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1

Natural convection in a vertical plane channel: DNS results for high Grashof numbers  

NASA Astrophysics Data System (ADS)

The turbulent natural convection of a gas ( Pr = 0.71) between two vertical infinite walls at different but constant temperatures is investigated by means of direct numerical simulation for a wide range of Grashof numbers (6.0 × 106 > Gr > 1.0 × 103). The maximum Grashof number is almost one order of magnitude higher than those of computations reported in the literature so far. Results for the turbulent transport equations are presented and compared to previous studies with special attention to the study of Verteegh and Nieuwstadt (Int J Heat Fluid Flow 19:135-149, 1998). All turbulence statistics are available on the TUHH homepage (http://www.tu-harburg.de/tt/dnsdatabase/dbindex.en.html). Accuracy considerations are based on the time averaged balance equations for kinetic and thermal energy. With the second law of thermodynamics Nusselt numbers can be determined by evaluating time averaged wall temperature gradients as well as by a volumetric time averaged integration. Comparing the results of both approaches leads to a direct measure of the physical consistency.

Kiš, P.; Herwig, H.

2014-07-01

2

On the finite element simulation of fluid motion with high Reynolds or Grashof number  

SciTech Connect

Numerical simulation of free convection problems with usual Finite Element (FE) formulations run into stability problems for large Grashof numbers. This is true even for simple models. In regions where the stream velocity or the temperature field is constant along the stream lines, the stiffness matrix may become ill-conditioned for large stream velocities although its physical contribution vanishes. Besides a costly increase in the number of elements and corresponding decrease of the length unit, a change in the unit system can not improve the matrix condition. The ill-conditioning arises from the usual decomposition of the nonlinear convective terms into a velocity-dependent stiffness matrix which represents a differential operator and a solution vector on which the stiffness matrix operates. The problem should be solved by an adapted choice of the matrix representation of the nonlinear convective terms. Alternatively and necessarily for Newton-Raphson iteration of the nonlinear equations - the ill-conditioning terms may be neglected within those elements, where their physical contribution is negligible.

Trautenberg, E.A.; Roeckelein, R. (SIEMENS Corporate Research Lab., Erlangen (Germany))

1993-03-01

3

Experimental investigation of free-convection heat transfer in vertical tube at large Grashof numbers / E. R. G. Eckert, A. J. Diaguila  

NASA Technical Reports Server (NTRS)

Local free-convection heat-transfer coefficients and temperature fields in the turbulent flow range were obtained within a vertical, stationary tube closed at the boom, heated along its walls, and having a length-to-diameter ratio of 5. Convective heat-transfer coefficients were correlated by the general relations for free-convection heat transfer. These coefficients, converted to dimensionless Nusselt numbers were 35 percent below known relations for vertical flat plates. Air temperature measurements within the tube indicated a thin boundary layer along the heated wall surface and unstable conditions in the air flow.

Eckert, E R G; Diaguila, A J

1952-01-01

4

Calibration of thermal anemometer at very low Reynolds numbers under microgravity  

Microsoft Academic Search

An experimental configuration is presented for conducting hot wire anemometer measurements at very low velocities, as demonstrated for the cases of a KC-135 aircraft in microgravity trajectory and a small drop-tower facility. It is noted that the influence of the Grashof number is more pronounced, even at relatively high velocities, than anticipated in the extant literature.

F. R. Stengele; A. Delgado; H. J. Rath

1992-01-01

5

Numbers  

NSDL National Science Digital Library

The purpose of this video tutorial is to review a couple ways in which we think about numbers. Thinking in terms of street numbers, money in bank accounts, and quantum particles (e.g. Bose-Einstein condensate) is contrasted with focusing on associating numbers with distinguishable manipulatives, as is more familiar in K-8 courses. This video concludes with a reminder that the symbol "infinity" is not, itself, a number.

2013-06-14

6

Numbers  

NSDL National Science Digital Library

This engaging web site contains information and interactive applets related to various number systems: Egyptian, Babylonian, Chinese, Greek, Roman, Mayan, and Arabic. Users learn the history and structure of each system as well as how to count and write numbers. The site also allows users to explore finger systems, calculating machines, other number bases, and "interesting numbers." A series of pages on data and graphs includes information and activities on gathering, analyzing, graphing and sorting data. (Because the section on the Arabic number system is so extensive, it is cataloged separately as a related resource.)

Edkins, Jo

2006-01-01

7

3D natural convection in circular horizontal cylinder: effect of Prandtl number  

NASA Astrophysics Data System (ADS)

The stability of three-dimensional (3-D) natural convection in circular cylinder with differentially heated vertical end walls and insulated lateral walls is investigated numerically. In such a configuration, which is a basic configuration of several crystal growth systems, the flow develops as soon as the temperature difference (? T) is non zero. When ? T is increased, we observe a gradual change in the structure of the flow and the flow structure undergoes a variety of steady or unsteady bifurcations. The onset of unsteadiness is investigated by direct numerical simulation and by linear stability approach which combines Newton's method, to determine the stable or unstable 3-D steady state, and Arnoldi's method to compute the eigenvalues of largest real part of the linearized evolution operator about this state. The continuation technique is then used to determine with precision the critical values of the governing parameters. Computations are carried out for a circular cylinder with an aspect ratio (length/diameter) equal to 3, and Prandtl number (Pr) ranging from 0.01 to 0.026. It is thus found that in the range of investigated Prandtl number, the steady state loses its stability through an unstable steady bifurcation followed by an unstable Hopf bifurcation which is found to occur at larger Grashof number. We also obtain a second branch which is stable and leads for a large value of Grashof to a stable Hopf bifurcation. A numerical integration is also conducted to supplement the 3-D linear stability analysis. The calculations were done for a circular cylinder with aspect ratio 3. Dependence of the steady and unsteady bifurcations on the Prandtl number is investigated in detail. The features of the results are that transport of the shear of the mean flow is found to be the main source of instability. However, thermal effects which are negligible for Pr=0, gain importance with increasing Prandtl number. For Pr=0.075, its contribution to the destabilisation of the initial steady flow is as important as that of the shear of the mean flow. The appearance of these bifurcations transforms an initial symmetric pattern to non-symmetric states. For instance, for Pr=0.01, the first bifurcation is steady and produces a symmetry breaking with respect to the transverse central horizontal axis. However, for Pr=0.055, the Hopf bifurcation produces a symmetry breaking with respect to the longitudinal vertical plane. Furthermore, oscillatory three-dimensional flow structure and heat transfer are analysed and the origins of the instabilities are clarified by means of energy stability analysis.

Vaux, S.; Ben Hadid, H.; Henry, D.

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.

Dan Bunker

2010-01-01

9

Number Sense  

NSDL National Science Digital Library

Hacker has given you a challenge. He’ll run his number machine to create a number. Then you’ll get three numbers between one and nine. The challenge is to make a number that is larger than the one on Hacker’s machine. Be careful though--Hacker will give you numbers that can’t be bigger than his!

2008-01-01

10

Number Line  

NSDL National Science Digital Library

This iOS app helps students to visualize number sentences and create models for addition, subtractions, multiplication, and division. The number line can be adjusted to represent multiples of numbers from one to one hundred.

Clarity Innovations, Inc.

2013-11-22

11

Mystery Number  

NSDL National Science Digital Library

This game for 2-3 players (K-5) combines logic and numbers. Players start with a 10x10 grid of the numbers 1 to 100. One person chooses a secret number and announces the range in which it falls. Other players ask yes or no questions to identify the number. They cross out the numbers on the board that are no longer possibilities. The player who identifies the secret number wins. Available as a downloadable pdf in English or in Spanish.

2011-01-01

12

Number Explorer  

NSDL National Science Digital Library

This interactive application helps students to learn visually about numbers from their possible arrangements and how those arrangements relate to division, multiplication, and factors. The web applet divides numbers and displays calculation to show the remainder as a number, fraction, or decimal value and allows demonstration of types of numbers such as prime, square, and triangular. The number explorer has automated tests for divisibility, factor pairs, or prime factors. Three different shapes can be used, the original fish swim around and obediently arrange themselves to show number properties. However balls or cards cards can be used instead, these animate faster and are better for displaying numbers.

2012-01-01

13

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.

2013-12-04

14

Number Tracks  

NSDL National Science Digital Library

This problem provides an opportunity for children to explore and visualize number patterns and sequences and to reinforce key number concepts and vocabulary such as odd and even, factors and multiples. Students cut consecutive number tracks into equal length pieces in several ways and investigate the patterns that emerge among the sums of the tracks. The Teachers' Notes page explains number tracks and offers suggestions for implementation, discussion questions, a printable sheet of number tracks (pdf), and ideas for extension and support.

15

Number Flash  

NSDL National Science Digital Library

This iOS app helps students make the transition from counting to number recognition by thinking of a number of objects in relation to five and ten. The app displays a set number of items from one to twenty in ten frames then flashes away after the preset number of seconds. The user must identify the number that was shown on the ten frames.

Mark, Mitchell

2013-03-10

16

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

17

Number Cruncher  

NSDL National Science Digital Library

This Science NetLinks interactive game helps students increase their logic and decision making skills by challenging a player to consider a series of mathematical processes to find a path from a starting number to a goal number in a math maze. The activity appears as a 5x5 matrix of numbers, each of which has an operation symbol next to it, indicating whether it will be added to, subtracted from, or multiplied by the previous number. Starting in the center with a given number, players choose an adjoining number to complete the next step and they proceed until successfully reaching the goal number or until they have run out of usable numbers on the game board. To add an additional challenge to the game, a player can limit each level to reaching the target in seven or fewer steps.

2011-10-13

18

Complex Numbers  

NSDL National Science Digital Library

This is a short study guide from the University of Maryland's Physics Education Research Group on introducing, interpreting, and using complex numbers. Mathematical equations are included to help students understand the nature of complex numbers.

2010-04-01

19

Number Theory  

Microsoft Academic Search

Comments on the article by Gardner Murphy , which considered the psychological sources of Pythagorean number theory. The current author offers some supplementary information, noting that there are some additional meanings attached to some numbers in the culture of India.

Santokh S. Anant

1968-01-01

20

Tooth Numbering  

MedlinePLUS

... numbered as well. Illustrations created by Simple Steps designer Michael Becker Universal Numbering System Adults In this ... indicates that it is a deciduous (primary or "baby") tooth. So, a child's first tooth on the ...

21

Negative Numbers  

NSDL National Science Digital Library

This article is an account of how negative numbers became part of the "vocabulary" of mathematicians and of some of the earliest appearances of negative numbers in calculations of the ancient civilizations of China, India and Greece. Although negative numbers were used in calculations, negative answers to mathematical problems were considered meaningless or impossible. The troubled history of negative numbers presented in this article shows how the simple mathematical principles taken for granted today have taken thousands of years to develop.

Howard, Jill

2009-05-01

22

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

23

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.

Dan Bunker

2005-01-01

24

Number Sense  

NSDL National Science Digital Library

Students will practice counting to 100 and making numbers with base ten blocks Let\\'s have some fun with math! First, practice counting to 100. Listen to the instructions on this website. Count to 100 Now that you have worked on counting to 100, let\\'s make some numbers! Use the base ten blocks to make the numbers shown on the screen! Base Ten Blocks Great work! The next ...

Black, Mrs.

2007-10-03

25

Complex Numbers  

NSDL National Science Digital Library

The objective of this lesson is to gain a better understanding of complex numbers and their graphs Situation: The Swiss Mathemation, Jean Robert Argand developed a means to graphically represent complex numbers. This led to solving problems related to altenating electrical current, which provides current day luxuries. Could you do the same? Current Knowledge: Use your knowledge of complex number and the coordinate system and with your partner, ...

Mrs. Pierce

2010-11-16

26

Index Numbers  

Microsoft Academic Search

Index numbers are used to aggregate detailed information on prices and quantities into scalar measures of price and quantity levels or their growth. The paper reviews four main approaches to bilateral index number theory where two price and quantity vectors are to be aggregated: fixed basket and average of fixed baskets, stochastic, test or axiomatic and economic approaches. The paper

Erwin Diewert

2007-01-01

27

Number Line  

NSDL National Science Digital Library

In this brief article the numerous uses of the number line are detailed: counting, measurement, addition, subtraction, decimals, and fractions. The article contains visual representations of the some of the concepts and links to related topics.

2012-08-27

28

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

29

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

30

Numbers & Operation  

NSDL National Science Digital Library

Let's get speedy with number use. Click on the game Going Bananas with Divsion which is in bold letters below. Using the mouse, click on Instructions and read them carefully. Then, click on Start Game . Then select 3-12 as your level to play. Use the mouse to select ...

Mrs. Fincher

2010-03-07

31

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

32

Table Numbers  

NSDL National Science Digital Library

This interactive applet helps students develop fluency with multiplication facts. Users chose a factor from among the digits 1-9, each of which is associated with a mnemonic graphic. The applet then displays three numbers and the user selects the one which is a multiple of the chosen factor. The player must respond correctly to ten examples to complete a round. A one-point penalty for selecting an incorrect product discourages guessing. The few words that are displayed are in Dutch.

2008-01-01

33

Fibonacci numbers and Lucas numbers in graphs  

Microsoft Academic Search

A subset S?V(G) is independent if no two vertices of S are adjacent in G. In this paper we study the number of independent sets in graphs with two elementary cycles. In particular we determine the smallest number and the largest number of these sets among n-vertex graphs with two elementary cycles. The extremal values of the number of independent

Mariusz Startek; Andrzej Wloch; Iwona Wloch

2009-01-01

34

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

35

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.

36

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

37

1 -Routing Number 2 -Account Number  

E-print Network

ACCOUNT Fill out the form above. If you have questions about the transit/routing number or the account and SAVE, you will still be able to access all the information via online, under View Paycheck Click on ADD

38

Hyper Space Complex Number  

E-print Network

A new kind of numbers called Hyper Space Complex Numbers and its algebras are defined and proved. It is with good properties as the classic Complex Numbers, such as expressed in coordinates, triangular and exponent forms and following the associative and commutative laws of addition and multiplication. So the classic Complex Number is developed from in complex plane with two dimensions to in complex space with N dimensions and the number system is enlarged also.

Shanguang Tan

2007-04-23

39

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 ...

Ms. Nielsen

2008-09-02

40

Elements of number theory  

E-print Network

The dissertation argues for the necessity of a morphosemantic theory of number, that is, a theory of number serviceable both to semantics and morphology. The basis for this position, and the empirical core of the dissertation, ...

