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1

Heat Transfer at Small Grashof Numbers  

Microsoft Academic Search

Rough physical arguments suggest that the heat transfer from a body, immersed in a fluid, should be determined by the heat-conduction equation alone whenever the Grashof number, G, associated with the problem is small. However, heat-transfer rates predicted in this fashion are not always in accordance with the experimentally determined values. It is shown that, while convection is negligible in

J. J. Mahony

1957-01-01

2

Efficient parallel computations ofows of arbitraryuids for all regimes of Reynolds, Mach and Grashof numbers  

Microsoft Academic Search

Thispaperpresents auni®ed numerical method able to address a wide class ofuidow problems of engineering interest. Arbitraryuids are treated specifying totally arbitrary equations of state, either in analytical form or through look-up tables. The most general system of the unsteady Navier-Stokes equations is integrated with a coupled implicit preconditioned method. The method can stand in®nite CFL number and shows the ef®ciency

M. Mulas; S. Chibbaro

3

Free convection from a point source of heat, and heat transfer from spheres at small Grashof numbers  

Microsoft Academic Search

A numerical description, based on the Boussinesq equations, is given for the steady free convection flow due to a point source of heat and heated spheres. We begin with the non-dimensional formulation of the problem for the point source giving the numerical solution for a wide range of values of the Prandtl number, the remaining parameter. The analytical description of

V. N. Kurdyumov; A. Liñán

1999-01-01

4

Laminar free convection induced by a line heat source, and heat transfer from wires at small Grashof numbers  

Microsoft Academic Search

The buoyancy-induced laminar flow and temperature fields associated with a line source of heat in an unbounded environment are described by numerically solving the non-dimensional Boussinesq equations with the appropriate boundary conditions. The solution is given for values of the Prandtl number, the single parameter, ranging from zero to infinity. The far-field form of the solution is well known, including

Amable Liñán; Vadim N. Kurdyumov

1998-01-01

5

Experimental study of low Prandtl number natural convection in an array of uniformly heated vertical cylinders  

Microsoft Academic Search

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

J. C. Dutton; J. R. Welty

1975-01-01

6

Low-Prandtl number natural convection in volumetrically heated rectangular enclosures  

Microsoft Academic Search

Following a previous study for a slender enclosure (AR=4), direct numerical two-dimensional simulations were conducted for the free convective flow of a low-Prandtl number fluid (Pr=0.0321) with internal heat generation in a square cavity having adiabatic top and bottom walls and isothermal side walls. The Grashof number, Gr, based on conductive maximum temperature and cavity width, ranged from 105 to

Salvatore Arcidiacono; Ivan Di Piazza; Michele Ciofalo

2001-01-01

7

Rayleigh-Bénard-Marangoni Instabilities of Low-Prandtl-Number Fluid in a Vertical Cylinder with Lateral Heating  

Microsoft Academic Search

A stability analysis of Rayleigh-Bénard-Marangoni flow of a low-Prandtl-number fluid in an open vertical cylinder is presented. The cylinder is heated laterally and cooled at the free surface by radiation. The governing equations are solved for axisymmetric base flow using a high-order finite-difference scheme. Small perturbations are applied to the base flow to determine the critical Marangoni number and Grashof

B. Xu; X. Ai; B. Q. Li

2007-01-01

8

Number Track  

NSDL National Science Digital Library

Students can use this interactive Flash applet to practice ordering whole numbers within 20. The applet displays a track and number tiles, which the user drags to create the correct sequence of numbers 1 through 20. Users may choose from four levels: place 5 missing numbers, place 10 numbers, arrange all 20 numbers, or create your own challenge.

Bunker, Dan

2010-01-01

9

Number Models  

NSDL National Science Digital Library

Students are given a worksheet with a representation of a number in base-ten blocks. Students are asked to write the number with numerals and determine how the number changes, when blocks are added and taken away.

Sherdan, Danielle

2010-07-26

10

Number Factory  

NSDL National Science Digital Library

This interactive game develops fluency and flexibility with whole number operations. In each round the player is given 4 single-digit whole numbers, presented in the context of a factory. The player uses each number exactly once with the interactive calculator to arrive as close as possible to a given target number.

Doorman, Michiel

2003-01-01

11

Number Sense  

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.

Wnet.org

2011-01-01

12

NUMBER SENSE  

NSDL National Science Digital Library

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 ...

Simpson, Ms.

2007-10-27

13

Leftist Numbers  

ERIC Educational Resources Information Center

|The leftist number system consists of numbers with decimal digits arranged in strings to the left, instead of to the right. This system fails to be a field only because it contains zerodivisors. The same construction with prime base yields the p-adic numbers.|

Rich, Andrew

2008-01-01

14

Number Time  

ERIC Educational Resources Information Center

|This article features Number Time, a site developed by the British Broadcasting Corporation (BBC) for young mathematics learners, located at www.bbc.co.uk/schools/numbertime. The site uses interactive animation to help children in pre-K through grade 2 understand and practice number basics. Users will find online games, videos that tell number

Herrera, Terese A.

2004-01-01

15

Number theory  

Microsoft Academic Search

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

M. R. Schroeder

1989-01-01

16

Number Factory  

NSDL National Science Digital Library

This interactive Java applet promotes number sense, estimation, and provides practice with order of operations. The player's goal is to make a numerical expression using the four given numbers and the four basic operations with the result being the target number (or as close as they can get to it). The student can also use brackets in their calculation.

Doorman, Michiel

2012-01-07

17

Superharmonic numbers  

NASA Astrophysics Data System (ADS)

Let tau(n) denote the number of positive divisors of a natural number n>1 and let sigma(n) denote their sum. Then n is superharmonic if sigma(n)mid n^ktau(n) for some positive integer k . We deduce numerous properties of superharmonic numbers and show in particular that the set of all superharmonic numbers is the first nontrivial example that has been given of an infinite set that contains all perfect numbers but for which it is difficult to determine whether there is an odd member.

Cohen, Graeme L.

2009-03-01

18

Number Balance  

NSDL National Science Digital Library

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.

Bunker, Dan

2005-01-01

19

Number Patterns  

NSDL National Science Digital Library

This Java applet allows users to practice recognizing patterns with integers and completing a sequence of numbers by adding or subtracting a common difference. The user is given the first five terms of a number pattern and asked to complete the pattern with the next two numbers. There is a check answer button for feedback and a new pattern button for additional practice. Instructions for users and teacher information are available through links at the top of the page.

2005-09-30

20

Number Grid  

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.

2012-01-01

21

Number Cruncher  

NSDL National Science Digital Library

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.

Science, American A.

2009-01-01

22

Number Grids and Number Triangles  

NSDL National Science Digital Library

Practice counting, counting by tens, place value, and fact families by entering your answers into the blank boxes; click the big blue and green buttons to check your work. Each of the five levels of Number Grid activities displays a section of a matrix containing a set of of consecutive whole numbers. A move from one number to the next within a row corresponds to a change of one; a move from one number to the next within a column refers to a change of ten. The three levels of Number Triangle activities provide practice with fact families and inverse relationships through flash cards. An addition/subtraction Number Triangle has two addends and a sum; a multiplication/division Number Triangle has two factors and a product.

Brown, Quincy; Fetter, Annie

2006-08-01

23

Number Watch  

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_.

24

Complex Numbers  

NSDL National Science Digital Library

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.

Kuphaldt, Tony R.

2008-07-15

25

Number Patterns  

NSDL National Science Digital Library

Students are given a worksheet and asked to identify and extend the growing or repeating numerical patterns. Students develop their own number pattern and create a model showing the pattern and the next three stages of the pattern.

Cornwell, Susan

2010-07-22

26

Number Fun  

NSDL National Science Digital Library

We will work on number sense. Play a fun counting game. IXL Counting Review Help Curious George count chicks! Count Your Chickens! Help Sagwa count the fish. Counting Fish Rescue the octopi by counting! Octopus Count Play the five frame games! Five Frame Game ...

Hoffmann, Mrs.

2011-08-05

27

Number Patterns  

NSDL National Science Digital Library

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.

Scotchmoor, Judy

2010-01-01

28

Numbers Sense  

ERIC Educational Resources Information Center

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…

Kathotia, Vinay

2009-01-01

29

Number Cruncher  

NSDL National Science Digital Library

Similar to the original "Function Machine" but lists input and output in a table and will not let the user attempt to guess the rule without having at least two data points. Number Cruncher is one of the Interactivate assessment explorers.

30

Number Sense!  

NSDL National Science Digital Library

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 ...

Painter, Ms.

2006-10-27

31

Number Pairs  

NSDL National Science Digital Library

With this interactive Flash applet students make use of complements of 10 to develop fluency with addition within 100. Users "repair" a water slide by selecting pairs of numbers that add to 20 in the first round, and then to 100. In successive rounds they may choose to practice with any multiple of 10 from 30 to 90.

Bunker, Dan

2010-01-01

32

Bead Numbers  

NSDL National Science Digital Library

This page links to an interactive Flash abacus that helps develop and reinforce pupils' understanding of place value. [Click "Start the Activity" to begin.] The abacus has three pegs (representing units, tens and hundreds) onto which users drop beads. The activity has two areas: a "free" (unstructured) area where pupils can represent 3-digit numbers, and a "computer questions" area that presents six challenging tasks to carry out. The page includes notes for teachers and pupils.

Netmedia

2011-01-01

33

Value Numbering  

Microsoft Academic Search

SUMMARY Value numbering is a compiler-based program analysis method that allows redundant computations to be removed. This paper compares hash-based approaches derived from the classic local algorithm1 with partitioning approaches based on the work of Alpern, Wegman, and Zadeck2. Historically, the hash-based algorithm has been applied to single basic blocks or extended basic blocks. We have improved the technique to

Preston Briggs; Keith D. Cooper; L. Taylor Simpson

1997-01-01

34

Fermat Numbers and Mersenne Numbers.  

National Technical Information Service (NTIS)

An IBM 7090 computer program, and results of testing Mersenne numbers M sub p = (2 raised to the power p) - 1 with p prime, p < 5000, have been described by Hurwitz. This paper describes modifications made to his program, and further computational results...

J. L. Selfridge A. Hurwitz

1968-01-01

35

Transitions in Convection of a Low Prandtl Number Fluid Driven by a Horizontal Temperature Gradient  

NASA Astrophysics Data System (ADS)

The transitions in convection of a low Prandtl number fluid (mercury) contained in enclosed rectangular cavities driven by horizontal temperature gradients were investigated. These cavities have insulating top, bottom and side boundaries. The other two end walls are highly conducting. The temperatures on the conducting walls were varied to control the temperature gradient inside. Both the temperature and the velocity of the fluid inside the cavity were measured. A traversing system allowed the probe position to be changed with the cavity always sealed. The temperature gradient, controlled by a computer, was ramped very slowly. At every 0.2 or 0.12 degree the ramping was held and a data file of several hours was taken. The Prandtl number of the fluid was varied from 0.025 to 0.035 by changing the average temperature. The cavity size effect on the transitions was investigated. The primary (large) cavity had aspect ratio (length:height:width) of 17.8:1:17.8 (height = 0.9 cm). The other cavities for size effect investigation were shorter and narrower. Fourier transform was used to analyze the time series. Phase portraits were constructed in 3d using time delay method and correlation dimensions were computed for some trajectories. For the large cavity, the observed onset of the longitudinal oscillatory state at Grashof number Gr = 18490 was far above the predicted value of 10610 for an infinite long cavity (height/length = 0). At low Grashof numbers, the flow was time independent. As Gr was increased, it changed to a noisy state with a periodic component and then became purely chaotic. Finally the longitudinal oscillatory state appeared with two frequencies and noise. The longitudinal oscillatory state was observed to be a standing wave with a wavelength of about 3 cm. The critical Gr was affected by the cavity width and length. The narrower the cavity, the more stable the flow. The critical Gr for oscillation decreased as the length was increased. An unusual subharmonic transition sequence was observed for the cavity with aspect ratio 4:1:2. With frequency components f and f/2 appear at the onset of oscillation, they were followed by f/3, f/6, f/9 and f/18. After the appearance of f/18, the subharmonics started to disappear and noise background kept increasing. Finally, it became pure chaotic.

Hung, Ming-Cheng

36

MHD Natural Convection Flow of Fluids of Different Prandtl Numbers in the Stokes Problem for a Vertical Porous Plate  

NASA Astrophysics Data System (ADS)

This paper investigates the effects of different Prandtl numbers on the MHD natural convection flow of fluids in the Stokes problem for the impulsive motion of a porous vertical plate. Both cases of the applied magnetic field being fixed either to the fluid or to the moving plate are considered. Unified closed form expressions are obtained for the temperature and the velocity, which are used to compute the Nusselt number and the skin friction respectively. These equations are solved semi-analytically using the Laplace transform technique along with the Riemann-sum approximation method. The influence of different flow parameters such as Prandtl number, Grashof number and the suction/injection parameter on velocity, temperature, skin friction and the rate of heat transfer are discussed for the two cases (i.e., when the magnetic field is fixed relative to the fluid or to the moving wall) with the aid of graphs. The result obtained through this method is found to be in excellent agreement with earlier results obtained analytically.

Jha, Basant K.; Apere, Clement A.

2012-06-01

37

Number Sense Series: Developing Early Number Sense  

NSDL National Science Digital Library

The author of this one-page article discusses early number sense and how it develops. She provides research background and suggests teaching strategies that promote early number sense, including instructions for simple games using dot cards. The article includes a list of references and a link to a follow-up article, "A Sense of 'ten' and Place Value" (cataloged separately).

Way, Jenni

2005-10-01

38

Number Square Puzzle: 10 Missing Numbers  

NSDL National Science Digital Library

This activity for the interactive white board (free access with registration) allows the learner to explore the patterns in the hundreds chart and notice the relationships between the numbers in the horizontal and vertical puzzles. Users drag and drop the individual numbers back in their correct places in the blank 10 X 10 grid.

2012-07-19

39

Kindergarten Number Sense  

NSDL National Science Digital Library

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 ...

Estes, Mrs.

2007-11-02

40

Number and Operations  

NSDL National Science Digital Library

The study of numbers and operations is the cornerstone of the mathematics curriculum. Learning what numbers mean, how they may be represented, relationships among them, and computations with them is central to developing number sense.

K-12 Outreach,

41

Multiplication Series: Number Arrays  

NSDL National Science Digital Library

This one-page article describes and illustrates how arrays can be used to represent many number concepts, including building multiplication facts, commutativity, parity (odd/even), and exploring factors, prime numbers, and square numbers.

2002-10-01

42

Sum-Difference Numbers  

ERIC Educational Resources Information Center

|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

Shi, Yixun

2010-01-01

43

Children's psychology of number  

Microsoft Academic Search

This paper is about the method by which young children learn the nature of number. By arguments in the language of the primitives, in the history of number, and in the modern approaches to teaching number concepts, we establish that numbers are understood by most people to be qualitative, rather than quantitative. Accordingly, we employ this idea to conduct real

Tong Monbill; Chiu Souyung

1983-01-01

44

Numbers and Operations  

NSDL National Science Digital Library

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 ...

Williams, Mrs.

2008-04-03

45

Operations on fuzzy numbers  

Microsoft Academic Search

A fuzzy number is a fuzzy subset of the real line whose highest membership values are clustered around a given real number called the mean value ; the membership function is monotonia on both sides of this mean value. In this paper, the usual algebraic operations on real numbers are extended to fuzzy numbers by the use of a fuzzification

DIDIER DUBOIS; HENRI PRADE

1978-01-01

46

The Kaprekar Numbers  

NASA Astrophysics Data System (ADS)

The (decimal) n-Kaprekar numbers are defined and are shown to be in one-one correspondence with the unitary divisors of 10^n - 1. In particular, this establishes the correctness of an algorithm for generating the Kaprekar numbers proposed by Charosh in 1981. The even perfect numbers are shown to be Kaprekar numbers in the binary base.

Iannucci, Douglas E.

2000-01-01

47

Guess The Number  

NSDL National Science Digital Library

This Flash applet is an interactive version of the classic game that develops number sense and strategic thinking. The computer generates a random secret number. The user makes guesses, taking advantage of the higher or lower clues provided, until the number is discovered. The goal is to find the secret number with as few attempts as possible. Three levels allow the user to adjust the range of possible numbers: up to 100, 500, or 1000.

Bunker, Dan

2010-01-01

48

Dividing Rational Numbers  

NSDL National Science Digital Library

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 ...

Nielsen, Ms.

2008-09-02

49

PET: [number sign]1 is number one  

SciTech Connect

Subsidized in the beginning by bottle deposits, now spurred by the ability of curbside recycling to collect more than soda bottles, polyethylene terephthalate (PET) recycling has made great strides in the last 10 years. Its growth rate and increased market demand are the envy of many other materials. Appropriate, if not deliberately, this number-one resin is listed under the Society for the Plastics Industry's resin identification code as [number sign]1. Unlike most recyclables, the market demand for recycled PET is greater than the supply. As a result, demand not supply, is fueling the increase in PET recycling.

Miller, C.

1994-09-01

50

Number Sense Made Simple Using Number Patterns  

ERIC Educational Resources Information Center

|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…

Su, Hui Fang Huang; Marinas, Carol; Furner, Joseph

2011-01-01

51

Narrow it Down: Numbers  

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: âIâm thinking of a number between 1 and 50.â 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 âmore thanâ and âless thanâ (Is it less than 7? Is there a 1 in the 10âs 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.

Terc

2010-01-01

52

Place Value Number Line  

NSDL National Science Digital Library

With this interactive applet students can develop their understanding of place value and the relative position and magnitude of numbers in the base-10 number system. Users drag given numbers to their position on a number line, zooming in and out to increase precision. They can select from six levels of difficulty (Tens, Hundreds, Thousands, Millions, Billions, Decimals) and from 1 to 3 dots. There are three modes: Explore, Practice, Test.

1999-01-01

53

The Numbered Forest.  

ERIC Educational Resources Information Center

|Describes the activity of numbering trees in which students number trees or find the numbered trees and observe other features according to class time. This activity aims to increase student tracking, mapping, and writing skills and integrate them with math skills. Suggests follow up activities that focus on reading, writing, and language skills.…

Kissner, Emily

2000-01-01

54

Discovery: Prime Numbers  

ERIC Educational Resources Information Center

|Prime numbers are important as the building blocks for the set of all natural numbers, because prime factorisation is an important and useful property of all natural numbers. Students can discover them by using the method known as the Sieve of Eratosthenes, named after the Greek geographer and astronomer who lived from c. 276-194 BC. Eratosthenes…

de Mestre, Neville

2008-01-01

55

Random Number Generation  

NSDL National Science Digital Library

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.

Joiner, David; The Shodor Education Foundation, Inc.

56

Law of Large Numbers  

NSDL National Science Digital Library

The controls on this applet let you change the number of trials, the probability of success in each trial, and toggle between viewing either the difference between the number of successes and the expected number of successes, or the difference between the percentage of successes and the probability of success in each trial.

Stark, Philip B.

2009-10-26

57

Theory of Numbers  

NSDL National Science Digital Library

This course provides an introduction to number theory, including topics such as prime numbers, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions and elliptic curves. The materials include lecture notes, exams and assignments with solutions. MIT presents OpenCourseWare as free educational material online. No registration or enrollment is required to use the materials.

Olsson, Martin

2010-12-27

58

Sign Language Number Recognition  

Microsoft Academic Search

Sign language number recognition system lays down foundation for handshape recognition which addresses real and current problems in signing in the deaf community and leads to practical applications. The input for the sign language number recognition system is 5000 Filipino sign language number video file with 640 x 480 pixels frame size and 15 frame\\/second. The color-coded gloves uses less

Iwan Njoto Sandjaja; Nelson Marcos

2009-01-01

59

Are numbers gendered?  

PubMed

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 that influence judgments of stimuli arbitrarily paired with numerical cues; specifically, babies' faces and foreign names were more likely to be judged as "male" when paired with odd versus even numbers. The power of logically irrelevant numerical stimuli to connote masculinity or femininity reflects the pervasiveness of gender as a social scaffolding for generating understandings of abstract concepts. PMID:21767039

Wilkie, James E B; Bodenhausen, Galen V

2011-07-18

60

Convoluted convolved Fibonacci numbers  

Microsoft Academic Search

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),

Pieter Moree

2003-01-01

61

Estimating large numbers.  

PubMed

Despite their importance in public discourse, numbers in the range of 1 million to 1 trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitical scenarios. Prior theoretical conceptions predict a log-to-linear shift: People will either place numbers linearly or will place numbers according to a compressive logarithmic or power-shaped function (Barth & Paladino, ; Siegler & Opfer, ). While about half of people did estimate numbers linearly over this range, nearly all the remaining participants placed 1 million approximately halfway between 1 thousand and 1 billion, but placed numbers linearly across each half, as though they believed that the number words "thousand, million, billion, trillion" constitute a uniformly spaced count list. Participants in this group also tended to be optimistic in evaluations of largely ineffective political strategies, relative to linear number-line placers. The results indicate that the surface structure of number words can heavily influence processes for dealing with numbers in this range, and it can amplify the possibility that analogous surface regularities are partially responsible for parallel phenomena in children. In addition, these results have direct implications for lawmakers and scientists hoping to communicate effectively with the public. PMID:23819823

Landy, David; Silbert, Noah; Goldin, Aleah

2013-03-05

62

Fun With Numbers!  

NSDL National Science Digital Library

Today we are going to play some games that will teach us Number Place Value and Number Words. First, use the Blocks to match the numbers that are given to you. You can either use a 3 column, a 2 column, or a 1 column problem. Do five of these problems. Play Catch a Ten. To play this game, you must count the blocks that you are picking up for the bear. ...

Holmgren, Ms.

2006-10-27

63

Biggest Number Game  

NSDL National Science Digital Library

In this game, learners build a multi-digit number by rolling dice and deciding which place value box to place each number. This requires strategy and planning as they must consider what they may roll in the future and which boxes are still open. Learners can compete to make the largest or smallest numbers during each round of play. Educators can use this game to introduce and/or practice strategy, risk, and place value.

Houston, Children'S M.

2013-05-15

64

Complex Numbers and Trigonometry  

NSDL National Science Digital Library

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.

Hillman, Abraham P.; Alexanderson, Gerald L.; Newton, Mervin E.

65

Prime Numbers Video  

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.

2010-01-01

66

Distance Domination Numbers of  

Microsoft Academic Search

The distance ?-domination number ??(G) of a strongly connected digraph G is the minimum number ? for which there is a set DV (G) with cardinality ? such that any vertex v \\/ 2 D can be reached within distance ? from some vertex in D. In this paper, we establish a lower bound and an upper bound for ??

Tian Fang; Xu Junming

67

Numbers as Shapes  

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.

2011-08-01

68

Numbers, taxonomy, and judgment  

Microsoft Academic Search

From the earliest times man has endowed numbers with magical properties. We all know that misfortunes come in threes, that the seventh son of a seventh son has remarkable gifts, and that it is unlucky to sit down thirteen at table. Even in more erudite spheres the tendency is discernible: how else can we explain the interest in perfect numbers,

W. T. Williams

1967-01-01

69

The Fibonacci Numbers.  

ERIC Educational Resources Information Center

|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)|

Onstad, Torgeir

1991-01-01

70

Beyond the number domain  

Microsoft Academic Search

In a world without numbers, we would be unable to build a skyscraper, hold a national election, plan a wed- ding or pay for a chicken at the market. The numerical symbols used in all these behaviors build on the approxi- mate number system (ANS) which represents the num- ber of discrete objects or events as a continuous mental magnitude.

Jessica F. Cantlon; Michael L. Platt; Elizabeth M. Brannon

2008-01-01

71

Subdivision Froude Number.  

National Technical Information Service (NTIS)

A Froude number that is applicable to subdivisions of a cross section is developed assuming one-dimensional flow. The subdivision Froude number is shown to be an accurate index of the flow regime in subdivisions of a cross section. An imaginary Froude num...

D. H. Schoellhamer J. C. Peters B. E. Larock

1985-01-01

72

MAA NumberADay  

NSDL National Science Digital Library

How much can you really learn from one number a day? Quite a bit actually, and this fun feature from the Mathematical Association of America (MAA) may prove to be rather addictive. Posted daily since September 2008, the MAA posts a number (for example, the number 11,185,272) and then offers a selection of that number's properties. Visitors to the site can click on some of the external links, look over the weblog archive, and also subscribe to their RSS feed. First-time visitors may wish to start by looking at the number 1529 (September 12, 2008), which happens to be the numerical address of MAA headquarters in Washington, D.C.

73

Introduction to Negative Numbers  

NSDL National Science Digital Library

This lesson plan based on a Cyberchase activity, first addresses a common misconception: starting measurement from 1 instead of 0. Then, it introduces negative numbers by extending a number line beyond 0 in the negative (left) direction. It is motivated by the Cyber Squadâs mission to find the captured Cyberchase Council on a particular floor of a tall building as seen in two quicktime videos: âImportance of the Origin" and "Inventing Negative Numbers" (each are cataloged separately). In addition to the learning activity, other support materials are included: handouts, assessments and answer keys.

Wnet.org

2006-01-01

74

The Numbers Game.  

ERIC Educational Resources Information Center

Describes a simple activity that explores and reveals the principles of significant figures and scientific notation using a 500 gram bag of unpopped popcorn. Students must devise a method for determining the number of kernels in the bag. (DDR)

Lustick, David

1997-01-01

75

The magical Fibonacci number  

Microsoft Academic Search

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

D. R. Mack

1990-01-01

76

Fibonacci's Forgotten Number  

ERIC Educational Resources Information Center

|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…

Brown, Ezra; Brunson, Cornelius

2008-01-01

77

SeanNumbers-Ofala  

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.

2010-02-01

78

Art by Numbers  

Microsoft Academic Search

\\u000a The number, object and subject of paintings, sculptures, drawings, video, films, photographs and installations have revealed\\u000a an aesthetic potential that had remained latent and unexpressed up until the first decades of the last century. For a long\\u000a time, the number in figurative arts was only the result of a transitive counting, an answer to the question “How many?” Virtues,\\u000a planets,

Mel Bochner; Roman Opalka

79

Report number codes  

SciTech Connect

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.

Nelson, R.N. (ed.)

1985-05-01

80

Third Grade Number Actiivities  

NSDL National Science Digital Library

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.

Godwin, Nicola

2012-01-01

81

Positive About Negative Numbers  

NSDL National Science Digital Library

This article is devoted to the mathematical topic of negative numbers and provides a series of primary resources designed to familiarize children with the notion of counting on either side of a central point. The article presents that the activities listed should be played sequentially to build precursory ideas in understanding negative numbers. All the games discussed in the article are linked on the page and have been cataloged separately: Incy Wincy Spider, Tug of War, Swimming Pool, Tug Harder, First Connect Three and lastly Sea Level.

Woodham, Liz

2011-01-01

82

Number Systems for Computers  

NSDL National Science Digital Library

Understanding number systems, especially Binary and Hexadecimal, is important to comprehending how computers function. It all begins with the magic circle we call ZERO. Work through the exercises in the order listed to gain some background in number systems and what makes it possible for computers to work. The magic of ZeroPlace Value Place Value Fun!Place Value Fun! One if by land, Two if by sea.The Binary System And then there were sixteen....hexadecimal Hexadecimal Headquarters Mr Booth s Computer Systems Class Student Learning Domain ...

Mrbooth

2007-09-19

83

Poissonian copy numbers  

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.

Liao, David

84

Stability in Numbers  

NSDL National Science Digital Library

In this Illuminations lesson, students apply their knowledge of addition equations to investigate the equivalence of two numeric expressions using the "Pan Balance-Numbers" applet (cataloged separately). An instructional plan, questions for the students, assessment options, extensions, and teacher reflections are given for the lesson as well as links to the applet and a student activity sheet(word format).

Keller, Gary M.

2011-01-01

85

Number2.com  

NSDL National Science Digital Library

Free online SAT, ACT, and GRE test preparation courses. Register for tutorials and practice sessions that dynamically adapt to performance, providing customized feedback for every response and monitoring overall student progress in the coaching system. Number2.com also offers a vocabulary builder, question of the day, and word of the day; and links to financial aid, college application, and career planning resources.

2007-11-26

86

Houses with Height Numbers  

NSDL National Science Digital Library

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.

Boon, Peter; Van Den Brink, Jan

2004-01-01

87

Fibonacci numbers and words  

Microsoft Academic Search

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,

Giuseppe Pirillo

1997-01-01

88

Why Delannoy numbers?  

