed, at least for x being not close to zero.
Direct methods compute the solution to a problem in a finite number of steps. These methods would give the precise answer if they were performed in infinite precision arithmetic. Examples include Gaussian elimination, the QR factorization method for solving systems of linear equations, and the simplex method of linear programming. In practice, finite precision is used and the result is an approximation of the true solution (assuming stability).
In contrast to direct methods, iterative methods are not expected to terminate in a number of steps. Starting from an initial guess, iterative methods form successive approximations that converge to the exact solution only in the limit. A convergence test is specified in order to decide when a sufficiently accurate solution has (hopefully) been found. Even using infinite precision arithmetic these methods would not reach the solution within a finite number of steps (in general). Examples include Newton's method, the bisection method, and Jacobi iteration. In computational matrix algebra, iterative methods are generally needed for large problems.
Iterative methods are more common than direct methods in numerical analysis. Some methods are direct in principle but are usually used as though they were not, e.g. GMRES and the conjugate gradient method. For these methods the number of steps needed to obtain the exact solution is so large that an approximation is accepted in the same manner as for an iterative method.
Furthermore, continuous problems must sometimes be replaced by a discrete problem whose solution is known to approximate that of the continuous problem; this process is called discretization. For example, the solution of a differential equation is a function. This function must be represented by a finite amount of data, for instance by its value at a finite number of points at its domain, even though this domain is a continuum.
The generation and propagation of errors
The study of errors forms an important part of numerical analysis. There are several ways in which error can be introduced in the solution of the problem.
Round-off errors arise because it is impossible to represent all real numbers exactly on a machine with finite memory (which is what all practical digital computers are).
Truncation and discretization error
Truncation errors are committed when an iterative method is terminated or a mathematical procedure is approximated, and the approximate solution differs from the exact solution. Similarly, discretization induces a discretization error because the solution of the discrete problem does not coincide with the solution of the continuous problem. For instance, in the iteration in the sidebar to compute the solution of 3x3 + 4 = 28, after 10 or so iterations, we conclude that the root is roughly 1.99 (for example). We therefore have a truncation error of 0.01.
Once an error is generated, it will generally propagate through the calculation. For instance, we have already noted that the operation + on a calculator (or a computer) is inexact. It follows that a calculation of the type a+b+c+d+e is even more inexact.
What does it mean when we say that the truncation error is created when we approximate a mathematical procedure? We know that to integrate a function exactly requires one to find the sum of infinite trapezoids. But numerically one can find the sum of only finite trapezoids, and hence the approximation of the mathematical procedure. Similarly, to differentiate a function, the differential element approaches to zero but numerically we can only choose a finite value of the differential element.
Numerical stability and well-posed problems
Numerical stability is an important notion in numerical analysis. An algorithm is called numerically stable if an error, whatever its cause, does not grow to be much larger during the calculation. This happens if the problem is well-conditioned, meaning that the solution changes by only a small amount if the problem data are changed by a small amount. To the contrary, if a problem is ill-conditioned, then any small error in the data will grow to be a large error.
Both the original problem and the algorithm used to solve that problem can be well-conditioned and/or ill-conditioned, and any combination is possible.
So an algorithm that solves a well-conditioned problem may be either numerically stable or numerically unstable. An art of numerical analysis is to find a stable algorithm for solving a well-posed mathematical problem. For instance, computing the square root of 2 (which is roughly 1.41421) is a well-posed problem. Many algorithms solve this problem by starting with an initial approximation x1 to , for instance x1=1.4, and then computing improved guesses x2, x3, etc.. One such method is the famous Babylonian method, which is given by xk+1 = xk/2 + 1/xk. Another iteration, which we will call Method X, is given by xk + 1 = (xk2−2)2 + xk.[3] We have calculated a few iterations of each scheme in table form below, with initial guesses x1 = 1.4 and x1 = 1.42.
Babylonian Babylonian Method X Method X x1 = 1.4 x1 = 1.42 x1 = 1.4 x1 = 1.42 x2 = 1.4142857... x2 = 1.41422535... x2 = 1.4016 x2 = 1.42026896 x3 = 1.414213564... x3 = 1.41421356242... x3 = 1.4028614... x3 = 1.42056... ... ... x1000000 = 1.41421... x28 = 7280.2284... Observe that the Babylonian method converges fast regardless of the initial guess, whereas Method X converges extremely slowly with initial guess 1.4 and diverges for initial guess 1.42. Hence, the Babylonian method is numerically stable, while Method X is numerically unstable.