Harbour, Daniel, 1975-

2003-01-01

41

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

42

Reform by the Numbers.  

ERIC Educational Resources Information Center

Although numbers such as average test scores or dropout rates can capture part of a school system's success or failure, school statistics seldom tell the whole story. School board members should realize that numbers might measure compliance or process, rather than improvement. Also, improvements in numbers might reflect changes in assessment…

Hanford, Terry; White, Kathleen

1991-01-01

43

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

44

The Remarkable Number "1"  

ERIC Educational Resources Information Center

In human history, the origin of the numbers came from definite practical needs. Indeed, there is strong evidence that numbers were created before writing. The number "1", dating back at least 20,000 years, was found as a counting symbol on a bone. The famous statement by the German mathematician Leopold Kronecker (1823-1891), "God…

Allen, G. Donald

2014-01-01

45

On Number Representation  

E-print Network

Place value numbers, such as the binary or decimal numbers can be represented by the end vertices (leaf or pendant vertices) of rooted symmetrical trees. Numbers that consist of at most a fixed number of digits are represented by vertices that are equidistant from the root vertex and the corresponding number representations do not depend on the distance from the root vertex. In this paper, we introduce place value number systems which are representable by rooted symmetrical trees and in which the representation of a number depends on the distance of the corresponding vertex from the root vertex. Such dependence activates the role of zero in such a way as to render its function equivalent to that of any other single digit number. Thus, in addition to being a place value holder, the digit zero (just as any other single digit numeral) affects the value of a number regardless of its position. For example 012 is different, in the new systems, from 12. As such, these new number systems could be thought of as a natural development for the role of zero. We also illustrate how addition is performed in these newly constructed number systems. In addition to being mathematical structures which could be of mathematical interest, these new number systems could possibly have applications in computing and computing security.

Rafael I. Rofa

2013-10-30

46

Decompose That Teen Number!  

NSDL National Science Digital Library

The students will receive explicit instruction from the teacher on the definition of decomposing a number and how to represent a decomposition with manipulatives, drawings, and equations. The students will use linking cubes to reflect numbers from 11-19, and to show their understanding of how to decompose a number. Students will record decompositions as an equation.

ROBIN MARMITT

2012-09-03

47

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

48

Convoluted Convolved Fibonacci Numbers  

NASA Astrophysics Data System (ADS)

The convolved Fibonacci numbers F_j^(r) are defined by (1-x-x^2)^{-r}=sum_{j>= 0}F_{j+1}^(r)x^j. In this note we consider some related numbers that can be expressed in terms of convolved Fibonacci numbers. These numbers appear in the numerical evaluation of a constant arising in the study of the average density of elements in a finite field having order congruent to a (mod d). We derive a formula expressing these numbers in terms of ordinary Fibonacci and Lucas numbers. The non-negativity of these numbers can be inferred from Witt's dimension formula for free Lie algebras. This note is a case study of the transform 1/n sum_{d|}n mu(d)f(z^d)^{n/d} (with f any formal series), which was introduced and studied in a companion paper by Moree.

Moree, Pieter

2004-04-01

49

Decimal Number Line  

NSDL National Science Digital Library

This interactive Flash applet helps students explore place value and develop number sense within whole numbers, integers and decimals. It allows a child or teacher to select an interval in the given number line and show that interval divided into ten equal parts but on a larger scale, which can then be repeated. Users may choose the size of the interval between markers on the first number line and the starting number of that line, as well as whether to hide or show individual number lines and the numbers on them. This applet lends itself well for use on an interactive white board. A pdf guide to this collection of teaching applets is cataloged separately.

2006-01-01

50

Guess the Number  

NSDL National Science Digital Library

This interactive game gives students practice in counting and ordering numbers. Users try to determine the magician's secret number in as few tries as possible by adjusting their successive guesses according to feedback (too high or too low). Solvers can choose from three ranges of numbers (1 to 10, 1 to 100, or -1000 to 1000) and choose whether or not to view previous guesses.

2011-01-01

51

Number Line Bars  

NSDL National Science Digital Library

Teachers and students can use this interactive Java applet to model and carry out arithmetic operations on the number line. Users manipulate the size, position, and direction of color bars to represent addition, subtraction, multiplication and division with whole numbers, integers and fractions. Options include the ability to zoom in and out, change the colors of the bars, and adjust the step size of the bars and number line increments.

2000-01-01

52

Computing with Real Numbers  

Microsoft Academic Search

We introduce, in Part I, a number representation suitable for exact real number computation, consisting of an exponent and\\u000a a mantissa, which is an infinite stream of signed digits, based on the interval [?1,1]. Numerical operations are implemented\\u000a in terms of linear fractional transformations (LFT’s). We derive lower and upper bounds for the number of argument digits that are needed

Abbas Edalat; Reinhold Heckmann

2000-01-01

53

Interactive Fraction Number Lines  

NSDL National Science Digital Library

In this lesson students make models of fractions, including a human number line. Using a number line, students develop conceptual understanding of fractions. Students use the number line to represent and compare fractions less than one. The activities are engaging and include full participation/engagement of all students. The fractions are limited to positive fractions less than one with a denominator of 2 or 4 including 0 and 1 whole.

Green, Michael

2012-05-25

54

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.

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

2005-12-07

55

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.

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

56

Law of Large Numbers  

NSDL National Science Digital Library

Created by Charles M. Grinstead and J. Laurie Snell of Dartmouth College, this website is part of an online statistics textbook. Topics include: (1) Law of Large Numbers for Discrete Random Variables, (2) Chebyshev Inequality, (3) Law of Averages, (4) Law of Large Numbers for Continuous Random Variables, (5) Monte Carlo Method. There are several examples and exercises that accompany the material.

Grinstead, Charles M.

57

Numbers and Operations  

NSDL National Science Digital Library

Counting numbers 1-10 Help Champ the Monkey Count the Bananas! The higher you count the harder it gets when you Count the Fish In Pirate numbers count the barrels and then press the red button to launch the cannon. Make sure you're right or your ship will sink! Help count with Counting with Elmo and Zoe! ...

Gribbin, Miss

2010-11-10

58

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

59

Definitions Numbered Space  

E-print Network

Definitions · Numbered Space ­ a single space marked with a number and reserved for a single permit 24/7 · Unnumbered Space ­ a space which can be used by any customer allowed to park in that lot. High Low Average Question 4: If I buy a staff permit for an UNNUMBERED* space in a non-gated surface

Behmer, Spencer T.

60

Templates, Numbers & Watercolors.  

ERIC Educational Resources Information Center

Describes how a second-grade class used large templates to draw and paint five-digit numbers. The lesson integrated artistic knowledge and vocabulary with their mathematics lesson in place value. Students learned how draftspeople use templates, and they studied number paintings by Charles Demuth and Jasper Johns. (KM)

Clemesha, David J.

1990-01-01

61

Avogadro's Number Ferromagnetically  

ERIC Educational Resources Information Center

Avogadro's number, usually denoted by N[subscript A], plays a fundamental role in both physics and chemistry. It defines the extremely useful concept of the mole, which is the base unit of the amount of matter in the international system of units. The fundamental character of this number can also be illustrated by its appearance in the definitions…

Houari, Ahmed

2010-01-01

62

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

63

Counting whole numbers  

NSDL National Science Digital Library

Identify and use whole numbers up to 100 Here are some links to help you learn more about counting Teach R Kids Math counting and number activity themes Here are some games to help you practice your counting counting cherrios Bunny Count Connect the Dots Game ...

Hirst, Ms.

2007-10-12

64

Inventing Negative Numbers  

NSDL National Science Digital Library

In this quick time video segment from Cyberchase, viewers learn about extending a vertical number line below zero as they watch the CyberSquad rescue the Cyberspace Council, which is being held captive by Hacker in a tall building. This video is also featured in the lesson plan: "Introducing Negative Numbers" (cataloged separately). Teaching Tips and a transcript are included.

2008-10-10

65

Numbers in the News  

NSDL National Science Digital Library

All those numbers in the newspaper: what do they mean? Challenge learners to find out as they develop their number sense. Distribute newspaper pages to learners so that each pair gets a section with numbers at the right level of difficulty: easy—weather or sports scores; medium—clothing ads or event listings with times and dates; hard—automobile ads, monetary exchange rates. Learners try to find the smallest and largest numbers on the page (including best deal/best rate) and explain to others what they found. Variation for younger learners: look for the largest or smallest number on a walk around the building or around the block. Available as a web page and downloadable pdf.

TERC

2010-01-01

66

Number Conveyor Belt  

NSDL National Science Digital Library

This activity for the interactive white board (free access with registration) allows a teacher to create an arithmetic sequence for students to watch being built as the sequence of numbers moves along a conveyor. Learners must determine the pattern being used so when the belt randomly stops, the missing number in the sequence can be dragged/ dropped into its place. The teacher sets the start number (0-19), the interval or common difference (1-10) and if the sequence will count up or down. This last option provides an opportunity to display patterns with integers.

2012-01-01

67

1.NBT Ordering 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: Malik is given a list of numbers: 1 \\ \\ 5 \\ \\ 10 \\ \\ 50 \\ \\ 100 He wants to include the following numbers so all numbers will be listed in order from l...

2012-05-01

68

Genetics by the Numbers  

MedlinePLUS

... genome is larger than any other known species. Credit: Open Cage That's how many base pairs—or ... of chromosomes, which are made up of DNA. Credit: NHGRI That's the approximate number of genes in ...

69

On Hultman Numbers  

NASA Astrophysics Data System (ADS)

Finding a sequence of transpositions that transforms a given permutation into the identity permutation and is of the shortest possible length is an important problem in bioinformatics. Here, a transposition consists in exchanging two contiguous intervals of the permutation. Bafna and Pevzner introduced the cycle graph as a tool for working on this problem. In particular, they took advantage of the decomposition of the cycle graph into so-called alternating cycles. Later, Hultman raised the question of determining the number of permutations with a cycle graph containing a given quantity of alternating cycles. The resulting number is therefore similar to the Stirling number of the first kind. We provide an explicit formula for computing what we call the Hultman numbers, and give a few numerical values. We also derive formulae for related cases, as well as for a much more general problem. Finally, we indicate a counting result related to another operation on permutations called the "block-interchange".

Doignon, Jean-Paul; Labarre, Anthony

2007-06-01

70

Two Symmetric Properties of Mersenne Numbers and Fermat Numbers  

E-print Network

Mersenne numbers and Fermat numbers are two hot and difficult issues in number theory. This paper constructs a special group for every positive odd number other than 1, and discovers an algorithm for determining the multiplicative order of 2 modulo q for each positive odd number q. It is worth mentioning that this paper discovers two symmetric properties of Mersenne numbers and Fermat numbers.

Shi Yongjin

2013-04-27

71

Exploring Number Sequences  

NSDL National Science Digital Library

This series of activities can be used to introduce number sequences and patterns and to reinforce parity (even and odd numbers) and its application in addition. The resources are intended for use on an interactive whiteboard but may also be used individually or in small groups. They can be accessed online or downloaded (zip) to a local computer. The pack includes teacher notes, background information on the content, and a student worksheet.

2011-01-01

72

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.

73

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

74

Addictive Number Theory  

Microsoft Academic Search

\\u000a In 1996, just after Springer-Verlag published my books Additive Number Theory: The Classical Bases [34] and Additive Number Theory: Inverse Problems and the Geometry of Sumsets [35], I went into my local Barnes and Noble superstore on Route 22 in Springfield, New Jersey, and looked for them on the\\u000a shelves. Suburban bookstores do not usually stock technical mathematical books, and,

Melvyn B. Nathanson

75

Dangerous Doubles (Doubling Numbers)  

NSDL National Science Digital Library

This lesson teaches students to use the strategy doubling numbers and doubles plus or minus one in order to use mental math to add one digit numbers. The students are engaged in learning through the read aloud of Double the Ducks by Stephen Murphy and then get to work with a partner to draw doubles and write equations that relate to their drawings. Students individually work on solving word problems using these strategies and manipulatives as necessary to solve.

Sharrer, Stephanie

2012-07-14

76

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

77

Beyond the Number Domain  

PubMed Central

In a world without numbers, we would be unable to build a skyscraper, hold a national election, plan a wedding, or pay for a chicken at the market. The numerical symbols used in all these behaviors build on the approximate number system (ANS) which represents the number of discrete objects or events as a continuous mental magnitude. In this review, we first discuss evidence that the ANS bears a set of behavioral and brain signatures that are universally displayed across animal species, human cultures, and development. We then turn to the question of whether the ANS constitutes a specialized cognitive and neural domain--a question central to understanding how this system works, the nature of its evolutionary and developmental trajectory, and its physical instantiation in the brain. PMID:19131268

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

2009-01-01

78

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

79

Expansion of rational numbers in Mobius number systems Petr Kurka  

E-print Network

Expansion of rational numbers in M¨obius number systems Petr K°urka Center for Theoretical Study- tions. We say that a M¨obius number system is rational, if it represents rational numbers by periodic. In the present paper we study expansions of rational numbers in the integer M¨obius number systems, whose

Kurka, Petr

80

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

81

"Better than Their Numbers"  

ERIC Educational Resources Information Center

This article discusses College Summit, a nonprofit effort centered around the premise that there is a sizable number of students who are more capable of college academics than their test scores and grade point averages suggest. Its four-day summer sessions are focused not on ramping up students' academic performance but in mining students'…

Cech, Scott J.

2008-01-01

82

IN NUMBERS: Biostatistics Faculty  

E-print Network

STRENGTH IN NUMBERS: Biostatistics Faculty Are in Great Demand in the SPH and Beyond of the school's Department of Biostatistics faculty (clockwise starting from lower left): Drs. Catherine Sugar specialize in other aspects of clinical trials design. With this expertise, the Department of Biostatistics

Grether, Gregory

83

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

84

Emergency Numbers DANFORTH CAMPUS  

E-print Network

Fire Safety Active Shooter Natural Disasters Hazardous Material Spills Flu Information PreparingEmergency Numbers DANFORTH CAMPUS Ambulance · Fire · Police (314) 935-5555 Emergency Health Service 911 MEDICAL CAMPUS Ambulance · Fire · Police (314) 362-HELP (4357) Safety and Security 2012-2013 Guide

Subramanian, Venkat

85

Emergency Numbers DANFORTH CAMPUS  

E-print Network

Fire Safety Active Shooter Natural Disasters Hazardous Material Spills Flu Information PreparingEmergency Numbers DANFORTH CAMPUS Ambulance · Fire · Police (314) 935-5555 Emergency Health Service 911 MEDICAL CAMPUS Ambulance · Fire · Police (314) 362-HELP (4357) Safety and Security 2014-2015 Guide

Grant, Gregory

86

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.