Microsoft Academic Search

This article is not a research paper, but a little note on the history of combinatorics: We present here a tentative short biography of Henri De- lannoy, and a survey of his most notable works. This answers to the question raised in the title, as these works are related to lattice paths enumeration, to the so-called Delannoy numbers, and were

Cyril Banderier; Sylviane R. Schwer

2004-01-01

89

Electroweak baryon number violation  

Microsoft Academic Search

Electroweak baryon number violation may play a crucial role for the creation\\u000aof the matter-antimatter asymmetry in the early universe. In this talk, we\\u000areview the basic mechanism, which relies on the behavior of chiral fermions in\\u000anontrivial Yang-Mills gauge field backgrounds.

FRANS R. KLINKHAMER

2002-01-01

90

Electroweak baryon number violation  

Microsoft Academic Search

Electroweak baryon number violation may play a crucial role for the creation of the matter-antimatter asymmetry in the early universe. In this talk, we review the basic mechanism, which relies on the behavior of chiral fermions in nontrivial Yang-Mills gauge field backgrounds.

F. R. Klinkhamer

2002-01-01

91

The Net by Numbers.  

ERIC Educational Resources Information Center

The expansion of the commercial Internet has encouraged the interpretation of the Internet and its uses as a potential marketing medium. Examines statistical and demographic information about the Internet including number of Internet hosts and World Wide Web servers, and estimates of Internet users; and raises questions about definitions and…

McMurdo, George

1996-01-01

92

Sunspot Number Variations  

NSDL National Science Digital Library

In this activity students find the patterns that emerge when sunspot numbers are plotted over a period of time. Students learn about sunspot variations and the solar cycle, and are able to predict future solar minimums and solar maximums. The required sunspot charts can be downloaded along with the student worksheets.

Meier, Beverly

93

Making the Numbers? \\  

Microsoft Academic Search

Much recent work in strategy and popular discussion suggests that an excessive focus on “managing the numbers” --delivering quarterly earnings at the expense of longer term investments--makes it difficult for firms to make the investments necessary to build competitive advantage. “Short termism” has been blamed for everything from the decline of the US automobile industry to the low penetration of

Nelson P. Repenning; Rebecca M. Henderson

2010-01-01

94

By the numbers.  

PubMed

Any statement about the ability of the specialty to meet the future demand for orthodontic care based merely on a ratio of the projected number of orthodontists to the projected population is an oversimplification. Still, some inferences can be drawn from the data presented in this article. To be as prudent as possible, we will limit the scope of the discussion to the next 10 years. 1. It seems likely that the annual number of orthodontic graduates will remain about the same. 2. Considering the slow increase in the average age of orthodontists, the death rate will increase slightly, but not significantly. 3. The average annual number of retirees will be somewhere between 125 (the current rate) and 359 (the maximum projected by the JCO Retirement Survey). 4. The above assumptions would leave no less than 7,500 practicing orthodontists in the United States in 10 years. 5. The number of children age 9-17 will increase by 5-10%. In a worst-case scenario, could 7,500 orthodontists meet the orthodontic demand 10 years from now? The 1997 JCO Orthodontic Practice Study reported the annual median number of case starts to be 180. Multiplied by 9,000 orthodontists, that would equal 1,620,000 case starts. If we project a 10% increase in demand, there could be 1,782,000 case starts 10 years from now--an average of 238 starts per year for 7,500 orthodontists. Respondents to the Practice Studies have consistently indicated that they could handle 50 additional case starts with no increase in staff or facilities, which would mean current orthodontists could accommodate an average of 230 case starts. Moreover, orthodontic productivity is likely to increase due to delegation and improved technology. In conclusion, even if the sharp increase in the number of annual retirements anticipated in the JCO Retirement Survey turns out to be correct, it seems unlikely that it will affect the ability of the specialty to accomplish its mission in the foreseeable future. PMID:10535001

Gottlieb, E L

1999-05-01

95

CT number definition  

NASA Astrophysics Data System (ADS)

The accuracy of CT number plots has been found lacking in several medical applications. This is of concern since the ability to compare and evaluate results on a reproducible and standard basis is essential to long term development. Apart from the technical limitations arising from the CT scanner and the data treatment, there are fundamental issues with the definition of the Hounsfield number, namely the absence of a standard photon energy and the need to specify the attenuation mechanism for standard measurements. This paper presents calculations to demonstrate the shortcomings of the present definition with a brief discussion. The remedy is straightforward, but probably of long duration as it would require an international agreement.

Bryant, J. A.; Drage, N. A.; Richmond, S.

2012-04-01

96

Beware the numbers game.  

PubMed

Attention in England has turned again to the issue of staffing levels. As we report ( page 7 ), government adviser Don Berwick last month published the latest report calling on providers to make sure there are enough staff to deliver care. Professor Berwick falls short of recommending minimum staffing levels, as some had hoped, but he does demand 'appropriate numbers' to ensure services are safe. PMID:23980768

2013-09-01

97

Number patterns in Nature  

Microsoft Academic Search

Fibonacci phyllotaxis is one of many examples that demonstrate the relationship of biological growth patterns with the golden mean and self-similar symmetry, also observed in scale–rotational crystal growth. An equivalent relationship of natural-number patterns with the structure and periodicity of atomic matter is demonstrated. A generalized, closed periodic law that reveals the hidden symmetry in the periodicity of atomic matter

Jan C. A. Boeyens

2003-01-01

98

Separation numbers of trees  

Microsoft Academic Search

Let G be a graph on n vertices. Given a bijection f : V (G) ! {1,2,...,n}, let |f| = min{|f(u) f(v)| : uv 2 E(G)}. The separation number s(G) (also known as antibandwidth (1, 7)) of G is then max{|f|} over all such bijections f of G. We study the case when G is a forest, obtaining the following

Tao Jiang; Zevi Miller; Dan Pritikin

2009-01-01

99

Hypergraph Ramsey numbers  

Microsoft Academic Search

The Ramsey number r_k(s,n) is the minimum N such that every red-blue coloring of the k -tuples of an N -element set contains a red set of size s or a blue set of size n , where a set is called red (blue) if all k -tuples from this set are red (blue). In this paper we obtain new

David Conlon; Jacob Fox; Benny Sudakov

2010-01-01

100

All About 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.

2012-01-01

101

Prime Number Races  

Microsoft Academic Search

This is a survey article on prime number races. Chebyshev noticed in the first half of the nineteenth century that for any given value of x, there always seem to be more primes of the form 4n+3 less than x then there are of the form 4n+1. Similar observations have been made with primes of the form 3n+2 and 3n+1,

Andrew Granville; Greg Martin

2004-01-01

102

On Circuits and Numbers  

Microsoft Academic Search

Abstract We establish new, yet intimate relationships between the 2adic integers Z from arithmetics and digital circuits, finite and infinite, from electronics. (a) Rational numbers,with an odd denominator,correspond to output only synchronous,circuits. (b) Bit-wise 2ading mappings,correspond to combinational circuits. (c) On-line functions, N Z : ( ) ( ) (mod ) correspond to synchronous,circuits. (d) Continuous functions Z Z, correspond

Jean E. Vuillemin

1994-01-01

103

Paint by Number  

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.

2001-01-01

104

The radiative Reynolds number  

NASA Astrophysics Data System (ADS)

The radiative Reynolds number (RRN) is defined as a parameter characterizing the stability of low-temperature current-carrying plasma in high-current radiating discharges (such as are used for the pumping of high-power lasers). The RRN approach is used to examine the stability of plasmas and other objects in fields of intrinsic thermal emission; processes in MHD converters, gas lasers, and the cosmic plasma are examined. It is shown that in all cases where the RRN is sufficiently large the overheating instability (such as occurs in the solar photosphere) arises and the plasma becomes turbulent.

Rozanov, V. B.; Rukhadze, A. A.

105

History of Prime Numbers  

NSDL National Science Digital Library

The School of Mathematics and Statistics at the University of St Andrews, Scotland has developed an extensive collection of articles on the history of mathematics (See also NSDL Scout Report for Math, Engineering, and Technology, June 4, 2004). This article, written by J J O'Connor and E F Robertson, reviews the history of Prime Numbers. The article includes hyperlinks to topics addressed further in other sections of the website. For example, from this website visitors can also find articles on Pythagoras and Euclid.

106

By the Numbers  

NSDL National Science Digital Library

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.

Science, American A.

2009-01-01

107

q Numbers of quantum groups, Fibonacci numbers, and orthogonal polynomials  

Microsoft Academic Search

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

I. I. Kachurik

1998-01-01

108

Lepton family number violation  

SciTech Connect

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.

Herczeg, P.

1999-03-01

109

7 and Happy Numbers - Numberphile  

NSDL National Science Digital Library

In this 1.5-minute video, mathematician Dr Ria Symonds describes a characteristic of numbers such as 7, which after repeated squaring of digits and summing of the squares, result in the number 1, the first natural number. This introduction invites an investigation to find other "happy" numbers, and to find out what happens to "sad" numbers.

Symonds, Ria

2012-02-10

110

Wizard's Number (0-100)  

NSDL National Science Digital Library

This interactive Flash applet helps students develop number sense and basic number concepts. Players attempt to guess the wizard's number by clicking on dragons to get clues related to the number of digits, a more/less comparison with a benchmark, rounding, how far it is to the next ten, comparison of tens and units, and parity. Clicking on the wizard opens a keypad on which to type the secret number. A version covering numbers 0-1000 is cataloged separately.

2011-01-01

111

Number Games, Magnitude Representation, and Basic Number Skills in Preschoolers  

ERIC Educational Resources Information Center

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…

Whyte, Jemma Catherine; Bull, Rebecca

2008-01-01

112

PERFECT NUMBERS: AN ELEMENTARY INTRODUCTION  

Microsoft Academic Search

This serves as an elementary introduction to the history and the- ory surrounding even perfect numbers. One would be hard put to find a set of whole numbers with a more fascinating history and more elegant properties surrounded by greater depths of mystery—and more totally useless—than the perfect numbers. —Martin Gardner (2) The number 6 is unique in that 6

JOHN VOIGHT

113

Number Forms in the Brain  

Microsoft Academic Search

Mental images of number lines, Galton's ''number forms'' (NF), are a useful way of investigating the relation between number and space. Here we report the first neuroimaging study of number-form synesthesia, investigating 10 synesthetes with NFs going from left to right compared with matched controls. Neuroimaging with functional magnetic resonance imaging re- vealed no difference in brain activation during a

Joey Tang; Jamie Ward; Brian Butterworth

2008-01-01

114

New Enhanced Chaotic Number Generators  

Microsoft Academic Search

We introduce new families of enhanced chaotic number generators in order to compute very fast long series of pseudorandom numbers. The key feature of these generators being the use of chaotic numbers themselves for sampling chaotic subsequence of chaotic numbers in order to hide the generating function. We explore numerically the properties of these new families and underline their very

René Lozi

2007-01-01

115

Divisibility - Prime and Composite Numbers  

NSDL National Science Digital Library

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 ...

Harris, Mrs.

2007-11-05

116

A Study of Hyperperfect Numbers  

NASA Astrophysics Data System (ADS)

A number n is k-hyperperfect for some integer k if n = 1 + k s(n), where s(n) is the sum of the proper divisors of n. The 1-hyperperfect numbers are the familiar perfect numbers. This paper presents some theorems, conjectures and tables concerning hyperperfect numbers. All hyperperfect numbers less than 1011 have been computed. Evidence is presented suggesting that a published conjecture is false.

McCranie, Judson S.

2000-01-01

117

Numbers to the people: regulation, ownership and local number portability  

Microsoft Academic Search

Local number portability (LNP) is a key factor in the promotion of local call competition in telecommunications. By allowing a consumer to retain their number when moving between local telephone providers, LNP reduces customers’ switching costs and makes it easier for new providers to compete for customers. But regulators face a number of important choices when implementing LNP — what

Joshua S. Gans; Stephen P. King; Graeme Woodbridge

2001-01-01

118

Toddlers' Spontaneous Attention to Number and Verbal Number Quantification  

ERIC Educational Resources Information Center

|"S"pontaneous "a"ttention to "n"umber (SAN) is 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 before they acquire language. According…

Li, Xia

2009-01-01

119

The iodine number and the unsaturation number of fats  

Microsoft Academic Search

Summary  In order to determine the degree of unsaturation of fats and to study the kinetics of their hydrogenation, it is proposed\\u000a to use instead of the iodine number an index which is called the unsaturation number and shows the total number of double\\u000a bonds in 100 molecules of fatty acids.

A. I. Glushenkova; A. L. Markman

1970-01-01

120

Know Your Blood Sugar Numbers  

MedlinePLUS

... Numbers If you have diabetes, keeping your blood glucose (sugar) numbers in your target range can help you ... a lab test that measures your average blood glucose level over the last 2 to 3 months. ...

121

Three Cubes in One Number  

ERIC Educational Resources Information Center

|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.)|

Jue, Brian

2010-01-01

122

Natural Numbers in Transclassic Systems.  

National Technical Information Service (NTIS)

The reason why natural numbers follow the unilinear sequence prescribed by the Peano axioms is that these axioms presuppose that natural numbers are mapped unto the classic two-valued system of logic. If the same numbers are mapped unto transclassic syste...

G. Gunther

1970-01-01

123

PLURIDICTA, Numbers 28-35.  

ERIC Educational Resources Information Center

|The eight titles in this document include the following: "Comprehension and Input Processing as Useful Terms in the Field of SLA" (number 28) (Teresa Cadierno); "On the Role of Instruction in SLA: Research Results and Theoretical Explanations" (number 29) (Teresa Cadierno); "Can Writing Be Taught" (number 30) (Stuart Greene); "Academic Listening"…

Wagner, Johannes, Ed.

1998-01-01

124

DOMATIC NUMBER OF GRAPH PRODUCTS  

Microsoft Academic Search

A partition of V (G), all of whose classes are dominating sets in G, is called a domatic partition of G. The maximum number of classes of a domatic partition of G is called the domatic number of G. The concept of a domatic number was introduced in (1). More interesting results on domatically full graphs, domatically critical, domatically cocritical

Monika Kijewska; Maria Kwasnik

2002-01-01

125

PLURIDICTA, Numbers 28-35.  

ERIC Educational Resources Information Center

The eight titles in this document include the following: "Comprehension and Input Processing as Useful Terms in the Field of SLA" (number 28) (Teresa Cadierno); "On the Role of Instruction in SLA: Research Results and Theoretical Explanations" (number 29) (Teresa Cadierno); "Can Writing Be Taught" (number 30) (Stuart Greene); "Academic Listening"…

Wagner, Johannes, Ed.

1998-01-01

126

Do you know your numbers?  

NSDL National Science Digital Library

Let\\'s make sure we can recognize our numbers 0-10! Watch them swim by and Count the Fish! Let\\'s catch some fish in our very own Fishing Mission! A number is missing! Can you help Find the Missing Number? ...

Stringfield, Miss

2008-11-17

127

Perfect, Amicable and Sociable Numbers  

NSDL National Science Digital Library

These friendly sounding numbers are defined by their divisibility and sums. A perfect number is a number whose positive divisors (except for itself) sum to itself; an amicable number is a pair of numbers each of which equals the sum of the other's aliquot parts; and the members of aliquot cycles of length greater than two are often called sociable numbers. This page, housed at (but not officially affiliated with) the Institute for Materials Science at the University of Connecticut, defines and describes perfect, amicable, and sociable numbers and introduces aliquot sequences. The text has links to a bibliography and to numeric tables. This site might be interesting to college-level mathematics students or anyone into mathematical puzzles.

128

Quantum random number generator using photon-number path entanglement  

NASA Astrophysics Data System (ADS)

We report an experimental implementation of quantum random number generator based on the photon-number-path entangled state. The photon-number-path entangled state is prepared by means of two-photon Hong-Ou-Mandel quantum interference at a beam splitter. The randomness in our scheme is of truly quantum mechanical origin as it comes from the projection measurement of the entangled two-photon state. The generated bit sequences satisfy the standard randomness test.

Kwon, Osung; Cho, Young-Wook; Kim, Yoon-Ho

2010-08-01

129

Catalan Numbers, the Hankel Transform, and Fibonacci Numbers  

Microsoft Academic Search

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.

Aleksandar Cvetkovic; Predrag Rajkovic; Milos Ivkovic

2002-01-01

130

Finite Prandtl number 2-D convection at high Rayleigh numbers  

Microsoft Academic Search

Finite Prandtl number thermal convection is important to the dynamics of planetary bodies in the solar system. For example, the complex geology on the surface of the Jovian moon Europa is caused by a convecting, brine-rich global ocean that deforms the overlying icy “lithosphere”. We have conducted a systematic study on the variations of the convection style, as Prandtl numbers

Catherine A. Hier Majumder; David A. Yuen; Erik O. Sevre; John M. Boggs; Stephen Y. Bergeron

2002-01-01

131

Chaotic Nonlinear Prime Number Function  

NASA Astrophysics Data System (ADS)

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.

Mateos, Luis A.

2011-06-01

132

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.

2008-01-01

133

Number Line Bars--Fractions  

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.

2005-01-01

134

Familial sinistrals avoid exact numbers.  

PubMed

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

Sauerland, Uli; Gotzner, Nicole

2013-03-27

135

Higher-order Fibonacci numbers  

Microsoft Academic Search

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

Milan Randi?; Daniel A. Morales; Oswaldo Araujo

1996-01-01

136

PCF Extended with Real Numbers  

Microsoft Academic Search

We extend the programming language PCF with a type for (total and partial)real numbers. By a partial real number we mean an element of a cpo of intervals,whose subspace of maximal elements (single-point intervals) is homeomorphic tothe Euclidean real line. We show that partial real numbers can be considered as"continuous words". Concatenation of continuous words corresponds to refinementof partial information.

Martín Hötzel Escardó

1996-01-01

137

Schmidt number for quantum operations  

SciTech Connect

To understand how entangled states behave under local quantum operations is an open problem in quantum-information theory. The Jamiolkowski isomorphism provides a natural way to study this problem in terms of quantum states. We introduce the Schmidt number for quantum operations by this duality and clarify how the Schmidt number of a quantum state changes under a local quantum operation. Some characterizations of quantum operations with Schmidt number k are also provided.

Huang Siendong [Department of Applied Mathematics, National Dong Hwa University, Hualien 974, Taiwan (China)

2006-05-15

138

Familial Sinistrals Avoid Exact Numbers  

PubMed Central

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.

Sauerland, Uli; Gotzner, Nicole

2013-01-01

139

Power Series of Fuzzy Numbers  

NASA Astrophysics Data System (ADS)

Following Talo and Ba?ar [Determination of the duals of classical sets of sequences of fuzzy numbers and related matrix transformations, Comput. Math. Appl. 58(2009), 717-733], we essentially deal with the power series of fuzzy numbers with real or fuzzy coefficients. We consider the different cases of power series of fuzzy numbers to be convergent and give the theorem on the term by term differentiation of power series of fuzzy numbers. Finally, we present a result on the Taylor expansion of a fuzzy valued function.

Kadak, U?ur; Ba?ar, Feyzi

2010-11-01

140

Measuring Distance of Fuzzy Numbers by Trapezoidal Fuzzy Numbers  

NASA Astrophysics Data System (ADS)

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.

Hajjari, Tayebeh

2010-11-01

141

Cosmic Numbers and Quantum Theory.  

National Technical Information Service (NTIS)

The cosmic numbers are considered, with emphasis on the relation N approx.= rho sup 2 . (Here N is the number of nucleons in the universe, and rho, its radius in atomic units). This relation is interpreted in terms of a quantum-mechanical model. (Atominde...

J. Tarski

1985-01-01

142

Toddlers' Spontaneous Attention to Number  

ERIC Educational Resources Information Center

|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…

Baroody, Arthur J.; Li, Xia; Lai, Meng-lung

2008-01-01

143

Toddlers' Spontaneous Attention to Number  

ERIC Educational Resources Information Center

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…

Baroody, Arthur J.; Li, Xia; Lai, Meng-lung

2008-01-01

144

Rational Numbers and Proportional Reasoning  

NSDL National Science Digital Library

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.

Findell, Carol R.

2007-12-12

145

On Counting the Rational Numbers  

ERIC Educational Resources Information Center

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…

Almada, Carlos

2010-01-01

146

Understanding Rational Numbers and Proportions  

NSDL National Science Digital Library

The three activities in this investigation center on situations involving rational numbers and proportions that students encounter at a bakery. These activities involve several important concepts of rational numbers and proportions, including partitioning a unit into equal parts, the quotient interpretation of fractions, the area model of fractions, determining fractional parts of a unit not cut into equal-sized pieces, and equivalence.

Illuminations, Nctm

2000-01-01

147

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.

Technology, National C.

2012-12-13

148

On Counting the Rational Numbers  

ERIC Educational Resources Information Center

|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…

Almada, Carlos

2010-01-01

149

Quick Images: Visualizing Number Combinations  

NSDL National Science Digital Library

In this 6-minute video kindergarten teacher Stephanie Latimer describes and models techniques for developing children's number sense and visual recognition of number combinations. After quickly displaying groups of objects on a ten frame, she asks her students to describe the ways that they see the objects grouped. The resource includes reflection questions for viewers and a transcript of the video (doc).

2012-01-01

150

Investigating the Randomness of Numbers  

ERIC Educational Resources Information Center

|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…

Pendleton, Kenn L.

2009-01-01

151

Spontaneous Number Representation in Mosquitofish  

ERIC Educational Resources Information Center

|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…

Dadda, Marco; Piffer, Laura; Agrillo, Christian; Bisazza, Angelo

2009-01-01

152

Efficient Generation of Prime Numbers  

Microsoft Academic Search

The generation of prime numbers underlies the use of most public-key schemes, essentially as a major primitive needed for the cre- ation of key pairs or as a computation stage appearing during various cryptographic setups. Surprisingly, despite decades of intense mathemat- ical studies on primality testing and an observed progressive intensi- cation of cryptographic usages, prime number generation algorithms remain

Marc Joye; Pascal Paillier; Serge Vaudenay

2000-01-01

153

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.

2012-01-01

154

Number line compression and the illusory perception of random numbers.  

PubMed

Developmental studies indicate that children initially possess a compressed intuition of numerical distances, in which larger numbers are less discriminable than small ones. Education then "linearizes" this responding until by about age eight, children become able to map symbolic numerals onto a linear spatial scale. However, this illusion of compression of symbolic numerals may still exist in a dormant form in human adults and may be observed in appropriate experimental contexts. To investigate this issue, we asked adult participants to rate whether a random sequence of numbers contained too many small numbers or too many large ones. Participants exhibited a large bias, judging as random a geometric series that actually oversampled small numbers, consistent with a compression of large numbers. This illusion resisted training on a number-space mapping task, even though performance was linear on this task. While the illusion was moderately reduced by explicit exposure to linear sequences, responding was still significantly compressed. Thus, the illusion of compression is robust in this task, but linear and compressed responding can be exhibited in the same participants depending on the experimental context. PMID:20382625

Viarouge, Arnaud; Hubbard, Edward M; Dehaene, Stanislas; Sackur, Jérôme

2010-01-01

155

Graspable Objects Shape Number Processing  

PubMed Central

The field of numerical cognition represents an interesting case for action-based theories of cognition, since number is a special kind of abstract concept. Several studies have shown that within the parietal lobes adjacent neural regions code numerical magnitude and grasping-related information. This anatomical proximity between brain areas involved in number and sensorimotor processes may account for interactions between numerical magnitude and action. In particular, recent studies have demonstrated a causal role of action perception on numerical magnitude processing. If objects are represented in terms of actions (affordances), the causal role of action on number processing should extend to the case of objects affordances. This study investigates the relationship between numbers and objects affordances in two experiments, without (Experiment 1) or with (Experiment 2) the requirement of an action (i.e., participants were asked to hold an object in their hands during the task). The task consisted in repeating aloud the odd or even digit within a pair depending on the type of the preceding or following object. Order of presentation (object–number vs. number–object), Object type (graspable vs. ungraspable), Object size (small vs. large), and Numerical magnitude (small vs. large) were manipulated for each experiment. Experiment 1 showed a facilitation – in terms of quicker responses – for graspable over ungraspable objects preceded by numbers, and an effect of numerical magnitude after the presentation of graspable objects. Experiment 2 demonstrated that the action execution enhanced overall the sensitivity to numerical magnitude, and that at the same time it interfered with the effects of objects affordances on number processing. Overall, these findings demonstrate that numbers and graspable objects are strongly interrelated, supporting the view that abstract concepts may be grounded in the motor experience.

Ranzini, Mariagrazia; Lugli, Luisa; Anelli, Filomena; Carbone, Rossella; Nicoletti, Roberto; Borghi, Anna M.

2011-01-01

156

Graspable objects shape number processing.  

PubMed

The field of numerical cognition represents an interesting case for action-based theories of cognition, since number is a special kind of abstract concept. Several studies have shown that within the parietal lobes adjacent neural regions code numerical magnitude and grasping-related information. This anatomical proximity between brain areas involved in number and sensorimotor processes may account for interactions between numerical magnitude and action. In particular, recent studies have demonstrated a causal role of action perception on numerical magnitude processing. If objects are represented in terms of actions (affordances), the causal role of action on number processing should extend to the case of objects affordances. This study investigates the relationship between numbers and objects affordances in two experiments, without (Experiment 1) or with (Experiment 2) the requirement of an action (i.e., participants were asked to hold an object in their hands during the task). The task consisted in repeating aloud the odd or even digit within a pair depending on the type of the preceding or following object. Order of presentation (object-number vs. number-object), Object type (graspable vs. ungraspable), Object size (small vs. large), and Numerical magnitude (small vs. large) were manipulated for each experiment. Experiment 1 showed a facilitation - in terms of quicker responses - for graspable over ungraspable objects preceded by numbers, and an effect of numerical magnitude after the presentation of graspable objects. Experiment 2 demonstrated that the action execution enhanced overall the sensitivity to numerical magnitude, and that at the same time it interfered with the effects of objects affordances on number processing. Overall, these findings demonstrate that numbers and graspable objects are strongly interrelated, supporting the view that abstract concepts may be grounded in the motor experience. PMID:22164141

Ranzini, Mariagrazia; Lugli, Luisa; Anelli, Filomena; Carbone, Rossella; Nicoletti, Roberto; Borghi, Anna M

2011-12-06

157

Objective Calibration of Sunspot Numbers  

NASA Astrophysics Data System (ADS)

Waldmeier [1971] found a very tight relationship between the F10.7 solar radio flux and the sunspot number and suggested using the flux for an objective calibration of the sunspot number. He suggested that if this relationship changed later on, the sunspot number should be re-calibrated, assuming that the calibration must have drifted with time. I repeat his analysis using data up to the present and it is, indeed, clear that the relationship has changed significantly. This could be due to a drift of the calibration or to a secular change in the visibility of sunspots, or both.

Svalgaard, L.

2010-12-01

158

Muon Number Violating Rare Decays.  

National Technical Information Service (NTIS)

The experimental status of rare decays that violate muon number conservation is summarized, giving upper limits of their branching ratios with 90% confidence. All of the muon experiments share several common elements. They aim to identify the process soug...

M. D. Cooper

1985-01-01

159

Fibonacci Numbers and the Spreadsheet.  

ERIC Educational Resources Information Center

|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)|

Verderber, Nadine L.

1991-01-01

160

Trapezoidal approximations of fuzzy numbers  

Microsoft Academic Search

The problem of the trapezoidal approximation of fuzzy numbers is discussed. A set of criteria for approximation operators is formulated. These constraints can be used for direct operator derivation. A new nearest trapezoidal approximation operator preserving expected interval is suggested.

Przemyslaw Grzegorzewski; Edyta Mrówka

2005-01-01

161

What Is a Prime Number?  

NSDL National Science Digital Library

This blog page explains prime and composite numbers. It contains a music video about primes and additional pages with an activity, vocabulary, and links to an online game and a Sieve of Eratosthenes applet (both cataloged separately).

2011-04-11

162

Small Differences Between Prime Numbers  

Microsoft Academic Search

Let p_n denote the nth prime number. The present investigation relates to the existence of relatively small values of pn+1-p_n when n is large, and establishes more precise results than those previously known.

E. Bombieri; H. Davenport

1966-01-01

163

Pre-Assigned Application number  

Center for Drug Evaluation (CDER)

... If requesting for an ANDA, please include the following: Note: ANDA pre-assigned numbers expire after 60 days. Reference ... More results from www.fda.gov/drugs/developmentapprovalprocess/formssubmissionrequirements

164

Integral Presentations of Catalan Numbers  

ERIC Educational Resources Information Center

We compute in three different ways the same definite parametric integral. By-products are the derivation of a combinatorial identity and two integral presentations of Catalan numbers. One of them leads to a presentation using the [gamma] function.