- Numerical stability is affected by the number of the significant digits the machine keeps on, if we use a machine that keeps on the first four floating-point digits, a good example on loss of significance is given by these two equivalent functions
- If we compare the results of
- and
- by looking to the two above results, we realize that loss of significance which is also called Subtractive Cancelation has a huge effect on the results, even though both functions are equivalent; to show that they are equivalent simply we need to start by f(x) and end with g(x), and so
- The true value for the result is 11.174755..., which is exactly g(500) = 11.1748 after rounding the result to 4 decimal digits.
- Now imagine that lots of terms like these functions are used in the program; the error will increase as one proceeds in the program, unless one uses the suitable formula of the two functions each time one evaluates either f(x), or g(x); the choice is dependent on the parity of x.
- The example is taken from Mathew; Numerical methods using matlab, 3rd ed.
Areas of study
The field of numerical analysis is divided into different disciplines according to the problem that is to be solved.
Computing values of functions
Interpolation: We have observed the temperature to vary from 20 degrees Celsius at 1:00 to 14 degrees at 3:00. A linear interpolation of this data would conclude that it was 17 degrees at 2:00 and 18.5 degrees at 1:30pm.
Extrapolation: If the gross domestic product of a country has been growing an average of 5% per year and was 100 billion dollars last year, we might extrapolate that it will be 105 billion dollars this year.
Regression: In linear regression, given n points, we compute a line that passes as close as possible to those n points.
Optimization: Say you sell lemonade at a lemonade stand, and notice that at $1, you can sell 197 glasses of lemonade per day, and that for each increase of $0.01, you will sell one glass of lemonade less per day. If you could charge $1.485, you would maximize your profit, but due to the constraint of having to charge a whole cent amount, charging $1.49 per glass will yield the maximum income of $220.52 per day.
Differential equation: If you set up 100 fans to blow air from one end of the room to the other and then you drop a feather into the wind, what happens? The feather will follow the air currents, which may be very complex. One approximation is to measure the speed at which the air is blowing near the feather every second, and advance the simulated feather as if it were moving in a straight line at that same speed for one second, before measuring the wind speed again. This is called the Euler method for solving an ordinary differential equation.
One of the simplest problems is the evaluation of a function at a given point. The most straightforward approach, of just plugging in the number in the formula is sometimes not very efficient. For polynomials, a better approach is using the Horner scheme, since it reduces the necessary number of multiplications and additions. Generally, it is important to estimate and control round-off errors arising from the use of floating point arithmetic.
Interpolation, extrapolation, and regression
Interpolation solves the following problem: given the value of some unknown function at a number of points, what value does that function have at some other point between the given points?
Extrapolation is very similar to interpolation, except that now we want to find the value of the unknown function at a point which is outside the given points.
Regression is also similar, but it takes into account that the data is imprecise. Given some points, and a measurement of the value of some function at these points (with an error), we want to determine the unknown function. The least squares-method is one popular way to achieve this.
Solving equations and systems of equations
Another fundamental problem is computing the solution of some given equation. Two cases are commonly distinguished, depending on whether the equation is linear or not. For instance, the equation 2x + 5 = 3 is linear while 2x2 + 5 = 3 is not.
Much effort has been put in the development of methods for solving systems of linear equations. Standard direct methods, i.e., methods that use some matrix decomposition are Gaussian elimination, LU decomposition, Cholesky decomposition for symmetric (or hermitian) and positive-definite matrix, and QR decomposition for non-square matrices. Iterative methods such as the Jacobi method, Gauss–Seidel method, successive over-relaxation and conjugate gradient method are usually preferred for large systems.
Root-finding algorithms are used to solve nonlinear equations (they are so named since a root of a function is an argument for which the function yields zero). If the function is differentiable and the derivative is known, then Newton's method is a popular choice. Linearization is another technique for solving nonlinear equations.
Solving eigenvalue or singular value problems
Several important problems can be phrased in terms of eigenvalue decompositions or singular value decompositions. For instance, the spectral image compression algorithm[4] is based on the singular value decomposition. The corresponding tool in statistics is called principal component analysis.
Main article: Mathematical optimizationOptimization problems ask for the point at which a given function is maximized (or minimized). Often, the point also has to satisfy some constraints.
The field of optimization is further split in several subfields, depending on the form of the objective function and the constraint. For instance, linear programming deals with the case that both the objective function and the constraints are linear. A famous method in linear programming is the simplex method.