2013-06-21

87

A Highly Random Number  

Microsoft Academic Search

In his celebrated 1936 paper Turing defined a machine to becircular iff it performs an infinite computation outputting only finitelymany symbols. We define ( as the probability that an arbitrary machinebe circular and we prove that is a random number that goes beyond$2, the probability that a universal self alelimiting machine halts. Thealgorithmic complexity of c is strictly greater than

Facultad De Ciencias Exactas; Gregory Chaitin; Sergio Daicz I; Vernica Becher

2001-01-01

88

Paint by Numbers Revived!  

ERIC Educational Resources Information Center

Remember paint by numbers? This revived trend was a perfect solution to teaching geometric shapes to the author's first-grade students. Geometric shapes are identified and used in early elementary art classrooms, but this lesson gives students a deeper understanding of shape, encourages problem-solving, and makes a strong correlation between math…

Hahn, Nic

2012-01-01

89

Large number hypothesis  

NASA Astrophysics Data System (ADS)

Dirac's large number hypothesis (LNH) and the Whitrow-Randall-Sciama relation are related to some cosmological models. The LNH and Whitrow-Randall-Sciama relations are neither equivalent nor consistent in general relativity, but they may both be valid in the Brans-Dicke theory and in another theory considered in this paper.

Berman, Marcelo Samuel

1992-08-01

90

CHEMICAL SAFETY Emergency Numbers  

E-print Network

- 1 - CHEMICAL SAFETY MANUAL 2010 #12;- 2 - Emergency Numbers UNBC Prince George Campus Security Prince George Campus Chemstores 6472 Chemical Safety 6472 Radiation Safety 5530 Biological Safety 5530 use, storage, handling, waste and emergency management of chemicals on the University of Northern

Bolch, Tobias

91

ALARA notes, Number 8  

SciTech Connect

This document contains information dealing with the lessons learned from the experience of nuclear plants. In this issue the authors tried to avoid the `tyranny` of numbers and concentrated on the main lessons learned. Topics include: filtration devices for air pollution abatement, crack repair and inspection, and remote handling equipment.

Khan, T.A.; Baum, J.W.; Beckman, M.C. [eds.] [eds.

1993-10-01

92

Generalized van der Waerden numbers  

Microsoft Academic Search

Certain generalizations of arithmetic progressions are used to define numbers analogous to the van der Waerden numbers. Several exact values of the new numbers are given, and upper bounds for these numbers are obtained. In addition, a comparison is made between the number of different arithmetic progressions and the number of different generalized arithmetic progressions.

Bruce M. Landman

1986-01-01

93

On normal numbers Veronica Becher  

E-print Network

On normal numbers Ver´onica Becher Universidad de Buenos Aires & CONICET Workshop on Logic Language and Information, July 2014 #12;Normal numbers Normality is a basic form of randomness for real numbers. It asks that the expansions of real numbers obey the Law of Large Numbers. Ver´onica Becher On normal numbers 1 / 30 #12

Becher, Verónica

94

ACCOUNTS PAYABLE VENDOR NUMBER GUIDE  

E-print Network

ACCOUNTS PAYABLE VENDOR NUMBER GUIDE FOR DEPARTMENTS W-9 AND W-8BEN FORMS TAXPAYER ID NUMBER (TIN), FEDERAL EMPLOYER ID NUMBER (FEIN), AND EMPLOYER'S ID NUMBER (EIN) HOW TO FIND A VENDOR'S ID NUMBER IN BANNER HOW TO DETERMINE IF A VENDOR IS IN BANNER UPDATED MAY 2013 #12;Vendor Number Guide

95

First Grade Number Actiivities  

NSDL National Science Digital Library

This page provides examples of First Grade Number (Operations and Algebraic Thinking, and Number and Operations in Base Ten) 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

96

Second grade Number Activities  

NSDL National Science Digital Library

This page provides examples of Second Grade Number (Operations and Algebraic Thinking, and Number and Operations in Base Ten) 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

97

On canonical number systems  

Microsoft Academic Search

Let P(x) = pdxd + ::: + p0 2 Z(x) be such that d ‚ 1;pd = 1;p0 ‚ 2 and N = f0;1;:::;p0 ¡ 1g. We are proving in this note a new criterion for the pair fP(x);Ng to be a canonical number system. This enables us to prove that if p2;:::;pd¡1; Pd i=1 pi ‚ 0 and p0

Shigeki Akiyama; Attila Pethö

2002-01-01

98

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

99

Maths Doctor: Number  

NSDL National Science Digital Library

The Maths Doctor website from Macmillan Publishers contains more than 250 lessons that are free for anyone. Each lesson includes a three to five minute video tutorial on the topic and a related worksheet for the student to complete. Each worksheet has a convenient QR code that a student can scan to access the video. The Number section contains numerous lessons ranging from Conversion of Units to Dividing Fractions to Subtracting Negative Integers.

2014-06-20

100

Nature by Numbers  

NSDL National Science Digital Library

This 4-minute computer animation highlights three forms in nature that have connections with numbers and geometry. The Fibonacci sequence and the golden ratio are shown relating to the chambered nautilus shell and the sunflower seed pattern. The Delaunay triangulation and Voronoi tessellation are shown to simulate the capillary distribution on a dragonfly wing. Included are descriptions of the mathematics and stills from the production.

101

Greek Number Theory  

Microsoft Academic Search

\\u000a Number theory is the second large field of mathematics that comes to us from the Pythagoreans via Euclid. The Pythagorean\\u000a theorem led mathematicians to the study of squares and sums of squares; Euclid drew attention to the primes by proving that there are infinitely many of them. Euclid’s investigations were based on the so-called Euclidean algorithm, a method for finding

John Stillwell

102

The Remarkable Number "1"  

NASA Astrophysics Data System (ADS)

In human history, the origin of the numbers came from definite practical needs. Indeed, there is strong evidence that numbers were created before writing. The number "1", dating back at least 20,000 years, was found as a counting symbol on a bone. The famous statement by the German mathematician Leopold Kronecker (1823-1891), "God made the integers; all else is the work of man," has spawned a lively modern philosophical discussion, and this discussion begins by trying to get a philosophical handle on "1." This approach remains under heavy discussion, and is more-or-less unresolved (Frege in Die Grundlagen der Arithmetik (English: The foundations of arithmetic). Polhman, 1884). In this note, we consider the many facets of "one" in it many guises and applications. Nonetheless, "one" has multiple meanings, from the very practical to the abstract, from mathematics to science to basically everything. We examine here a mere slice of mathematical history with a focus on the most basic and applicable concept therein. It troubles many, particularly students, even today.

Allen, G. Donald

2014-09-01

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

Variation in Plastid Number  

PubMed Central

Changes in the physiological state of the multiplastidic alga Olisthodiscus luteus result in a shift in chloroplast complement from 33 to 21 plastids. The effect of this induced change in organelle complement on nuclear and chloroplast DNA levels has been analyzed. Data suggest that the absolute amount of chloroplast and nuclear DNA found within a cell remains constant but that the amount of chloroplast DNA per plastid is inversely proportional to the number of chloroplasts to which that DNA must be distributed. ImagesFig. 1 PMID:16660558

Cattolico, Rose Ann

1978-01-01

105

Displaying Number Patterns  

NSDL National Science Digital Library

This applet from the E-Examples of NCTM, which could be used as an interactive presentation tool, allows the student to link numerical patterns to a visual display as a number pattern is displayed on a calculator and on a hundred board simultaneously. The learner's task is to compare counting sequences on the calculator with the patterns they generate on the hundred board with the goal of helping students to see patterns and then make predictions. Instructions for using the applet are provided as well as background for the teacher.

Bill Kreahling, Bob Panoff, and the Shodor Education Foundation

2011-05-05

106

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.

107

New normal numbers Veronica Becher  

E-print Network

New normal numbers Ver´onica Becher Universidad de Buenos Aires & CONICET, Argentina Joint work Departamento de Matem´atica, FCEyN, UBA, julio 2014 Ver´onica Becher New normal numbers 0 / 15 #12;Normal numbers Ver´onica Becher New normal numbers 1 / 15 #12;Normal numbers A base is an integer b greater than

Becher, Verónica

108

Generalized Maxwell Love numbers  

E-print Network

By elementary methods, I study the Love numbers of a homogeneous, incompressible, self-gravitating sphere characterized by a generalized Maxwell rheology, whose mechanical analogue is represented by a finite or infinite system of classical Maxwell elements disposed in parallel. Analytical, previously unknown forms of the complex shear modulus for the generalized Maxwell body are found by algebraic manipulation, and studied in the particular case of systems of springs and dashpots whose strength follows a power-law distribution. We show that the sphere is asymptotically stable for any choice of the mechanical parameters that define the generalized Maxwell body and analytical forms of the Love numbers are always available for generalized bodies composed by less than five classical Maxwell bodies. For the homogeneous sphere, real Laplace inversion methods based on the Post-Widder formula can be applied without performing a numerical discretization of the n-th derivative, which can be computed in a "closed-form" with the aid of the Faa di Bruno formula.

Giorgio Spada

2009-11-04

109

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

110

Wizard's Number (0-1000)  

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 digit sum, a more/less range comparison, rounding, how far it is to the next hundred, comparison of tens and units, the number of units, and parity. Clicking on the wizard opens a keypad on which to type the secret number. A version covering numbers 0-100 is cataloged separately.

2011-01-01

111

Modular redundant number systems  

SciTech Connect

With the increased use of public key cryptography, faster modular multiplication has become an important cryptographic issue. Almost all public key cryptography, including most elliptic curve systems, use modular multiplication. Modular multiplication, particularly for the large public key modulii, is very slow. Increasing the speed of modular multiplication is almost synonymous with increasing the speed of public key cryptography. There are two parts to modular multiplication: multiplication and modular reduction. Though there are fast methods for multiplying and fast methods for doing modular reduction, they do not mix well. Most fast techniques require integers to be in a special form. These special forms are not related and converting from one form to another is more costly than using the standard techniques. To this date it has been better to use the fast modular reduction technique coupled with standard multiplication. Standard modular reduction is much more costly than standard multiplication. Fast modular reduction (Montgomery`s method) reduces the reduction cost to approximately that of a standard multiply. Of the fast multiplication techniques, the redundant number system technique (RNS) is one of the most popular. It is simple, converting a large convolution (multiply) into many smaller independent ones. Not only do redundant number systems increase speed, but the independent parts allow for parallelization. RNS form implies working modulo another constant. Depending on the relationship between these two constants; reduction OR division may be possible, but not both. This paper describes a new technique using ideas from both Montgomery`s method and RNS. It avoids the formula problem and allows fast reduction and multiplication. Since RNS form is used throughout, it also allows the entire process to be parallelized.

NONE

1998-05-31

112

The Number of Planets, a Number-Referring Term?  

Microsoft Academic Search

singular terms referring to numbers as abstract objects: (1) The number of planets is eight. Frege took it as obvious that (1) is an identity statement. In this paper I will argue that Frege’s view about reference to numbers in natural language is fundamentally mistaken. The number of planets, I like to show, while it in general is a referential

Friederike Moltmann

113

Pauli Pascal Pyramids, Pauli Fibonacci Numbers, and Pauli Jacobsthal Numbers  

E-print Network

The three anti-commutative two-dimensional Pauli Pascal triangles can be generalized into multi-dimensional Pauli Pascal hyperpyramids. Fibonacci and Jacobsthal numbers are then generalized into Pauli Fibonacci numbers, Pauli Jacobsthal numbers, and Pauli Fibonacci numbers of higher order. And the question is: are Pauli rabbits killer rabbits?

Martin Erik Horn

2007-11-26

114

Generalized Lucas Numbers and Relations with Generalized Fibonacci Numbers  

E-print Network

In this paper, we present a new generalization of the Lucas numbers by matrix representation using Genaralized Lucas Polynomials. We give some properties of this new generalization and some relations between the generalized order-k Lucas numbers and generalized order-k Fibonacci numbers. In addition, we obtain Binet formula and combinatorial representation for generalized order-k Lucas numbers by using properties of generalized Fibonacci numbers.

Kaygisiz, Kenan

2011-01-01

115

Number Theoretic Background  

NASA Astrophysics Data System (ADS)

Contents: 1. Introduction 2. Divisibility 2.1. Basics on Divisibility 2.2. The Greatest Common Divisor 2.3. The Euclidean Algorithm 2.4. The Diophantine Equation ax+by=c 3. Prime Numbers 3.1. The Fundamental Theorem of Arithmetic 3.2. There Are Infinitely Many Primes 3.3. The Density of Primes 3.4. Primes in Arithmetic Progressions 4. Continued Fractions 5. Modular Arithmetic 5.1. Congruences 5.2. Modular Inverses 5.3. The Chinese Remainder Theorem 5.4. The Structure of the Multiplicative Group (Z/NZ)^* 5.5. Primitive Roots 6. Quadratic Congruences 6.1. Euler's Criterion 6.2. The Legendre Symbol and Quadratic Reciprocity 7. Pell's Equation 7.1. The Group Law 7.2. Integer Solutions 7.3. Finding the Fundamental Solution 8. The Riemann Zeta Function 8.1 Analytic Continuation and Functinal Equation of ?(s) 8.2 Connecting the Primes and the Zeros of ?(s) 8.3 The Riemann Hypothesis References

Rudnick, Z.

116

Generalized Compositions of Natural Numbers  

E-print Network

We consider compositions of natural numbers when there are different types of each natural number. Several recursions as well as some closed formulas for the number of compositions is derived. We also find its relationships with some known classes of integers such as Fibonacci, Catalan, Pell, Pell-Lucas, and Jacobsthal numbers.

Janjic, Milan

2010-01-01

117

Algebraic properties of number theories  

Microsoft Academic Search

Among other things we prove the following. (A) A number theory is convex if and only if it is inductive. (B) No r.e. number\\u000a theory has JEP. (C) No number theory has AP. We also give some information about the hard cores of number theories.