Dana-Picard, Thierry

2010-01-01

165

Baryon number violating nuclear decay  

Microsoft Academic Search

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

C S Warke

1984-01-01

166

High Mode Number VIV Experiments  

Microsoft Academic Search

\\u000a A simple equation is presented which provides the maximum achievable mode number for a flexible cylinder, towed by the top\\u000a end with a weight at the bottom end. The maximum achievable mode number, while towing in still water, is shown to depend primarily\\u000a on mass ratio, length to diameter ratio and the maximum allowable angle of departure from vertical at

J. Kim Vandiver; Ayden Marcollo

167

Neural Addition and Fibonacci Numbers  

Microsoft Academic Search

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

Valeriu Beiu

1999-01-01

168

Copy number variation and mutation  

NASA Astrophysics Data System (ADS)

Until very recently, the standard model of DNA included two genes for each trait. This dated model has given way to a model that includes copies of some genes well in excess of the canonical two. Copy number variations in the human genome play critical roles in causing or aggravating a number of syndromes and diseases while providing increased resistance to others. We explore the role of mutation, crossover, inversion, and reproduction in determining copy number variations in a numerical simulation of a population. The numerical model consists of a population of individuals, where each individual is represented by a single strand of DNA with the same number of genes. Each gene is initially assigned to one of two traits. Fitness of the individual is determined by the two most fit genes for trait one, and trait two genetic material is treated as a reservoir of junk DNA. After a sufficient number of generations, during which the genetic distribution is allowed to reach a steady-state, the mean numberof genes per trait and the copy number variation are recorded. Here, we focus on the role of mutation and compare simulation results to theory.

Clark, Brian; Weidner, Jacob; Wabick, Kevin

2009-11-01

169

Finite Prandtl Number 2-D Convection at High Rayleigh Number  

Microsoft Academic Search

Finite Prandtl number thermal convection is important to the dynamics of planetary bodies in the solar system. For example, the complex geology on the surface of the Jovian moon Europa is caused by a convecting, brine-rich global ocean that deforms the overlying icy \\

Catherine Hier Majumder; David A. Yuen; Erik O. Sevre; John M. Boggs; Stephen Y. Bergeron

170

Experimental Determination of Ramsey Numbers  

NASA Astrophysics Data System (ADS)

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.

Bian, Zhengbing; Chudak, Fabian; Macready, William G.; Clark, Lane; Gaitan, Frank

2013-09-01

171

Negative Numbers and Antimatter Particles  

NASA Astrophysics Data System (ADS)

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.

Tsan, Ung Chan

172

Nanoplasmonics of prime number arrays.  

PubMed

In this paper, we investigate the plasmonic near-field localization and the far-field scattering properties of non-periodic arrays of Ag nanoparticles generated by prime number sequences in two spatial dimensions. In particular, we demonstrate that the engineering of plasmonic arrays with large spectral flatness and particle density is necessary to achieve a high density of electromagnetic hot spots over a broader frequency range and a larger area compared to strongly coupled periodic and quasi-periodic structures. Finally, we study the far-field scattering properties of prime number arrays illuminated by plane waves and we discuss their angular scattering properties. The study of prime number arrays of metal nanoparticles provides a novel strategy to achieve broadband enhancement and localization of plasmonic fields for the engineering of nanoscale nano-antenna arrays and active plasmonic structures. PMID:20052140

Forestiere, Carlo; Walsh, Gary F; Miano, Giovanni; Dal Negro, Luca

2009-12-21

173

Experimental determination of ramsey numbers.  

PubMed

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. PMID:24116761

Bian, Zhengbing; Chudak, Fabian; Macready, William G; Clark, Lane; Gaitan, Frank

2013-09-25

174

1.OA Equality Number Sentences  

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: Compare the number of circles in each box. If they are equal, write a number sentence. For example: 4+3=5+1+1 If they are not equal, write "not equal."...

175

2.NBT Largest Number Game  

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: Dona had cards with the numbers 0 to 9 written on them. She flipped over three of them. Her teacher said: If those three numbers are the digits in anot...

176

7.EE Guess My Number  

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: Laila tells Julius to pick a number between one and ten. �Add three to your number and multiply the sum by five,� she tells him. Next she says, �Now ta...

177

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.

Liao, David

178

Count the Dots: Binary Numbers  

NSDL National Science Digital Library

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.

Technology, National C.

2012-12-13

179

Learning math: Number and operations  

NSDL National Science Digital Library

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.

Findell, Carol R.

2007-12-12

180

Project Solo; Newsletter Number Eleven.  

ERIC Educational Resources Information Center

An experimental 9th grade computer science syllabus is proposed. The syllabus would include the technical information needed for controlling and programing the computer in a number of modes and would preview some of the areas covered in the high school curriculum. A sample module of a topic not normally taught in high school--distance and…

Pittsburgh Univ., PA. Project Solo.

181

The Number of Discriminable Colours  

Microsoft Academic Search

ALTHOUGH a calculation of the approximate number of discriminable colours must depend upon the individual concerned, `normal' persons may be expected to furnish data which agree to the correct order of magnitude. The method used here involves the choice of an arbitrary colour solid, the well-known Titchener-Ebbhighaus double pyramid, to which available experimental data are applied with simplifying assumptions, in

George B. Welch

1937-01-01

182

Hemispheric lateralization of number comparison  

Microsoft Academic Search

In order to clarify the respective contribution of the right and left posterior parietal cortex (PPC) to number comparison, transcranial magnetic stimulation (TMS) was used to disrupt PPC processing in subjects instructed to determine whether a digit was smaller or larger than 5. Single pulse TMS was applied over the PPC, either unilaterally or bilaterally, 150, 200, or 250 ms

Michael Andres; Xavier Seron; Etienne Olivier

2005-01-01

183

Solar System Number-Crunching.  

ERIC Educational Resources Information Center

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…

Albrecht, Bob; Firedrake, George

1997-01-01

184

Generalized Fibonacci Numbers and Applications  

Microsoft Academic Search

The present paper relates to the methods for data encoding and the reading of coded information represented by colored (including monochrome\\/black, gray) symbols (bars, triangles, circles, or other symbols). It also introduces new algorithms for generating secure, reliable, and high capacity color barcodes by using so called weighted n-dimensional random Fibonacci number based representations of data. The representation, symbols, and

Sarkis Agaian

2009-01-01

185

Estimating Number of Narcotic Addicts.  

National Technical Information Service (NTIS)

The study was undertaken because there was an obvious need for an estimation of the number of narcotic abusers for the United States and for major subdivisions. The method used was an old one known variously as the capture-recapture, or dilution technique...

J. A. Greenwood

1974-01-01

186

Yupno Number System and Counting  

Microsoft Academic Search

The starting point of this study is the apparent contradiction between the existence in Yupno (Papua New Guinea) culture of an elaborate number system and the lack of importance attributed to counting in everyday life. The study is designed to answer two questions: To what extent is the model described by the socially most prestigious expert shared by other Yupno

Jürg Wassmann; Pierre R. Dasen

1994-01-01

187

Oxidation Numbers and Their Limitations.  

ERIC Educational Resources Information Center

|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)|

Woolf, A. A.

1988-01-01

188

Materiales. Numbers 21-23.  

ERIC Educational Resources Information Center

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…

Materiales, 1997

1997-01-01

189

Human subtelomeric copy number variations  

Microsoft Academic Search

Copy number variation is a defining characteristic of human subtelomeres. Human subtelomeric segmental duplication regions (‘Subtelomeric Repeats’) comprise about 25% of the most distal 500 kb and 80% of the most distal 100 kb in human DNA. Huge allelic disparities seen in subtelomeric DNA sequence content and organization are postulated to have an impact on the dosage of transcripts embedded

H. Riethman

2008-01-01

190

Prandtl number of toroidal plasmas.  

National Technical Information Service (NTIS)

Theory of the L-mode confinement in toroidal plasmas is developed. The Prandtl number, the ratio between the ion viscosity and the thermal conductivity is obtained for the anomalous transport process which is caused by the self-sustained turbulence in the...

K. Itoh S. Itoh A. Fukuyama M. Yagi M. Azumi

1993-01-01

191

Adjuncts Build Strength in Numbers  

ERIC Educational Resources Information Center

|When professors in positions that offer no chance of earning tenure begin to stack the faculty, campus dynamics start to change. Growing numbers of adjuncts make themselves more visible. They push for roles in governance, better pay and working conditions, and recognition for work well done. And they do so at institutions where tenured faculty,…

June, Audrey Williams

2012-01-01

192

Fibonacci numbers and trigonometric identities  

Microsoft Academic Search

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.

N. Garnier; O. Ramare

2006-01-01

193

Questioning Zero and Negative Numbers  

ERIC Educational Resources Information Center

After experiencing a Developing Mathematical Ideas (DMI) class on the construction of algebraic concepts surrounding zero and negative numbers, the author conducted an interview with a first grader to determine the youngster's existing level of understanding about these topics. Uncovering young students' existing understanding can provide focus…

Wilcox, Virginia B.

2008-01-01

194

Time to Make the Numbers  

ERIC Educational Resources Information Center

|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.)|

Surrena, Michelle

2011-01-01

195

Not Just a Number Anymore  

ERIC Educational Resources Information Center

|In the Essex, Cincinnati retirement center where they both worked as nurses, Holly Doherty and Michele Schavoir often heard aides complain about one longtime resident in particular. The patient kicks and screams and nurses can not stand to be around her. After a year of playing detective, Doherty found a number of the patient's relatives in…

Henderson, Nancy

2008-01-01

196

Whole Number Subtraction -- An Analysis.  

ERIC Educational Resources Information Center

|This document is intended as a resource for persons using, designing, or evaluating instructional materials in whole number subtraction. Its purpose is to provide conceptual machinery: (1) for describing/specifying subtraction tests and exercises and (2) for formulating related questions and conjectures. It is mainly a logical analysis subject to…

Gilpin, John B.

197

20 CFR 404.1220 - Identification numbers.  

Code of Federal Regulations, 2013 CFR

...special identification number to each political subdivision...Notice of Identifying Number,â to inform the State of the special identification number(s). The special number...paid prior to 1987, the employer shall show the...

2013-04-01

198

Cosmic Rays and Sunspot Numbers  

NSDL National Science Digital Library

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.

Higley, Susan

199

Number-phase uncertainty relations  

Microsoft Academic Search

The minimization problem of finding the number-phase minimum uncertainty states (MUS) is considered and its solutions are found either numerically or, under some special conditions, analytically. The phase uncertainty measure is based on the Bandilla-Paul dispersion. The problem is treated (i) in a finite-dimensional Hilbert space and (ii) for a countably infinite-dimensional Hilbert space (i.e. the standard quantum harmonic oscillator),

T. Opatrny

1995-01-01

200

Determination of the Schmidt number  

NASA Astrophysics Data System (ADS)

Optimized, necessary, and sufficient conditions for the identification of the Schmidt number will be derived in terms of general Hermitian operators. These conditions apply to arbitrary mixed quantum states. The optimization procedure delivers equations similar to the eigenvalue problem of an operator. The properties of the solution of these equations will be studied. We solve these equations for classes of operators. The solutions will be applied to phase randomized two-mode squeezed-vacuum states in continuous variable systems.

Sperling, J.; Vogel, W.

2011-04-01

201

Ultrafilters and combinatorial number theory  

Microsoft Academic Search

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

Neil Hindman; Los Amgeles

202

Algorithms in algebraic number theory  

Microsoft Academic Search

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

Hendrik W. Lenstra Jr.

1992-01-01

203

Fibonacci numbers and orthogonal polynomials  

Microsoft Academic Search

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

Christian Berg

2006-01-01

204

Determination of the Schmidt number  

SciTech Connect

Optimized, necessary, and sufficient conditions for the identification of the Schmidt number will be derived in terms of general Hermitian operators. These conditions apply to arbitrary mixed quantum states. The optimization procedure delivers equations similar to the eigenvalue problem of an operator. The properties of the solution of these equations will be studied. We solve these equations for classes of operators. The solutions will be applied to phase randomized two-mode squeezed-vacuum states in continuous variable systems.

Sperling, J.; Vogel, W. [Arbeitsgruppe Quantenoptik, Institut fuer Physik, Universitaet Rostock, D-18051 Rostock (Germany)

2011-04-15

205

Recalibration of Zurich Sunspot Number  

NASA Astrophysics Data System (ADS)

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.

Svalgaard, Leif; Bertello, L.

2009-05-01

206

A Pseudo-Random Number Generator Based on Normal Numbers  

SciTech Connect

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.

Bailey, David H.

2004-12-31

207

Mass Transfer with Chemical Reaction on Flow Past an Accelerated Vertical Plate with Variable Temperature and Thermal Radiation  

NASA Astrophysics Data System (ADS)

An exact solution of an unsteady radiative flow past a uniformly accelerated infinite vertical plate with variable temperature and mass diffusion is presented here, taking into account the homogeneous chemical reaction of first order. The plate temperature as well as concentration near the plate is raised linearly with time. The dimensionless governing equations are solved using the Laplace-transform technique. The velocity, temperature and concentration fields are studied for different physical parameters such as the thermal Grashof number, mass Grashof number, Schmidt number, Prandtl number, radiation parameter, chemical reaction parameter and time. It is observed that the velocity increases with increasing values of the thermal Grashof number or mass Grashof number. But the trend is just reversed with respect to the thermal radiation parameter. It is also observed that the velocity increases with the decreasing chemical reaction parameter

Muthucumaraswamy, R.; Balachandran, P.; Ganesan, K.

2013-08-01

208

The Number of Tectonic Plates  

NASA Astrophysics Data System (ADS)

The number of tectonic plates on Earth described in the literature has expanded greatly since the early days of plate tectonics, when only a dozen or so plates were considered in global models of present day plate motions. Recently, with new techniques of more accurate earthquake epicenter locations, modern ways of measuring ocean bathymetry using swath mapping, the use of space based geodetic techniques &c, there has been a huge growth in the number of plates thought to exist. Bird (2003) proposed 52 plates, many of which were delineated on the basis of earthquake locations. Because of the pattern of areas of these plates, he suggested that there should be more small plates than he could identify. In this paper, I gather together publications that have proposed additional plates and discuss the new area arrangement which has been produced by the addition of these 23 new plates to Bird's catalogue. In addition I have measured the areas of the very small plates along the San Andreas fault identified by Bird and Rosenstock (1984) and added these 17 plates to the list as well as five plates proposed by Meade and Hager (2005). Sorting the plates by size allows us to investigate how size varies as a function of order. There are several changes of slope in the log-log plots of plate number (largest to smallest) against plate linear dimension. One set of relatively small plates shows a negative slope of -2.5, the same slope that has been found by modelling studies of two-dimensional structures such as rifted margins as well as three dimensional fragmentation models. Plates were characterized by what types of boundary they had. On looking at boundary type as a function of plate order, there seems to be no obvious pattern apart from what has been caused by non-uniform study of Earth's plate tectonic boundaries.

Harrison, C. G.

2011-12-01

209

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...

210

Propulsion at low Reynolds number  

NASA Astrophysics Data System (ADS)

We study the propulsion of two model swimmers at low Reynolds number. Inspired by Purcell's model, we propose a very simple one-dimensional swimmer consisting of three spheres that are connected by two arms whose lengths can change between two values. The proposed swimmer can swim with a special type of motion, which breaks the time-reversal symmetry. We also show that an ellipsoidal membrane with tangential travelling wave on it can also propel itself in the direction preferred by the travelling wave. This system resembles the realistic biological animals like Paramecium.

Najafi, Ali; Golestanian, Ramin

2005-04-01

211

High Rayleigh number porous convection  

NASA Astrophysics Data System (ADS)

Convective flow in porous media undergoes a transition around Rayleigh number Ra = 1300, from predominantly large-scale (quasi-) periodic rolls to vigorous columnar exchange flow driven by unsteady plume formation in boundary layers. The dynamics of these structures determine the flux of heat or solute through the system, as described by the Nusselt number Nu. This is of particular interest for understanding how convection affects the rate of dissolution of sequestered CO2 in a saline aquifer. High resolution 2D numerical simulations of porous media Rayleigh-Benard convection are presented, which show that, for 2000

Hewitt, Duncan; Lister, John; Neufeld, Jerome

2011-11-01

212

Access to emergency number services.  

PubMed

Access to emergency services is mandated by Title II of the Americans with Disabilities Act (ADA). The Department of Justice oversees the accessibility of public safety answering points (PSAPs), popularly called 9-1-1 centers. The Federal Communications Commission (FCC) has at least two roles in emergency number access: (1) as regulator of the ADA's Title IV on telecommunications access, and (2) as regulator of communications companies with regard to support of and interconnection with PSAPs. The rules of both agencies contributed significantly to the improvement during the 1990s of access to 9-1-1 for people who are deaf, hard of hearing, or speech disabled. However, as new technologies for text wireless communications and relay services have moved quickly to Internet protocol (IP)-based technologies over the past 5-8 years, the use of traditional wireline telephones and text telephones among deaf, hard of hearing, and speech-disabled people has declined. PSAPs cannot be contacted via the newer forms of telecommunications, such as e-mail, instant messaging, and IP-based forms of relay services, including video relay services. The gap between the technology supported by policy and the technologies currently being used by deaf and hard of hearing people has become a serious problem that is difficult to solve because of the separate jurisdictions of the two agencies, the need for coordination within the FCC, technological challenges, and funding issues. In this article, the key policy and technology challenges will be analyzed and recommendations made for short-and long-term solutions to this dilemma. PMID:18751576

Harkins, Judith E; Strauss, Karen Peltz

2008-01-01

213

Ranking fuzzy numbers by preference ratio  

Microsoft Academic Search

We propose a ranking method for fuzzy numbers. In this method a preference function is defined by which fuzzy numbers are measured point by point and at each point the most preferred number is identified. Then, these numbers are ranked on the basis of their preference ratio. Therefore, fuzzy numbers are compared relatively and not necessarily one is preferred absolutely

Mohammad Modarres; Soheil Sadi-nezhad

2001-01-01

214

Integrals of fuzzy-number-valued functions  

Microsoft Academic Search

Using the representation theorem of fuzzy numbers, we give an alternative approach for the integrals of fuzzy-number-valued functions, and for the Radon-Nikodym theorem of the fuzzy-number-valued measures.

Yun Kyong Kim; Byung Moon Ghil

1997-01-01

215

Trapezoidal approximations of fuzzy numbers - revisited  

Microsoft Academic Search

Fuzzy number approximation by trapezoidal fuzzy numbers which preserve expected interval is discussed. The previously proposed approximation operator is improved so as to always produce a well formed trapezoidal fuzzy number.

Przemyslaw Grzegorzewski; Edyta Mrówka

2007-01-01

216

Number line bounce (grades 6-8)  

NSDL National Science Digital Library

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

Mathematics, Utah S.

2003-01-01

217

Fascinating Fibonaccis: Mystery and Magic in Numbers.  

ERIC Educational Resources Information Center

|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

Garland, Trudi Hammel

218

Avogadro Number and Mole: A Royal Confusion.  

ERIC Educational Resources Information Center

|There is a great deal of confusion in physics and chemistry textbooks, dictionaries, manuals, and handbooks about the definition of Avogadro's number and the term "mole." Avogadro's number is defined simply as the number of atomic mass units in one gram. Mole is defined as the mass of one Avogadro number of identical items. (Author/PR)|

Emiliani, Cesare

1991-01-01

219

The Decimal Number System and Young Children  

ERIC Educational Resources Information Center

|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…

Harrison, John

2006-01-01

220

Representation and application of fuzzy numbers  

Microsoft Academic Search

In this paper we present the theoretical background of fuzzy numbers connected with the possibility and Dempster-Shafer theories. We describe some types of representation of fuzzy numbers and we study the notions of the distance and orders between fuzzy numbers based on these representations. The second part is devoted to the application of fuzzy numbers in data analysis, artificial intelligence

Stanis?aw Heilpern

1997-01-01

221

Some remarks on distances between fuzzy numbers  

Microsoft Academic Search

In this paper we consider different approaches to assigning distances between fuzzy numbers. A pseudo-metric on the set of fuzzy numbers arising from the idea of the value of a fuzzy number is described, and some of its topological properties are noted. Reducing functions are used to define a family of metrics on the space of fuzzy numbers; some convergent

William Voxman

1998-01-01

222

The Magic of a Number System  

NASA Astrophysics Data System (ADS)

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.

Elmasry, Amr; Jensen, Claus; Katajainen, Jyrki

223

Leading Digits, Lattice Points, and Algebraic Numbers.  

National Technical Information Service (NTIS)

Contents: Introduction and statement of results; Summation formulas; Pisot and Contents: Introduction and statement of results; Summation formulas; Pisot and Salem numbers; The Trace; A class of Pisot numbers; Lattice points; Repeated averages, and Leadin...

I. Vardi

1998-01-01

224

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.

Richard H. Jarman, College O.

2011-01-01

225

Number Theory in the High School Classroom.  

ERIC Educational Resources Information Center

|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)|

Dence, Thomas

1999-01-01

226

Fisheries Review Volume 35, Number 4, 1990.  

National Technical Information Service (NTIS)

Fisheries Review is intended to furnish fishery biologists with abstracts of current literature in sport, fishery research, and management. One volume, consisting of four numbers, is issued each year. Each number contains separate Author, Geographic, Taxo...

J. Humphrey

1990-01-01

227

Number Systems. Popular Lectures in Mathematics.  

ERIC Educational Resources Information Center

The origin, properties, and applications of various number systems are discussed. Among the 15 topics discussed are: tests for divisibility, the binary system, the game of Nim, computers, and infinite number representations. (MK)

Fomin, S. V.

228

Nearest interval approximation of a fuzzy number  

Microsoft Academic Search

The problem of the interval approximation of fuzzy numbers is discussed. A new interval approximation operator, which is the best one with respect to a certain measure of distance between fuzzy numbers, is suggested.

Przemyslaw Grzegorzewski

2002-01-01

229

Low Reynolds Number Airfoil Survey, Volume 1.  

National Technical Information Service (NTIS)

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 crit...

B. H. Carmichael

1981-01-01

230

Measurement Corner Mass, Moles and Avogadro's Number  

ERIC Educational Resources Information Center

Discusses and clarifies the confusion arising from the use of the terms "mass,""volume,""matter,""mole," and "Avogadro's number." Suggests three laboratory activities concerning mass, volume, and number of particles in a given volume. (CS)

Todd, Robert M.

1977-01-01

231

46 CFR Sec. 7 - Job order numbering.  

Code of Federal Regulations, 2010 CFR

...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 order thereto awarded to a...

2009-10-01

232

46 CFR Sec. 7 - Job order numbering.  

Code of Federal Regulations, 2010 CFR

...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 order thereto awarded to a...

2010-10-01

233

Requesting a Pre-Assigned Application number  

Center for Drug Evaluation (CDER)

... If YES, answer question below: Please specify the ANDA Number, Drug, Dosage Form, Strength. A pre-assigned number ... More results from www.fda.gov/drugs/developmentapprovalprocess/formssubmissionrequirements

234

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...

2011-10-01

235

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...

2012-10-01

236

Symmetry numbers and chemical reaction rates  

Microsoft Academic Search

This article shows how to evaluate rotational symmetry numbers for different molecular configurations and how to apply them\\u000a to transition state theory. In general, the symmetry number is given by the ratio of the reactant and transition state rotational\\u000a symmetry numbers. However, special care is advised in the evaluation of symmetry numbers in the following situations: (i)\\u000a if the reaction

Antonio Fernández-Ramos; Benjamin A. Ellingson; Rubén Meana-Pañeda; Jorge M. C. Marques; Donald G. Truhlar

2007-01-01

237

Positional number system (Babylonian) Session 5  

NSDL National Science Digital Library

In this session you will learn about the positional number system (Babylonian) Read Babylonian number system information. Read Babylonian Numerals. 1.What is the base? 2. Why was that base chosen? 3.How easy is the system to learn and to write? 4.Is there any ambiguity in the interpretation of symbols? 5.Does the culture use spoken numbers, body counting, or counting devices? Explain for each. 6.What patterns exist in the number systems? 7.How do ...

Nunes-Bufford, Mrs.

2008-12-01

238

On Anti-Elite Prime Numbers  

NASA Astrophysics Data System (ADS)

An odd prime number p is called anti-elite if only finitely many Fermat numbers are quadratic non-residues to p. This concept is the exact opposite to that of elite prime numbers. We study some fundamental properties of anti-elites and show that there are infinitely many of them. A computational search among all the numbers up to 100 billion yielded 84 anti-elite primes.

M"Uller, Tom

2007-09-01

239

Pearl Diver: A number line math game  

NSDL National Science Digital Library

In this Java application students must identify several points on a number line. The number line positions may include integers, fractional values, decimal values, and whole numbers. In the more advanced levels the number line does not begin with a 0 in all cases. Between levels students are asked to cut the eel into fractional parts and given points for their accuracy. This game is also available as an iOS app for a fee.

Lab, Nm S.

2013-01-01

240

The Decimal Representation of Real Numbers  

ERIC Educational Resources Information Center

|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…

Kalapodi, A.

2010-01-01

241

Developing Young Children's Multidigit Number Sense.  

ERIC Educational Resources Information Center

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)

Diezmann, Carmel M.; English, Lyn D.

2001-01-01

242

Developing Young Children's Multidigit Number Sense.  

ERIC Educational Resources Information Center

|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.)…

Diezmann, Carmel M.; English, Lyn D.

2001-01-01

243

Congruences for Bernoulli, Euler, and Stirling Numbers  

Microsoft Academic Search

We use properties of p-adic integrals and measures to obtain congruences for higher-order Bernoulli and Euler numbers and polynomials, as well as for certain generalizations and for Stirling numbers of the second kind. These congruences are analogues and generalizations of the usual Kummer congruences for the ordinary Bernoulli numbers.

Paul Thomas Young

1999-01-01

244

Reading the World through Very Large Numbers  

ERIC Educational Resources Information Center

|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…

Greer, Brian; Mukhopadhyay, Swapna

2010-01-01

245

Insights into Our Understandings of Large Numbers  

ERIC Educational Resources Information Center

|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…

Kastberg, Signe E.; Walker, Vicki

2008-01-01

246

Random number generator architecture and VLSI implementation  

Microsoft Academic Search

Security protocols and encryption algorithms are basically based on random number generators. In this paper, a new random number generator architecture is introduced. The produced number word length is equal to 160 bits. The philosophy architecture relies on the usage of the SHA hash function. The offered security strength of this certain hash function ensures the unpredictability of the produced

Nicolas Sklavos; Paris Kitsos; K. Papadomanolakis; Odysseas G. Koufopavlou

2002-01-01

247

Transient droplet heating at high Peclet number  

Microsoft Academic Search

The transient heating of a spherical liquid particle at high Peclet number has been calculated with the use of adaptive grids for low Reynolds numbers. The use of adaptive grids greatly enhances the efficiency of the calculations and allows for the large Peclet numbers to be studied. The results of the calculations show that the transient period of internal isotherm

H. A. Dwyer; R. J. Kee; P. K. Barr; B. R. Sanders

1981-01-01

248

46 CFR Sec. 7 - Job order numbering.  

Code of Federal Regulations, 2012 CFR

...2012-10-01 2012-10-01 false Job order numbering. Sec. 7 Section 7...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 order...

2012-10-01

249

46 CFR Sec. 7 - Job order numbering.  

Code of Federal Regulations, 2011 CFR

...2011-10-01 2011-10-01 false Job order numbering. Sec. 7 Section Sec...CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP...Contract number shall be inserted in every job order and supplemental job order...

2011-10-01

250

Mathematical and Behavioral Foundations of Number  

Microsoft Academic Search

The principal aim of this report has been to clear the air with regard to number development theory and research. We began with a brief overview of the status of the number concept in pure mathematics and psychology. It was argued that although there are clear methological differences between pure mathematical and psychological approaches to the study of number, the

Charles J. Brainerd

1973-01-01

251

On a canonical representation of fuzzy numbers  

Microsoft Academic Search

Fuzzy numbers, and more generally linguistic values, are approximate assessments, given by experts and accepted by decision-makers when obtaining more accurate values is impossible or unnecessary. To simplify the task of representing and handling fuzzy numbers, several authors have introduced real indices in order to capture the information contained in a fuzzy number. In this paper we propose two parameters,

M. Delgado; M. A. Vila; W. Voxman

1998-01-01

252

Teach Kids about Numbers All around Us  

ERIC Educational Resources Information Center

|Recognizing the role numbers play in people's everyday lives is crucial to students' math understanding now and down the road. That's why Bob Krech, a curriculum specialist in New Jersey's West Windsor-Plainsboro district, likes to teach a lesson he calls "Numbers All Around Us." This lesson uses real-world examples to show that numbers help…

Hudson, Hannah Trierweiler

2011-01-01

253

Number-operator approximation for pairing  

SciTech Connect

Conservation of particle number in the number-operator approximation of Otsuka and Arima is shown to require a particular normalization for the pair-creation operator. Even with this normalization, two difficulties arise: (a) the average number of particles in a shell can easily violate the Pauli principle, and (b) the mean square fluctuation of the particle number can be negative. As a consequence of the tendency to Pauli violation, the approximate ground-state expectation of the single-particle energy per particle is too low and fails to increase with the number of particles.