The method of Lagrange multipliers can be used to reduce optimization problems with constraints to unconstrained optimization problems.
Evaluating integrals
Main article: Numerical integrationNumerical integration, in some instances also known as numerical quadrature, asks for the value of a definite integral. Popular methods use one of the Newton–Cotes formulas (like the midpoint rule or Simpson's rule) or Gaussian quadrature. These methods rely on a "divide and conquer" strategy, whereby an integral on a relatively large set is broken down into integrals on smaller sets. In higher dimensions, where these methods become prohibitively expensive in terms of computational effort, one may use Monte Carlo or quasi-Monte Carlo methods (see Monte Carlo integration), or, in modestly large dimensions, the method of sparse grids.
Differential equations
Main articles: Numerical ordinary differential equations and Numerical partial differential equationsNumerical analysis is also concerned with computing (in an approximate way) the solution of differential equations, both ordinary differential equations and partial differential equations.
Partial differential equations are solved by first discretizing the equation, bringing it into a finite-dimensional subspace. This can be done by a finite element method, a finite difference method, or (particularly in engineering) a finite volume method. The theoretical justification of these methods often involves theorems from functional analysis. This reduces the problem to the solution of an algebraic equation.
Main articles: List of numerical analysis software and Comparison of numerical analysis softwareSince the late twentieth century, most algorithms are implemented in a variety of programming languages. The Netlib repository contains various collections of software routines for numerical problems, mostly in Fortran and C. Commercial products implementing many different numerical algorithms include the IMSL and NAG libraries; a free alternative is the GNU Scientific Library.
There are several popular numerical computing applications such as MATLAB, S-PLUS, LabVIEW, and IDL as well as free and open source alternatives such as FreeMat, Scilab, GNU Octave (similar to Matlab), IT++ (a C++ library), R (similar to S-PLUS) and certain variants of Python. Performance varies widely: while vector and matrix operations are usually fast, scalar loops may vary in speed by more than an order of magnitude.[5][6]
Many computer algebra systems such as Mathematica also benefit from the availability of arbitrary precision arithmetic which can provide more accurate results.
Also, any spreadsheet software can be used to solve simple problems relating to numerical analysis.
See also
- Scientific computing
- List of numerical analysis topics
- Gram-Schmidt process
- Numerical differentiation
- Symbolic-numeric computation
- Analysis of algorithms
- Numerical Recipes
- ^ Photograph, illustration, and description of the root(2) tablet from the Yale Babylonian Collection
- ^ The New Zealand Qualification authority specifically mentions this skill in document 13004 version 2, dated 17 October 2003 titled CARPENTRY THEORY: Demonstrate knowledge of setting out a building
- ^ This is a fixed point iteration for the equation x = (x2 − 2)2 + x = f(x), whose solutions include . The iterates always move to the right since . Hence converges and diverges.
- ^ The Singular Value Decomposition and Its Applications in Image Compression
- ^ Speed comparison of various number crunching packages
- ^ Comparison of mathematical programs for data analysis Stefan Steinhaus, ScientificWeb.com
- Gilat, Amos (2004). MATLAB: An Introduction with Applications (2nd edition ed.). John Wiley & Sons. ISBN 0-471-69420-7.
- Hildebrand, F. B. (1974). Introduction to Numerical Analysis (2nd edition ed.). McGraw-Hill. ISBN 0-070-28761-9.
- Leader, Jeffery J. (2004). Numerical Analysis and Scientific Computation. Addison Wesley. ISBN 0-201-73499-0.
- Trefethen, Lloyd N. (2006). "Numerical analysis", 20 pages. In: Timothy Gowers and June Barrow-Green (editors), Princeton Companion of Mathematics, Princeton University Press.