A. Macintyre; H. Simmons

1975-01-01

118

HOPF ALGEBRAS AND TRANSCENDENTAL NUMBERS  

E-print Network

HOPF ALGEBRAS AND TRANSCENDENTAL NUMBERS Michel Waldschmidt Universit´e P. et M. Curie (Paris VI clear, but we point out that it already plays a role in transcendental number theory: St´ephane Fischler-Lindemann). If is a non-zero algebraic number, then e is a transcendental number. Equivalently, if is a non

119

On normal numbers Veronica Becher  

E-print Network

On normal numbers Ver´onica Becher Universidad de Buenos Aires & CONICET, Argentina 16 Latin American Symposium on Mathematical Logic July 2014 Ver´onica Becher On normal numbers 0 / 22 #12;Normal numbers Normality is a basic form of randomness for real numbers. It asks that the expansions of real

Becher, Verónica

120

On normal numbers Veronica Becher  

E-print Network

On normal numbers Ver´onica Becher Universidad de Buenos Aires & CONICET Coloquio del Departamento de Matem´atica, FCEN, UBA, 2 octubre 2014 #12;Normal numbers Normality is a basic form of randomness´onica Becher On normal numbers 1 / 33 #12;Normal numbers Normality is a basic form of randomness for real

Becher, Verónica

121

Topological completions of the field of rational numbers which consist of Liouville numbers and rational numbers  

Microsoft Academic Search

Some subfields of the field of real numbers which consist exclusively of rational numbers and Liouville numbers are given. Each of these fields is a completion of the rational number field endowed with a field topology finer than the usual topology.

J. E. Marcos

1999-01-01

122

Truly Hypercomplex Numbers: Unification of Numbers and Vectors  

E-print Network

Since the beginning of the quest of hypercomplex numbers in the late eighteenth century, many hypercomplex number systems have been proposed but none of them succeeded in extending the concept of complex numbers to higher dimensions. This paper provides a definitive solution to this problem by defining the truly hypercomplex numbers of dimension N greater than or equal to 3. The secret lies in the definition of the multiplicative law and its properties. This law is based on spherical and hyperspherical coordinates. These numbers which I call spherical and hyperspherical hypercomplex numbers define Abelian groups over addition and multiplication. Nevertheless, the multiplicative law generally does not distribute over addition, thus the set of these numbers equipped with addition and multiplication does not form a mathematical field. However, such numbers are expected to have a tremendous utility in mathematics and in science in general.

Redouane Bouhennache

2014-09-15

123

Concatenated Fibonacci and Lucas numbers do not form normal numbers  

E-print Network

We show that the infinite decimal numbers $\\mathcal{F} = 0.F_{1}F_{2}F_{3}...$ and $\\mathcal{L} = 0.L_{1}L_{2}L_{3}...$ obtained by concatenating respectively the Fibonacci and the Lucas numbers for their fractional parts are not normal numbers to base 10.

Mendonça, J Ricardo G

2011-01-01

124

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 to…

Li, Xia

2009-01-01

125

Butterflies and topological quantum numbers  

E-print Network

The Hofstadter model illustrates the notion of topological quantum numbers and how they account for the quantization of the Hall conductance. It gives rise to colorful fractal diagrams of butterflies where the colors represent the topological quantum numbers.

J. E. Avron; D. Osadchy

2001-10-20

126

Butterflies and topological quantum numbers  

Microsoft Academic Search

The Hofstadter model illustrates the notion of topological quantum numbers and how they account for the quantization of the Hall conductance. It gives rise to colorful fractal diagrams of butterflies where the colors represent the topological quantum numbers.

J. E. Avron; D. Osadchy

2001-01-01

127

Graphs, partitions and Fibonacci numbers  

Microsoft Academic Search

Abstract The Fibonacci number of a graph is the number of independent vertex subsets. In this paper, we investigate trees with large Fibonacci number. In particular, we show that all trees with n edges and Fibonacci number,> 2,\\/4 for constants A,B as n ! 1. This is proved by using a natural correspondence between partitions of integers and star-like trees.

Arnold Knopfmacher; Robert F. Tichy; Stephan Wagner; Volker Ziegler

2007-01-01

128

A Lesson in Number Pattern  

ERIC Educational Resources Information Center

This article presents a guided investigation into the spacial relationships between the centres of the squares in a Fibonacci tiling. It is essentially a lesson in number pattern, but includes work with surds, coordinate geometry, and some elementary use of complex numbers. The investigation could be presented to students in a number of ways…

Fletcher, Rodney

2008-01-01

129

Numbers and Math. Beginnings Workshop.  

ERIC Educational Resources Information Center

Presents five articles addressing numbers and math instruction for young children: "Math Talk with Young Children: One Parent's Experience" (Fred E. Gross); "How Children Build Their Understanding of Numbers" (David Elkind); "Early Math: It's More than Numbers" (Ann S. Epstein); "Assessing Mathematical Learning: Observing and Listening to…

Gross, Fred E.; Elkind, CavidEpstein, Ann S.; Copley, Juanita V.; Haugen, Ginny; Haugen, Kirsten

2003-01-01

130

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

131

Random Numbers and Quantum Computers  

ERIC Educational Resources Information Center

The topic of random numbers is investigated in such a way as to illustrate links between mathematics, physics and computer science. First, the generation of random numbers by a classical computer using the linear congruential generator and logistic map is considered. It is noted that these procedures yield only pseudo-random numbers since…

McCartney, Mark; Glass, David

2002-01-01

132

Transcendental L2 -Betti numbers  

E-print Network

Transcendental L2 -Betti numbers Atiyah's question Thomas Schick G¨ottingen OA Chennai 2010 Thomas Schick (G¨ottingen) Transcendental L2 -Betti numbers Atiyah's question OA Chennai 2010 1 / 24 #12). Thomas Schick (G¨ottingen) Transcendental L2 -Betti numbers Atiyah's question OA Chennai 2010 2 / 24 #12

Sunder, V S

133

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

134

Data Compression with Prime Numbers  

E-print Network

A compression algorithm is presented that uses the set of prime numbers. Sequences of numbers are correlated with the prime numbers, and labeled with the integers. The algorithm can be iterated on data sets, generating factors of doubles on the compression.

Gordon Chalmers

2005-11-16

135

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.

136

Perceiving numbers influences actions in number-space synesthesia.  

PubMed

Number and space are spontaneously linked in human cognition and have been metaphorically described as a 'mental number line'. In number-space synesthetes (NSS), numbers are visualized in specific spatial arrays, in an idiosyncratic and explicit manner. Here we tested whether the numerical-spatial association that characterizes NSS has the potential to affect individual's actions when the number is not a task-relevant feature. We used a Simon task that implies stimulus-response matching. Task-irrelevant Arabic numerals (1, 4, 6, 9) appeared simultaneously at the same location as a colored target. A group of 15 age-matched controls and 4 NSS completed a 2×2 within-subjects design consisting of Simon (compatible and incompatible) and number-space (congruent and incongruent) trials. Mean reaction time (RT) and RT cumulative distribution functions across Simon and number-space conditions for both NSS and controls were analyzed. Relative to controls, synesthetes' RTs were overall affected by the number-space mapping. Moreover, synesthetes' Simon effects occurred at later response times. These results provide strong evidence that numbers are cognitively represented as action codes and that the strength of the association shapes the impact of the numerical representation on individuals' actions. PMID:22800399

Arend, Isabel; Gertner, Limor; Henik, Avishai

2013-01-01

137

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

138

Nonliteral understanding of number words  

PubMed Central

One of the most puzzling and important facts about communication is that people do not always mean what they say; speakers often use imprecise, exaggerated, or otherwise literally false descriptions to communicate experiences and attitudes. Here, we focus on the nonliteral interpretation of number words, in particular hyperbole (interpreting unlikely numbers as exaggerated and conveying affect) and pragmatic halo (interpreting round numbers imprecisely). We provide a computational model of number interpretation as social inference regarding the communicative goal, meaning, and affective subtext of an utterance. We show that our model predicts humans’ interpretation of number words with high accuracy. Our model is the first to our knowledge to incorporate principles of communication and empirically measured background knowledge to quantitatively predict hyperbolic and pragmatic halo effects in number interpretation. This modeling framework provides a unified approach to nonliteral language understanding more generally. PMID:25092304

Kao, Justine T.; Wu, Jean Y.; Bergen, Leon; Goodman, Noah D.

2014-01-01

139

Dynamic Virtual Credit Card Numbers  

E-print Network

Abstract. Theft of stored credit card information is an increasing threat to e-commerce. We propose a dynamic virtual credit card number scheme that reduces the damage caused by stolen credit card numbers. A user can use an existing credit card account to generate multiple virtual credit card numbers that are either usable for a single transaction or are tied with a particular merchant. We call the scheme dynamic because the virtual credit card numbers can be generated without online contact with the credit card issuers. These numbers can be processed without changing any of the infrastructure currently in place; the only changes will be at the end points, namely, the card users and the card issuers. We analyze the security requirements for dynamic virtual credit card numbers, discuss the design space, propose a scheme using HMAC, and prove its security under the assumption that HMAC is a PRF. Key words: e-commerce, credit card theft 1

Ian Molloy; Jiangtao Li; Ninghui Li

140

Dynamic Virtual Credit Card Numbers  

NASA Astrophysics Data System (ADS)

Theft of stored credit card information is an increasing threat to e-commerce. We propose a dynamic virtual credit card number scheme that reduces the damage caused by stolen credit card numbers. A user can use an existing credit card account to generate multiple virtual credit card numbers that are either usable for a single transaction or are tied with a particular merchant. We call the scheme dynamic because the virtual credit card numbers can be generated without online contact with the credit card issuers. These numbers can be processed without changing any of the infrastructure currently in place; the only changes will be at the end points, namely, the card users and the card issuers. We analyze the security requirements for dynamic virtual credit card numbers, discuss the design space, propose a scheme using HMAC, and prove its security under the assumption the underlying function is a PRF.

Molloy, Ian; Li, Jiangtao; Li, Ninghui

141

FIBONACCI NUMBERS, LUCAS NUMBERS AND INTEGRALS OF CERTAIN GAUSSIAN PROCESSES  

Microsoft Academic Search

We study the distributions of integrals of Gaussian processes aris- ing as limiting distributions of test statistics proposed for treating a goodness of t or symmetry problem. We show that the cumulants of the distributions can be expressed in terms of Fibonacci numbers and Lucas numbers. 1 n P n k=1 exp(it 0 Xk), t2 Rd, be the empirical Fourier

LUDWIG BARINGHAUS; Wei-Yin Loh

142

Ergodic theory and number theory Ergodic theory and number theory  

E-print Network

fruit in old age, they will stay fresh and green. Psalm 92:14 1 / 18 #12;Ergodic theory and number theory They will still bear fruit in old age, they will stay fresh and green. Psalm 92:14 It is not only and number theory They will still bear fruit in old age, they will stay fresh and green. Psalm 92

Wirosoetisno, Djoko

143

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

2013-01-01

144

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. PMID:23544052

Sauerland, Uli; Gotzner, Nicole

2013-01-01

145

DIAGNOSIS NUMBER OF CASES CARDIOVASCULAR  

E-print Network

DIAGNOSIS NUMBER OF CASES CARDIOVASCULAR Cardiovascular disease .........................................................36 Crop Disorder.....................................................12 Digestive Disease/Plant/worms...........................14 Liver disease ......................................................14 Liver tumor

Schladow, S. Geoffrey

146

Compendium of Experimental Cetane Numbers  

SciTech Connect

This report is an updated version of the 2004 Compendium of Experimental Cetane Number Data and presents a compilation of measured cetane numbers for pure chemical compounds. It includes all available single compound cetane number data found in the scientific literature up until March 2014 as well as a number of unpublished values, most measured over the past decade at the National Renewable Energy Laboratory. This Compendium contains cetane values for 389 pure compounds, including 189 hydrocarbons and 201 oxygenates. More than 250 individual measurements are new to this version of the Compendium. For many compounds, numerous measurements are included, often collected by different researchers using different methods. Cetane number is a relative ranking of a fuel's autoignition characteristics for use in compression ignition engines; it is based on the amount of time between fuel injection and ignition, also known as ignition delay. The cetane number is typically measured either in a single-cylinder engine or a constant volume combustion chamber. Values in the previous Compendium derived from octane numbers have been removed, and replaced with a brief analysis of the correlation between cetane numbers and octane numbers. The discussion on the accuracy and precision of the most commonly used methods for measuring cetane has been expanded and the data has been annotated extensively to provide additional information that will help the reader judge the relative reliability of individual results.

Yanowitz, J.; Ratcliff, M. A.; McCormick, R. L.; Taylor, J. D.; Murphy, M. J.

2014-08-01

147

numbers and SAT Oliver Kullmann  

E-print Network

(diagonal form), created by the OKlibrary: c 2 parts, arithmetic progressions of size 3, and 9 prime numbers extensions The generic boolean translation On the history of the Green-Tao theorem Arithmetic progressions n prime numbers contain an arithmetic progression of length k. Trivially grt1(1) = 1 and grt1(2) = 2

Martin, Ralph R.

148

numbers and SAT Oliver Kullmann  

E-print Network

, 7, 11, 13, 17, 19, 23} into two parts such that no part contains an arithmetic progression of size 3 by the OKlibrary: c 2 parts, arithmetic progressions of size 3, and 9 prime numbers. c Variables and associated numbers, there exists some i {1, . . . , m} such that f-1(i) contains an arithmetic progression of size

Martin, Ralph R.

149

Organizing, Concerns and Control Numbers.  

ERIC Educational Resources Information Center

A heuristic procedure can be used to teach organizational skills to students of technical writing. Designed to allow students on their own to explore ways that numbers can be used to give a definite shape to technical information, its central feature is a matrix composed of a series of control numbers (horizontal axis) and organizing concerns…

Washington, Gene

150

Computational Number Theory C. Pomerance  

E-print Network

Computational Number Theory C. Pomerance 1 Introduction Historically, computation has been invented geometry. To help predict the positions of the planets, the Greeks invented trigonometry. Algebra this trend. One mathematical area where the new emphasis on computation can be clearly felt is number theory

Pomerance, Carl

151

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

152

Wild Partitions and Number Theory  

Microsoft Academic Search

We introduce the notion of wild partition to describe in combinatorial language an important situation in the theory of p-adic fields. For Q a power of p, we get a sequence of numbers ! Q,n counting the number of certain wild partitions of n. We give an explicit formula for the corresponding generating function ! Q(x) = ! ! Q,nxn

David P. Roberts

153

Whole Numbers - When in Rome  

NSDL National Science Digital Library

The students perform the Sieve of Eratosthenes in class to find the prime number between 1 and 100. They also look for patterns such as where the multiples of 2 or 5 appear in the sieve. At home or in a computer lab they then research the Fibonacci Sequence and other number systems.