Vincent, C.M.

1983-01-01

254

Object-based neglect in number processing  

PubMed Central

Recent evidence suggests that neglect patients seem to have particular problems representing relatively smaller numbers corresponding to the left part of the mental number line. However, while this indicates space-based neglect for representational number space little is known about whether and - if so - how object-based neglect influences number processing. To evaluate influences of object-based neglect in numerical cognition, a group of neglect patients and two control groups had to compare two-digit numbers to an internally represented standard. Conceptualizing two-digit numbers as objects of which the left part (i.e., the tens digit should be specifically neglected) we were able to evaluate object-based neglect for number magnitude processing. Object-based neglect was indicated by a larger unit-decade compatibility effect actually reflecting impaired processing of the leftward tens digits. Additionally, faster processing of within- as compared to between-decade items provided further evidence suggesting particular difficulties in integrating tens and units into the place-value structure of the Arabic number system. In summary, the present study indicates that, in addition to the spatial representation of number magnitude, also the processing of place-value information of multi-digit numbers seems specifically impaired in neglect patients.

2013-01-01

255

Maximum Sunspot Numbers and Active Days  

NASA Astrophysics Data System (ADS)

Parameters associated with solar minimum have been studied to relate them to solar activity at solar maximum so that one could possibly predict behaviors of an upcoming solar cycle. The number of active days has been known as a reliable indicator of solar activity around solar minimum. Active days are days with sunspots reported on the solar disk. In this work, we have explored the relationship between the sunspot numbers at solar maximum and the characteristics of the monthly number of active days. Specifically, we have statistically examined how the maximum monthly sunspot number of a given solar cycle is correlated with the slope of the linear relationship between monthly sunspot numbers and the monthly number of active days for the corresponding solar cycle. We have calculated the linear correlation coefficient r and the Spearman rank-order correlation coefficient rs for data sets prepared under various conditions. Even though marginal correlations are found, they turn out to be insufficiently significant (r ~ 0.3). Nonetheless, we have confirmed that the slope of the linear relationship between monthly sunspot numbers and the monthly number of active days is less steep when solar cycles belonging to the "Modern Maximum" are considered compared with rests of solar cycles. We conclude, therefore, that the slope of the linear relationship between monthly sunspot numbers and the monthly number of active days is indeed dependent on the solar activity at its maxima, but that this simple relationship should be insufficient as a valid method to predict the following solar activity amplitude.

Chang, Heon-Young

2013-09-01

256

On the binary expansions of algebraic numbers  

SciTech Connect

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}.

Bailey, David H.; Borwein, Jonathan M.; Crandall, Richard E.; Pomerance, Carl

2003-07-01

257

Relativistic theory of tidal Love numbers  

SciTech Connect

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.

Binnington, Taylor; Poisson, Eric [Department of Physics, University of Guelph, Guelph, Ontario, N1G 2W1 (Canada) and Department of Physics, University of Guelph, Guelph, Ontario, N1G 2W1 (Canada) and Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario, M5S 3H8 (Canada)

2009-10-15

258

Generation of large prime numbers from a sequence of previous prime numbers  

NASA Astrophysics Data System (ADS)

A prime number is co-prime with all the primes as well. This paper utilizes this fact by generating larger prime numbers based on a set of smaller prime numbers. The prime numbers are ordered and each two consecutive primes are coupled to generate their co-prime number formula extending this process larger prime sequence is established. Will the process help us produce larger prime numbers faster and more efficiently? This paper investigates the described process.

Samir, Brahim Belhaouari; Rezk, Youssef A. Y.

2012-09-01

259

Towards even and odd squeezed number states  

SciTech Connect

The time evolution of even and odd squeezed states, as well as that of squeezed number states, has been given in simple, analytic form. This follows experimental work on trapped ions which has demonstrated even and odd coherent states, number states, and squeezed (but not displaced) ground states. The authors review this situation and consider the extension to even and odd squeezed number states. Questions of uncertainty relations are also discussed.

Nieto, M.M. [Los Alamos National Lab., NM (United States). Theoretical Div.]|[Universitaet Ulm (Germany). Abteilung fuer Quantenphysik

1998-03-01

260

Particle-number-projected thermal pairing  

SciTech Connect

Particle-number projection is applied to the modified BCS (MBCS) theory. The resulting particle-number-projected MBCS theory, taking into account the effects due to fluctuations of particle and quasiparticle numbers at finite temperature, is tested within the exactly solvable multilevel model for pairing as well as the realistic {sup 120}Sn nucleus. The signature of the pseudogap in the crossover region above the critical temperature of superfluid-normal phase transition is discussed in terms of the pairing spectral function.

Nguyen Dinh Dang [Heavy-Ion Nuclear Physics Laboratory, Nishina Center for Accelerator-Based Science, RIKEN, 2-1 Hirosawa, Wako city, 351-0198 Saitama, Japan and Institute for Nuclear Science and Technique, Hanoi (Viet Nam)

2007-12-15

261

Factoring numbers with a single interferogram  

SciTech Connect

We construct an analog computer based on light interference to encode the hyperbolic function f({zeta}){identical_to}1/{zeta} into a sequence of skewed curlicue functions. The resulting interferogram when scaled appropriately allows us to find the prime number decompositions of integers. We implement this idea exploiting polychromatic optical interference in a multipath interferometer and factor seven-digit numbers. We give an estimate for the largest number that can be factored by this scheme.

Tamma, Vincenzo [Department of Physics, University of Maryland, Baltimore County, Baltimore, Maryland 21250 (United States); Dipartimento Interateneo di Fisica, Universita degli Studi di Bari, IT-70100 Bari (Italy); Zhang Heyi; He Xuehua; Shih Yanhua [Department of Physics, University of Maryland, Baltimore County, Baltimore, Maryland 21250 (United States); Garuccio, Augusto [Dipartimento Interateneo di Fisica, Universita degli Studi di Bari, IT-70100 Bari (Italy); INFN-Sezione di Bari, Bari (Italy); Schleich, Wolfgang P. [Institut fuer Quantenphysik, Universitaet Ulm, Albert-Einstein-Allee 11, D-89081 Ulm (Germany)

2011-02-15

262

On the Number of Latin Squares  

Microsoft Academic Search

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\\u000a\\u000a (3) provide a formula for the

Brendan D. McKay; Ian M. Wanless

2005-01-01

263

Canonical number systems, counting automata and fractals  

Microsoft Academic Search

In this paper we study properties of the fundamental domain [script F][beta] of number systems, which are defined in rings of integers of number fields. First we construct addition automata for these number systems. Since [script F][beta] defines a tiling of the n-dimensional vector space, we ask, which tiles of this tiling `touch' [script F][beta]. It turns out that the

Klaus Scheicher; Jörg M. Thuswaldner

2002-01-01

264

Help With Fractions: Seeing Them As Numbers  

NSDL National Science Digital Library

In this informative webpage, teachers are given ideas on how to test what their students know about fractions on a number line, as well as some easy ideas to get students comfortable with placing fractions on a number line. There is a 2:50 minute video explaining how to place fractions on a number line. Two printable practice sheets are available in PDF format.

Roger

2011-01-01

265

On the centroids of fuzzy numbers  

Microsoft Academic Search

Abstract In a paper by Cheng [A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and Systems 95 (1998) 307–317], a centroid-based distance method was suggested for ranking fuzzy numbers, both normal and non-normal, where the fuzzy numbers are compared,and ranked in terms of their Euclidean distances from their centroid points to the origin. It is found

Ying-ming Wang; Jian-bo Yang; Dong-ling Xu; Kwai-sang Chin

2006-01-01

266

Factoring numbers with a single interferogram  

NASA Astrophysics Data System (ADS)

We construct an analog computer based on light interference to encode the hyperbolic function f(?)?1/? into a sequence of skewed curlicue functions. The resulting interferogram when scaled appropriately allows us to find the prime number decompositions of integers. We implement this idea exploiting polychromatic optical interference in a multipath interferometer and factor seven-digit numbers. We give an estimate for the largest number that can be factored by this scheme.

Tamma, Vincenzo; Zhang, Heyi; He, Xuehua; Garuccio, Augusto; Schleich, Wolfgang P.; Shih, Yanhua

2011-02-01

267

An integrated multiplier for complex numbers  

Microsoft Academic Search

In this article we consider a design of a multiplier for the multiplication of complex numbers. The complex numbers are packed\\u000a into one 32-bit word. They are represented by two 13-bit parts with the same 6-bit exponent. Multiplication of complex numbers\\u000a is examined from the perspectives of performance, complexity and silicon area. The design is unique and combines shared Booth

Vojin G. Oklobdzija; David Villeger; Thierry Soulas

1994-01-01

268

Physical tests for random numbers in simulations  

NASA Astrophysics Data System (ADS)

We propose three physical tests to measure correlations in random numbers used in Monte Carlo simulations. The first test uses autocorrelation times of certain physical quantities when the Ising model is simulated with the Wolff algorithm. The second test is based on random walks, and the third on blocks of n successive numbers. We apply the tests to show that recent errors in high precision Ising simulations using generalized feedback shift register algorithms are due to short range correlations in random number sequences.

Vattulainen, I.; Ala-Nissila, T.; Kankaala, K.

1994-11-01

269

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...

270

THE DISCOUNTED REPRODUCTIVE NUMBER FOR EPIDEMIOLOGY  

PubMed Central

The basic reproductive number, , and the effective reproductive number, , are commonly used in mathematical epidemiology as summary statistics for the size and controllability of epidemics. However, these commonly used reproductive numbers can be misleading when applied to predict pathogen evolution because they do not incorporate the impact of the timing of events in the life-history cycle of the pathogen. To study evolution problems where the host population size is changing, measures like the ultimate proliferation rate must be used. A third measure of reproductive success, which combines properties of both the basic reproductive number and the ultimate proliferation rate, is the discounted reproductive number . The discounted reproductive number is a measure of reproductive success that is an individual’s expected lifetime offspring production discounted by the background population growth rate. Here, we draw attention to the discounted reproductive number by providing an explicit definition and a systematic application framework. We describe how the discounted reproductive number overcomes the limitations of both the standard reproductive numbers and proliferation rates, and show that is closely connected to Fisher’s reproductive values for different life-history stages

Reluga, Timothy C.; Medlock, Jan; Galvani, Alison

2013-01-01

271

Number puzzles (grades 6-8)  

NSDL National Science Digital Library

This virtual manipulative challenges students to solve number puzzles using one- and two-digit addition. Each puzzle requires students to arrange a given set of numbers on either a triangular or square grid so that sides or the rows, columns, and diagonals add up to a given number. Students are able to check their answers on the web site, which includes instructions for using the applet, a description of related activities, and information for parents and teachers. There is also a link to the National Council of Teachers of Mathematics (NCTM) Standard for Number and Operations. Copyright 2005 Eisenhower National Clearinghouse

Mathematics, Utah S.

2003-01-01

272

The Fibonacci Numbers and the Golden Section  

NSDL National Science Digital Library

This award-winning site explores not only who Fibonacci was, but also the Fibonacci number properties, where they occur in nature, and much, much more. Puzzles with answers, illustrations, diagrams, and graphs are included. The Golden Ratio and Lucas numbers are addressed here as well. This site contains over 200 pages of information.

Knott, Ron

2007-12-12

273

7 CFR 46.20 - Lot numbers.  

Code of Federal Regulations, 2013 CFR

...2013-01-01 false Lot numbers. 46.20 Section 46.20 Agriculture Regulations of the...Records of Market Receivers § 46.20 Lot numbers. An identifying...purchased shipment of similar produce on hand at that time or received...

2013-01-01

274

Seedbed, Numbers 29-31, 1988.  

ERIC Educational Resources Information Center

|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…

Goldenhersh, Barbara, Ed.

275

The Writhing Number of a Space Curve  

PubMed Central

A geometric invariant of a space curve, the writhing number, is defined and studied. For the central curve of a twisted cord the writhing number measures the extent to which coiling of the central curve has relieved local twisting of the cord. This study originated in response to questions that arise in the study of supercoiled double-stranded DNA rings.

Fuller, F. Brock

1971-01-01

276

Deafness for the Meanings of Number Words  

ERIC Educational Resources Information Center

We describe the performance of an aphasic individual who showed a selective impairment affecting his comprehension of auditorily presented number words and not other word categories. His difficulty in number word comprehension was restricted to the auditory modality, given that with visual stimuli (written words, Arabic numerals and pictures) his…

Cano, Agnes; Rapp, Brenda; Costa, Albert; Juncadella, Montserrat

2008-01-01

277

On the Concept Image of Complex Numbers  

ERIC Educational Resources Information Center

|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…

Nordlander, Maria Cortas; Nordlander, Edvard

2012-01-01

278

Search for lepton-family-number nonconservation  

SciTech Connect

A review of the status of lepton-family-number nonconservation is given. After a brief historical and theoretical discussion, a description of how experimental searches for lepton-family-number nonconservation are performed is presented. Finally, a summary of the results from past experiments and prospects for future experiments is given.

Hoffman, C.M.

1986-01-01

279

Infinite Sums of M-Bonacci Numbers  

ERIC Educational Resources Information Center

|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-iru, Muniru A.

2009-01-01

280

The covering number in learning theory  

Microsoft Academic Search

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 Kðx; t Þ¼ kðxtÞ on ½0; 1? n; we provide estimates depending on

Ding-xuan Zhou

2002-01-01

281

Activities: Recursion and the Central Polygonal Numbers.  

ERIC Educational Resources Information Center

Provided is a teacher's guide for a problem-solving activity that establishes a link between number patterns and geometry by focusing on the development of recurrence relations established when generating central polygonal numbers. Reproducible worksheets and a 3.0 BASIC program for the activity are given. (MDH)

Miller, William A.

1991-01-01

282

Families of Linear Recurrences for Catalan Numbers  

ERIC Educational Resources Information Center

|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…

Gauthier, N.

2011-01-01

283

Fast Complex Convolution Using Number Theoretic Transforms.  

National Technical Information Service (NTIS)

It is shown that discrete circular convolution of complex number sequences may be carried out without arithmetic roundoff error using a family of number theoretic transforms defined in a finite ring. In certain cases the arithmetic of this transform may i...

E. Vegh L. M. Leibowitz

1975-01-01

284

THE NEW ELEMENT CALIFORNIUM (ATOMIC NUMBER 98)  

Microsoft Academic Search

Definite identification has been made of an isotope of the element with atomic number 98 through the irradiation of Cm²² with about 35-Mev helium ions in the Berkeley Crocker Laboratory 60-inch cyclotron. The isotope which has been identified has an observed half-life of about 45 minutes and is thought to have the mass number 244. The observed mode of decay

S. G. Thompson; A. Ghiorso; G. T. Seaborg

1950-01-01

285

7 CFR 1.414 - Docket number.  

Code of Federal Regulations, 2013 CFR

...Formal Review of Sourcing Areas Pursuant to the Forest Resources Conservation and Shortage Relief Act of 1990 (16 U.S.C. 620 et seq.) § 1.414 Docket number. Each proceeding, following its institution, shall be assigned a docket number by...

2013-01-01

286

7 CFR 1.414 - Docket number.  

Code of Federal Regulations, 2012 CFR

...Formal Review of Sourcing Areas Pursuant to the Forest Resources Conservation and Shortage Relief Act of 1990 (16 U.S.C. 620 et seq.) § 1.414 Docket number. Each proceeding, following its institution, shall be assigned a docket number by...

2012-01-01

287

Contests with an unknown number of contestants  

Microsoft Academic Search

This paper studies rent-seeking contests where the contestants do not know the number of actively competing contestants. Two models are compared. In the first, all players are risk neutral; in the second, all have constant absolute risk aversion. If the expected fraction of active contestants is low, an increase in the number of potential contestants increases individual rent-seeking efforts. This

Johannes Münster

2006-01-01

288

New Copy Number Variations in Schizophrenia  

Microsoft Academic Search

Genome-wide screenings for copy number variations (CNVs) in patients with schizophrenia have demonstrated the presence of several CNVs that increase the risk of developing the disease and a growing number of large rare CNVs; the contribution of these rare CNVs to schizophrenia remains unknown. Using Affymetrix 6.0 arrays, we undertook a systematic search for CNVs in 172 patients with schizophrenia

Chiara Magri; Emilio Sacchetti; Michele Traversa; Paolo Valsecchi; Rita Gardella; Cristian Bonvicini; Alessandra Minelli; Massimo Gennarelli; Sergio Barlati

2010-01-01

289

California Articulation Number System. Plan, Prepare, Transfer.  

ERIC Educational Resources Information Center

|The California Articulation Number (CAN) Project was initiated in 1985 by the three public segments of higher education in California: the University of California (UC), the California State Universities (CSU), and the California Community Colleges (CCC). The CAN System provides a cross reference number for lower-division, transferable,…

California Articulation Number System Project Office, Sacramento.

290

Factoring Large Numbers: Stealing Your Secrets.  

National Technical Information Service (NTIS)

The purpose of this research has been to explore the methods and techniques currently used to factor large numbers. The RSA cryptosystem employs large numbers which are the product of two primes to encrypt and decrypt private messages. In order to break t...

K. S. Currie

2000-01-01

291

A Partition Formula for Fibonacci Numbers  

Microsoft Academic Search

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.

Philipp Fahr; Claus Michael Ringerl

2008-01-01

292

Ultra Low Reynolds Number Airfoil Testing Facility  

Microsoft Academic Search

This paper documents research being performed under a SBIR Phase II program funded by NASA Dryden Flight Research Center. The paper will discuss the design, set-up, and initial testing of a new ultra low Reynolds number water tunnel airfoil testing facility. The new water tunnel 2-D airfoil facility is designed to test airfoil sections at low Reynolds numbers ranging from

Michael Kerho

293

Octane number prediction for gasoline blends  

Microsoft Academic Search

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

Nikos Pasadakis; Vassilis Gaganis; Charalambos Foteinopoulos

2006-01-01

294

Almost periodic fuzzy-number-valued functions  

Microsoft Academic Search

In this paper we develop a theory of almost periodic fuzzy functions, i.e. of the almost periodic functions of real variable and with values fuzzy real numbers, Although the class of fuzzy real numbers does not form a linear normed space, the majority of main properties of almost periodic functions with values in Banach spaces are extended to this case.

Barnabás Bede; Sorin G. Gal

2004-01-01

295

Fostering At-Risk Preschoolers' Number Sense  

ERIC Educational Resources Information Center

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…

Baroody, Arthur; Eiland, Michael; Thompson, Bradley

2009-01-01

296

Fostering At-Risk Preschoolers' Number Sense  

ERIC Educational Resources Information Center

|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…

Baroody, Arthur; Eiland, Michael; Thompson, Bradley

2009-01-01

297

Counting integral ideals in a number field  

Microsoft Academic Search

Let K be an algebraic number field. We discuss the problem of counting the number of integral ideals below a given norm and obtain effective error estimates. The approach is elementary and follows a classical line of argument of Dedekind and Weber. The novelty here is that explicit error estimates can be obtained by fine tuning this classical argument without

M. Ram Murty; Jeanine Van Order

2007-01-01

298

A prime number approach to biological sequencing.  

PubMed

Computational sequencing of nucleic acid and amino acid sequences is placing increasing demands on computer resources. The use of prime numbers is explored as a convenient means of improving program speed and reducing storage requirements. It is concluded that the application of the prime number approach leads to significant increases in speed and some reduction in storage requirements. PMID:3840126

Greer, W; Barrett, A N; Sowden, J M

1985-03-01

299

Infinite Sums of M-Bonacci Numbers  

ERIC Educational Resources Information Center

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-iru, Muniru A.

2009-01-01

300

Dividing Fraction by a Whole Number  

NSDL National Science Digital Library

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. ...

West, Mrs.

2013-01-04

301

Whole Word, Phrase or Number Reading.  

National Technical Information Service (NTIS)

An object of this invention is to provide a method of reading text, which locates and recognizes phrases, individual words, or numbers as single units. Another object is to provide a method of recognizing words or numbers like a person with dyslexia, whic...

M. A. O'Hair

1986-01-01

302

Nonclassicality in phase-number uncertainty relations  

SciTech Connect

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.

Matia-Hernando, Paloma; Luis, Alfredo [Departamento de Optica, Facultad de Ciencias Fisicas, Universidad Complutense, 28040 Madrid (Spain)

2011-12-15

303

Understanding a Child's Development of Number Sense  

NSDL National Science Digital Library

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.

Burns, Marilyn

2011-01-01

304

Dynamic hydration numbers for biologically important ions  

Microsoft Academic Search

The role of ionized groups in biological systems is determined by their affinity for water [Biophys. J. 72 (1997) 65–76]. The tightly bound water associated with biologically important ions increases their apparent size. We define the apparent dynamic hydration number of an ion here as the number of tightly bound water molecules that must be assigned to the ion to

Michael Y Kiriukhin; Kim D Collins

2002-01-01

305

How to read floating point numbers accurately  

Microsoft Academic Search

Converting decimal scientific notation into binary floating point is nontrivial, but this conversion can be performed with the best possible accuracy without sacrificing efficiency.Consider the problem of converting decimal scientific notation for a number into the best binary floating point approximation to that number, for some fixed precision. This problem cannot be solved using arithmetic of any fixed precision. Hence

William D. Clinger

2004-01-01

306

How to read floating point numbers accurately  

Microsoft Academic Search

Consider the problem of converting decimal scientific notation for a number into the best binary floating point approximation to that number, for some fixed precision. This problem cannot be solved using arithmetic of any fixed precision. Hence the IEEE Standard for Binary Floating-Point Arithmetic does not require the result of such a conversion to be the best approximation.This paper presents

William D. Clinger

1990-01-01

307

The factorization of the ninth Fermat number  

Microsoft Academic Search

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

H. W. Lenstra; M. S. Manasse; J. M. Pollard

1993-01-01

308

Hardware realization of a Fermat number transform  

Microsoft Academic Search

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.

J. McClellan

1976-01-01

309

Ground state number fluctuations of trapped particles  

NASA Astrophysics Data System (ADS)

This thesis encompasses a number of problems related to the number fluctuations from the ground state of ideal particles in different statistical ensembles. In the microcanonical ensemble most of these problems may be solved using number theory. Given an energy E, the well-known problem of finding the number of ways of distributing N bosons over the excited levels of a one-dimensional harmonic spectrum, for instance, is equivalent to the number of restricted partitions of E. As a result, the number fluctuation from the ground state in the microcanonical ensemble for this system may be found analytically. When the particles are fermions instead of bosons, however, it is difficult to calculate the exact ground state number fluctuation because the fermionic ground state consists of many levels. By breaking up the energy spectrum into particle and hole sectors, and mapping the problem onto the classic number partitioning theory, we formulate a method of calculating the particle number fluctuation from the ground state in the microcanonical ensemble for fermions. The same quantity is calculated for particles interacting via an inverse-square pairwise interaction in one dimension. In the canonical ensemble, an analytical formula for the ground state number fluctuation is obtained by using the mapping of this system onto a system of noninteracting particles obeying the Haldane-Wu exclusion statistics. In the microcanonical ensemble, however, the result can be obtained only for a limited set of values of the interacting strength parameter. Usually, for a discrete set of a mean-field single-particle quantum spectrum and in the microcanonical ensemble, there are many combinations of exciting particles from the ground state. The spectrum given by the logarithms of the prime number sequence, however, is a counterexample to this rule. Here, as a consequence of the fundamental theorem of arithmetic, there is a one-to-one correspondence between the microstate and the macrostate, resulting in the vanishing of number fluctuation for all excitations. The use of the canonical or grand canonical ensembles, on the other hand, gives a substantial number fluctuation from the ground state. For a related spectrum, that given by the logarithms of an integer n, the microcanonical number fluctuation is non-zero but the application of the other ensembles is still not valid. These two spectra are examples of systems where canonical and grand canonical ensembles averagings yield answers different from the microcanonical result. (Abstract shortened by UMI.)

Tran, Muoi N.

310

Compendium of Experimental Cetane Number Data  

SciTech Connect

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.

Murphy, M. J.; Taylor, J. D.; McCormick, R. L.

2004-09-01

311

ColE1 copy number mutants.  

PubMed Central

A deletion mutant of the colicin E1-derived plasmid, pDMS6642, exhibited an approximately fourfold increase in copy number. We subsequently isolated hydroxylamine-induced mutants of that plasmid that had a further increase in copy number. Analysis of them suggests that the increased copy number of pDMS6642 is associated with transcriptional readthrough from a Tn3 transposon into the region of ColE1 containing information that influences plasmid replication. The hydroxylamine mutation in one copy number mutant appeared to increase the plasmid copy number by stimulating readthrough transcription from the Tn3 transposon into the ColE1 replication control region, whereas the other hydroxylamine mutation acts by another mechanism.

Schmidt, L; Inselburg, J

1982-01-01

312

Random numbers spring from alpha decay  

SciTech Connect

Congruential random number generators, which are widely used in Monte Carlo simulations, are deficient in that the number they generate are concentrated in a relatively small number of hyperplanes. While this deficiency may not be a limitation in small Monte Carlo studies involving a few variables, it introduces a significant bias in large simulations requiring high resolution. This bias was recognized and assessed during preparations for an accident analysis study of nuclear power plants. This report describes a random number device based on the radioactive decay of alpha particles from a /sup 235/U source in a high-resolution gas proportional counter. The signals were fed to a 4096-channel analyzer and for each channel the frequency of signals registered in a 20,000-microsecond interval was recorded. The parity bits of these frequency counts (0 for an even count and 1 for an odd count) were then assembled in sequence to form 31-bit binary random numbers and transcribed to a magnetic tape. This cycle was repeated as many times as were necessary to create 3 million random numbers. The frequency distribution of counts from the present device conforms to the Brockwell-Moyal distribution, which takes into account the dead time of the counter (both the dead time and decay constant of the underlying Poisson process were estimated). Analysis of the count data and tests of randomness on a sample set of the 31-bit binary numbers indicate that this random number device is a highly reliable source of truly random numbers. Its use is, therefore, recommended in Monte Carlo simulations for which the congruential pseudorandom number generators are found to be inadequate. 6 figures, 5 tables.

Frigerio, N.A.; Sanathanan, L.P.; Morley, M.; Clark, N.A.; Tyler, S.A.

1980-05-01

313

Verification plan for equipment installation, full scale heater tests. number sign. 1 and. number sign. 2  

SciTech Connect

This Verification Plan for Equipment Installation, Full Scale Heater Test {number sign}1 and {number sign}2 (VP-FS {number sign}1 {number sign}2) presents the Hold Points and equipment items (check sheets) to document the installation effort. This plan complements, but does not duplicate, the Title 3 inspection.

Not Available

1980-01-01

314

Thermal fluctuations of induced fermion number  

SciTech Connect

We analyze the phenomenon of induced fermion number at finite temperature. At finite temperature, the induced fermion number > is a thermal expectation value, and we compute the finite temperature fluctuations ({Delta}N){sup 2}=-{sup 2}. While the zero temperature induced fermion number is topological and is a sharp observable, the finite temperature induced fermion number is generically nontopological, and is not a sharp observable. The fluctuations are due to the mixing of states inherent in any finite temperature expectation value. We analyze in detail two different cases in (1+1)-dimensional field theory: fermions in a kink background, and fermions in a chiral sigma model background. At zero temperature the induced fermion numbers for these two cases are very similar, but at finite temperature they are very different. The sigma model case is generic and the induced fermion number is nontopological, but the kink case is special and the fermion number is topological, even at finite temperature. There is a simple physical interpretation of all these results in terms of the spectrum of the fermions in the relevant background, and many of the results generalize to higher dimensional models.