External links
- Numerische Mathematik, volumes 1-66, Springer, 1959-1994 (searchable; pages are images). (English) (German)
- Numerische Mathematik at SpringerLink, volumes 1-112, Springer, 1959–2009
- SIAM Journal on Numerical Analysis, volumes 1-47, SIAM, 1964–2009
Software and Code
- Numerical methods for Fortran programmers
- Java Number Cruncher features free, downloadable code samples that graphically illustrate common numerical algorithms
- Excel Implementations
- Several Numerical Mathematical Utilities (in Javascript)
Online Texts
- Numerical Recipes, William H. Press (free, downloadable previous editions)
- First Steps in Numerical Analysis, R.J.Hosking, S.Joe, D.C.Joyce, and J.C.Turner
- Numerical Analysis for Engineering, D. W. Harder
- CSEP (Computational Science Education Project), U.S. Department of Energy
Online Course Material
- Numerical Methods, Stuart Dalziel University of Cambridge
- Lectures on Numerical Analysis, Dennis Deturck and Herbert S. Wilf University of Pennsylvania
- Numerical methods, John D. Fenton University of Karlsruhe
- Numerical Methods for Science, Technology, Engineering and Mathematics, Autar Kaw University of South Florida
- Numerical Analysis Project, John H. Mathews California State University, Fullerton
- Numerical Methods - Online Course, Aaron Naiman Jerusalem College of Technology
- Numerical Methods for Physicists, Anthony O'Hare Oxford University
- Lectures in Numerical Analysis, R. Radok Mahidol University
- Introduction to Numerical Analysis for Engineering, Henrik Schmidt Massachusetts Institute of Technology
Areas of mathematics Areas Arithmetic · Algebra (elementary – linear – multilinear – abstract) · Geometry (Discrete geometry – Algebraic geometry – Differential geometry) · Calculus/Analysis · Set theory · Logic · Category theory · Number theory · Combinatorics · Graph theory · Topology · Lie theory · Differential equations/Dynamical systems · Mathematical physics · Numerical analysis · Computation · Information theory · Probability · Statistics · Optimization · Control theory · Game theory
Wikimedia Foundation. 2010.


text:
Researchers at Harvard University have taken inspiration from the swarm construction method used by termites to create TERMES. These robots are intended as the first step in a project with the ultimate goal of creating a fully automated robotic workforce that can create complex structures without the need for centralized control.
The robots are designed "with a philosophy of simplicity" needing to perform only a few simple functions with a high degree of reliability. Each robot houses ten sensors and three actuators in order to detect its position relative to the blocks used in the project as building materials.
TERMES units are only aware of their immediate vicinity and have no concept of the progression on the structure as a whole, or of the work conducted by their fellow robots. They simply progress what is in front of them to its final state.
If necessary, an individual worker robot has the ability to build a structure without the aide of other units as each robot is identical with no central command unit directing or coordinating the workers. Each TERMES has the ability to maneuver both on the structure it is creating, and in unstructured environments, but in their current design, can only operate in flat, obstacle-free areas.
Each robot measures 175 mm (6.8 in) in length with its gripping claw raised and is 110 mm ( 4.3 in) wide by 100 mm (4 in) high, excluding the supporting shelf. Each robot weighs 810g (28.5oz).
Construction and design
Each robot is constructed via a mixture of 3D printed components and off the shelf items with only a few hand crafted components. The team has used foam construction blocks to test the abilities of its robots. The blocks are built to easily stack together, sliding naturally into place with the help of neodymium magnets attached to each face.
The worker units are fitted with a motorized arm and gripper in order to pick up and manipulate the blocks with a padded shelf on the back to aid in stability and the robots are propelled via two micro metal gear motors. They're also fitted with mercury tilt switch, allowing them to retain a sense of position relative to the blocks if they slip while climbing.
After extensive testing it was decided that the workers would have four small whegs (a combination of a wheel and a leg) angled to fit the notches in the building blocks which would allow them to climb the highest block relative to their size. As well as allowing the robots to climb the blocks, the design also gives them the best chance of traversing more challenging terrain.
The whegs were given a curved shape in order to allow them to turn on the spot with the aide of circular grooves in the construction blocks, allowing them to maneuver on structures without toppling off. Robots are fitted with a motorized arm and gripper in order to pick up and manipulate the blocks with a padded shelf on the back to aide in carrying them.
All of these features combine to create a highly autonomous and reliable robot with the ability to climb, navigate, manipulate the construction blocks, and combine these abilities to autonomously produce a structure based on the user's design.
Potential benefits
The TERMES project represents a modest first step to the ultimate goal of a fully automated work force. This would remove the necessity of constant human oversight and has the potential to improve speed and efficiency of a building project.The lack of a central control unit would be useful if the robots were to be sent to a high-risk construction area. Ordinarily, if in such circumstances the command unit were to be destroyed, the entire operation would stop. However with the TERMES, each unit is entirely expendable allowing others to simply carry on the work regardless of losses.
Applications for this robotic construction crew could include tasks such as stacking sandbags in a flood or undertaking simple building tasks in harsh environments or on another planet.