2010-01-01

154

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.

NCTM Illuminations

2000-01-01

155

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.

Carol R. Findell

2007-12-12

156

"JUST THE MATHS" UNIT NUMBER  

E-print Network

) Rounding to a specified number of significant figures The first significant figure of a decimal quantity to a specified number of significant figures, we use the same principle as in (a), but starting from the first significant figure, then working to the right. EXAMPLES 1. 362.5863 = 362.59 to 5 significant figures; 362

Davies, Christopher

157

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

158

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

159

OFFICE USE ONLY Reference number  

E-print Network

of $ Credit or Check Card Please debit my card to the sum of $ Card number Expiration date M M / Y Y Y Y I) Card number Expiration date M M / Y Y Y Y Your credit or check card will be automatically charged of stocks or shares B. Regular Giving By Credit or Check Card Please debit my card to the sum of $ Monthly

Dixon, Peter

160

Number of Part D Enrollees  

Cancer.gov

The following tables list the number of persons appearing in the SEER-Medicare data who are enrolled in Medicare Part D as well as the total number of patients who were eligible to enroll according to the PEDSF file. The tables were generated separately for patients not enrolled in Managed Care and for those enrolled in Managed Care only.

161

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

162

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

163

INDEXING THE APPROXIMATE NUMBER SYSTEM Indexing the Approximate Number System  

E-print Network

; Pica, Lemer, Izard, & Dehaene, 2004). Some researchers have hypothesised that the ANS is the cognitive, suggesting that an ANS deficit may #12;INDEXING THE APPROXIMATE NUMBER SYSTEM 4 be the cause of mathematical

Inglis, Matthew

164

Number without a language model  

PubMed Central

Cross-cultural studies suggest that access to a conventional language containing words that can be used for counting is essential to develop representations of large exact numbers. However, cultures that lack a conventional counting system typically differ from cultures that have such systems, not only in language but also in many other ways. As a result, it is difficult to isolate the effects of language on the development of number representations. Here we examine the numerical abilities of individuals who lack conventional language for number (deaf individuals who do not have access to a usable model for language, spoken or signed) but who live in a numerate culture (Nicaragua) and thus have access to other aspects of culture that might foster the development of number. These deaf individuals develop their own gestures, called homesigns, to communicate. We show that homesigners use gestures to communicate about number. However, they do not consistently extend the correct number of fingers when communicating about sets greater than three, nor do they always correctly match the number of items in one set to a target set when that target set is greater than three. Thus, even when integrated into a numerate society, individuals who lack input from a conventional language do not spontaneously develop representations of large exact numerosities. PMID:21300893

Spaepen, Elizabet; Coppola, Marie; Spelke, Elizabeth S.; Carey, Susan E.; Goldin-Meadow, Susan

2011-01-01

165

Number without a language model.  

PubMed

Cross-cultural studies suggest that access to a conventional language containing words that can be used for counting is essential to develop representations of large exact numbers. However, cultures that lack a conventional counting system typically differ from cultures that have such systems, not only in language but also in many other ways. As a result, it is difficult to isolate the effects of language on the development of number representations. Here we examine the numerical abilities of individuals who lack conventional language for number (deaf individuals who do not have access to a usable model for language, spoken or signed) but who live in a numerate culture (Nicaragua) and thus have access to other aspects of culture that might foster the development of number. These deaf individuals develop their own gestures, called homesigns, to communicate. We show that homesigners use gestures to communicate about number. However, they do not consistently extend the correct number of fingers when communicating about sets greater than three, nor do they always correctly match the number of items in one set to a target set when that target set is greater than three. Thus, even when integrated into a numerate society, individuals who lack input from a conventional language do not spontaneously develop representations of large exact numerosities. PMID:21300893

Spaepen, Elizabet; Coppola, Marie; Spelke, Elizabeth S; Carey, Susan E; Goldin-Meadow, Susan

2011-02-22

166

Reynolds number influences in aeronautics  

NASA Technical Reports Server (NTRS)

Reynolds number, a measure of the ratio of inertia to viscous forces, is a fundamental similarity parameter for fluid flows and therefore, would be expected to have a major influence in aerodynamics and aeronautics. Reynolds number influences are generally large, but monatomic, for attached laminar (continuum) flow; however, laminar flows are easily separated, inducing even stronger, non-monatomic, Reynolds number sensitivities. Probably the strongest Reynolds number influences occur in connection with transitional flow behavior. Transition can take place over a tremendous Reynolds number range, from the order of 20 x 10(exp 3) for 2-D free shear layers up to the order of 100 x 10(exp 6) for hypersonic boundary layers. This variability in transition behavior is especially important for complex configurations where various vehicle and flow field elements can undergo transition at various Reynolds numbers, causing often surprising changes in aerodynamics characteristics over wide ranges in Reynolds number. This is further compounded by the vast parameterization associated with transition, in that any parameter which influences mean viscous flow development (e.g., pressure gradient, flow curvature, wall temperature, Mach number, sweep, roughness, flow chemistry, shock interactions, etc.), and incident disturbance fields (acoustics, vorticity, particulates, temperature spottiness, even electro static discharges) can alter transition locations to first order. The usual method of dealing with the transition problem is to trip the flow in the generally lower Reynolds number wind tunnel to simulate the flight turbulent behavior. However, this is not wholly satisfactory as it results in incorrectly scaled viscous region thicknesses and cannot be utilized at all for applications such as turbine blades and helicopter rotors, nacelles, leading edge and nose regions, and High Altitude Long Endurance and hypersonic airbreathers where the transitional flow is an innately critical portion of the problem.

Bushnell, Dennis M.; Yip, Long P.; Yao, Chung-Sheng; Lin, John C.; Lawing, Pierce L.; Batina, John T.; Hardin, Jay C.; Horvath, Thomas J.; Fenbert, James W.; Domack, Christopher S.

1993-01-01

167

Numbered nasal discs for waterfowl  

USGS Publications Warehouse

Numbered nasal discs were successfully used in studies requiring large numbers of individually marked waterfowl. The procedure for constructing these discs is outlined. Blue-winged teal (Anas discors) with 5/8-inch discs, and canvasback (Aythya valisineria) and redhead (A. americana) with 3/4-inch discs can be individually identified up to 50 and 80 yards, respectively, with a gunstock-mounted, 20-power spotting scope. The particular value of these markers is their durability, the number of combinations possible, and the apparent absence of behavioral or mortality influence among such species as the blue-winged teal.

Bartonek, J.C.; Dane, C.W.

1964-01-01

168

BKP and projective Hurwitz numbers  

E-print Network

We consider $d$-fold branched coverings of the projective plane $\\mathbb{RP}^2$ and show that the hypergeometric tau function of the BKP hierarchy of Kac and van de Leur is the generating function for the weighted sums of the related Hurwitz numbers. In particular we get the $\\mathbb{RP}^2$ analogue of the $\\mathbb{CP}^1$ generating functions proposed by Okounkov. Hurwitz numbers weighted by the Hall-Littlewood and by the Macdonald polynomials are the other examples. We also consider integrals of tau functions which generate projective Hurwitz numbers.

Sergei Natanzon; Alexander Orlov

2015-01-19

169

Incomplete Fibonacci and Lucas numbers  

Microsoft Academic Search

A particular use of well-known combinatorial expressions for Fibonacci and Lucas numbers gives rise to two interesting classes\\u000a of integers (namely, the numbersF\\u000a n(k) andL\\u000a n(k)) governed by the integral parametersn andk. After establishing the main properties of these numbers and their interrelationship, we study some congruence properties\\u000a ofL\\u000a n(k), one of which leads to a supposedly new characterisation of

Piero Filipponi

1996-01-01

170

Large Number Hypothesis: A Review  

E-print Network

Large dimensionless numbers, arising out of ratios of various physical constants, intrigued many scientists, especially Dirac. Relying on the coincidence of large numbers, Dirac arrived at the revolutionary hypothesis that the gravitational constant $G$ should vary inversely as the cosmic time $t$. This hypothesis of Dirac, known as Large Number Hypothesis (LNH), sparked off many speculations, arguments and new ideas in terms of applications. Works done by several authors with LNH as their basic platform are reviewed in this work. Relationship between some of those works are pointed out here. Possibility of time-variations of physical constants other than $G$ are also discussed.

Saibal Ray; Utpal Mukhopadhyay; Partha Pratim Ghosh

2007-05-13

171

4th Grade Number Activities  

NSDL National Science Digital Library

This page provides examples of 4th Grade Number (Operations and Algebraic Thinking, Number and Operations in Base Ten, and Number Operations-Fractions) activities aligned with the Common Core State Standards. A CCSS standard is stated and the possible activities are listed below and linked. All activities are suitable for use in Math Centers, small group or whole class settings and are designed to elicit a range of responses and provide opportunities for students to communicate their reasoning and mathematical thinking. Instructions for each task are typed in large print and written in child-friendly language to enable students to work on activities independently after a brief introduction to the task. All files for the 4th Grade Number Activities listed are in PDF format.

Godwin, Nicola

2012-01-01

172

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

173

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

174

The Jacobi-Stirling Numbers  

E-print Network

The Jacobi-Stirling numbers were discovered as a result of a problem involving the spectral theory of powers of the classical second-order Jacobi differential expression. Specifically, these numbers are the coefficients of integral composite powers of the Jacobi expression in Lagrangian symmetric form. Quite remarkably, they share many properties with the classical Stirling numbers of the second kind which, as shown in LW, are the coefficients of integral powers of the Laguerre differential expression. In this paper, we establish several properties of the Jacobi-Stirling numbers and its companions including combinatorial interpretations thereby extending and supplementing known contributions to the literature of Andrews-Littlejohn, Andrews-Gawronski-Littlejohn, Egge, Gelineau-Zeng, and Mongelli.

Andrews, George E; Gawronski, Wolfgang; Littlejohn, Lance L

2011-01-01

175

Avogadro's Number and Avogadro's Constant  

ERIC Educational Resources Information Center

Discusses three possible methods of thinking about the implications of the definitions of the Avogadro constant and number. Indicates that there is only one way to arrive at a simple and standard conclusion. (CC)

Davies, R. O.

1973-01-01

176

Comparing Two 3-Digit Numbers  

NSDL National Science Digital Library

This whole-class lesson will reinforce the concept of comparing two 3-digit numbers as well as provide practice for students to become comparing experts. Students will use playing cards to practice their skills.

2013-01-31

177

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

178

Young Students Investigate Number Cubes.  

ERIC Educational Resources Information Center

Describes a series of learning activities built around number cubes. Sample activities introduce elementary properties of the cube, the magic rule of seven, and basic concepts related to graphs in the plane coordinate system. (PVD)

Friedlander, Alex

1997-01-01

179

5th Grade Number Activities  

NSDL National Science Digital Library

This page provides examples of 5th Grade Number (Operations and Algebraic Thinking, Number and Operations in Base Ten, and Number Operations-Fractions) activities aligned with the Common Core State Standards. A CCSS standard is stated and the possible activities are listed below and linked. All activities are suitable for use in Math Centers, small group or whole class settings and are designed to elicit a range of responses and provide opportunities for students to communicate their reasoning and mathematical thinking. Instructions for each task are typed in large print and written in child-friendly language to enable students to work on activities independently after a brief introduction to the task. All files for the 5th Grade Number Activities listed are in PDF format.

Nicola Godwin

2012-01-01

180

Number Sense Games and Activities  

NSDL National Science Digital Library

Students will select online games related to number sense and play them individually or with a partner Odd or Even Can you tell the difference between odd or even? Choose one of these games for some practice! Don\\'t be afraid. The ghosts in this game only haunt those who don\\'t know odd or even numbers. Surely that\\'s not YOU! Even Ghostblasters Odd Ghostblasters Odd/Even Building Game Counting Patterns I know you can count ...

Mrs. Barker

2005-10-18

181

Why are airport runways numbered?  

NSDL National Science Digital Library

This Figure This! activity provides students an opportunity to apply their knowledge of angles and compass directions to solve a problem in the context of airport runways. The introduction calls students' attention to the numbers assigned to both ends of runways. Students are asked to find a missing runway number. The activity includes links to a solution hint, the solution, related math questions, and additional resources.

2012-01-01

182

Euclid's Number-Theoretical Work  

E-print Network

When people mention the mathematical achievements of Euclid, his geometrical achievements always spring to mind. But, his Number-Theoretical achievements (See Books 7, 8 and 9 in his magnum opus \\emph{Elements} [1]) are rarely spoken. The object of this paper is to affirm the number-theoretical role of Euclid and the historical significance of Euclid's algorithm. It is known that almost all elementary number-theoretical texts begin with Division algorithm. However, Euclid did not do like this. He began his number-theoretical work by introducing his algorithm. We were quite surprised when we began to read the \\emph{Elements} for the first time. Nevertheless, one can prove that Euclid's algorithm is essentially equivalent with the Bezout's equation and Division algorithm. Therefore, Euclid has preliminarily established Theory of Divisibility and the greatest common divisor. This is the foundation of Number Theory. After more than 2000 years, by creatively introducing the notion of congruence, Gauss published his \\emph{Disquisitiones Arithmeticae} in 1801 and developed Number Theory as a systematic science. Note also that Euclid's algorithm implies Euclid's first theorem (which is the heart of `the uniqueness part' of the fundamental theorem of arithmetic) and Euclid's second theorem (which states that there are infinitely many primes). Thus, in the nature of things, Euclid's algorithm is the most important number-theoretical work of Euclid. For this reason, we further summarize briefly the influence of Euclid's algorithm. Knuth said `we might call Euclid's method the granddaddy of all algorithms'. Based on our discussion and analysis, it leads to the conclusion Euclid's algorithm is the greatest number-theoretical achievement of the Euclidean age.