Dunne, Gerald V.; Rao, Kumar

2001-07-15

315

Low Nephron Number and Its Clinical Consequences  

PubMed Central

Epidemiologic studies now strongly support the hypothesis, proposed over two decades ago, that developmental programming of the kidney impacts an individual’s risk for hypertension and renal disease in later life. Low birth weight is the strongest current clinical surrogate marker for an adverse intrauterine environment and, based on animal and human studies, is associated with a low nephron number. Other clinical correlates of low nephron number include female gender, short adult stature, small kidney size, and prematurity. Low nephron number in Caucasian and Australian Aboriginal subjects has been shown to be associated with higher blood pressures, and, conversely, hypertension is less prevalent in individuals with higher nephron numbers. In addition to nephron number, other programmed factors associated with the increased risk of hypertension include salt sensitivity, altered expression of renal sodium transporters, altered vascular reactivity, and sympathetic nervous system overactivity. Glomerular volume is universally found to vary inversely with nephron number, suggesting a degree of compensatory hypertrophy and hyperfunction in the setting of a low nephron number. This adaptation may become overwhelmed in the setting of superimposed renal insults, e.g. diabetes mellitus or rapid catch-up growth, leading to the vicious cycle of on-going hyperfiltration, proteinuria, nephron loss and progressive renal functional decline. Many millions of babies are born with low birth weight every year, and hypertension and renal disease prevalences are increasing around the globe. At present, little can be done clinically to augment nephron number; therefore adequate prenatal care and careful postnatal nutrition are crucial to optimize an individual’s nephron number during development and potentially to stem the tide of the growing cardiovascular and renal disease epidemics worldwide.

Luyckx, Valerie A.; Shukha, Khuloud; Brenner, Barry M.

2011-01-01

316

Nontopological Finite Temperature Induced Fermion Number  

SciTech Connect

We show that while the zero temperature induced fermion number in a chiral sigma model background depends only on the asymptotic values of the chiral field, at finite temperature the induced fermion number depends also on the detailed shape of the chiral background. We resum the leading low temperature terms to all orders in the derivative expansion, producing a simple result that can be interpreted physically as the different effect of the chiral background on virtual pairs of the Dirac sea and on the real particles of the thermal plasma. By contrast, for a kink background, not of sigma model form, the finite T induced fermion number is temperature dependent but topological.

Aitchison, I. J. R.; Dunne, G. V.

2001-02-26

317

RANEXP: experimental random number generator package  

NASA Astrophysics Data System (ADS)

A library containing highly portable implementations of most algorithms for (pseudo) random number generation has been developed, which might be used in any area of simulation which requires random number generators. Each generator is freely configurable by the user, so the RANEXP library is particularly well-suited for applications requiring different random number generators. The algorithms are implemented in C, but are callable from Fortran application program also. Supported by ODIN, a joint project of the University of Karlsruhe and Siemens Nixdorf Informationssysteme AG.

Hennecke, Michael

1994-04-01

318

Multiplication: An Adventure in Number Sense  

NSDL National Science Digital Library

This activity helps students learn their multiplication tables, but also build their reasoning about numbers, their relationships and their patterns in the multiplication table. The tutorial begins with a multiplication applet and leads the student through a number of different strategies for stream lining the number of multiplication facts from 100 down to thirteen. Each page in the unit consists of dialogs between a student and a mentor, as well as illustrations, summaries and suggestions for further explorations and activities. Users can skip dialogs if they wish, going directly for the summaries and activities.

2005-01-01

319

VLSI binary multiplier using residue number systems  

SciTech Connect

The idea of performing multiplication of n-bit binary numbers using a hardware based on residue number systems is considered. This paper develops the design of a VLSI chip deriving area and time upper bounds of a n-bit multiplier. To perform multiplication using residue arithmetic, numbers are converted from binary to residue representation and, after residue multiplication, the result is reconverted to the original notation. It is shown that the proposed design requires an area a=o(n/sup 2/ log n) and an execution time t=o(log/sup 2/n). 7 references.

Barsi, F.; Di Cola, A.

1982-01-01

320

Quantum numbers and band topology of nanotubes  

NASA Astrophysics Data System (ADS)

Nanotubes as well as polymers and quasi-1D subsystems of 3D crystals have line group symmetry. This allows two types of quantum numbers: roto-translational and helical. The roto-translational quantum numbers are linear and total angular (not conserved) momenta, while the helical quantum numbers are helical and complementary angular momenta. Their mutual relations determine some topological properties of energy bands, such as systematic band sticking or van Hove singularities related to parities. The importance of these conclusions is illustrated by the optical absorption in carbon nanotubes: parity may prevent absorption peaks at van Hove singularities.

Damnjanovic, M.; Milosevic, I.; Vukovic, T.; Maultzsch, J.

2003-05-01

321

The roles of cell size and cell number in determining ovariole number in Drosophila.  

PubMed

All insect ovaries are composed of functional units called ovarioles, which contain sequentially developing egg chambers. The number of ovarioles varies between and within species. Ovariole number is an important determinant of fecundity and thus affects individual fitness. Although Drosophila oogenesis has been intensively studied, the genetic and cellular basis for determination of ovariole number remains unknown. Ovariole formation begins during larval development with the morphogenesis of terminal filament cells (TFCs) into stacks called terminal filaments (TFs). We induced changes in ovariole number in Drosophila melanogaster by genetically altering cell size and cell number in the TFC population, and analyzed TF morphogenesis in these ovaries to understand the cellular basis for the changes in ovariole number. Increasing TFC size contributed to higher ovariole number by increasing TF number. Similarly, increasing total TFC number led to higher ovariole number via an increase in TF number. By analyzing ovarian morphogenesis in another Drosophila species we showed that TFC number regulation is a target of evolutionary change that affects ovariole number. In contrast, temperature-dependent plasticity in ovariole number was due to changes in cell-cell sorting during TF morphogenesis, rather than changes in cell size or cell number. We have thus identified two distinct developmental processes that regulate ovariole number: establishment of total TFC number, and TFC sorting during TF morphogenesis. Our data suggest that the genetic changes underlying species-specific ovariole number may alter the total number of TFCs available to contribute to TF formation. This work provides for the first time specific and quantitative developmental tools to investigate the evolution of a highly conserved reproductive structure. PMID:22200592

Sarikaya, Didem Pelin; Belay, Abel A; Ahuja, Abha; Dorta, Aisha; Green, Delbert André; Extavour, Cassandra G

2011-12-19

322

48 CFR 304.7001 - Numbering acquisitions.  

Code of Federal Regulations, 2012 CFR

...servicing agency. (6) A one-digit code describing the type of contract action. For example, the National Cancer Institute, NIH, may number its first contract for fiscal year 2009 as HHSN261200900001C. (Note: When more than one...

2012-10-01

323

Experimental Study of Low Reynolds Number Nozzles.  

National Technical Information Service (NTIS)

High-performance electrothermal thrusters operate in a low nozzle-throat Reynolds number regime. Under these conditions, the flow boundary layer occupies a large volume inside the nozzle, contributing to large viscous losses. Four nozzles (conical, bell, ...

S. P. Grisnik T. A. Smith L. E. Saltz

1987-01-01

324

46 CFR 169.515 - Number required.  

Code of Federal Regulations, 2011 CFR

...GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) NAUTICAL SCHOOLS SAILING SCHOOL VESSELS Lifesaving and Firefighting... (a) Except as provided in paragraph (c) of this...number of persons accommodated in the largest lifeboat or...

2012-10-01

325

47 CFR 1.1405 - File numbers.  

Code of Federal Regulations, 2012 CFR

...1405 Section 1.1405 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Grants by Random Selection Pole Attachment Complaint Procedures § 1.1405 File numbers. Each complaint which appears to...

2012-10-01

326

A physicist's approach to number partitioning  

Microsoft Academic Search

The statistical physics approach to the number partioning problem, a classical NP- hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase boundary that separates the \\

Stephan Mertens

2001-01-01

327

46 CFR 169.515 - Number required.  

Code of Federal Regulations, 2011 CFR

...GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) NAUTICAL SCHOOLS SAILING SCHOOL VESSELS Lifesaving and Firefighting... (a) Except as provided in paragraph (c) of this...number of persons accommodated in the largest lifeboat or...

2011-10-01

328

Being Number One Nation: Primacy and Detente.  

National Technical Information Service (NTIS)

This article is a short version of a study investigating American's status as Number One Nation in rankings of power and influence among all the world's nations. Factors determining international rankings are explored, as well as major attributes in which...

A. L. Wermuth

1975-01-01

329

Links to Literature: Popping Up Number Sense.  

ERIC Educational Resources Information Center

Describes a school-wide project using popcorn to gain number sense by learning more about a million. Used the books "How Much Is a Million?" and "If You Made a Million" to introduce the project. (MKR)

Hopkins, Lindy

1995-01-01

330

Large Number of Air Vehicles Simulation (LNAVSIM).  

National Technical Information Service (NTIS)

The Large Number of Air Vehicles Simulation (LNAVSIM) is an environment for modeling, planning, and simulating an air war. LNAVSIM addresses the Air Force's need for command and control tools for unmanned combat air vehicles (ucavs) and unmanned air vehic...

R. Johnson

2003-01-01

331

Numbers, Please! The Telephone Directory and Probability.  

ERIC Educational Resources Information Center

|Presents a Monte Carlo simulation on probability using a telephone directory as a pseudorandom-number generator. Claims that Monte Carlo simulations offer a way to teach probability concretely and with understanding and that students enjoy the probability experiments. (ASK)|

Brunner, Regina Baron

1997-01-01

332

Selecting Random Number Seeds in Practice.  

National Technical Information Service (NTIS)

A pseudorandom number generator, like a multiplicative congruential generator, depends on its initial value or seed. The computer may select a seed using its internal clock. Alternatively the simulation analyst may use Fishman's tables with seeds spaced 1...

J. P. C. Kleijnen

1985-01-01

333

Key and Sequence Number Extensions to GRE  

Microsoft Academic Search

GRE (Generic Routing Encapsulation) specifies a protocol for encapsulation of an arbitrary protocol over another arbitrary network layer protocol. This document describes extensions by which two fields, Key and Sequence Number, can be optionally carried in the GRE Header (1).

G. Dommety

2000-01-01

334

Application Type Supplemental NDA Application Number 201 ...  

Center for Drug Evaluation (CDER)

Text Version... Application Number 201-152/S-004 Submission Code SE-5 ... Another limitation of the NNRTIs is their relatively low genetic barrier to resistance. ... More results from www.fda.gov/downloads/drugs/developmentapprovalprocess

335

Infiltration formulas by curve number procedure.  

USGS Publications Warehouse

The Soil Conservation Service (SCS) curve number procedure for estimating runoff volume is examined in terms of the validity and applicability of the derived infiltration equations. -from ASCE Publications Abstracts

Chen, C. -L.

1982-01-01

336

Restriction Endonucleases/Variable Number Tandem Repeats.  

National Technical Information Service (NTIS)

Lecture I - Restriction Endonucleases by B. Howard, NIH, describes action of restriction endonucleases, nomenclature, availability of these materials, and certain difficulties. Lecture II - Variable Number Tandem Repeats (VNTR) by S. Odelberg, University ...

1994-01-01

337

Short-term memory for numbers.  

PubMed

Each of 52 (25 female and 27 male) high school students reproduced from memory 1000 eight-digit numbers after viewing each number for 5 s. Subjects were given unlimited time to reproduce the numbers and were allowed to change their reproductions. The range of errors was very large: from 71 to 2231 out of 8000 digits reproduced by each subject. Every subject showed a serial position effect and almost the same effect--about 70% of subjects made the greatest number of errors at the seventh digit. Female subjects made significantly more errors than did the males. Every subject improved his or her score by making changes. Data are given on the relative difficulty of recalling each of the 10 digits, the 100 doublets (pairs of digits), and the 1000 triplets (sets of three digits). PMID:2210770

Chapanis, A; Moulden, J V

1990-04-01

338

48 CFR 304.7001 - Numbering acquisitions.  

Code of Federal Regulations, 2011 CFR

...within the servicing agency. (6) A one-digit code describing the type of contract action. For example, the National Cancer Institute, NIH, may number its first contract for fiscal year 2009 as HHSN261200900001C. (Note: When more than...

2011-10-01

339

An Application of Number Theory to Cryptology.  

ERIC Educational Resources Information Center

|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)|

Snow, Joanne R.

1989-01-01

340

4.NBT Ordering 4-digit 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: Arrange these numbers in order, beginning with the smallest to the greatest. 2400 \\ 4002 \\ 2040 \\ 420 \\ 2004 Arrange these numbers in order, beginning ...

341

Mingle & Count: A Game of Number Sense  

NSDL National Science Digital Library

In this 5-minute video Barbara McCormick demonstrates an activity that helps her kindergarten students develop number sense. Students mingle and, on the teacher's signal, form themselves into groups of a given number. This active experience with equal groups helps build the foundation for multiplication and division with remainders. A sidebar provides reflection questions for viewers. A downloadable transcript (doc) of the video is included.

2012-01-01

342

New element californium (atomic number 98)  

Microsoft Academic Search

Definite identification has been made of an isotope of the element with atomic number 98 through the irradiation of Cm(242) with about 35-MeV helium ions in the Berkeley Crocker Laboratory 60-inch cyclotron. The isotope which has been identified has an observed half-life of about 45 minutes and is thought to have the mass number 244. The observed mode of decay

S. G. Thompson; A. Ghiroso; G. T. Seaborg

1950-01-01

343

The New Element Californium (Atomic Number 98)  

Microsoft Academic Search

Definite identification has been made of an isotope of the element with atomic number 98 through the irradiation of Cm242 with about 35-Mev helium ions in the Berkeley Crocker Laboratory 60-inch cyclotron. The isotope which has been identified has an observed half-life of about 45 min. and is thought to have the mass number 244. The observed mode of decay

S. G. Thompson; A. Ghiorso; G. T. Seaborg

1950-01-01

344

Factoring: A Visual Representation of Number  

NSDL National Science Digital Library

This Focus on Math blog post presents a dot diagram by Brent Yorgey of the consecutive natural numbers. The configuration of each number of dots reveals quickly whether it is prime or composite and provides information about its prime factorization. Included are two links: one to Stephen Von Wordley's animated factorization diagrams and the other to Malke Rosenfeld's blog describing a game based on the diagram.

Norris, Carollee

2013-01-08

345

SESAME equation of state number 7740: Polycarbonate  

SciTech Connect

An equation of state (EOS) for polycarbonate (a widely used polymer) has been generated with the computer code GRIZZLY and will be added to the SESAME library as material number 7740. Although a number of the input parameter used in the calculations are based on rough estimates. 7740 provides a good match to experimental Hugoniot data and should be reliable on or near the principal Hugoniot. 6 refs., 1 fig.

Boettger, J.C.

1991-06-01

346

A feeling for the numbers in biology  

PubMed Central

Although the quantitative description of biological systems has been going on for centuries, recent advances in the measurement of phenomena ranging from metabolism to gene expression to signal transduction have resulted in a new emphasis on biological numeracy. This article describes the confluence of two different approaches to biological numbers. First, an impressive array of quantitative measurements make it possible to develop intuition about biological numbers ranging from how many gigatons of atmospheric carbon are fixed every year in the process of photosynthesis to the number of membrane transporters needed to provide sugars to rapidly dividing Escherichia coli cells. As a result of the vast array of such quantitative data, the BioNumbers web site has recently been developed as a repository for biology by the numbers. Second, a complementary and powerful tradition of numerical estimates familiar from the physical sciences and canonized in the so-called “Fermi problems” calls for efforts to estimate key biological quantities on the basis of a few foundational facts and simple ideas from physics and chemistry. In this article, we describe these two approaches and illustrate their synergism in several particularly appealing case studies. These case studies reveal the impact that an emphasis on numbers can have on important biological questions.

Phillips, Rob; Milo, Ron

2009-01-01

347

Ion stopping powers and CT numbers.  

PubMed

One of the advantages of ion beam therapy is the steep dose gradient produced near the ion's range. Use of this advantage makes knowledge of the stopping powers for all materials through which the beam passes critical. Most treatment planning systems calculate dose distributions using depth dose data measured in water and an algorithm that converts the kilovoltage X-ray computed tomography (CT) number of a given material to its linear stopping power relative to water. Some materials present in kilovoltage scans of patients and simulation phantoms do not lie on the standard tissue conversion curve. The relative linear stopping powers (RLSPs) of 21 different tissue substitutes and positioning, registration, immobilization, and beamline materials were measured in beams of protons accelerated to energies of 155, 200, and 250 MeV; carbon ions accelerated to 290 MeV/n; and iron ions accelerated to 970 MeV/n. These same materials were scanned with both kilovoltage and megavoltage CT scanners to obtain their CT numbers. Measured RLSPs and CT numbers were compared with calculated and/or literature values. Relationships of RLSPs to physical densities, electronic densities, kilovoltage CT numbers, megavoltage CT numbers, and water equivalence values converted by a treatment planning system are given. Usage of CT numbers and substitution of measured values into treatment plans to provide accurate patient and phantom simulations are discussed. PMID:19931030

Moyers, Michael F; Sardesai, Milind; Sun, Sean; Miller, Daniel W

2009-06-21

348

Ion Stopping Powers and CT Numbers  

SciTech Connect

One of the advantages of ion beam therapy is the steep dose gradient produced near the ion's range. Use of this advantage makes knowledge of the stopping powers for all materials through which the beam passes critical. Most treatment planning systems calculate dose distributions using depth dose data measured in water and an algorithm that converts the kilovoltage X-ray computed tomography (CT) number of a given material to its linear stopping power relative to water. Some materials present in kilovoltage scans of patients and simulation phantoms do not lie on the standard tissue conversion curve. The relative linear stopping powers (RLSPs) of 21 different tissue substitutes and positioning, registration, immobilization, and beamline materials were measured in beams of protons accelerated to energies of 155, 200, and 250 MeV; carbon ions accelerated to 290 MeV/n; and iron ions accelerated to 970 MeV/n. These same materials were scanned with both kilovoltage and megavoltage CT scanners to obtain their CT numbers. Measured RLSPs and CT numbers were compared with calculated and/or literature values. Relationships of RLSPs to physical densities, electronic densities, kilovoltage CT numbers, megavoltage CT numbers, and water equivalence values converted by a treatment planning system are given. Usage of CT numbers and substitution of measured values into treatment plans to provide accurate patient and phantom simulations are discussed.

Moyers, Michael F., E-mail: MFMoyers@roadrunner.co [Department of Proton Therapy, Inc., Colton, CA (United States); Sardesai, Milind [Department of Long Beach Memorial Medical Center, Long Beach, CA (United States); Sun, Sean [Department of City of Hope National Medical Center, Duarte, CA (United States); Miller, Daniel W. [Department of Loma Linda University Medical Center, Loma Linda, CA (United States)

2010-10-01

349

Persistent consequences of atypical early number concepts.  

PubMed

How does symbolic number knowledge performance help identify young children at risk for poor mathematics achievement outcomes? In research and practice, classification of mathematics learning disability (MLD, or dyscalculia) is typically based on composite scores from broad measures of mathematics achievement. These scores do predict later math achievement levels, but do not specify the nature of math difficulties likely to emerge among students at greatest risk for long-term mathematics failure. Here we report that gaps in 2nd and 3rd graders' number knowledge predict specific types of errors made on math assessments at Grade 8. Specifically, we show that early whole number misconceptions predict slower and less accurate performance, and atypical computational errors, on Grade 8 arithmetic tests. We demonstrate that basic number misconceptions can be detected by idiosyncratic responses to number knowledge items, and that when such misconceptions are evident during primary school they persist throughout the school age years, with variable manifestation throughout development. We conclude that including specific qualitative assessments of symbolic number knowledge in primary school may provide greater specificity of the types of difficulties likely to emerge among students at risk for poor mathematics outcomes. PMID:24027540

Mazzocco, Michèle M M; Murphy, Melissa M; Brown, Ethan C; Rinne, Luke; Herold, Katherine H

2013-09-04

350

A new pseudorandom number generator based on a complex number chaotic equation  

NASA Astrophysics Data System (ADS)

In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and proved to be chaotic in the imaginary axis. And a pseudorandom number generator is constructed based on the chaotic equation. The alteration of the definitional domain of the chaotic equation from the real number field to the complex one provides a new approach to the construction of chaotic equations, and a new method to generate pseudorandom number sequences accordingly. Both theoretical analysis and experimental results show that the sequences generated by the proposed pseudorandom number generator possess many good properties.

Liu, Yang; Tong, Xiao-Jun

2012-09-01

351

Effects of condition number on preconditioning for low Mach number flows  

NASA Astrophysics Data System (ADS)

The effects of the condition number on convergence characteristics and solution quality for the preconditioned Navier-Stokes equations are studied. A general approach to the construction of preconditioning parameters is proposed to account for the effects of the condition number on these parameters. To verify this technique, laminar flows past a circular cylinder at Reynolds numbers of 20 and 40, and laminar flows past a NACA0012 airfoil at Reynolds numbers of 2500 and 5000 are solved. It is shown that the condition number has effects on the convergence characteristics and solution qualities, and also that a condition number exists that optimizes the convergence characteristics and solution quality.

Lee, Sang-Hyeon

2012-05-01

352

The applications of interval-valued fuzzy numbers and interval-distribution numbers  

Microsoft Academic Search

In this paper, we first define interval-valued fuzzy numbers and interval-distribution numbers, and then their extended operations are given. Next, we discuss some applications of generalized pseudo-probability metric spaces and pseudo-metric spaces.

Wang Guijun; Li Xiaoping

1998-01-01

353

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,...

2013-04-01

354

76 FR 60789 - Local Number Portability Porting Interval and Validation Requirements; Telephone Number Portability  

Federal Register 2010, 2011, 2012, 2013

...Interval and Validation Requirements; Telephone Number Portability AGENCY: Federal Communications...requests that involve a large quantity of telephone numbers. Specifically, the Commission...documents may also be purchased from BCPI, telephone (202) 488-5300, facsimile...

2011-09-30

355

Nonlinear dynamos at infinite magnetic Prandtl number.  

PubMed

The dynamo instability is investigated in the limit of infinite magnetic Prandtl number. In this limit the fluid is assumed to be very viscous so that the inertial terms can be neglected and the flow is enslaved to the forcing. The forcing consist of an external forcing function that drives the dynamo flow and the resulting Lorentz force caused by the back reaction of the magnetic field. The flows under investigation are the Archontis flow and the ABC flow forced at two different scales. The investigation covers roughly 3 orders of magnitude of the magnetic Reynolds number above onset. All flows show a weak increase of the averaged magnetic energy as the magnetic Reynolds number is increased. Most of the magnetic energy is concentrated in flat elongated structures that produce a Lorentz force with small solenoidal projection so that the resulting magnetic field configuration is almost force free. Although the examined system has zero kinetic Reynolds number at sufficiently large magnetic Reynolds number the structures are unstable to small scale fluctuations that result in a chaotic temporal behavior. PMID:21517581

Alexakis, Alexandros

2011-03-03

356

MOIRCS Deep Survey. I: DRG Number Counts  

NASA Astrophysics Data System (ADS)

We used very deep near-infrared imaging data taken with the Multi-Object InfraRed Camera and Spectrograph (MOIRCS) on the Subaru Telescope to investigate the number counts of Distant Red Galaxies (DRGs). We observed a 4' × 7' field in the Great Observatories Origins Deep Survey-North (GOODS-N), and our data reached J=24.6 and K=23.2 (5?, Vega magnitude). The surface density of DRGs selected by J - K > 2.3 is 2.35 ± 0.31 arcmin-2 at K < 22 and 3.54 ± 0.38 arcmin-2 at K < 23, respectively. These values are consistent with those in the GOODS-South and FIRES. Our deep and wide data suggest that the number counts of DRGs turn over at K ˜ 22, and the surface density of the faint DRGs with K > 22 is smaller than that expected from the number counts at the brighter magnitude. The result indicates that while there are many bright galaxies at 2 < z < 4 with the relatively old stellar population and/or heavy dust extinction, the number of faint galaxies with a similar red color is relatively small. Different behavior patterns of the number counts of the DRGs and bluer galaxies with 2 < zphot < 4 at K > 22 suggest that the mass-dependent color distribution, where most of the low-mass galaxies are blue, while more massive galaxies tend to have redder colors, had already been established at that epoch.

Kajisawa, Masaru; Konishi, Masahiro; Suzuki, Ryuji; Tokoku, Chihiro; Uchimoto, Yuka; Katsuno; Yoshikawa, Tomohiro; Akiyama, Masayuki; Ichikawa, Takashi; Ouchi, Masami; Omata, Koji; Tanaka, Ichi; Nishimura, Tetsuo; Yamada, Toru

2006-12-01

357

Beyond the Mental Number Line: A Neural Network Model of Number-Space Interactions  

ERIC Educational Resources Information Center

|It is commonly assumed that there is an interaction between the representations of number and space (e.g., [Dehaene et al., 1993] and [Walsh, 2003]), typically ascribed to a mental number line. The exact nature of this interaction has remained elusive, however. Here we propose that spatial aspects are not inherent to number representations, but…

Chen, Qi; Verguts, Tom

2010-01-01

358

The Numbers Game: Phasing in Generated ID Numbers at the University of Oregon  

ERIC Educational Resources Information Center

|With all the recent headlines about security breaches and information loss at financial and educational institutions, the higher education community needs to address the issue of using social security numbers as ID numbers. The University of Oregon undertook a change process to assign generated ID numbers to all records in their information…

Eveland, Sue

2005-01-01

359

78 FR 36725 - Numbering Policies for Modern Communications; IP-Enabled Services; Telephone Number Requirements...  

Federal Register 2010, 2011, 2012, 2013

...6/11/3078598/ios-6-unified-apple-id-phone-number (``Now, if someone...to your cell phone number and not your Apple ID email.''). 25. In light of these...direct access to numbers if they are ``red-lighted'' by the Commission for...

2013-06-19

360

Parallel Region Prime Number Computation Model  

NSDL National Science Digital Library

The Parallel Region Prime Number Computation Model uses the prime division algorithm to decide if a number is prime.  The prime division algorithm is inefficient and we use it here only to test the EJS implementation of the Parallel Region Element in EJS.  A parallel region executes independent code in a separate thread and these threads can execute simultaneously on a multi-core processor.  The screen capture shows that the total execution time for four computations on a quad-core processor is only one millisecond longer than the execution time for the longest single computation.  This linear speedup is close to the theoretical maximum. The Parallel Region Prime Number Computation Model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the model's jar file will run the simulation if Java is installed.

Christian, Wolfgang

2012-01-19

361

Congruent numbers with many prime factors  

PubMed Central

Mohammed Ben Alhocain, in an Arab manuscript of the 10th century, stated that the principal object of the theory of rational right triangles is to find a square that when increased or diminished by a certain number, m becomes a square [Dickson LE (1971) History of the Theory of Numbers (Chelsea, New York), Vol 2, Chap 16]. In modern language, this object is to find a rational point of infinite order on the elliptic curve . Heegner constructed such rational points in the case that m are primes congruent to 5,7 modulo 8 or twice primes congruent to 3 modulo 8 [Monsky P (1990) Math Z 204:45–68]. We extend Heegner's result to integers m with many prime divisors and give a sketch in this report. The full details of all the proofs will be given in ref. 1 [Tian Y (2012) Congruent Numbers and Heegner Points, arXiv:1210.8231].

Tian, Ye

2012-01-01

362

Compact disc serial number inspection system  

NASA Astrophysics Data System (ADS)

This paper presents a reliable neural network based system for compact disc serial number inspection. Four major steps are performed in this system, namely polar image conversion, segmentation, recognition, and verification. Polar image conversion straightens the circular stripe images containing the serial numbers to horizontally linear images, segmentation divides the images into separate character segments, recognition classifies the separate character segments by a trained neural network, and verification double checks the characters with their verification neural networks if the serial number is known. Special back-propagation training processes for recognition and verification neural networks are used to increase the system's performance. Excellent recognition results for this system implemented in the Sony SUPER vision system have been obtained. Moreover, this system can process more than 3 compact discs in one second.

Oki, Toru; Paolella, Philip; Chiu, Chinchuan

1993-09-01

363

PHD filtering with localised target number variance  

NASA Astrophysics Data System (ADS)

Mahler's Probability Hypothesis Density (PHD filter), proposed in 2000, addresses the challenges of the multipletarget detection and tracking problem by propagating a mean density of the targets in any region of the state space. However, when retrieving some local evidence on the target presence becomes a critical component of a larger process - e.g. for sensor management purposes - the local target number is insufficient unless some confidence on the estimation of the number of targets can be provided as well. In this paper, we propose a first implementation of a PHD filter that also includes an estimation of localised variance in the target number following each update step; we then illustrate the advantage of the PHD filter + variance on simulated data from a multiple-target scenario.

Delande, Emmanuel; Houssineau, Jérémie; Clark, Daniel

2013-05-01

364

Prime number variant of concealed trigeminy.  