A paper outlining the research was published this month in the journal Science.
The robot construction team can be seen in action in the Harvard video below.
Source: Harvard University


text:
Sometimes, when I am a step ahead of my email (yes, this is a rare occurrence), I get a chance to spend some time just browsing all the great online products OUP publishes. This morning, I spent some time in Oxford Biblical Studies Online and found an article about the relationship between medicine and the bible that I thought you would all enjoy. The article is from The Oxford Companion to the Bible and was written by J. Keir Howard. Check it out below.
It is generally agreed that modern Western medicine takes its origin from two main sources, the Greek ideals enshrined in the Hippocratic tradition, to which was added the influence of the biblical teaching of love of one's neighbor (Lev. 19.18; Luke 10.25–37). Thus, although Western medicine owes much to its classical heritage, especially as this has been reinterpreted since the Renaissance, it was the added dimension of a biblically based ethic that gave it a distinctive approach, centered in a profound respect for the person.
The pragmatism of Greek ideals is reflected in writings dealing with the exposure of unwanted or weak infants and with solutions to the problems of the chronically ill. The latter, being useless to themselves and to the state, should be allowed to die without medical attention (Plato, Republic 407). Biblical religion, on the other hand, had the frame of reference of a transcendent God to whom humankind was ultimately answerable; this gives rise to a profound respect for the dignity and innate value of the individual, seen as created in the image of God (Gen. 1.27). The responsibilities of biblical faith, whether Jewish or Christian, in the relations of people with one another are summed up in texts like "you shall love your neighbor as yourself" (Lev. 19.18) and "Do to others as you would have them do to you" (Matt. 7.12;…). From the standpoint of medicine, this was admirably summed up in the prayer of the great Jewish physician Maimonides (1135–1204 CE): "May I never see in my patient anything else than a fellow creature in pain."
The influence of such biblical precepts introduces an element of moral obligation into medical ethics as it developed in parallel with the rising influence of Christianity in the later Roman empire and throughout the medieval period in Europe. It also provided the spur to the church to establish hospitals that provided care for the sick; refuges that gave shelter to the blind, sufferers from leprosy, the mentally ill, and others outcast from society; and dispensaries for the poor. This same obligation, at a much later stage, led to the development of medical missionary work in conjunction with, yet distinct from, the growth of evangelistic concern that took place in the nineteenth century.
In providing a moral base for such developments, the Bible has given to modern medicine a great deal more than it might now care to acknowledge. Nevertheless, the centrality of respect for the person that originates in the Bible has now become enshrined in modern medical codes, such as the Geneva Convention Code of Ethics (1949) and the Helsinki Convention (1964) of the World Medical Association.
On the other hand, as a result of the ways in which the Bible has been interpreted and applied, there have been times when its influence on medicine has been negative. Until there was any proper understanding of the causative factors in disease and the actual disease processes themselves, there was a tendency to see sickness as the result of divine visitations and punishment for wrongdoing. The Bible itself knows little of physicians as such (see Medicine), and in the faith of Israel it was God alone who was the healer and giver of life. Most references to physicians are uncomplimentary (as in Mark 5.25–26, more temperately put in Luke 8.43) or at best neutral. Other than the reference to Luke "the beloved physician" (Col. 4.14), the only positive remarks about medical practitioners occur in Sirach 38.1–15, where the reader is exhorted to "honor physicians for their services." Even in this passage, however, the emphasis is on the need for confession of sin before any true healing could take place and the role of God as healer. (Note the much later dictum of Ambroise Paré [1510–1590]: "I treated the patient, but God healed him.")
In the Bible itself, it is the religious component that dominates in a situation where religion and medicine are inextricably bound together. This is seen particularly in Israel's legal codes, which did not separate physical disease from ritual purity. Thus, while the sanitary code of the Torah contains regulations that were of major importance in the promotion of health and the prevention of epidemic diseases in the community, they are set within a religious framework. Ultimately, it was God alone who sent disease and disaster as a punishment for wrongdoing or, alternatively, rewarded the good with health and well‐being (see, e.g., Exod. 15.26; Deut. 7.12–15).