Shaohua Zhang

2009-02-14

183

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

184

Overpseudoprimes, and Mersenne and Fermat numbers as primover numbers  

E-print Network

We introduce a new class of pseudoprimes-so called "overpseudoprimes to base $b$", which is a subclass of strong pseudoprimes to base $b$. Denoting via $|b|_n$ the multiplicative order of $b$ modulo $n$, we show that a composite $n$ is overpseudoprime if and only if $|b|_d$ is invariant for all divisors $d>1$ of $n$. In particular, we prove that all composite Mersenne numbers $2^{p}-1$, where $p$ is prime, are overpseudoprime to base 2 and squares of Wieferich primes are overpseudoprimes to base 2. Finally, we show that some kinds of well known numbers are overpseudoprime to a base $b$.

Shevelev, Vladimir; Velásquez-Soto, Juan Miguel; Castillo, John H

2012-01-01

185

Searching for the highest number.  

PubMed

When viewing a collection of products how does a consumer decide which one to buy? To do this task, the consumer not only needs to evaluate the desirability of the products, taking into account factors such as quality and price, but also needs to search through the products to find the most desirable one. We studied the search process using an abstraction of a common consumer choice task. In our task, observers searched an array of numbers for the highest. Crucially, the observers did not know in advance what this number would be, which made it difficult to know when the search should be terminated. In this way, our search task mimicked a problem often faced by consumers in a supermarket setting where they also may not know in advance what the most desirable product will be. We compared several computational models. We found that our data was best described by a process that assumes that observers terminate their search when they find a number that exceeds an internal threshold. Depending on the observer and the circumstances, this threshold appeared either to be fixed or to decrease over the course of the trial. This threshold can explain why in some situations the observers terminate the search without inspecting all the numbers in the display, whereas in other situations observers act in a seemingly irrational manner, continuing the search even after inspecting all the numbers. PMID:25427843

Howe, Piers D L; Little, Daniel R

2014-11-27

186

On converting numbers to the double-base number system  

Microsoft Academic Search

This paper is an attempt to bring some theory on the top of some previously unproved experimental statements about the double-base number system (DBNS). We use results from diophantine approximation to address the problem of converting integers into DBNS. Although the material presented in this article is mainly theoretical, the proposed algorithm could lead to very efficient implementations.

Valerie Berthe; Laurent Imbert

2004-01-01

187

8 Generalized Carmichael Numbers ON GENERALIZED CARMICHAEL NUMBERS  

E-print Network

exist which are squares. 1 Introduction: Historical Background On October 18th, 1640, Pierre de Fermat wrote in a letter to Bernard Frenicle de Bessy that if p is a prime number, then p divides ap,1 , 1 for all integers a not divisible by p, a result now known as Fermat's Little Theorem". An equivalent

Halbeisen, Lorenz

188

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

189

Concurrent Prime Number Test Model  

NSDL National Science Digital Library

The Concurrent Prime Number Test Model uses the trial 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 threads that 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 Concurrent Prime Number Test 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

190

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...

2012-05-01

191

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.

2013-06-21

192

Biotechnology at low Reynolds numbers.  

PubMed Central

The shrinking of liquid handling systems to the micron and submicron size range entails moving into the area of small Reynolds numbers. The fluid dynamics in this regime are very different from the macroscale. We present an intuitive explanation of how the different physics of small Reynolds numbers flow, along with microscopic sizes, can influence device design, and give examples from our own work using fluid flow in microfabricated devices designed for biological processing. Images FIGURE 1 FIGURE 9 FIGURE 10 FIGURE 11 FIGURE 12 FIGURE 13 PMID:8968612

Brody, J P; Yager, P; Goldstein, R E; Austin, R H

1996-01-01

193

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."...

194

Sharp bounds for harmonic numbers  

E-print Network

In the paper, we first survey some results on inequalities for bounding harmonic numbers or Euler-Mascheroni constant, and then we establish a new sharp double inequality for bounding harmonic numbers as follows: For $n\\in\\mathbb{N}$, the double inequality -\\frac{1}{12n^2+{2(7-12\\gamma)}/{(2\\gamma-1)}}\\le H(n)-\\ln n-\\frac1{2n}-\\gamma<-\\frac{1}{12n^2+6/5} is valid, with equality in the left-hand side only when $n=1$, where the scalars $\\frac{2(7-12\\gamma)}{2\\gamma-1}$ and $\\frac65$ are the best possible.

Qi, Feng

2010-01-01

195

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

196

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. âAdd three to your number and multiply the sum by five,â she tells him. Next she says, âNow ta...

197

900 Numbers: A Controversial Industry.  

ERIC Educational Resources Information Center

Pay-per-call telephone services through 900 numbers have given rise to criticism of their content and complaints of consumer fraud. The Federal Communications Commission, legislative initiatives, industry self-regulation, and consumer educators are attempting to protect consumers. (SK)

Galvez, Nancy D.

1992-01-01

198

Symmetry in Numbers David Marshall  

E-print Network

Symmetry in Numbers David Marshall Monmouth University April 13, 2005 808 -2 3 + 3 -169 54 + 1007 18 + 3 -169 54 - 1007 18 ­ Typeset by FoilTEX ­ #12;Symmetry One of the guiding principles group of symmetries. -Paul Yale, in Geometry and Symmetry 2. Due or just proportion; harmony of parts

Marshall, David

199

Winding Number Constrained Contour Detection.  

PubMed

Salient contour detection can benefit from the integration of both contour cues and region cues. However, this task is difficult due to different nature of region representations and contour representations. To solve this problem, this paper proposes an energy minimization framework based on winding number constraints. In this framework, both region cues, such as color/texture homogeneity, and contour cues, such as local contrast and continuity, are represented in a joint objective function, which has both region and contour labels. The key problem is how to design constraints that ensure the topological consistency of the two kinds of labels. Our technique is based on the topological concept of winding number. Using a fast method for winding number computation, a small number of linear constraints are derived to ensure label consistency. Our method is instantiated by ratio-based energy functions. By successfully integrating both region and contour cues, our method shows advantages over competitive methods. Our method is extended to incorporate user interaction, which leads to further improvements. PMID:25420265

Ming, Yansheng; Li, Hongdong; He, Xuming

2015-01-01

200

Name Number Email Location Abeysirigunawardena,  

E-print Network

-Espinoza, Harry 516-6757 Hgs1@jhu.edu 117 Mudd Hall Sandlin, Cliff 516-5452 Csandli1@jhu.edu 417 Jenkins HallName Number Email Location Abeysirigunawardena, Sanjaya 516-7348 Sabeysi1@jhu.edu 404 Jenkins Hall Hall Bailey, Jessica 516-7243 jessbailey@jhu.edu 110 Jenkins Hall Barrick, Doug 516-0409 barrick

von der Heydt, Rüdiger

201

"JUST THE MATHS" UNIT NUMBER  

E-print Network

.1.1 Arithmetic progressions 2.1.2 Arithmetic series 2.1.3 Geometric progressions 2.1.4 Geometric series 2 - ELEMENTARY PROGRESSIONS AND SERIES 2.1.1 ARITHMETIC PROGRESSIONS The "sequence" of numbers, a, a + d, a + 2d, a + 3d, ... is said to form an "arithmetic progression". The symbol a represents the "first term

Davies, Christopher

202

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

203

Class addresses, phone numbers, biographical-  

E-print Network

the engine to search for the selected college students only. #12;Class addresses, phone numbers, biographical the "Student Status" option, select "AS- Active." This will tell the engine to search for active students only Student Academic Search Criteria" to expand these options. · Under the "Student Classification" option

Cui, Yan

204

Number Crunching: A Sheep's Tale  

ERIC Educational Resources Information Center

In this article, the author talks about an allegorical tale which he has written as a message for teachers of mathematics. The story is about Gordon, who led a flock of small sheep. Gordon was a mathematics genius; however, his flock criticized his teaching of numbers and his boring lectures. His furry-god-farmer advised him to share his…

Sam, Chris Lam

2005-01-01

205

A generalized sense of number  

PubMed Central

Much evidence has accumulated to suggest that many animals, including young human infants, possess an abstract sense of approximate quantity, a number sense. Most research has concentrated on apparent numerosity of spatial arrays of dots or other objects, but a truly abstract sense of number should be capable of encoding the numerosity of any set of discrete elements, however displayed and in whatever sensory modality. Here, we use the psychophysical technique of adaptation to study the sense of number for serially presented items. We show that numerosity of both auditory and visual sequences is greatly affected by prior adaptation to slow or rapid sequences of events. The adaptation to visual stimuli was spatially selective (in external, not retinal coordinates), pointing to a sensory rather than cognitive process. However, adaptation generalized across modalities, from auditory to visual and vice versa. Adaptation also generalized across formats: adapting to sequential streams of flashes affected the perceived numerosity of spatial arrays. All these results point to a perceptual system that transcends vision and audition to encode an abstract sense of number in space and in time. PMID:25377454

Arrighi, Roberto; Togoli, Irene; Burr, David C.

2014-01-01

206

"JUST THE MATHS" UNIT NUMBER  

E-print Network

"JUST THE MATHS" UNIT NUMBER 2.2 SERIES 2 (Binomial series) by A.J.Hobson 2.2.1 Pascal's Triangle 2.2.1 PASCAL'S TRIANGLE Initially, we consider some simple illustrations obtainable from very elementary expansions follow the diagramatic pattern called PASCAL'S TRIANGLE: 1 1 1 2 1 1 3 3 1 1 4 6 4 1

Davies, Christopher

207

"JUST THE MATHS" UNIT NUMBER  

E-print Network

is z. 6 ? z Surface P Ignoring atmospheric pressure, the pressure, p, at P is measured as the thrust"JUST THE MATHS" UNIT NUMBER 13.16 INTEGRATION APPLICATIONS 16 (Centres of pressure) by A.J.Hobson 13.16.1 The pressure at a point in a liquid 13.16.2 The pressure on an immersed plate 13

Davies, Christopher

208

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

209

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

210

The elephant brain in numbers.  

PubMed

What explains the superior cognitive abilities of the human brain compared to other, larger brains? Here we investigate the possibility that the human brain has a larger number of neurons than even larger brains by determining the cellular composition of the brain of the African elephant. We find that the African elephant brain, which is about three times larger than the human brain, contains 257 billion (10(9)) neurons, three times more than the average human brain; however, 97.5% of the neurons in the elephant brain (251 billion) are found in the cerebellum. This makes the elephant an outlier in regard to the number of cerebellar neurons compared to other mammals, which might be related to sensorimotor specializations. In contrast, the elephant cerebral cortex, which has twice the mass of the human cerebral cortex, holds only 5.6 billion neurons, about one third of the number of neurons found in the human cerebral cortex. This finding supports the hypothesis that the larger absolute number of neurons in the human cerebral cortex (but not in the whole brain) is correlated with the superior cognitive abilities of humans compared to elephants and other large-brained mammals. PMID:24971054

Herculano-Houzel, Suzana; Avelino-de-Souza, Kamilla; Neves, Kleber; Porfírio, Jairo; Messeder, Débora; Mattos Feijó, Larissa; Maldonado, José; Manger, Paul R

2014-01-01

211

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

212

Several problems in number theory  

Microsoft Academic Search

For a long time, number theory has influenced information security and cryptography. This thesis adds examples of its influence.^ The first topic is related with Broadcast Group Key Management (BGKM) in cryptography. After the Access Control Polynomial (ACP) BGKM scheme was proposed [38], people tried to check its basic security properties in BGKM [28]. They found that it has a

Sangil Nahm

2011-01-01

213

Gummy vs. Gum (Number Pattern)  

NSDL National Science Digital Library

"In this lesson, students use gummy bears and sticks of gum to discover a number pattern and write an equation that describes it. This lesson should be conducted after students have worked with patterns and one- and two-step equations." from the Beacon Learning Center.

Center, Beacon L.

2009-10-13

214

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

215

Numbering in Personal Communications Services  

Microsoft Academic Search

—This paper presents a novel location management technique, HOP- PER, that is designed to support in a scalable and efficient manner non- geographical (lifelong) personal numbers in Personal Communications Ser- vices (PCS). Performance comparisons between our scheme and other schemes are derived from large scale simulations using a realistic traffic modeling framework for the ten largest cities of the United

Derek Lam; Yingwei Cui; Donald C. Cox; Jennifer Widom

216

Topology of Numbers Allen Hatcher  

E-print Network

of the connection with the Pythagorean Theorem. Our goal will be a formula that gives them all. The ancient GreeksTopology of Numbers Allen Hatcher Chapter 0. Preview Pythagorean Triples. Rational Points on Other Quadratic Curves. Rational Points on a Sphere. Pythagorean Triples and Quadratic Forms. Pythagorean Triples

Hatcher, Allen

217

The elephant brain in numbers  

PubMed Central

What explains the superior cognitive abilities of the human brain compared to other, larger brains? Here we investigate the possibility that the human brain has a larger number of neurons than even larger brains by determining the cellular composition of the brain of the African elephant. We find that the African elephant brain, which is about three times larger than the human brain, contains 257 billion (109) neurons, three times more than the average human brain; however, 97.5% of the neurons in the elephant brain (251 billion) are found in the cerebellum. This makes the elephant an outlier in regard to the number of cerebellar neurons compared to other mammals, which might be related to sensorimotor specializations. In contrast, the elephant cerebral cortex, which has twice the mass of the human cerebral cortex, holds only 5.6 billion neurons, about one third of the number of neurons found in the human cerebral cortex. This finding supports the hypothesis that the larger absolute number of neurons in the human cerebral cortex (but not in the whole brain) is correlated with the superior cognitive abilities of humans compared to elephants and other large-brained mammals. PMID:24971054

Herculano-Houzel, Suzana; Avelino-de-Souza, Kamilla; Neves, Kleber; Porfírio, Jairo; Messeder, Débora; Mattos Feijó, Larissa; Maldonado, José; Manger, Paul R.

2014-01-01

218

Real numbers. Constants, variables, and mathematical modeling.  