PubMed

A 53-year-old man with myocardial infarction was found to have frequent premature ventricular beats. The predominant pattern was classical concealed trigeminy; i.e., the number of conducted sinus beats, S, between extrasystoles satisfied the equation S = 3n + 2, where "n" is zero or any positive integer. Two other transient patterns also occurred. The first one was characterized by exceptional values of S, which satisfied the equation S = 3n + 3. In the second transient pattern, all values of S fitted the classical equation, but there were singularly absent values; i.e., the "n" in the equation was exclusively an odd number, giving rise to only prime numbers of interectopic conducted sinus beats. It is proposed in this last form that there are two sites of fixed block proximal to a variable distal block in a re-entry loop responsible for the ventricular extrasystoles. PMID:2415650

Medeiros, C M; Medeiros, N P; de Nonohay, N C; Rodrigues, R

1985-10-01

365

Algebraic Expressions - Number Line Model for Multiplication  

NSDL National Science Digital Library

This interactive Java learning tool allows a teacher to demonstrate and explore with students number line models for two simple variable expressions for multiplication. The first expression is a variable with an understood coefficient of one and the second is the multiplication of a variable by a coefficient. Sliders are used to select the value of the variable (-10 to 10) and the coefficient (0 to 10). Check boxes show or hide the algebraic expression, the expression with substitution, the notation shown for multiplication, the result, and a model for the multiplication, shown as jumps along a number line.

Maine, Edc I.

2010-08-26

366

Statistical Analysis of Random Number Generators  

NASA Astrophysics Data System (ADS)

In many applications, for example cryptography and Monte Carlo simulation, there is need for random numbers. Any procedure, algorithm or device which is intended to produce such is called a random number generator (RNG). What makes a good RNG? This paper gives an overview on empirical testing of the statistical properties of the sequences produced by RNGs and special software packages designed for that purpose. We also present the results of applying a particular test suite--TestU01-- to a family of RNGs currently being developed at the Centro Interdipartimentale Vito Volterra (CIVV), Roma, Italy.

Accardi, Luigi; Gäbler, Markus

2011-01-01

367

On Fibonacci numbers with few prime divisors  

Microsoft Academic Search

If $n$ is a positive integer, write $F_n$ for the $n$th Fibonacci\\u000anumber, and $\\\\omega(n)$ for the number of distinct prime divisors\\u000aof $n$. We give a description of Fibonacci numbers satisfying\\u000a$\\\\omega(F_n) \\\\leq 2$. Moreover, we prove that the inequality\\u000a$\\\\omega(F_n) \\\\geq (\\\\log n)^{\\\\log 2 + o(1)}$ holds for almost\\u000aall $n$. We conjecture that $\\\\omega(F_n) \\\\gg \\\\log n$

Yann Bugeaud; Florian Luca; Maurice Mignotte; Samir Siksek

2005-01-01

368

Simulations of motor unit number estimation techniques  

NASA Astrophysics Data System (ADS)

Motor unit number estimation (MUNE) is an electrodiagnostic procedure used to evaluate the number of motor axons connected to a muscle. All MUNE techniques rely on assumptions that must be fulfilled to produce a valid estimate. As there is no gold standard to compare the MUNE techniques against, we have developed a model of the relevant neuromuscular physiology and have used this model to simulate various MUNE techniques. The model allows for a quantitative analysis of candidate MUNE techniques that will hopefully contribute to consensus regarding a standard procedure for performing MUNE.

Major, Lora A.; Jones, Kelvin E.

2005-06-01

369

Multiplicative conservation of baryon number and baryogenesis  

NASA Astrophysics Data System (ADS)

In the canonical seesaw mechanism of neutrino mass, lepton number is only multiplicatively conserved, which enables the important phenomenon of leptogenesis to occur, as an attractive explanation of the present baryon asymmetry of the Universe. A parallel possibility, hitherto unrecognized, also holds for baryon number and baryogenesis. This new idea is shown to be naturally realized in the context of a known supersymmetric string-inspired extension of the Standard Model, based on E particle content, and having an extra U1 gauge symmetry. Within this framework, two-loop radiative neutrino masses are also possible, together with a new form of very long-lived matter.

Ma, Ernest

2008-03-01

370

Turbulent pipe flow at extreme Reynolds numbers.  

PubMed

Both the inherent intractability and complex beauty of turbulence reside in its large range of physical and temporal scales. This range of scales is captured by the Reynolds number, which in nature and in many engineering applications can be as large as 10(5)-10(6). Here, we report turbulence measurements over an unprecedented range of Reynolds numbers using a unique combination of a high-pressure air facility and a new nanoscale anemometry probe. The results reveal previously unknown universal scaling behavior for the turbulent velocity fluctuations, which is remarkably similar to the well-known scaling behavior of the mean velocity distribution. PMID:22463643

Hultmark, M; Vallikivi, M; Bailey, S C C; Smits, A J

2012-02-28

371

Developing forecasting charts for sunspot numbers  

SciTech Connect

A new statistical modeling approach is used to fit models to 200 years of sunspot data and the adequate models for yearly, monthly, and daily sunspot numbers are employed to obtain the minimum mean squared error forecasts. The analysis of new models revealed a long-term 76-year period, a short-term 27-year period, and a 2.5-year period due to stratospheric winds in addition to a commonly known 11-year periodicity of the sunspots. The forecasting charts are developed in a format that can be easily read to obtain the long-term (yearly average) and short-term (daily average) predictions of sunspot numbers.

Kapoor, S.G.; Wu, S.M.

1982-01-01

372

K.CC Number Line Up  

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: The teacher will need a set of number cards (easily created using large index cards) that begin with 1 and end with the number of students in the class...

373

Transverse galloping at low Reynolds numbers  

NASA Astrophysics Data System (ADS)

The possibility of transverse galloping of a square cylinder at low Reynolds numbers (Re?200, so that the flow is presumably laminar) is analysed. Transverse galloping is here considered as a one-degree-of-freedom oscillator subjected to fluid forces, which are described by using the quasi-steady hypothesis (time-averaged data are extracted from previous numerical simulations). Approximate solutions are obtained by means of the method of Krylov-Bogoliubov, with two major conclusions: (i) a square cylinder cannot gallop below a Reynolds number of 159 and (ii) in the range 159?Re?200 the response exhibits no hysteresis.

Barrero-Gil, A.; Sanz-Andrés, A.; Roura, M.

2009-10-01

374

Two-bit quantum random number generator based on photon-number-resolving detection  

NASA Astrophysics Data System (ADS)

Here we present a new fast two-bit quantum random number generator based on the intrinsic randomness of the quantum physical phenomenon of photon statistics of coherent light source. Two-bit random numbers were generated according to the number of detected photons in each light pulse by a photon-number-resolving detector. Poissonian photon statistics of the coherent light source guaranteed the complete randomness of the bit sequences. Multi-bit true random numbers were generated for the first time based on the multi-photon events from a coherent light source.

Jian, Yi; Ren, Min; Wu, E.; Wu, Guang; Zeng, Heping

2011-07-01

375

Number Concepts without Number Lines in an Indigenous Group of Papua New Guinea  

PubMed Central

Background The generic concept of number line, which maps numbers to unidimensional space, is a fundamental concept in mathematics, but its cognitive origins are uncertain. Two defining criteria of the number line are that (i) there is a mapping of each individual number (or numerosity) under consideration onto a specific location on the line, and (ii) that the mapping defines a unidimensional space representing numbers with a metric — a distance function. It has been proposed that the number line is based on a spontaneous universal human intuition, rooted directly in brain evolution, that maps number magnitude to linear space with a metric. To date, no culture lacking this intuition has been documented. Methodology/Principal Findings By means of a number line task, we investigated the universality proposal with the Yupno of Papua New Guinea. Unschooled adults did exhibit a number-to-space mapping (criterion i) but, strikingly, despite having precise cardinal number concepts, they located numbers only on the endpoints, thus failing to use the extent of the line. The produced mapping was bi-categorical and metric-free, in violation of criterion ii. In contrast, Yupnos with scholastic experience used the extent of the segment according to known standards, but they did so not as evenly as western controls, exhibiting a bias towards the endpoints. Conclusions/Significance Results suggest that cardinal number concepts can exist independently from number line representations. They also suggest that the number line mapping, although ubiquitous in the modern world, is not universally spontaneous, but rather seems to be learned through — and continually reinforced by — specific cultural practices.

Nunez, Rafael; Cooperrider, Kensy; Wassmann, Jurg

2012-01-01

376

Automaticity of Two-Digit Numbers  

ERIC Educational Resources Information Center

|Automatic processing of 2-digit numbers was demonstrated using the size congruency effect (SiCE). The SiCE indicates the processing of the irrelevant (numerical) dimension when 2 digits differing both numerically and physically are compared on the relevant (physical) dimension. The SiCE was affected by the compatibility between unit and decade…

Ganor-Stern, Dana; Tzelgov, Joseph; Ellenbogen, Ravid

2007-01-01

377

Synesthesia and Number Cognition in Children  

ERIC Educational Resources Information Center

|Grapheme-color synesthesia, when achromatic digits evoke an experience of a specific color (photisms), has been shown to be consistent, involuntary, and linked with number concept in adults, yet there have been no comparable investigations with children. We present a systematic study of grapheme-color synesthesia in children aged between 7 and 15…

Green, Jennifer A. K.; Goswami, Usha

2008-01-01

378

Polish Endocrinology. Volume 22, Number 3, 1971.  

National Technical Information Service (NTIS)

Contents: Growth dynamics of ovarian grafts in the kidneys and spleen of rats; Histological and morphometric studies on ovarian grafts in the kidneys and spleen in rats; Changes in the number of ovarian cells transplanted into the spleen in castrated fema...

1971-01-01

379

Analytic surface germs with minimal Pythagoras number  

Microsoft Academic Search

We determine all complete intersection surface germs whose Pythagoras number is 2, and find that they are all embedded in R3 and have the property that every positive semidefinite analytic function germ is a sum of squares of analytic function germs. In addition, we discuss completely these properties for mixed surface germs in R3. Finally, we find in higher embedding

José F. Fernando; F. Ciencias Matematicas

2003-01-01

380

A Fast Number Theoretic Finite Radon Transform  

Microsoft Academic Search

This paper presents a new fast method to map between images and their digital projections based on the Number Theoretic Transform (NTT) and the Finite Radon Transform (FRT). The FRT is a Discrete Radon Transform (DRT) defined on the same finite geometry as the Finite or Discrete Fourier Transform (DFT). Consequently, it may be inverted directly and exactly via the

Shekhar Chandra; Imants D. Svalbe

2009-01-01

381

Number of people with glaucoma worldwide  

Microsoft Academic Search

AIM: To estimate the prevalence of glaucoma among people worldwide. METHODS: Available published data on glaucoma prevalence were reviewed to determine the relation of open angle and angle closure glaucoma with age in people of European, African, and Asian origin. A comparison was made with estimated world population data for the year 2000. RESULTS: The number of people with primary

H. A. Quigley

1996-01-01

382

Phylogenetic diversity measures based on Hill numbers  

PubMed Central

We propose a parametric class of phylogenetic diversity (PD) measures that are sensitive to both species abundance and species taxonomic or phylogenetic distances. This work extends the conventional parametric species-neutral approach (based on ‘effective number of species’ or Hill numbers) to take into account species relatedness, and also generalizes the traditional phylogenetic approach (based on ‘total phylogenetic length’) to incorporate species abundances. The proposed measure quantifies ‘the mean effective number of species’ over any time interval of interest, or the ‘effective number of maximally distinct lineages’ over that time interval. The product of the measure and the interval length quantifies the ‘branch diversity’ of the phylogenetic tree during that interval. The new measures generalize and unify many existing measures and lead to a natural definition of taxonomic diversity as a special case. The replication principle (or doubling property), an important requirement for species-neutral diversity, is generalized to PD. The widely used Rao's quadratic entropy and the phylogenetic entropy do not satisfy this essential property, but a simple transformation converts each to our measures, which do satisfy the property. The proposed approach is applied to forest data for interpreting the effects of thinning.

Chao, Anne; Chiu, Chun-Huo; Jost, Lou

2010-01-01

383

Understanding Quantum Numbers in General Chemistry Textbooks  

ERIC Educational Resources Information Center

|Quantum numbers and electron configurations form an important part of the general chemistry curriculum and textbooks. The objectives of this study are: (1) Elaboration of a framework based on the following aspects: (a) Origin of the quantum hypothesis, (b) Alternative interpretations of quantum mechanics, (c) Differentiation between an orbital…

Niaz, Mansoor; Fernandez, Ramon

2008-01-01

384

Golden Proportions for the Generalized Tribonacci Numbers  

ERIC Educational Resources Information Center

|It is known that the ratios of consecutive terms of Fibonacci and Tribonacci sequences converge to the fixed ratio. In this article, we consider the generalized form of Tribonacci numbers and derive the "golden proportion" for the whole family of this generalized sequence. (Contains 2 tables.)|

Shah, Devbhadra V.; Mehta, Darshana A.

2009-01-01

385

Fibonacci numbers when counting chord diagrams  

Microsoft Academic Search

1. Introduction. The combinatorics of drawing some chords in some circles arises in a section of knot theory called invariants of finite-type. We will see that the Fibonacci numbers are useful for counting certain forms of these chord diagrams. We also prove that most of the chord diagrams are null. 2. Definitions We begin with a vector space of chord

Jane Kraemer

386

Radical Software. Number Two. The Electromagnetic Spectrum.  

ERIC Educational Resources Information Center

In an effort to foster the innovative uses of television technology, this tabloid format periodical details social, educational, and artistic experiments with television and lists a large number of experimental videotapes available from various television-centered groups and individuals. The principal areas explored in this issue include cable…

Korot, Beryl, Ed.; Gershuny, Phyllis, Ed.

1970-01-01

387

Odd numbers of photons and teleportation  

SciTech Connect

Several teleportation protocols, namely those using entangled coherent states, entangled squeezed states, and the single-photon Einstein-Podolsky-Rosen state, are all shown to be particular instances of a more general scheme that relies on the detection of an odd number of photons.

Enk, S.J. van [Bell Labs, Lucent Technologies, 600-700 Mountain Avenue, Murray Hill, New Jersy 07974 (United States)

2003-02-01

388

Maple Explorations, Perfect Numbers, and Mersenne Primes  

ERIC Educational Resources Information Center

Some examples from different areas of mathematics are explored to give a working knowledge of the computer algebra system Maple. Perfect numbers and Mersenne primes, which have fascinated people for a very long time and continue to do so, are studied using Maple and some questions are posed that still await answers.

Ghusayni, B.

2005-01-01

389

Computation of semantic number from morphological information  

Microsoft Academic Search

The distinction between singular and plural enters into linguistic phenomena such as morphology, lexical semantics, and agreement and also must interface with perceptual and conceptual systems that assess numerosity in the world. Three experiments examine the computation of semantic number for singulars and plurals from the morphological properties of visually presented words. In a Stroop-like task, Hebrew speakers were asked

Iris Berent; Steven Pinker; Joseph Tzelgov; Uri Bibi; Liat Goldfarb

2005-01-01

390

Abstract number and arithmetic in preschool children.  

PubMed

Educated humans use language to express abstract number, applying the same number words to seven apples, whistles, or sins. Is language or education the source of numerical abstraction? Claims to the contrary must present evidence for numerical knowledge that applies to disparate entities, in people who have received no formal mathematics instruction and cannot express such knowledge in words. Here we show that preschool children can compare and add large sets of elements without counting, both within a single visual-spatial modality (arrays of dots) and across two modalities and formats (dot arrays and tone sequences). In two experiments, children viewed animations and either compared one visible array of dots to a second array or added two successive dot arrays and compared the sum to a third array. In further experiments, a dot array was replaced by a sequence of sounds, so that participants had to integrate quantity information presented aurally and visually. Children performed all tasks successfully, without resorting to guessing strategies or responding to continuous variables. Their accuracy varied with the ratio of the two quantities: a signature of large, approximate number representations in adult humans and animals. Addition was as accurate as comparison, even though children showed no relevant knowledge when presented with symbolic versions of the addition tasks. Abstract knowledge of number and addition therefore precedes, and may guide, language-based instruction in mathematics. PMID:16172388

Barth, Hilary; La Mont, Kristen; Lipton, Jennifer; Spelke, Elizabeth S

2005-09-19

391

A Framework for Remediating Number Combination Deficits  

ERIC Educational Resources Information Center

This article introduces a framework for the remediation of number combination (NC) deficits. Research on the remediation of NC deficits is summarized, and research program studies are used to illustrate the 3 approaches to remediation. The Framework comprises a 2-stage system of remediation. The less intensive stage implementing 1 of 3…

Fuchs, Lynn S.; Powell, Sarah R.; Seethaler, Pamela M.; Fuchs, Douglas; Hamlett, Carol L.; Cirino, Paul T.; Fletcher, Jack M.

2010-01-01

392

Science Books & Films, Volume XIII, Number 3.  

ERIC Educational Resources Information Center

|This document provides annotated bibliographies of 205 books, 61 children's books, and 87 films all of which are science related. Each annotation includes author, publisher, title, number of pages, cost, an appraisal from highly recommended to not recommended, and level of difficulty from preschool to professional. Entries are grouped by topics…

Finch, Shari, Ed.

393

VORTEX INDUCED VIBRATIONS AT HIGH REYNOLDS NUMBERS  

Microsoft Academic Search

Vortex induced vibrations of circular section structures are a well known and deeply studied phenomenon because many engineering applications are involved by this kind of prob- lems. Up to now most part of the experimental results belong to a Reynolds Number range be- tween 500 and 6 ¢ 104 and no reliable numerical simulations are available for Reynolds higher than

Giorgio Diana; Marco Belloli; Stefano Giappino; Sara Muggiasca

394

Preparing nanoparticle assemblies with number density gradients  

NASA Astrophysics Data System (ADS)

We report on preparing assemblies of gold nanoparticles with gradient in number densities on flat silica-covered substrates. The methodology consists of : i) first forming a molecular gradient of amino groups (-NH2) on the substrate by vapor deposition of amine-terminated silane molecules, followed by ii) attachment of gold nanoparticles to -NH2 functional groups by immersing the substrate in a colloidal gold solution. Experiments using atomic force microscopy (AFM) reveal that the number density of nanoparticles on the substrate varies gradually as a function of the position on the substrate. Near edge x-ray absorption fine structure (NEXAFS) studies confirm that the decrease of the nanoparticle density is associated with the decrease of the number of the -NH2 groups anchored to the substrate. We demonstrate that the number density and spatial distribution of the nanoparticles within the gradients can be tuned by contolling the vapor diffusion of silane molecules. In addition we show that this simple methodology can be further extended to create "double gradients" of nanoparticles.

Bhat, Rajendra; Fischer, Daniel; Genzer, Jan

2002-03-01

395

On the Number and Size of Nations  

Microsoft Academic Search

This paper studies the equilibrium determination of the number of countries in different political regimes, and in different economic environments, with more or less economic integration. The authors focus on the trade-off between the benefits of large jurisdictions and the costs of heterogeneity of large and diverse populations. Their model implies that (1) democratization leads to secessions; (2) in equilibrium

Alberto Alesina; Enrico Spolaore

1997-01-01

396

Mechanisms of change in gene copy number  

Microsoft Academic Search

Deletions and duplications of chromosomal segments (copy number variants, CNVs) are a major source of variation between individual humans and are an underlying factor in human evolution and in many diseases, including mental illness, developmental disorders and cancer. CNVs form at a faster rate than other types of mutation, and seem to do so by similar mechanisms in bacteria, yeast

James R. Lupski; Susan M. Rosenberg; Grzegorz Ira; P. J. Hastings

2009-01-01

397

Copy number variation in Parkinson's disease  

Microsoft Academic Search

ABSTRACT: A central theme of human genetic studies is to understand genomic variation and how this underlies the inherited basis of disease. Genomic variation can provide increased biological understanding of disease processes, which is necessary to develop future treatments. Recent technological advances have highlighted the role of copy number variants in normal and pathological phenotypic expression. These applications have been

Mathias Toft; Owen A Ross

2010-01-01

398

Computation of Semantic Number from Morphological Information  

ERIC Educational Resources Information Center

|The distinction between singular and plural enters into linguistic phenomena such as morphology, lexical semantics, and agreement and also must interface with perceptual and conceptual systems that assess numerosity in the world. Three experiments examine the computation of semantic number for singulars and plurals from the morphological…

Berent, Iris; Pinker, Steven; Tzelgov, Joseph; Bibi, Uri; Goldfarb, Liat

2005-01-01

399

On gauged Baryon and Lepton numbers  

SciTech Connect

The observation that Baryon number and Lepton number are conserved in nature provides strong motivation for associating gauge symmetries to these conserved numbers. This endeavor requires that the gauge group of electroweak interactions be extended from SU(2){sub L} X U(1){sub Y} to SU(2){sub L} X U(1){sub R} X U(1){sub Lepton} where U(1){sub R} couples only to the right-handed quarks and leptons. If it furthur postulated that right-handed currents exist on par with the left-handed ones, then the full electroweak symmetry is SU(2){sub L} X SU(2){sub R} X U(1){sub Baryon} X U(1){sub Lepton}. The SU(2){sub L} X SU(2){sub R} X U(1){sub Baryon} X U(1){sub Lepton} model is described in some detail. The triangle anomalies of the three families of quarks and leptons in the model are cancelled invoking leptoquark matter which is new fermionic matter that carries baryon as well as lepton numbers. In addition to the standard neutral boson (Z {degree}), the theory predicts two neutral gauge bosons with mass lower bounds of 120 GeV and 210 GeV which makes these particles prospective candidates for production at LEP, the TEVATRON and the SSC.

Rajpoot, S.

1990-01-01

400

Sustaining Student Numbers in the Competitive Marketplace  

ERIC Educational Resources Information Center

|The climate of competition for students in the higher education sector makes it imperative that institutions increase their marketing efforts, both domestically and internationally, to help sustain student numbers. In Australia, the Bradley Report and the government response, which will do away with quotas, allows for a much freer market than…

Szekeres, Judy

2010-01-01

401

Julian day numbers and calendar dates.  

NASA Astrophysics Data System (ADS)

The simple algorithms of Hatcher (1984, 1985) serving the purpose of forward and reverse transformation between calendar dates and the Julian day numbers are presented. A slightly modified version of the algorithms implemented in FORTRAN programming language has been tested to be valid for all dates since the year 100100 BC. The printouts of these subroutines are appended.

Borkowski, K. M.

402

Computation of Semantic Number from Morphological Information  

ERIC Educational Resources Information Center

The distinction between singular and plural enters into linguistic phenomena such as morphology, lexical semantics, and agreement and also must interface with perceptual and conceptual systems that assess numerosity in the world. Three experiments examine the computation of semantic number for singulars and plurals from the morphological…

Berent, Iris; Pinker, Steven; Tzelgov, Joseph; Bibi, Uri; Goldfarb, Liat

2005-01-01

403

Science Sampler: Pick-a-number  

NSDL National Science Digital Library

The Pick-a-number activity, a variation of the game 20 Questions, provides a way to address challenges at the beginning of the school year, in a standards-based way. It also helps students develop the essential skill of asking questions as part of the scientific inquiry process.

Sitzman, Daniel

2005-09-01

404

Cylinder drag at low Reynolds number  

Microsoft Academic Search

From terminal velocity measurements of solitary finite length circular cylinders settling in a large rectangular tank of fluid, drag values for infinite length circular cylinders translating at constant speed through an unbounded fluid were obtained. The drag was determined as the effective weight of the cylinder in the liquid and the Reynolds number was determined from the terminal velocity measurements

B. Huner

1977-01-01

405

Low Reynolds Number Particle-Fluid Interactions  

Microsoft Academic Search

The focus of this dissertation is the analysis of torque and drag coefficients, for the steady rotation of spheres in an infinite viscous fluid, and for axisymmetric viscous flow past linear arrays of spheres, respectively. The exact solutions for such torque and drag coefficients are unknown if the number of spheres under consideration is greater than two. A new approximation

Andrea Claire Bodnar

1994-01-01

406

The LSS Review. Volume 3, Number 1  

ERIC Educational Resources Information Center

|A growing number of American students are nonnative English speakers. These students are vulnerable to early school exit and schools are facing more and more such students each year. Presently, about 56% of all public school teachers in the United States have at least one English language learner (ELL) student in their class, but less than 20% of…

Hoag, Lydia, Ed.

2004-01-01

407

Genomic characteristics of cattle copy number variations  

Technology Transfer Automated Retrieval System (TEKTRAN)

We performed a systematic analysis of cattle copy number variations (CNVs) using the Bovine HapMap SNP genotyping data, including 539 animals of 21 modern cattle breeds and 6 outgroups. After correcting genomic waves and considering the trio information, we identified 682 candidate CNV regions (CNVR...

408

Estimate octane numbers using an enhanced method  

SciTech Connect

An improved model, based on the Twu-Coon method, is not only internally consistent, but also retains the same level of accuracy as the previous model in predicting octanes of gasoline blends. The enhanced model applies the same binary interaction parameters to components in each gasoline cut and their blends. Thus, the enhanced model can blend gasoline cuts in any order, in any combination or from any splitting of gasoline cuts and still yield the identical value of octane number for blending the same number of gasoline cuts. Setting binary interaction parameters to zero for identical gasoline cuts during the blending process is not required. The new model changes the old model`s methodology so that the same binary interaction parameters can be applied between components inside a gasoline cut as are applied to the same components between gasoline cuts. The enhanced model is more consistent in methodology than the original model, but it has equal accuracy for predicting octane numbers of gasoline blends, and it has the same number of binary interaction parameters. The paper discusses background, enhancement of the Twu-Coon interaction model, and three examples: blend of 2 identical gasoline cuts, blend of 3 gasoline cuts, and blend of the same 3 gasoline cuts in a different order.

Twu, C.H.; Coon, J.E. [Simulation Sciences Inc., Brea, CA (United States)

1997-03-01

409

ML Estimation under Misspecified Number of Signals  

Microsoft Academic Search

The maximum likelihood (ML) approach for estimating direction of arrival (DOA) is a well known and popular technique in array processing. Its statistical properties such as consistency and efficiency have been extensively studied in the literature. A common assumption made in previous works is that the assumed number of signals equals the true one. However, this information is not always

Pei-Jung Chung

2005-01-01

410

Ranking of fuzzy numbers by sign distance  

Microsoft Academic Search

Several different strategies have been proposed for ranking of fuzzy numbers. These include methods based on the coefficient of variation (CV index), distance between fuzzy sets, centroid point and original point, and weighted mean value. Each of these techniques has been shown to produce non-intuitive results in certain cases. In this paper we propose a modification of the distance based

Saeid Abbasbandy; B. Asady

2006-01-01

411

T-sum of LR fuzzy numbers  

Microsoft Academic Search

The sum of L-R fuzzy numbers based on a given Archimedian continuous t-norm T is studied. A series of improving sufficient conditions of several authors ensuring an analytical form of the output sum is completed by a sufficient and necessary condition, i.e., the best sufficient condition. Some applications are indicated.

Andrea Marková

1997-01-01

412

Preston Probe Calibrations at High Reynolds Number.  

National Technical Information Service (NTIS)

The overall goal of the research effort is to study the performance of two Preston probes designed by NASA Langley Research Center across an unprecedented range of Reynolds number (based on friction velocity and probe diameter), and perform an accurate ca...

A. J. Smits

1998-01-01

413

Oxidation Numbers in the Study of Metabolism  

ERIC Educational Resources Information Center

|The calculation and use of oxidation numbers in the study of metabolic reactions are discussed for normal oxidations (alcohol dehydrogenase and the NAD+/NADH couple, propanediol dehydratase) and for enzymatic reactions with a "hidden" redox component (transamination, the coupled conversion of ethylamine to ethanol, and the biomethylation of…

Bentley, Ronald; Franzen, James; Chasteen, Thomas G.

2002-01-01

414

Secular Love numbers of the major planets  

Microsoft Academic Search

Secular Love numbers of the major planets have been determined by solving the first (Dirichlet's) boundary — value problem for the level ellipsoid as the boundary surface. It has been demonstrated that the rotational distortions are responsible for the actual figure of the bodies above. The 6th degree Stokes zonal parameter for Uranus and for Neptune have been predicted.

Milan Bursa

1992-01-01

415

Curve Numbers for Golf Course Watersheds  

Technology Transfer Automated Retrieval System (TEKTRAN)

Storm event runoff is a critical component to the environmental and structural design related to hydrology. The curve number (CN) method is a robust and accepted method for determining excess rainfall. Measured CNs for golf course watersheds and for that matter hydrologic data from golf course wate...