The establishment of such a causal relationship between disease and a failure to meet religious and moral obligations was, in some sense, an attempt to answer the unanswerable question, "Why me?" It was seen especially with regard to contagious and disfiguring diseases, of which the best example is the disease complex unfortunately called leprosy in most English translations. Various ritual prescriptions were applied to such diseases in order to avoid the contamination of the community, which was seen as more important than the healing of the sick person. Similar ritual restrictions were also imposed in relation to normal physiological functions (see, e.g., Lev. 12; 15.16–33). Thus, consulting a physician for help could be construed as denial of the primary role of God and evidence of lack of faith in him, as well as lack of willingness to acknowledge personal sin (2 Chron. 16.12).
Many of these concepts were perpetuated in Christianity, even though such a simplistic viewpoint was challenged in the Bible (e.g., in the book of Job and John 9.1–3). The early church, however, undoubtedly interpreted such views too literally, and medical treatment was displaced by an emphasis on prayer and fasting in order to chasten the individual. From the Renaissance onward, however, medicine and theology became increasingly divorced from one another, allowing the development of medicine along the now‐familiar lines of scientific principles from the sixteenth or seventeenth centuries onward. Nonetheless, there has always been in Christianity a healing ministry that has been seen as biblically based (see, e.g., Luke 10.9). In general, this has not been considered as in competition with orthodox medicine but rather as complementary to it. Some more recent developments in healing ministries derived from biblical literalism, however, seem to be an attempt to return to a prescientific worldview, and will inevitably be in conflict with modern medical practice.


text:
Nation on alert as bushfires spread, Gillard warns NSW residents to be vigilant
NSW firefighter injured near Gundaroo
07 January 2013
published by www.news.com.au
Australia — A firefighter has been badly burned while battling an out-of-control fire north of Canberra.
The grassfire on Gundaroo Road, between the NSW town of Gundaroo and Gunning has burnt 50 hectares.
The NSW Rural Fire Services firefighter was taken by helicopter on Monday afternoon to Concord Hospital in Sydney with severe burns.
Gundaroo Road is closed from the Hume Highway.
Meanwhile, ACT firefighters have put out one of three blazes they were battling in the Territory's south.
A cluster of small fires at Rendezvous Creek in Namadgi National Park was extinguished after the site was water-bombed.
Another fire of 26 hectares near Mount Ginini is contained and the ACT Rural Fire Service (ACT RFS) continues to work to extinguish it.
The ACT RFS is also working to put out a fire in the far southwest of Namadgi National Park, near Sentry Box Mountain.
Both those fires in Namadgi are controlled and pose no threat to property or lives.
Water-bombing helicopters and specialist remote firefighters are working in the area.
A total fire ban has been declared for Tuesday in the ACT, with fire danger rated at extreme due to forecast very hot and windy weather.
For information about fires, ACT residents can check the ESA website: www.esa.act.gov.au or its Facebook or Twitter accounts, or call Canberra Connect on 13 22 81.
All residents are urged to report any smoke or fire sightings by calling triple zero.


text:
Image courtesy of www.truenewsfromchangenyc.blogspot.com
One Sunday, this television host/singer was backstage with her fellow female performers getting ready for their song number. Out of the blue, she approached the others girls and suggested to them that they should all wear dresses in the same shade to make their number look more special.
The other girls agreed to her suggestion so they began going through their dresses to find a shade that is common in everyone's wardrobe. After agreeing on which shade to wear, the girls started getting ready for their number.
When the girls were about to leave their dressing rooms, they noticed that the host was missing. The next time they saw her was when they were already about to appear on stage. Much to their surprise, the host was wearing a dress in a shade that is different from everyone else's. She totally made the other girls look like her backup dancers on stage.
Do you have an idea as to who this host/singer is? She seems to enjoy giving inaccurate information to her rivals so that she can upstage them.
I suggest that you follow micsylim on Twitter if you need additional clues on this post. Please observe the guidelines in posting comments. Always keep in mind that initials and comments that are too explicit will not be allowed.
Thank you very much for making Fashion PULIS a daily habit. Kindly continue to send your juicy stories to firstname.lastname@example.com.


text:
The purpose of this page is to provide a search tool
for Utah Census records. This resource should only
be used as an index and a search of the original
should always be done to overcome transcription
errors and omissions.
Type in a surname only to search for a family.
For best results on the first name only enter just the first part of the name e.g.
Mary will match on Mary, Mary Jane, Mary J., etc.
You can do partial searches on surnames e.g. De will match on Dean, Dee, Dewey, Dewhurst etc.
You need to provide at least 2 letters and it will match on everything that begins with those letters.
Picture courtesy Utah State Historical Society.
Back to Tracing Mormon Pioneers.
Number of visits