E-print Network

with their multiplicative inverses we get Rational numbers, or numbers of the form m n , where m and n are integer numbers. It can be verified that all addition and multiplication properties make sense for the rational numbers and multiplicative inverses to m n ? The Irrational numbers is the next stage after the Rational numbers

Alekseenko, Alexander

219

Student Learning Centre Review of Number  

E-print Network

directions, { ... , -4 , -3 , -2 , -1 , 0 , 1, 2 , 3 , 4 , 5, ...} is the set of integers. Rational numbers are all the numbers on the real number line that are not rational, e.g. 2, -10, ,5 /2 Every real number) integers (d) negative real numbers (e) rational (f) irrational (g) prime (h) composite 2. Use a number line

220

Using Stokes expansion for natural convection inside a two-dimensional cavity  

NASA Astrophysics Data System (ADS)

We consider the two-dimensional problem of steady natural convection in a circular cavity filled with viscous fluid and subjected to a cosine temperature variation on the boundary. The solution is expanded for low Grashof number and extended to 35 terms by computer. Analysis shows that convergence is limited by a square root singularity on the negative real axis of the Grashof number. An Euler transformation and extraction of the leading, secondary, and tertiary singularities at infinity render the series accurate for all values of the Grashof number. The major conclusion of this investigation is that, while in previous works using the method of series extension (for example, the slowly rotating pipe studied by Mansour, 1985) the limiting values of the quantities of interest for high values of the similarity parameters disagreed with other techniques, partial agreement with other investigations is achieved in the present work.

Mansour, Kamyar

1993-07-01

221

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

222

Number-theory dark matter  

NASA Astrophysics Data System (ADS)

We propose that the stability of dark matter is ensured by a discrete subgroup of the U(1)B-L gauge symmetry, Z(B-L). We introduce a set of chiral fermions charged under the U(1)B-L in addition to the right-handed neutrinos, and require the anomaly-cancellation conditions associated with the U(1)B-L gauge symmetry. We find that the possible number of fermions and their charges are tightly constrained, and that non-trivial solutions appear when at least five additional chiral fermions are introduced. The Fermat theorem in the number theory plays an important role in this argument. Focusing on one of the solutions, we show that there is indeed a good candidate for dark matter, whose stability is guaranteed by Z(B-L).

Nakayama, Kazunori; Takahashi, Fuminobu; Yanagida, Tsutomu T.

2011-05-01

223

Weighted pebbling numbers on graphs  

E-print Network

We expand the theory of pebbling to graphs with weighted edges. In a weighted pebbling game, one player distributes a set amount of weight on the edges of a graph and his opponent chooses a target vertex and places a configuration of pebbles on the vertices. Player one wins if, through a series of pebbling moves, he can move at least one pebble to the target. A pebbling move of p pebbles across an edge with weight w leaves the floor of pw pebbles on the next vertex. We find the weighted pebbling numbers of stars, graphs with at least 2|V|-1 edges, and trees with given targets. We give an explicit formula for the minimum total weight required on the edges of a length-2 path, solvable with p pebbles and exhibit a graph which requires an edge with weight 1/3 in order to achieve its weighted pebbling number.

Jones, Stephanie; McLeman, Cameron; Nyman, Kathryn

2011-01-01

224

Analytic number theory Anirban Mukhopadhyay  

E-print Network

in arithematic progression 29 6. Least quadratic non-residue 30 7. Arithmetic large sieve 31 Introduction(x) = {p x : p - 2 0 mod d} = (x, d, 2) where (x, q, a) denone the number pf primes x in the arithmetic progression a mod q. Thus X = (x) and g(p) = 1/(p). The error d |rd| = d |(x, d, 2) - (x) (d) | can

Paris-Sud XI, Université de

225

Diophantine approximations with Fibonacci numbers  

E-print Network

Let $F_{n}$ be the $n$-th Fibonacci number. Put $\\varphi=\\frac{1+\\sqrt5}{2}$. We prove that the following inequalities hold for any real $\\alpha$: 1) $\\inf_{n \\in \\mathbb N} ||F_n\\alpha||\\le\\frac{\\varphi-1}{\\varphi+2}$, 2) $\\liminf_{n\\to \\infty}||F_n\\alpha||\\le 1/5$, 3) $\\liminf_{n \\to \\infty}||\\varphi^n \\alpha||\\le 1/5$. These results are the best possible.

Zhuravleva, Victoria

2011-01-01

226

Semantic alignment and number comparison.  

PubMed

Are the quantity representations activated by Arabic digits influenced by semantic context? We developed a novel paradigm to examine semantic alignment effects (e.g., Bassok et al. in J Exp Psychol Learn Mem Cogn 34:343-352, 2008) in number comparison. A horizontal word pair (either less more or few many) appeared for 480 ms to prime either relative magnitude (less more) or quantity (few many). Then a horizontal pair of single digits that were either successors (near) or differed by at least four (far) appeared above the word pair. Participants indicated verbally whether or not the word and digit pairs were congruent with respect to left-to-right ascending or descending relative magnitude. The RT advantage for far number pairs compared to near pairs (the distance effect) was greater with magnitude primes (81 ms) than quantity primes (17 ms), demonstrating a semantic alignment effect. This effect disappeared in Experiment 2 in which participants received identical stimuli but named the larger of the two digits and were free to ignore the primes. Nonetheless, mean RT in Experiment 2 was faster with prime and target pairs both ascending or both descending, but only with quantity primes. This prime-dependent order-congruity effect suggests that semantic alignment with respect to numerical order affected number comparison in Experiment 2. The results thereby demonstrate that number comparison exhibits task-dependent semantic alignment effects and recruits distinct numerical representations as a function of semantic context (e.g., Cohen Kadosh and Walsh in Behav Brain Sci 32:313-373, 2009). PMID:21461771

Campbell, Jamie I D; Sacher, Sean G

2012-01-01

227

Properties of proper rational numbers  

E-print Network

This short article is aimed at educators and teachers of mathematics.Its goal is simple and direct:to explore some of the basic/elementary properties of proper rational numbers.A proper rational number is a rational which is not an integer. A proper rational r can be written in standard form: r=c/b,where c and b are relatively prime integers; and with b greater than or equal to 2. There are seven theorems, one proposition, and one lemma; Lemma1, in this paper. Lemma1 is a very well known result, commonly known as Euclid's lemma.It is used repeatedly throughout this paper, and its proof can be found in reference[1]. Theorem4(i) gives precise conditions for the sum of two proper rationals to be an integer.Theorem5(a) gives exact conditions for the product to be an integer. Theorem7 states that there exist no two proper rationals both of whose sum and product are integers.This follows from Theorem6 which states that if two rational numbers have a sum being an integer; and a product being an integer;then these two rationals must both be in fact integers.

Konstantine Zelator

2011-09-29

228

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

229

Laurent polynomials and Eulerian numbers  

E-print Network

Duistermaat and van der Kallen show that there is no nontrivial complex Laurent polynomial all of whose powers have a zero constant term. Inspired by this, Sturmfels posed two questions: Do the constant terms of a generic Laurent polynomial form a regular sequence? If so, then what is the degree of the associated zero-dimensional ideal? In this note, we prove that the Eulerian numbers provide the answer to the second question. The proof involves reinterpreting the problem in terms of toric geometry.

Erman, Daniel; Várilly-Alvarado, Anthony

2009-01-01

230

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...

2012-05-01

231

Order in Number, Monograph No. 3.  

ERIC Educational Resources Information Center

This monograph attempts to provide the teacher with examples, techniques, and tips for developing order in number. Topics covered include pre-number order and classification; beginning number activities; number lines; the 100-square counting chart; ordering the integers; fractional numbers; and games, counting rhymes, and other activities. A…

Beardsley, Leeh M.

232

Indexing the approximate number system.  

PubMed

Much recent research attention has focused on understanding individual differences in the approximate number system, a cognitive system believed to underlie human mathematical competence. To date researchers have used four main indices of ANS acuity, and have typically assumed that they measure similar properties. Here we report a study which questions this assumption. We demonstrate that the numerical ratio effect has poor test-retest reliability and that it does not relate to either Weber fractions or accuracy on nonsymbolic comparison tasks. Furthermore, we show that Weber fractions follow a strongly skewed distribution and that they have lower test-retest reliability than a simple accuracy measure. We conclude by arguing that in the future researchers interested in indexing individual differences in ANS acuity should use accuracy figures, not Weber fractions or numerical ratio effects. PMID:24361686

Inglis, Matthew; Gilmore, Camilla

2014-01-01

233

Life at high Deborah number  

E-print Network

In many biological systems, microorganisms swim through complex polymeric fluids, and usually deform the medium at a rate faster than the inverse fluid relaxation time. We address the basic properties of such life at high Deborah number analytically by considering the small-amplitude swimming of a body in an arbitrary complex fluid. Using asymptotic analysis and differential geometry, we show that for a given swimming gait, the time-averaged leading-order swimming kinematics of the body can be expressed as an integral equation on the solution to a series of simpler Newtonian problems. We then use our results to demonstrate that Purcell's scallop theorem, which states that time-reversible body motion cannot be used for locomotion in a Newtonian fluid, breaks down in polymeric fluid environments.

Eric Lauga

2009-04-28

234

Small number preference in guiding attention.  

PubMed

Healthy individuals are usually biased toward small numbers when they are asked to mentally bisect number intervals or generate number sequences. Number magnitude may be represented spatially along a left-to-right mental number line. The preference for small numbers is believed to reflect the leftward spatial bias of this numerical representation. This study examined whether small numbers captured visual attention more than larger numbers. Participants were asked to detect a target pre-cued by a small or a large number. We found that the response was faster when the target was pre-cued by a small number than when pre-cued by a large number, suggesting that visual attention is preferentially allocated to small numbers. In addition, this attentional preference for small numbers was distinct for participants of different educational backgrounds. For science or engineering participants, this small number preference was enhanced by left-hand responding and was positively correlated with the small number preference in a random number generation task, suggesting that the small number preference was attributable to a leftward bias of the spatial representation. For liberal arts participants, however, left-hand responding did not enhance the small number preference and no correlations were found between the attention task and the random number generation task, suggesting that non-spatial processing mediated the small number preference. Our findings show that the small number preference occurs as early as the perceptual processing stage and distinct mechanisms underlie the preference for small numbers for participants with different educational backgrounds. PMID:25354972

Cai, Yong-Chun; Li, Shuang-Xia

2015-02-01

235

Verification Challenges at Low Numbers  

SciTech Connect

Many papers have dealt with the political difficulties and ramifications of deep nuclear arms reductions, and the issues of “Going to Zero”. Political issues include extended deterrence, conventional weapons, ballistic missile defense, and regional and geo-political security issues. At each step on the road to low numbers, the verification required to ensure compliance of all parties will increase significantly. Looking post New START, the next step will likely include warhead limits in the neighborhood of 1000 . Further reductions will include stepping stones at1000 warheads, 100’s of warheads, and then 10’s of warheads before final elimination could be considered of the last few remaining warheads and weapons. This paper will focus on these three threshold reduction levels, 1000, 100’s, 10’s. For each, the issues and challenges will be discussed, potential solutions will be identified, and the verification technologies and chain of custody measures that address these solutions will be surveyed. It is important to note that many of the issues that need to be addressed have no current solution. In these cases, the paper will explore new or novel technologies that could be applied. These technologies will draw from the research and development that is ongoing throughout the national laboratory complex, and will look at technologies utilized in other areas of industry for their application to arms control verification.

Benz, Jacob M.; Booker, Paul M.; McDonald, Benjamin S.

2013-06-01

236

Number systems, ?-splines and refinement  

NASA Astrophysics Data System (ADS)

This paper is concerned with the smooth refinable function on a plane relative with complex scaling factor . Characteristic functions of certain self-affine tiles related to a given scaling factor are the simplest examples of such refinable function. We study the smooth refinable functions obtained by a convolution power of such charactericstic functions. Dahlke, Dahmen, and Latour obtained some explicit estimates for the smoothness of the resulting convolution products. In the case ?=1+i, we prove better results. We introduce ?-splines in two variables which are the linear combination of shifted basic functions. We derive basic properties of ?-splines and proceed with a detailed presentation of refinement methods. We illustrate the application of ?-splines to subdivision with several examples. It turns out that ?-splines produce well-known subdivision algorithms which are based on box splines: Doo-Sabin, Catmull-Clark, Loop, Midedge and some -subdivision schemes with good continuity. The main geometric ingredient in the definition of ?-splines is the fundamental domain (a fractal set or a self-affine tile). The properties of the fractal obtained in number theory are important and necessary in order to determine two basic properties of ?-splines: partition of unity and the refinement equation.

Zube, Severinas

2004-12-01

237

Visuospatial Priming of the Mental Number Line  

ERIC Educational Resources Information Center

It has been argued that numbers are spatially organized along a "mental number line" that facilitates left-hand responses to small numbers, and right-hand responses to large numbers. We hypothesized that whenever the representations of visual and numerical space are concurrently activated, interactions can occur between them, before response…

Stoianov, Ivilin; Kramer, Peter; Umilta, Carlo; Zorzi, Marco

2008-01-01

238

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

239

Orbital elements of numbered minor planets  

Microsoft Academic Search

This list is a continuation of Abstr. 098.023. The numbered minor planets are listed according to their definitive number. Newly numbered objects are indicated by an asterisk. The names of the orbit computers are given behind the respective M.P.C. (or MPO) numbers:

G. V. Williams; B. G. Marsden; D. J. Asher; S. Nakano

2000-01-01

240

Orbital elements of numbered minor planets  

Microsoft Academic Search

This list is a continuation of Abstr. 098.035. The numbered minor planets are listed according to their definitive number. Newly numbered objects are indicated by an asterisk. The names of the orbit computers are given behind the respective M.P.C. numbers:

S. Nakano; G. V. Williams; B. G. Marsden; D. J. Asher; C. M. Bardwell; D. W. E. Green

1998-01-01

241

Contextual Effects on Number-Time Interaction  

ERIC Educational Resources Information Center

Time perception has long been known to be affected by numerical representations. Recent studies further demonstrate that when participants estimate the duration of Arabic numbers, number magnitude, though task-irrelevant, biases duration judgment to produce underestimation for smaller numbers and overestimation for larger numbers. Such effects…

Lu, Aitao; Hodges, Bert; Zhang, Jijia; Zhang, John X.

2009-01-01

242

NOTES ON COMPLEX NUMBERS DAVID M. MCCLENDON  

E-print Network

which solves the equation 2x = 3. 1.3. Rational numbers. To fix this, we consider the rational numbers divisors, and q = 0. What is great about the rational numbers is that you get all the pros of the integers and you can also divide one rational number by another (as long as the divisor is not zero) and get

McClendon, David M.