416

The Segregation Number in Polymer Reactor Engineering  

Microsoft Academic Search

Nauman defined in his review paper [1] that “the segregation number is… a ratio of characteristic times; a characteristic time for micromixing divided by a characteristic time for macromixing:” N = ?\\/?and has also selected as “a logical characteristic time for the macro-mixing is the mean residence time t.” The final result of his derivation for a spherical droplet is

J. M. Berty

1974-01-01

417

Gauss Linking Number and Electromagnetic Uncertainty Principle  

Microsoft Academic Search

It is shown that there is a precise sense in which the Heisenberg uncertainty between fluxes of electric and magnetic fields through finite surfaces is given by (one-halfh times) the Gauss linking number of the loops that bound these surfaces. To regularize the relevant operators, one is naturally led to assign a framing to each loop. The uncertainty between the

Abhay Ashtekar; Alejandro Corichi

1997-01-01

418

Bioinspired Corrugated Airfoil at Low Reynolds Numbers  

Microsoft Academic Search

An experimental study was conducted to investigate the flow behavior around a bioinspired corrugated airfoil compared with a traditional streamlined airfoil and a flat plate at the chord Reynolds number of Re 34; 000 to explore the potential application of such bioinspired corrugated airfoils for micro air vehicle applications. The experiments were conducted in a low-speed wind tunnel. A high-resolution

Hui Hu; Masatoshi Tamai

2008-01-01

419

Probability and the Law of Large Numbers  

NSDL National Science Digital Library

This probability activity guides students to discover the law of large numbers by having them consider why flipping a coin multiple times does not always produce equal results. The activity includes a 3 minute video featuring Bianca from Cyberchase, a document for data collection, and two assessment options (rtf format).

2012-01-01

420

A Knack for Numbers: Paquita Friday  

ERIC Educational Resources Information Center

|Back in middle school Dr. Paquita Friday began helping keep books at her grandmother's pharmacy during inventory. It was no chore, she recalls. It was fun. By then, of course, she already knew she had a knack for numbers. Today Friday is gaining recognition for her research in accounting stock market disclosures and winning awards for her…

Yates, Eleanor Lee

2005-01-01

421

ESTIMATES OF SINGULAR NUMBERS OF INTEGRAL OPERATORS  

Microsoft Academic Search

ContentsIntroduction § 1. Operator spaces and function spaces § 2. Estimates of singular numbers based on the method of piecewise-polynomial approximation § 3. Interpolation methods § 4. General results on estimates (statements) § 5. Proof of the main results on estimates § 6. Operators with a difference kernel § 7. Tests for nuclearity § 8. Multipliers in classes of kernels

M Sh Birman; M. Z. Solomjak

1977-01-01

422

Demonstrations of the Enormity of Avogadro's Number  

NASA Astrophysics Data System (ADS)

Most high-school students learn of Avogadro's number for the first time when they begin study of the mole concept. It is important to impress students with the enormity of Avogadro's number and the concomitant minuscularity of the atom, and papers addressing this need have regularly appeared in this Journal. The present article describes three new problems used annually at Trinity School to make the impression. The first two problems are suitable to be assigned as homework. The first of these uses Avogadro's number simply as a scaling factor; the second, requiring more attention to units, is a calculation of the number of moles of sand grains in the Sahara Desert. The third problem is a series of related calculations that requires some closer in-class mathematical analysis and culminates in an astonishing result. All calculations are done in familiar English units, because with them I have found the results to be more immediately impressive to American students. Conversion factors to metric units can be applied if teachers find that desirable.

Diemente, Damon

1998-12-01

423

Entanglement distillation protocols and number theory  

Microsoft Academic Search

We show that the analysis of entanglement distillation protocols for qudits of arbitrary dimension D benefits from applying basic concepts from number theory, since the set ZDn associated with Bell diagonal states is a module rather than a vector space. We find that a partition of ZDn into divisor classes characterizes the invariant properties of mixed Bell diagonal states under

H. Bombin; M. A. Martin-Delgado

2005-01-01

424

Combinatorics of generalized q-Euler numbers  

Microsoft Academic Search

New enumerating functions for the Euler numbers are considered. Sev- eral of the relevant generating functions appear in connection to entries in Ramanu- jan's Lost Notebook. The results presented here are, in part, a response to a conjec- ture made by M. E. H. Ismail and C. Zhang about the symmetry of polynomials in Ramanujan's expansion for a generalization of

Tim Huber; Ae Ja Yee

2010-01-01

425

Independence Number for the Generalized Petersen Graphs.  

National Technical Information Service (NTIS)

Given a graph G, an independent set I(G) is a subset of the vertices of G such that no two vertices in I(G) are adjacent. The independence number alpha(G) is the order of the largest set of independent vertices. In this paper, we study the independence nu...

J. Fox P. Stanica R. Gera

2011-01-01

426

Arithmetic Operations Beyond Floating Point Number Precision  

Microsoft Academic Search

In basic computational physics classes, students often raise the question of how to compute a number that exceeds the numerical limit of the machine. While technique of avoiding overflow\\/underflow has practical application in the electrical and electronics engineering industries, it is not commonly utilized in scientific computing, because scientific notation is adequate in most cases. We present an undergraduate project

Chih-Yueh Wang; Chen-Yang Yin; Hong-Yu Chen; Yung-Ko Chen

2010-01-01

427

Application of low copy number DNA profiling.  

PubMed

Low copy number (LCN) DNA profiling is a technique sensitive enough to analyze just a few cells. When this kind of analysis is carried out, special considerations are needed to interpret the results. In particular, it is important to consider the implications of allele dropout and the possibility of contamination from a laboratory source. A rationale for interpreting LCN DNA is described. PMID:11387628

Gill, P

2001-06-01

428

Quantum abacus for counting and factorizing numbers  

SciTech Connect

We generalize the binary quantum counting algorithm of Lesovik, Suslov, and Blatter [Phys. Rev. A 82, 012316 (2010)] to higher counting bases. The algorithm makes use of qubits, qutrits, and qudits to count numbers in a base-2, base-3, or base-d representation. In operating the algorithm, the number nnumber n in the base-d representation; the inverse transformation is fully quantum at the level of individual qudits, while a simpler semiclassical version can be used on the level of qudit registers. Combining registers of qubits, qutrits, and qudits, where d is a prime number, with a simpler single-shot measurement allows us to find the powers of 2, 3, and other primes d in the number n. We show that the counting task naturally leads to the shift operation and an algorithm based on the quantum Fourier transformation. We discuss possible implementations of the algorithm using quantum spin-d systems, d-well systems, and their emulation with spin-1/2 or double-well systems. We establish the analogy between our counting algorithm and the phase estimation algorithm and make use of the latter's performance analysis in stabilizing our scheme. Applications embrace a quantum metrological scheme to measure voltage (an analog to digital converter) and a simple procedure to entangle multiparticle states.

Suslov, M. V. [Moscow Institute of Physics and Technology, Institutskii per. 9, 141700 Dolgoprudny, Moscow District (Russian Federation); R and D Department, NIX Computer Company, Zvezdniy boulevard 19, 129085 Moscow (Russian Federation); Lesovik, G. B. [L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, 117940 Moscow (Russian Federation); Blatter, G. [Theoretische Physik, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zuerich (Switzerland)

2011-05-15

429

Quantum abacus for counting and factorizing numbers  

NASA Astrophysics Data System (ADS)

We generalize the binary quantum counting algorithm of Lesovik, Suslov, and Blatter [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.82.012316 82, 012316 (2010)] to higher counting bases. The algorithm makes use of qubits, qutrits, and qudits to count numbers in a base-2, base-3, or base-d representation. In operating the algorithm, the number nnumber n in the base-d representation; the inverse transformation is fully quantum at the level of individual qudits, while a simpler semiclassical version can be used on the level of qudit registers. Combining registers of qubits, qutrits, and qudits, where d is a prime number, with a simpler single-shot measurement allows us to find the powers of 2, 3, and other primes d in the number n. We show that the counting task naturally leads to the shift operation and an algorithm based on the quantum Fourier transformation. We discuss possible implementations of the algorithm using quantum spin-d systems, d-well systems, and their emulation with spin-1/2 or double-well systems. We establish the analogy between our counting algorithm and the phase estimation algorithm and make use of the latter’s performance analysis in stabilizing our scheme. Applications embrace a quantum metrological scheme to measure voltage (an analog to digital converter) and a simple procedure to entangle multiparticle states.

Suslov, M. V.; Lesovik, G. B.; Blatter, G.

2011-05-01

430

BioNumbers--the database of key numbers in molecular and cell biology.  

PubMed

BioNumbers (http://www.bionumbers.hms.harvard.edu) is a database of key numbers in molecular and cell biology--the quantitative properties of biological systems of interest to computational, systems and molecular cell biologists. Contents of the database range from cell sizes to metabolite concentrations, from reaction rates to generation times, from genome sizes to the number of mitochondria in a cell. While always of importance to biologists, having numbers in hand is becoming increasingly critical for experimenting, modeling, and analyzing biological systems. BioNumbers was motivated by an appreciation of how long it can take to find even the simplest number in the vast biological literature. All numbers are taken directly from a literature source and that reference is provided with the number. BioNumbers is designed to be highly searchable and queries can be performed by keywords or browsed by menus. BioNumbers is a collaborative community platform where registered users can add content and make comments on existing data. All new entries and commentary are curated to maintain high quality. Here we describe the database characteristics and implementation, demonstrate its use, and discuss future directions for its development. PMID:19854939

Milo, Ron; Jorgensen, Paul; Moran, Uri; Weber, Griffin; Springer, Michael

2009-10-23

431

The e-mail gossip number and the connected domination number  

Microsoft Academic Search

Our object is to introduce eg(G), the e-mail gossip number of a connected graph G, and derive a simple equation expressing this new invariant in terms of the known [1] connected domination number cd(G). As a corollary we see that determining each of these numbers is NP-hard. In general we follow the graph theoretic notation and terminology of [2]. Throughout

B. Raghavachari

1997-01-01

432

Teleportation-based number-state manipulation with number-sum measurement  

SciTech Connect

We examine various manipulations of photon number states which can be implemented by teleportation technique with number-sum measurement. The preparations of the Einstein-Podolsky-Rosen resources as well as the number-sum measurement resulting in projection to certain Bell state may be done conditionally with linear optical elements, i.e., beam splitters, phase shifters, and zero-one-photon detectors. Squeezed vacuum states are used as primary entanglement resource, while single-photon sources are not required.

Kitagawa, Akira; Yamamoto, Katsuji [Department of Nuclear Engineering, Kyoto University, Kyoto 606-8501 (Japan)

2003-10-01

433

Modeling low Reynolds number microgravity combustion problems  

NASA Astrophysics Data System (ADS)

The limit of low Reynolds number and low gravity allows a novel approximation to be developed for the equations of combustion theory. When the velocity field is separated into solenoidal and irrotational parts it is possible to show that the former is negligible to the lowest order in Reynolds number. Hence, the computation of the velocity field from the Navier Stokes equations may be replaced by the simpler task of solving Poissons equation for the irrotational field. This irrotational field is then substituted into the convective terms in energy and species equations, enabling solutions to be found for scalar quantities like the temperature and species mass fractions. The procedure is illustrated by examining two problems; the flow of air past a sphere blowing a light gas like helium, and combustion of volatiles blown from a porous sphere in an oxidizing crossfiow.

Baum, Howard R.

434

The MCNP5 Random number generator  

SciTech Connect

MCNP and other Monte Carlo particle transport codes use random number generators to produce random variates from a uniform distribution on the interval. These random variates are then used in subsequent sampling from probability distributions to simulate the physical behavior of particles during the transport process. This paper describes the new random number generator developed for MCNP Version 5. The new generator will optionally preserve the exact random sequence of previous versions and is entirely conformant to the Fortran-90 standard, hence completely portable. In addition, skip-ahead algorithms have been implemented to efficiently initialize the generator for new histories, a capability that greatly simplifies parallel algorithms. Further, the precision of the generator has been increased, extending the period by a factor of 10{sup 5}. Finally, the new generator has been subjected to 3 different sets of rigorous and extensive statistical tests to verify that it produces a sufficiently random sequence.

Brown, F. B. (Forrest B.); Nagaya, Y. (Yasunobu)

2002-01-01

435

An introduction to the Hilger quaternion numbers  

NASA Astrophysics Data System (ADS)

The classical time scales calculus used in applied mathematics was originated as the result of investigating calculus of variations on time scales. It was introduced by its originator Stefan Hilger in the late eighties as an attempt to unify continuous and discrete problems in one theory. The main purpose of this paper is to introduce the Hilger quaternion numbers and deduce some of their fundamental properties. We extend the definitions of Hilger pure imaginary number, Hilger real axis, the Hilger alternating axis, and the Hilger imaginary circle within this context. We further introduce a generalized cylinder transformation to give a definition of the quaternionic exponential function on time scales. To the best of our knowledge, this does not appear to have been done in literature before.

Georgiev, S.; Morais, J.

2013-10-01

436

Finite-particle-number approach to physics  

SciTech Connect

Starting from a discrete, self-generating and self-organizing, recursive model and self-consistent interpretive rules we construct: the scale constants of physics (3,10,137,1.7x10/sup 38/); 3+1 Minkowski space with a discrete metric and the algebraic bound ..delta.. is an element of ..delta.. tau is greater than or equal to 1; the Einstein-deBroglie relation; algebraic double slit interference; a single-time momentum-space scattering theory connected to laboratory experience; an approximation to wave functions; local phase severance and hence both distant correlations and separability; baryon number, lepton number, charge and helicity; m/sub p//m/sub e/; a cosmology not in disagreement with current observations.

Noyes, H.P.

1982-10-01

437

Nonequilibrium hadronization and constituent quark number scaling  

SciTech Connect

The constituent quark number scaling of elliptic flow is studied in a nonequilibrium hadronization and freeze-out model with rapid dynamical transition from ideal, deconfined, and chirally symmetric quark-gluon plasma, to final noninteracting hadrons. In this transition a bag model of constituent quarks is considered, where the quarks gain constituent quark mass while the background bag field breaks up and vanishes. The constituent quarks then recombine into simplified hadron states, while chemical, thermal, and flow equilibrium break down one after the other. In this scenario the resulting temperatures and flow velocities of baryons and mesons are different. Using a simplified few source model of the elliptic flow, we are able to reproduce the constituent quark number scaling, with assumptions on the details of the nonequilibrium processes.

Zschocke, Sven [TU Dresden, Institut fuer Planetare Geodaesie, Lohrmann-Observatorium, D-01062 Dresden (Germany); Horvat, Szabolcs [Department of Physics and Technology, University of Bergen, Allegaten 55, N-5007 Bergen (Norway); Faculty of Physics, Babes-Bolyai University, Kogalniceanu str 1, 400084 Cluj-Napoca (Romania); Mishustin, Igor N. [Frankfurt Institute for Advanced Studies (FIAS), D-60438 Frankfurt am Main (Germany); Russian Research Center, Kurchatov Institute, 123182 Moscow (Russian Federation); Csernai, Laszlo P. [Department of Physics and Technology, University of Bergen, Allegaten 55, N-5007 Bergen (Norway); Frankfurt Institute for Advanced Studies (FIAS), D-60438 Frankfurt am Main (Germany); MTA-KFKI Research Institute for Particle Physics and Nuclear Physics, H-1525 Budapest (Hungary)

2011-04-15

438

Entanglement distillation protocols and number theory  

SciTech Connect

We show that the analysis of entanglement distillation protocols for qudits of arbitrary dimension D benefits from applying basic concepts from number theory, since the set Z{sub D}{sup n} associated with Bell diagonal states is a module rather than a vector space. We find that a partition of Z{sub D}{sup n} into divisor classes characterizes the invariant properties of mixed Bell diagonal states under local permutations. We construct a very general class of recursion protocols by means of unitary operations implementing these local permutations. We study these distillation protocols depending on whether we use twirling operations in the intermediate steps or not, and we study them both analytically and numerically with Monte Carlo methods. In the absence of twirling operations, we construct extensions of the quantum privacy algorithms valid for secure communications with qudits of any dimension D. When D is a prime number, we show that distillation protocols are optimal both qualitatively and quantitatively.

Bombin, H.; Martin-Delgado, M.A. [Departamento de Fisica Teorica I, Universidad Complutense, 28040 Madrid (Spain)

2005-09-15

439

Optimal number of pigments in photosynthetic complexes  

NASA Astrophysics Data System (ADS)

We study excitation energy transfer in a simple model of a photosynthetic complex. The model, described by the Lindblad equation, consists of pigments interacting via dipole-dipole interaction. The overlapping of pigments induces an on-site energy disorder, providing a mechanism for blocking the excitation transfer. Based on the average efficiency as well as the robustness of random configurations of pigments, we calculate the optimal number of pigments that should be enclosed in a pigment-protein complex of a given size. The results suggest that a large fraction of pigment configurations are efficient as well as robust if the number of pigments is properly chosen. We compare the optimal results of the model to the structure of pigment-protein complexes as found in nature, finding good agreement.

Jesenko, Simon; Žnidari?, Marko

2012-09-01

440

Riemann zeros, prime numbers, and fractal potentials.  

PubMed

Using two distinct inversion techniques, the local one-dimensional potentials for the Riemann zeros and prime number sequence are reconstructed. We establish that both inversion techniques, when applied to the same set of levels, lead to the same fractal potential. This provides numerical evidence that the potential obtained by inversion of a set of energy levels is unique in one dimension. We also investigate the fractal properties of the reconstructed potentials and estimate the fractal dimensions to be D=1.5 for the Riemann zeros and D=1.8 for the prime numbers. This result is somewhat surprising since the nearest-neighbor spacings of the Riemann zeros are known to be chaotically distributed, whereas the primes obey almost Poissonlike statistics. Our findings show that the fractal dimension is dependent on both level statistics and spectral rigidity, Delta(3), of the energy levels. PMID:16241330

van Zyl, Brandon P; Hutchinson, David A W

2003-06-23

441

Quantum random-number generator based on a photon-number-resolving detector  

NASA Astrophysics Data System (ADS)

We demonstrated a high-efficiency quantum random number generator which takes inherent advantage of the photon number distribution randomness of a coherent light source. This scheme was realized by comparing the photon flux of consecutive pulses with a photon number resolving detector. The random bit generation rate could reach 2.4 MHz with a system clock of 6.0 MHz, corresponding to a random bit generation efficiency as high as 40%. The random number files passed all the stringent statistical tests.

Ren, Min; Wu, E.; Liang, Yan; Jian, Yi; Wu, Guang; Zeng, Heping

2011-02-01

442

Quantum random-number generator based on a photon-number-resolving detector  

SciTech Connect

We demonstrated a high-efficiency quantum random number generator which takes inherent advantage of the photon number distribution randomness of a coherent light source. This scheme was realized by comparing the photon flux of consecutive pulses with a photon number resolving detector. The random bit generation rate could reach 2.4 MHz with a system clock of 6.0 MHz, corresponding to a random bit generation efficiency as high as 40%. The random number files passed all the stringent statistical tests.

Ren Min; Wu, E; Liang Yan; Jian Yi; Wu Guang; Zeng Heping [State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062 (China)

2011-02-15

443

Mach number dependence of electron heating in high Mach number quasiperpendicular shocks  

NASA Astrophysics Data System (ADS)

The efficiency of electron heating through microinstabilities generated in the transition region of a quasiperpendicular shock for a wide range of Mach numbers is investigated by utilizing particle-in-cell (PIC) simulation and model analyses. In the model analyses saturation levels of effective electron temperature as a result of microinstabilities are estimated from an extended quasilinear (trapping) analysis for relatively low (high) Mach number shocks. Here, modified two-stream instability (MTSI) is assumed to become dominant in low Mach number regime, while Buneman instability (BI) is assumed to become dominant in high Mach number regime. It is revealed that Mach number dependence of the effective electron temperature in the MTSI dominant case is essentially different from that in the BI dominant case. The effective electron temperature through the MTSI does not depend much on the Mach number, although that through the BI increases with the Mach number as in the past studies. The results are confirmed to be consistent with the PIC simulations both in qualitative and quantitative levels. The model analyses predict that a critical Mach number, above which a steep rise in electron heating rate occurs, may arise at the Mach number of a few tens.

Matsukiyo, Shuichi

2010-04-01

444

2.NBT Ordering 3-digit 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: 1. Arrange the following numbers from least to greatest: 476 \\ \\ 647 \\ \\ 74 \\ \\ 674 \\ \\ 467 ______ ______ ______ ______ ______ 2. Arrange the following...

445

Rational Number Project: Initial Fraction Ideas  

NSDL National Science Digital Library

Twenty-eight lesson plans make up this research-based fourth and fifth grade fraction curriculum. It includes a teacher guide with theoretical framework and instructions and templates for making manipulatives. The Rational Number Project is an NSF-funded multi-university research project, and originally published this series of lessons in 1997 as "Fraction Lessons for the Middle Grades Level 1". This is an updated version, aligned to NCTM Standards for 2000.

Cramer, Kathleen; Behr, Merlyn; Post, Thomas; Lesh, Richard

2009-01-01

446

Fractions on the number line (grade 3)  

NSDL National Science Digital Library

This is a sample PARCC assessment task based on CCSS grade 3 fraction standards. In this interactive five-part task students reason about fractions used to represent part of a whole or a location on a number line, compare fractions with and without models, and construct arguments to defend their decisions. Included are the alignments to the CCSS, a scoring rubric, and background on the task itself.

2013-01-01

447

What is a closed-form number?  

Microsoft Academic Search

If a student asks for an antiderivative of exp(x^2), there is a standard reply: the answer is not an elementary function. But if a student asks for a closed-form expression for the real root of x = cos(x), there is no standard reply. We propose a definition of a closed-form expression for a number (as opposed to a *function*) that

Timothy Y. Chow

1998-01-01

448

Generating Random Numbers in Hostile Environments  

Microsoft Academic Search

\\u000a This paper discusses basic security aspects of distributed random number generation in potentially hostile environments. The\\u000a goal is to outline and discuss a distributed approach, which comes to question in the case of attacker being able to target\\u000a one or several mobile devices. We define communication paths and attacker models instead of providing technical details of\\u000a local generation. This paper

Jan Krhovjak; Andriy Stetsko; Vashek Matyas

449

Cold spray nozzle mach number limitation  

Microsoft Academic Search

The classic one-dimensional isentropic flow approach is used along with a two-dimensional axisymmetric numerical model to\\u000a show that the exit Mach number of a cold spray nozzle should be limited due to two factors. To show this, the two-dimensional\\u000a model is validated with experimental data. Although both models show that the stagnation temperature is an important limiting\\u000a factor, the one-dimensional

B. Jodoin

2002-01-01

450

Random.org: True Random Number Service  

NSDL National Science Digital Library

This random number service allows users to generate up to ten-thousand random integers with duplicates, randomized sequences without duplicates, or up to sixteen kilobytes of raw random bytes. Users can also flip virtual coins and generate random bitmaps. Most of the content on this site is free, but there are a few choice products which require log-in. Overall though, this is a great resource for anyone interested in mathematics.

Haahr, Mads

2009-08-28

451

On finding the number of clusters  

Microsoft Academic Search

We present a novel approach to finding the number of clusters in data based on the minimization of a regularized cost function. Minimization of the proposed cost function results in the minimization of the sum-of-squared distances of the data points from the respective nearest cluster center as well as the sum-of-squared distances of the individual cluster centers from neighborhood cluster

Ravi Kothari; Dax Pitts

1999-01-01

452

Novel quantum numbers in condensed matter physics  

Microsoft Academic Search

The physics understanding novel quantum numbers in condensed matter physics are discussed. Examples are given from the fields of conducting quasi-one-dimensional conductors 3He–A and the fractional quantum Hall effect. A common feature of these systems is a symmetry breaking whose under parameter describes a discrete symmetry breaking. This lead to flow of charge in the vacuum without excitation of carriers

J. R. Schrieffer

2004-01-01

453

Utility Priority Number Evaluation for FMEA  

Microsoft Academic Search

Traditionally, decisions on how to improve an operation are based on risk priority number (RPN) in the failure mode and effects\\u000a analysis (FMEA). Many scholars questioned the RPN method and proposed some new methods to improve the decision process, but\\u000a these methods are only measuring from the risks viewpoint while ignoring the importance of corrective actions. The corrective\\u000a actions may

Jih Kuang Chen

2007-01-01

454

Laser interrogation of latent vehicle registration number  

SciTech Connect

A recent investigation involved automobile registration numbers as important evidentiary specimens. In California, as in most states, small, thin metallic decals are issued to owners of vehicles each year as the registration is renewed. The decals are applied directly to the license plate of the vehicle and typically on top of the previous year`s expired decal. To afford some degree of security, the individual registration decals have been designed to tear easily; they cannot be separated from each other, but can be carefully removed intact from the metal license plate by using a razor blade. In September 1993, the City of Livermore Police Department obtained a blue 1993 California decal that had been placed over an orange 1992 decal. The two decals were being investigated as possible evidence in a case involving vehicle registration fraud. To confirm the suspicion and implicate a suspect, the department needed to known the registration number on the bottom (completely covered) 1992 decal. The authors attempted to use intense and directed light to interrogate the colored stickers. Optical illumination using a filtered white-light source partially identified the latent number. However, the most successful technique used a tunable dye laser pumped by a pulsed Nd:YAG laser. By selectively tuning the wavelength and intensity of the dye laser, backlit illumination of the decals permitted visualization of the underlying registration number through the surface of the top sticker. With optimally-tuned wavelength and intensity, 100% accuracy was obtained in identifying the sequence of latent characters. The advantage of optical techniques is their completely nondestructive nature, thus preserving the evidence for further interrogation or courtroom presentation.

Russo, R.E. [Lawrence Berkeley Lab., CA (United States). Energy and Environment Div.]|[Lawrence Livermore National Lab., CA (United States). Forensic Science Center; Pelkey, G.E. [City of Livermore Police Dept., CA (United States); Grant, P.; Whipple, R.E.; Andresen, B.D. [Lawrence Livermore National Lab., CA (United States). Forensic Science Center

1994-09-01

455

Number theory as the ultimate physical theory  

Microsoft Academic Search

At the Planck scale doubt is cast on the usual notion of space-time and one cannot think about elementary particles. Thus,\\u000a the fundamental entities of which we consider our Universe to be composed cannot be particles, fields or strings. In this\\u000a paper the numbers are considered as the fundamental entities. We discuss the construction of the corresponding physical theory.\\u000a A

Igor V. Volovich

2010-01-01

456

Airline network design with variable hub number  

Microsoft Academic Search

This paper addresses the non-strict hub-and-spoken airline network design problem in airline industry. Firstly, under the condition of the hub number not specified, an optimization model to minimize the sum of transportation cost and construct hub cost is established. Secondly, the classic algorithm can not solve the problem efficiently because the problem is NP-hard problem. An ant colony algorithm which

Yi Qin; Jinfu Zhu; Wei Zhang

2009-01-01

457

An Extendable Galaxy Number Count Model  

Microsoft Academic Search

I review galaxy number count models and present ncmod, an extendable and\\u000ageneral purpose model for comparing and interpreting the results of field\\u000agalaxy survey data. I develop techniques and software for converting the\\u000aresults of a survey done in one filter into another filter, for direct\\u000acomparison with other surveys. Comparison of the data from surveys which differ\\u000agreatly

1998-01-01

458

Titanium Superconducting Photon-Number-Resolving Detector  

Microsoft Academic Search

High-efficiency photon-number-resolving detectors have been developed using titanium-based transition-edge sensors. Device performances have been evaluated with respect to the response photon distribution, dark count, and timing jitter. In the analysis of the photon statistics, the observed detection probabili- ties were consistent with Poisson distributions. From a comparison of the measured distribution with theory, 98% detection efficiency was deduced at 850

Daiji Fukuda; Go Fujii; Takayuki Numata; Kuniaki Amemiya; Akio Yoshizawa; Hidemi Tsuchida; Hidetoshi Fujino; Hiroyuki Ishii; Taro Itatani; Shuichiro Inoue; Tatsuya Zama

2011-01-01

459

Preparing nanoparticle assemblies with number density gradients  

Microsoft Academic Search

We report on preparing assemblies of gold nanoparticles with gradient in number densities on flat silica-covered substrates. The methodology consists of : i) first forming a molecular gradient of amino groups (-NH2) on the substrate by vapor deposition of amine-terminated silane molecules, followed by ii) attachment of gold nanoparticles to -NH2 functional groups by immersing the substrate in a colloidal

Rajendra Bhat; Daniel Fischer; Jan Genzer

2002-01-01

460

Copy number polymorphisms and anticancer pharmacogenomics  

Microsoft Academic Search

Background  Recent studies have investigated the contribution of copy number variants (CNVs) to disease susceptibility in a multitude\\u000a of complex disorders, including systemic lupus erythematosus, Crohn's disease, and various neurodevelopmental disorders. Relatively\\u000a few CNV studies, however, have been conducted on pharmacologic phenotypes even though these structural variants are likely\\u000a to play an important role. We developed a genome-wide method to identify

Eric R Gamazon; R Stephanie Huang; M Eileen Dolan; Nancy J Cox

2011-01-01

461

Braess's Paradox, Fibonacci Numbers, and Exponential Inapproximability  

Microsoft Academic Search

\\u000a We give the first analyses in multicommodity networks of both the worst-case severity of Braess’s Paradox and the price of\\u000a anarchy of selfish routing with respect to the maximum latency. Our first main result is a construction of an infinite family\\u000a of two-commodity networks, related to the Fibonacci numbers, in which both of these quantities grow exponentially with the\\u000a size

Henry Lin; Tim Roughgarden; Éva Tardos; Asher Walkover

2005-01-01

462

On relative gain array and condition number  

Microsoft Academic Search

Deviations of open-loop properties in the presence of modeling uncertainties are studied. The aim is to gain insights into how open-loop properties and, thus, potentially closed-loop properties may vary in the face of a diagonally structured uncertainty. Several estimates are given for the worst-case deviations of the open-loop transfer function in terms of the scaled plant condition numbers, the relative

Jie Chen; J. S. Freudenberg; Carl N. Nett

1992-01-01

463

What is a closed-form number?  

Microsoft Academic Search

If a student asks for an antiderivative of exp(x^2), there is a standard\\u000areply: the answer is not an elementary function. But if a student asks for a\\u000aclosed-form expression for the real root of x = cos(x), there is no standard\\u000areply. We propose a definition of a closed-form expression for a number (as\\u000aopposed to a *function*) that

Timothy Y. Chow

1998-01-01

464

Detecting Prime Numbers via Roots of Polynomials  

ERIC Educational Resources Information Center

|It is proved that an integer n [greater than or equal] 2 is a prime (resp., composite) number if and only if there exists exactly one (resp., more than one) nth-degree monic polynomial f with coefficients in Z[subscript n], the ring of integers modulo n, such that each element of Z[subscript n] is a root of f. This classroom note could find use…

Dobbs, David E.

2012-01-01

465

Semantics and the Number of English Sentences.  

ERIC Educational Resources Information Center

It has long been said that there are an infinite number of English sentences. "This is the cat that caught the rat" is an Enqlish sentence. So is "This is the cat that caught the rat that stole the cheese.""This is the cat with white paws that caught the rat that stole the cheese" is unobjectionable as well. Since a clear cutoff point cannot be…

Bjurlof, Thomas; Jamieson, Dale

466

Redefining the number needed to excise.  

PubMed

The number needed to excise (NNE) is a metric used to convey the efficiency of dermatological practice by serving as a gauge for the diagnostic accuracy of melanoma. Rather than an NNE for melanoma alone, we assert that the NNE should measure all skin cancer types and we present data on NNE from two clinical sites demonstrating the utility and trends in NNE over time. PMID:23574144

Chen, Lucy; Dusza, Stephen; Grazzini, Marta; Blum, Andreas; Marghoob, Ashfaq

2013-04-10

467

Compound liquid jets at low Reynolds numbers  

Microsoft Academic Search

Asymptotic methods based on the slenderness ratio are used to obtain the leading-order equations which govern the fluid dynamics of axisymmetric, isothermal, Newtonian, compound liquid jets such as those employed in the manufacture of textile fibres, composite fibres and optical fibres, at low Reynolds numbers. It is shown that the leading-order equations are one-dimensional, and analytical solutions are obtained for

J. I Ramos

2002-01-01

468

Distribution of the number of consecutive records  

Microsoft Academic Search

We study the distribution of the number n;r of r consecutive records in a sequence of n independent and identically distributed random variables from a common continuous distribution, or equivalently, in a random permutation ofn elements. We show that the asymptotic distribution of n;r is Poisson for r = 1; 2 and non-Poisson for r 3. Precise asymptotic results are

Hua-huai Chern; Hsien-kuei Hwang; Yeong-nan Yeh

2000-01-01

469

Factorization of the tenth Fermat number  

Microsoft Academic Search

We describe the complete factorization of the tenth Fermat num- ber F10 by the elliptic curve method (ECM). F10 is a product of four prime factors with 8, 10, 40 and 252 decimal digits. The 40-digit factor was found after about 140 Mflop-years of computation. We also discuss the complete fac- torization of other Fermat numbers by ECM, and summarize

Richard P. Brent

1999-01-01

470

1NBT Number of the Day  

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: Materials Large chart paper, markers, math journals, pencils, 100 chart. Directions Students will count the "Number of the Day" beginning with 1 on the...

471

Tidal Love Numbers of Neutron Stars  

SciTech Connect

For a variety of fully relativistic polytropic neutron star models we calculate the star's tidal Love number k{sub 2}. Most realistic equations of state for neutron stars can be approximated as a polytrope with an effective index n {approx} 0.5-1.0. The equilibrium stellar model is obtained by numerical integration of the Tolman-Oppenheimer-Volkhov equations. We calculate the linear l = 2 static perturbations to the Schwarzschild spacetime following the method of Thorne and Campolattaro. Combining the perturbed Einstein equations into a single second-order differential equation for the perturbation to the metric coefficient g{sub tt} and matching the exterior solution to the asymptotic expansion of the metric in the star's local asymptotic rest frame gives the Love number. Our results agree well with the Newtonian results in the weak field limit. The fully relativistic values differ from the Newtonian values by up to {approx}24%. The Love number is potentially measurable in gravitational wave signals from inspiralling binary neutron stars.

Hinderer, Tanja [Center for Radiophysics and Space Research, Cornell University, Ithaca, NY 14853 (United States)], E-mail: tph25@cornell.edu

2008-04-20

472

Identification of copy number variants in horses.  

PubMed

Copy number variants (CNVs) represent a substantial source of genetic variation in mammals. However, the occurrence of CNVs in horses and their subsequent impact on phenotypic variation is unknown. We performed a study to identify CNVs in 16 horses representing 15 distinct breeds (Equus caballus) and an individual gray donkey (Equus asinus) using a whole-exome tiling array and the array comparative genomic hybridization methodology. We identified 2368 CNVs ranging in size from 197 bp to 3.5 Mb. Merging identical CNVs from each animal yielded 775 CNV regions (CNVRs), involving 1707 protein- and RNA-coding genes. The number of CNVs per animal ranged from 55 to 347, with median and mean sizes of CNVs of 5.3 kb and 99.4 kb, respectively. Approximately 6% of the genes investigated were affected by a CNV. Biological process enrichment analysis indicated CNVs primarily affected genes involved in sensory perception, signal transduction, and metabolism. CNVs also were identified in genes regulating blood group antigens, coat color, fecundity, lactation, keratin formation, neuronal homeostasis, and height in other species. Collectively, these data are the first report of copy number variation in horses and suggest that CNVs are common in the horse genome and may modulate biological processes underlying different traits observed among horses and horse breeds. PMID:22383489

Doan, Ryan; Cohen, Noah; Harrington, Jessica; Veazey, Kylee; Veazy, Kylee; Juras, Rytis; Cothran, Gus; McCue, Molly E; Skow, Loren; Dindot, Scott V

2012-03-01

473

Identification of copy number variants in horses  

PubMed Central

Copy number variants (CNVs) represent a substantial source of genetic variation in mammals. However, the occurrence of CNVs in horses and their subsequent impact on phenotypic variation is unknown. We performed a study to identify CNVs in 16 horses representing 15 distinct breeds (Equus caballus) and an individual gray donkey (Equus asinus) using a whole-exome tiling array and the array comparative genomic hybridization methodology. We identified 2368 CNVs ranging in size from 197 bp to 3.5 Mb. Merging identical CNVs from each animal yielded 775 CNV regions (CNVRs), involving 1707 protein- and RNA-coding genes. The number of CNVs per animal ranged from 55 to 347, with median and mean sizes of CNVs of 5.3 kb and 99.4 kb, respectively. Approximately 6% of the genes investigated were affected by a CNV. Biological process enrichment analysis indicated CNVs primarily affected genes involved in sensory perception, signal transduction, and metabolism. CNVs also were identified in genes regulating blood group antigens, coat color, fecundity, lactation, keratin formation, neuronal homeostasis, and height in other species. Collectively, these data are the first report of copy number variation in horses and suggest that CNVs are common in the horse genome and may modulate biological processes underlying different traits observed among horses and horse breeds.

Doan, Ryan; Cohen, Noah; Harrington, Jessica; Veazy, Kylee; Juras, Rytis; Cothran, Gus; McCue, Molly E.; Skow, Loren; Dindot, Scott V.

2012-01-01

474

Low-Reynolds-number swimming at pycnoclines  

PubMed Central

Microorganisms play pivotal functions in the trophic dynamics and biogeochemistry of aquatic ecosystems. Their concentrations and activities often peak at localized hotspots, an important example of which are pycnoclines, where water density increases sharply with depth due to gradients in temperature or salinity. At pycnoclines organisms are exposed to different environmental conditions compared to the bulk water column, including reduced turbulence, slow mass transfer, and high particle and predator concentrations. Here we show that, at an even more fundamental level, the density stratification itself can affect microbial ecology at pycnoclines, by quenching the flow signature, increasing the energetic expenditure, and stifling the nutrient uptake of motile organisms. We demonstrate this through numerical simulations of an archetypal low-Reynolds-number swimmer, the “squirmer.” We identify the Richardson number—the ratio of buoyancy forces to viscous forces—as the fundamental parameter that quantifies the effects of stratification. These results demonstrate an unexpected effect of buoyancy on low-Reynolds-number swimming, potentially affecting a broad range of abundant organisms living at pycnoclines in oceans and lakes.

Doostmohammadi, Amin; Stocker, Roman; Ardekani, Arezoo M.

2012-01-01

475

Vertebrate kinetochore protein architecture: protein copy number.  

PubMed

To define the molecular architecture of the kinetochore in vertebrate cells, we measured the copy number of eight kinetochore proteins that link kinetochore microtubules (MTs [kMTs]) to centromeric DNA. We used a fluorescence ratio method and chicken DT40 cell lines in which endogenous loci encoding the analyzed proteins were deleted and complemented using integrated green fluorescent protein fusion transgenes. For a mean of 4.3 kMTs at metaphase, the protein copy number per kMT is between seven and nine for members of the MT-binding KNL-1/Mis12 complex/Ndc80 complex network. It was between six and nine for four members of the constitutive centromere-associated network: centromere protein C (CENP-C), CENP-H, CENP-I, and CENP-T. The similarity in copy number per kMT for all of these proteins suggests that each MT end is linked to DNA by six to nine fibrous unit attachment modules in vertebrate cells, a conclusion that indicates architectural conservation between multiple MT-binding vertebrate and single MT-binding budding yeast kinetochores. PMID:20548100

Johnston, Katherine; Joglekar, Ajit; Hori, Tetsuya; Suzuki, Aussie; Fukagawa, Tatsuo; Salmon, E D

2010-06-14

476

Reynolds number effects in combustion noise  

SciTech Connect

Acoustic emission spectra have been obtained for non-premixed turbulent combustion from two small diameter laboratory gas burners, two commercial gas burners and a large gas burner in the firebox of a Babcock-Wilcox Boiler (50,000 lb steam/hr). The changes in burner size and firing rate represent changes in Reynolds number and changes in air/fuel ratio represent departure from stoichiometric proportions. The combustion efficiency was measured independently through gas analysis. The acoustic spectra obtained from the various burners exhibit a persistent shape over the Reynolds number range of 8200-82,000. The spectra were analyzed for identification of a predictable frequency domain that is most responsive to, and readily correlated with, combustion efficiency. A simple parameter (consisting of the ratio of the average acoustic power output in the most responsive frequency bandwidth to the acoustic power level of the loudest frequency) is proposed whose value increases significantly and unmistakably as combustion efficiency approaches 100%. The dependence of the most responsive frequency domain on the various Reynolds numbers associated with turbulent jets is discussed.

Seshan, P.K.

1981-01-01

477

Elementary complex number analysis of lung models.  

PubMed

Formulae from the complex number method of network analysis are used by respiratory physiologists with increasing frequency. As yet, however, no elementary derivation of these has been found in physiological journals, the reader usually being referred to electronic texts: the derivations in these texts are not directed to respiratory problems and are generally more involved than required for respiratory purposes. The present presentation of the complex number analysis method is elementary, the necessary grounding in the field of complex numbers being given in an Appendix. The analysis is directed first to a one-compartment lung, then to a simple two-compartment lung (effectively the same method applying also to simple multiple-compartment lungs), and finally an indication is given of the analysis of more complex models that include air-compression effects. By gaining an understanding of the underlying principles the respiratory physiologist will improve the extent and depth of application of this powerful method of analysis. In particular, he will be in a position to analyse the body plethysmographic measurement of the non-uniform lung. PMID:3975494

Imberger, H

1985-01-01

478

CONTRA: copy number analysis for targeted resequencing  

PubMed Central

Motivation: In light of the increasing adoption of targeted resequencing (TR) as a cost-effective strategy to identify disease-causing variants, a robust method for copy number variation (CNV) analysis is needed to maximize the value of this promising technology. Results: We present a method for CNV detection for TR data, including whole-exome capture data. Our method calls copy number gains and losses for each target region based on normalized depth of coverage. Our key strategies include the use of base-level log-ratios to remove GC-content bias, correction for an imbalanced library size effect on log-ratios, and the estimation of log-ratio variations via binning and interpolation. Our methods are made available via CONTRA (COpy Number Targeted Resequencing Analysis), a software package that takes standard alignment formats (BAM/SAM) and outputs in variant call format (VCF4.0), for easy integration with other next-generation sequencing analysis packages. We assessed our methods using samples from seven different target enrichment assays, and evaluated our results using simulated data and real germline data with known CNV genotypes. Availability and implementation: Source code and sample data are freely available under GNU license (GPLv3) at http://contra-cnv.sourceforge.net/ Contact: Jason.Li@petermac.org Supplementary information: Supplementary data are available at Bioinformatics online.

Li, Jason; Lupat, Richard; Amarasinghe, Kaushalya C.; Thompson, Ella R.; Doyle, Maria A.; Ryland, Georgina L.; Tothill, Richard W.; Halgamuge, Saman K.; Campbell, Ian G.; Gorringe, Kylie L.

2012-01-01

479

Sometimes area counts more than number  

PubMed Central

Using an interference paradigm, we show across three experiments that adults' order judgments of numbers, sizes, or combined area of dots in pairs of arrays occur spontaneously and automatically, but at different speeds and levels of accuracy. Experiment 1 used circles whose sizes varied between but not within arrays. Variation in circle size interfered with judgments of which array had more circles. Experiment 2 used displays in which circle size varied within and between arrays. Between-array differences in the amount of “circle stuff” (area occupied by circles) interfered with judgments of number. Experiment 3 examined whether variation in number also interferes with judgments of area. Interference between discrete and continuous stimulus dimensions occurred in both directions, although it was stronger from the continuous to the discrete than vice versa. These results bear on interpretations of studies with infants and preschoolers wherein subjects respond on the basis of continuous quantity rather than discrete quantity. In light of our results with adults, these findings do not license the conclusion that young children cannot represent discrete quantity. Absent data on attentional hierarchies and speed of processing, it is premature to conclude that infant and child quantity processes are fundamentally different from that of adults.

Hurewitz, Felicia; Gelman, Rochel; Schnitzer, Brian

2006-01-01

480

Congruent numbers with many prime factors.  

PubMed

Mohammed Ben Alhocain, in an Arab manuscript of the 10th century, stated that the principal object of the theory of rational right triangles is to find a square that when increased or diminished by a certain number, m becomes a square [Dickson LE (1971) History of the Theory of Numbers (Chelsea, New York), Vol 2, Chap 16]. In modern language, this object is to find a rational point of infinite order on the elliptic curve my2 = x3 - x. Heegner constructed such rational points in the case that m are primes congruent to 5,7 modulo 8 or twice primes congruent to 3 modulo 8 [Monsky P (1990) Math Z 204:45-68]. We extend Heegner's result to integers m with many prime divisors and give a sketch in this report. The full details of all the proofs will be given in ref. 1 [Tian Y (2012) Congruent Numbers and Heegner Points, arXiv:1210.8231]. PMID:23213259

Tian, Ye

2012-12-04

481

Variation of curve number with storm depth  

NASA Astrophysics Data System (ADS)

The NRCS Curve Number (known also as SCS-CN) method is well known as a tool in predicting flood runoff depth from small ungauged catchment. The traditional way of determination the CNs, based on soil characteristics, land use and hydrological conditions, seemed to have tendency to overpredict the floods in some cases. Over 30 year rainfall-runoff data, collected in two small (A=23.4 & 82.4 km2), lowland, agricultural catchments in Center of Poland (Banasik & Woodward 2010), were used to determine runoff Curve Number and to check a tendency of changing. The observed CN declines with increasing storm size, which according recent views of Hawkins (1993) could be classified as a standard response of watershed. The analysis concluded, that using CN value according to the procedure described in USDA-SCS Handbook one receives representative value for estimating storm runoff from high rainfall depths in the analyzes catchments. This has been confirmed by applying "asymptotic approach" for estimating the watershed curve number from the rainfall-runoff data. Furthermore, the analysis indicated that CN, estimated from mean retention parameter S of recorded events with rainfall depth higher than initial abstraction, is also approaching the theoretical CN. The observed CN, ranging from 59.8 to 97.1 and from 52.3 to 95.5, in the smaller and the larger catchment respectively, declines with increasing storm size, which has been classified as a standard response of watershed. The investigation demonstrated also changeability of the CN during a year, with much lower values during the vegetation season. Banasik K. & D.E. Woodward (2010). "Empirical determination of curve number for a small agricultural watrshed in Poland". 2nd Joint Federal Interagency Conference, Las Vegas, NV, June 27 - July 1, 2010 (http://acwi.gov/sos/pubs/2ndJFIC/Contents/10E_Banasik_ 28_02_10. pdf). Hawkins R. H. (1993). "Asymptotic determination of curve numbers from data". Journal of Irrigation and Drainage Division. American Society of Civil Engineers, 119(2). pp. 334-345. ACKNOWLEDGMENTS The investigation described in the paper is part of the research project no. N N305 396238 founded by PL-Ministry of Science and Higher Education. The support provided by this organization is gratefully acknowledged.

Banasik, K.; Hejduk, L.

2012-04-01

482

Number Sense and Number Nonsense: Understanding the Challenges of Learning Math  

ERIC Educational Resources Information Center

How do children learn math--and why do some children struggle with it? The answers are in "Number Sense and Number Nonsense," a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math…

Krasa, Nancy; Shunkwiler, Sara

2009-01-01

483

Language and Number Values: The Influence of Number Names on Children's Understanding of Place Value  

ERIC Educational Resources Information Center

|In recent years, the idea of language influencing the cognitive development of an understanding of place value has received increasing attention. This study explored the influence of using explicit number names on pre-kindergarten and kindergarten students' ability to rote count, read two-digit numerals, model two-digit numbers, and identify the…

Browning, Sandra T.; Beauford, Judith E.

2012-01-01

484

Piaget, Children, and Number: Applying Piaget's Theory to the Teaching of Elementary Number.  

ERIC Educational Resources Information Center

This paper proposes a method for teaching number applying the conservation theory of Piaget in the classroom. It is suggested that number facts cannot be taught by social transmission, since there is a fundamental distinction between logico-mathematical and social knowledge. Conservation cannot be taught to non-conservers, but there are ways to…

Kamii, Constance; DeVries, Rheta

485

How to Learn the Natural Numbers: Inductive Inference and the Acquisition of Number Concepts  

ERIC Educational Resources Information Center

|Theories of number concepts often suppose that the natural numbers are acquired as children learn to count and as they draw an induction based on their interpretation of the first few count words. In a bold critique of this general approach, Rips, Asmuth, Bloomfield [Rips, L., Asmuth, J. & Bloomfield, A. (2006). Giving the boot to the bootstrap:…

Margolis, Eric; Laurence, Stephen

2008-01-01

486

76 FR 79607 - Local Number Portability Porting Interval and Validation Requirements; Telephone Number Portability  

Federal Register 2010, 2011, 2012, 2013

...when the new service provider requests a CSR: any working telephone number associated...provider requests a Customer Service Record (CSR). Best Practice 70 provides that the transferring...when the new service provider requests a CSR: any working telephone number...

2011-12-22

487

Genetic Association Studies of Copy-Number Variation: Should Assignment of Copy Number States Precede Testing?  

Microsoft Academic Search

Recently, structural variation in the genome has been implicated in many complex diseases. Using genomewide single nucleotide polymorphism (SNP) arrays, researchers are able to investigate the impact not only of SNP variation, but also of copy-number variants (CNVs) on the phenotype. The most common analytic approach involves estimating, at the level of the individual genome, the underlying number of copies

Patrick Breheny; Prabhakar Chalise; Anthony Batzler; Liewei Wang; Brooke L. Fridley

2012-01-01

488

Approximations of fuzzy numbers by trapezoidal fuzzy numbers preserving the ambiguity and value  

Microsoft Academic Search

Value and ambiguity are two parameters which were introduced to represent fuzzy numbers. In this paper, we find the nearest trapezoidal approximation and the nearest symmetric trapezoidal approximation to a given fuzzy number, with respect to the average Euclidean distance, preserving the value and ambiguity. To avoid the laborious calculus associated with the Karush–Kuhn–Tucker theorem, the working tool in some

Adrian I. Ban; A. Brândas; Lucian C. Coroianu; C. Negrutiu; O. Nica

2011-01-01

489

Number Sense and Number Nonsense: Understanding the Challenges of Learning Math  

ERIC Educational Resources Information Center

|How do children learn math--and why do some children struggle with it? The answers are in "Number Sense and Number Nonsense," a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math…

Krasa, Nancy; Shunkwiler, Sara

2009-01-01

490

Influence of pole-pair number and rotor slot number on effects caused by cage faults  

Microsoft Academic Search

? ? Abstract -- This paper discusses the relationship between the pole-pair number ‘p’ and the slot number ’N’ as well as basic effects in stator currents caused by various cage faults. The analysis is performed using a model of a motor with faulty cage reduced to four equations. It is capable of operating with cage asymmetry factors. The authors

T. J. Sobczyk; W. Maciolek

2011-01-01

491

Video filtering with Fermat number theoretic transforms using residue number system  

Microsoft Academic Search

. Nevertheless, the transform length appears still to be useful especially with block-based image and video filtering ap- plications. We call these transforms the generalized FNT (GFNT). The second solution is to use a residue number system (RNS) to enlarge the effective modulus, while performing actual number theoretic transforms with smaller moduli. This approach appears to be particularly useful with

Tuukka Toivonen; Janne Heikkilä

2006-01-01

492

Making Numbers Your Friends: A Set of "Make This Number" Activities  

ERIC Educational Resources Information Center

Fluency with basic number facts is vital for students' progress in mathematics. Not only does it contribute to students' facility with mental computation and algorithms, but an understanding of numbers and their properties builds a foundation for future mathematical work including algebra. There are many activities that can help students "make…

Chick, Helen

2009-01-01

493

27 CFR 40.170 - Application for employer identification number.  

Code of Federal Regulations, 2013 CFR

...false Application for employer identification number. 40.170 Section...170 Application for employer identification number. Every manufacturer...has neither secured an employer identification number nor made...

2013-04-01

494

A Framework for Remediating Number Combination Deficits  

PubMed Central

This article introduces a framework for the remediation of number combination (NC) deficits. Research on the remediation of NC deficits is summarized, and research program studies are used to illustrate the 3 approaches to remediation. The Framework comprises a 2-stage system of remediation. The less intensive stage implementing 1 of 3 intervention approaches hypothesized to be most productive for a student uses a validated protocol while monitoring student response. The more intensive stage, which is reserved for nonresponders, involves integrating the 3 intervention approaches within a skills-based diagnostic-prescriptive scheme for individualizing intervention.

FUCHS, LYNN S.; POWELL, SARAH R.; SEETHALER, PAMELA M.; FUCHS, DOUGLAS; HAMLETT, CAROL L.; CIRINO, PAUL T.; FLETCHER, JACK M.

2011-01-01

495

Investigations in Number, Data, and Space  

NSDL National Science Digital Library

Investigations is a complete K-5 mathematics curriculum, developed at TERC in Cambridge, Mass. It is designed to help all children understand the fundamental ideas of number and operations, geometry, data, measurement, and early algebra. The curriculum has four major goals: to offer students meaningful mathematical problems; emphasize depth in mathematical thinking; communicate mathematics content and pedagogy to teachers; and expand the pool of mathematically literate students. This site includes descriptions of the units in each grade, K through 5; ordering information; and information on professional-development workshops designed to facilitate introduction of this curriculum.

Terc

496

Getting DNA copy numbers without control samples  

PubMed Central

Background The selection of the reference to scale the data in a copy number analysis has paramount importance to achieve accurate estimates. Usually this reference is generated using control samples included in the study. However, these control samples are not always available and in these cases, an artificial reference must be created. A proper generation of this signal is crucial in terms of both noise and bias. We propose NSA (Normality Search Algorithm), a scaling method that works with and without control samples. It is based on the assumption that genomic regions enriched in SNPs with identical copy numbers in both alleles are likely to be normal. These normal regions are predicted for each sample individually and used to calculate the final reference signal. NSA can be applied to any CN data regardless the microarray technology and preprocessing method. It also finds an optimal weighting of the samples minimizing possible batch effects. Results Five human datasets (a subset of HapMap samples, Glioblastoma Multiforme (GBM), Ovarian, Prostate and Lung Cancer experiments) have been analyzed. It is shown that using only tumoral samples, NSA is able to remove the bias in the copy number estimation, to reduce the noise and therefore, to increase the ability to detect copy number aberrations (CNAs). These improvements allow NSA to also detect recurrent aberrations more accurately than other state of the art methods. Conclusions NSA provides a robust and accurate reference for scaling probe signals data to CN values without the need of control samples. It minimizes the problems of bias, noise and batch effects in the estimation of CNs. Therefore, NSA scaling approach helps to better detect recurrent CNAs than current methods. The automatic selection of references makes it useful to perform bulk analysis of many GEO or ArrayExpress experiments without the need of developing a parser to find the normal samples or possible batches within the data. The method is available in the open-source R package NSA, which is an add-on to the aroma.cn framework. http://www.aroma-project.org/addons.

2012-01-01

497

Numbers Count Workshop at Agnes Scott College  

NSDL National Science Digital Library

These workshop resources were provided for faculty interested in addressing the gap between mathematics and its application in biological problem solving. To support the observation, experimentation and modeling of data, the Numbers Count workshop will provide an introduction to data, tools, and curricular materials for use with undergraduates. We also addressed the lack of context that impedes student learningâÂÂstudents rightfully ask themselves why should they need to integrate arcsin x if they want to become a physician? This event was held at Agnes Scott College in Atlanta in January 2009.

Claudia Neuhauser (University of Minnesota Rochester;Health Sciences)

2009-01-09

498

Resources for the UTK Numbers Count Workshop  

NSDL National Science Digital Library

These workshop resources were prepared for faculty interested in addressing the gap between mathematics and its application in biological problem solving. To support the observation, experimentation and modeling of data, the Numbers Count workshop provides an introduction to data, tools, and curricular materials for use with undergraduates. We also addressed the lack of context that impedes student learningâÂÂstudents rightfully ask themselves why should they need to integrate arcsin x if they want to become a physician? This event was held at the University of Tennessee at Knoxville in May 2009.

Claudia Neuhauser (University of Minnesota Rochester;Health Sciences)

2009-05-07

499

Turbulent Schmidt Numbers Above a Wheat Crop  

NASA Astrophysics Data System (ADS)

Measurements of vertical fluxes and concentration differences above a spring wheat crop (height h=0.9-0.95 m, row spacing 0.25 m, displacement height d=0.5-0.6 m) were analyzed to determine the Schmidt numbers for water vapour (S^v) and carbon dioxide (S^c) based on concentration differences between intakes 2.55 and 3.54 m above the ground. During nearly-neutral stratification S^v(0) = 0.68 ± 0.1 while S^c = 0.78 ± 0.2, implying that the roughness sublayer extended above 2.5 h.

Wilson, J. D.

2013-08-01

500

Turbulent Schmidt Numbers Above a Wheat Crop  

NASA Astrophysics Data System (ADS)

Measurements of vertical fluxes and concentration differences above a spring wheat crop (height h=0.9-0.95 m, row spacing 0.25 m, displacement height d=0.5-0.6 m) were analyzed to determine the Schmidt numbers for water vapour (S^v) and carbon dioxide (S^c) based on concentration differences between intakes 2.55 and 3.54 m above the ground. During nearly-neutral stratification S^v(0) = 0.68 ± 0.1 while S^c = 0.78 ± 0.2, implying that the roughness sublayer extended above 2.5 h.

Wilson, J. D.

2013-04-01