243

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 the…

Harrison, John

2006-01-01

244

Generalized Feedback Shift Register Pseudorandom Number Algorithm  

Microsoft Academic Search

The generalized feedback shift register pseudorandom number algorithm has several advantages over all other pseudorandom number generators. These advantages are: (1) it produces multidimensional pseudorandom numbers; (2) it has an arbitrarily long period independent of the word size of the computer on which it is implemented; (3) it is faster than other pseudorandom number generators; (4) the “same” floating-point pseudorandom

T. G. Lewis; W. H. Payne

1973-01-01

245

MATHEMATICAE Normal numbers and the Borel hierarchy  

E-print Network

FUNDAMENTA MATHEMATICAE 226 (2014) Normal numbers and the Borel hierarchy by Ver´onica Becher that the set of absolutely normal numbers is 0 3-complete in the Borel hierarchy of subsets of real numbers. Similarly, the set of absolutely normal numbers is 0 3-complete in the effective Borel hierarchy. 1

Slaman, Theodore A.

246

On Liouville Numbers Yet Another Application of Functional Analysis to Number Theory  

E-print Network

of Transcendental Numbers On Liouville Numbers ­ p.4/42 #12;Transcendental Numbers Gottfried Leibniz Leonhard Euler "omnem rationem transcendunt" (Gottfried Leibniz, 1682 - ? - 1704) On Liouville Numbers ­ p.5/42 #12

247

Heat transfer from a horizontal wafer-based disk of multi-chip modules  

Microsoft Academic Search

Convective heat transfer characteristics above a horizontal wafer-based disk heated with 15 simulated chips in unobstructed ambient air have been experimentally investigated under both stationary and rotating disk conditions. Relevant parameters influencing heat transfer performance studied are the Grashof number and rotational Reynolds number. Their effects on heat transfer characteristics in such configurations of stationary and rotational heated disks are

Y. R. Shieh; C. J. Li; Y. H. Hung

1999-01-01

248

On q-deformed Stirling numbers  

E-print Network

The purpose of this article is to introduce q-deformed Stirling numbers of the first and second kinds. Relations between these numbers, Riemann zeta function and q-Bernoulli numbers of higher order are given. Some relations related to the classical Stirling numbers and Bernoulli numbers of higher order are found. By using derivative operator to the generating function of the q-deformed Stirling numbers of the second kinds, a new function is defined which interpolates the q-deformed Stirling numbers of the second kinds at negative integers. The recurrence relations of the Stirling numbers of the first and second kind are given. In addition, relation between q-deformed Stirling numbers and q-Bell numbers is obtained.

Yilmaz Simsek

2007-11-03

249

h-analogue of Fibonacci Numbers  

E-print Network

In this paper, we introduce the h-analogue of Fibonacci numbers for non-commutative h-plane. For h h'= 1 and h = 0, these are just the usual Fibonacci numbers as it should be. We also derive a collection of identities for these numbers. Furthermore, h-Binet's formula for the h-Fibonacci numbers is found and the generating function that generates these numbers is obtained.

H. B. Benaoum

2009-09-30

250

Generating functions, Fibonacci numbers and rational knots  

Microsoft Academic Search

We describe rational knots with any of the possible combinations of the properties (a)chirality, (non-)positivity, (non-)fiberedness, and unknotting number one (or higher), and determine exactly their number for a given number of crossings in terms of their generating functions. We show in particular how Fibonacci numbers occur in the enumeration of fibered achiral and unknotting number one rational knots. Then

A. Stoimenow

2007-01-01

251

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

252

Prime number generation and factor elimination  

E-print Network

We have presented a multivariate polynomial function termed as factor elimination function,by which, we can generate prime numbers. This function's mapping behavior can explain the irregularities in the occurrence of prime numbers on the number line. Generally the different categories of prime numbers found till date, satisfy the form of this function. We present some absolute and probabilistic conditions for the primality of the number generated by this method. This function is capable of leading to highly efficient algorithms for generating prime numbers.

Vineet Kumar

2014-10-06

253

Grant Title: SOCIOLOGY Funding Opportunity Number: PD-98-1331. CFDA Number(s): 47.075.  

E-print Network

Grant Title: SOCIOLOGY Funding Opportunity Number: PD-98-1331. CFDA Number(s): 47.075. Agency Applicants: Unrestricted. Summary: The Sociology Program supports research on human social organization, socialization, gender roles, and the sociology of science and technology. In assessing the intrinsic merit

Farritor, Shane

254

Grant Title: COGNITIVE NEUROSCIENCE Funding Opportunity Number: NSG 09-563. (CFDA) Number(s): 47.075.  

E-print Network

Grant Title: COGNITIVE NEUROSCIENCE Funding Opportunity Number: NSG 09-563. (CFDA) Number(s): 47 of Support: Not listed. Eligible Applicants: Unrestricted. Summary: The Cognitive Neuroscience program seeks investigators. Investigators are invited to submit proposals that focus on cognitive neuroscience topics

Farritor, Shane

255

47 CFR 32.6622 - Number services.  

Code of Federal Regulations, 2011 CFR

...2011-10-01 false Number services. 32.6622 Section 32...CONTINUED) COMMON CARRIER SERVICES UNIFORM SYSTEM OF ACCOUNTS...Accounts § 32.6622 Number services. This account shall...disseminating those listings through directory assistance or other...

2011-10-01

256

47 CFR 32.6622 - Number services.  

Code of Federal Regulations, 2010 CFR

...2010-10-01 false Number services. 32.6622 Section 32...CONTINUED) COMMON CARRIER SERVICES UNIFORM SYSTEM OF ACCOUNTS...Accounts § 32.6622 Number services. This account shall...disseminating those listings through directory assistance or other...

2010-10-01

257

Computational Aspects of DNA Copy Number  

E-print Network

Computational Aspects of DNA Copy Number Measurement Doron Lipson Technion Aspects of DNA Copy Number Measurement Research Thesis Submitted in partial fulfillment . . . . . . . . . . . . . . . . . . . 36 2.2.4 Downstream Effects of Genomic Aberrations . . . . . . 42 2.2.5 DNA Replication Patterns

Shamir, Ron

258

Rockin' Round the Number Line: Lesson Two  

NSDL National Science Digital Library

After completing the formative assessments for proficiency with place value, the concept of "half-way", and estimation using a real world context, students will complete the lesson which uses their prior knowledge to support them in drawing conclusions about number patterns used in estimation and rounding numbers. Students will identify which "ten" or "hundred" the whole number falls closest to based on whether the number falls before or after a "half-way" number. Finally students will conclude that there are number patterns that guide estimation when one does not have a specific context that determines a need. Specifically we can use "half-way" numbers that are multiples of 5 to guide whether we "round up" or "round down" when estimating stand alone numbers.

Andreas Howell

2012-07-23

259

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.

2012-08-02

260

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

261

A determinant of generalized Fibonacci numbers  

E-print Network

We evaluate a determinant of generalized Fibonacci numbers, thus providing a common generalization of several determinant evaluation results that have previously appeared in the literature, all of them extending Cassini's identity for Fibonacci numbers.

Krattenthaler, Christian

2012-01-01

262

48 CFR 304.7001 - Numbering acquisitions.  

Code of Federal Regulations, 2012 CFR

...Officer shall also assign the letter contract number to the superseding definitized contract.) (2) Basic ordering agreements (BOAs) and BPAs. (3) Requests for proposals and invitations for bids. (4) Requests for quotations. (b) Numbering...

2012-10-01

263

48 CFR 304.7001 - Numbering acquisitions.  

Code of Federal Regulations, 2014 CFR

...Officer shall also assign the letter contract number to the superseding definitized contract.) (2) Basic ordering agreements (BOAs) and BPAs. (3) Requests for proposals and invitations for bids. (4) Requests for quotations. (b) Numbering...

2014-10-01

264

48 CFR 304.7001 - Numbering acquisitions.  

Code of Federal Regulations, 2013 CFR

...Officer shall also assign the letter contract number to the superseding definitized contract.) (2) Basic ordering agreements (BOAs) and BPAs. (3) Requests for proposals and invitations for bids. (4) Requests for quotations. (b) Numbering...

2013-10-01

265

48 CFR 304.7001 - Numbering acquisitions.  

Code of Federal Regulations, 2010 CFR

...Officer shall also assign the letter contract number to the superseding definitized contract.) (2) Basic ordering agreements (BOAs) and BPAs. (3) Requests for proposals and invitations for bids. (4) Requests for quotations. (b) Numbering...

2010-10-01

266

48 CFR 304.7001 - Numbering acquisitions.  

Code of Federal Regulations, 2011 CFR

...Officer shall also assign the letter contract number to the superseding definitized contract.) (2) Basic ordering agreements (BOAs) and BPAs. (3) Requests for proposals and invitations for bids. (4) Requests for quotations. (b) Numbering...

2011-10-01

267

49 CFR 230.47 - Boiler number.  

Code of Federal Regulations, 2010 CFR

...2010-10-01 2010-10-01 false Boiler number. 230.47 Section 230.47...LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges § 230.47 Boiler number. (a) Generally. The...

2010-10-01

268

Making Numbers in More Than One Way  

NSDL National Science Digital Library

In this lesson, students will find pairs of numbers that equal a number from 1-9. Students will represent these equalities with linking cubes, colored squares of construction paper, and written equations.

Brown, Kathleen

2012-07-20

269

On Ramachandra's Contributions to Transcendental Number Theory  

E-print Network

On Ramachandra's Contributions to Transcendental Number Theory Michel WALDSCHMIDT Universit P. et M(C) for the complex topology? The other contributions of Ramachandra to transcendental number theory are dealt

Paris-Sud XI, Université de

270

49 CFR 230.47 - Boiler number.  

Code of Federal Regulations, 2013 CFR

...2013-10-01 2013-10-01 false Boiler number. 230.47 Section 230.47...LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges § 230.47 Boiler number. (a) Generally. The...

2013-10-01

271

49 CFR 230.47 - Boiler number.  

Code of Federal Regulations, 2012 CFR

...2012-10-01 2012-10-01 false Boiler number. 230.47 Section 230.47...LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges § 230.47 Boiler number. (a) Generally. The...

2012-10-01

272

49 CFR 230.47 - Boiler number.  

Code of Federal Regulations, 2011 CFR

...2011-10-01 2011-10-01 false Boiler number. 230.47 Section 230.47...LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges § 230.47 Boiler number. (a) Generally. The...

2011-10-01

273

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

274

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

275

46 CFR Sec. 2 - Voyage numbers.  

Code of Federal Regulations, 2014 CFR

...with voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with berth...

2014-10-01

276

46 CFR Sec. 2 - Voyage numbers.  

Code of Federal Regulations, 2010 CFR

...with voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with berth...

2010-10-01

277

46 CFR Sec. 2 - Voyage numbers.  

Code of Federal Regulations, 2013 CFR

...with voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with berth...

2013-10-01

278

Using Simulated Annealing to Factor Numbers  

E-print Network

Almost all public secure communication relies on the inability to factor large numbers. There is no known analytic or classical numeric method to rapidly factor large numbers. Shor[1] has shown that a quantum computer can factor numbers in polynomial time but there is no practical quantum computer that can yet do such computations. We show that a simulated annealing[2] approach can be adapted to find factors of large numbers.

Eric Lewin Altschuler; Timothy J. Williams

2014-02-14

279

Let's Count! Learning Numbers in Multiple Ways  

NSDL National Science Digital Library

In this 5-minute video Pre-K teacher Rosemary Kungu demonstrates a variety of activities that develop early number skills, including number recognition, counting and ordering numbers. The activities involve active participation and incorporate multiple senses and learning styles, music, and collaboration. A downloadable transcript of the video (doc) is included along with reflection questions for viewers.

2013-01-01

280

When is a number Fibonacci? Phillip James  

E-print Network

When is a number Fibonacci? Phillip James Department of Computer Science, Swansea University January 25, 2009 Abstract This article looks into the importance of the Fibonacci numbers within Computer Science, commenting on how to compute a Fibonacci number. It introduces an efficient test as to whether

Berger, Ulrich

281

The competition numbers of complete tripartite graphs  

E-print Network

The competition numbers of complete tripartite graphs SUH-RYUNG KIM Department of Mathematics For a graph G, it is known to be a hard problem to compute the competition number k(G) of the graph G in general. In this paper, we give an explicit formula for the competition numbers of complete tripartite

282

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

283

46 CFR Sec. 7 - Job order numbering.  

Code of Federal Regulations, 2014 CFR

...2014-10-01 2014-10-01 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...

2014-10-01

284

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 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...

2011-10-01

285

46 CFR Sec. 7 - Job order numbering.  

Code of Federal Regulations, 2013 CFR

...2013-10-01 2013-10-01 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...

2013-10-01

286

46 CFR Sec. 7 - Job order numbering.  

Code of Federal Regulations, 2010 CFR

...2010-10-01 2010-10-01 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...

2010-10-01

287

Calculating Mach Numbers Using Ratios and Fractions  

NSDL National Science Digital Library

A mach number represents how many times the speed of sound a vehicle is traveling. NASA uses mach numbers to describe the speed of their planes. This video shows you how algebra can be used to determine the mach number of a NASA plane.

2004-01-01

288

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

289

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

290

A note on Quarks and numbers theory  

E-print Network

We express the basis vectors of Cartan fundamental representations of unitary groups by binary numbers. We determine the expression of Gel'fand basis of SU (3) based on the usual subatomic quarks notations and we represent it by binary numbers. By analogy with the mesons and quarks we find a new property of prime numbers.

Mehdi Hage-Hassan

2013-02-26

291

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

292

Irving Fisher and Index Number Theory  

Microsoft Academic Search

There are four main approaches to bilateral index number theory: the fixed basket, stochastic, test and economic approaches. The paper reviews the contributions of Irving Fisher to these approaches to index number theory which are still in use today. The paper also reviews Fisher’s contributions to multilateral index number theory. The main themes of the paper are developed in the

Erwin Diewert

2012-01-01

293

KIAS SEOUL, February 2004 Transcendental Number Theory  

E-print Network

KIAS SEOUL, February 2004 Transcendental Number Theory: the State of the Art Michel Waldschmidt of transcendental numbers. http://www.math.jussieu.fr/miw/ 2 #12;Early History ( 1934) J. Liouville(1844) ­ First examples of transcendental numbers. n1 10-n! is transcendental Idea of the proof. If is an algebraic

Waldschmidt, Michel

294

Number Pieces, by the Math Learning Center  

NSDL National Science Digital Library

This free iOS app uses virtual base-10 blocks to help students develop their understanding of place value and computation strategies with multi-digit numbers. Students use the number pieces to represent multi-digit numbers, regroup, add, subtract, multiply, and divide.

2013-11-23

295

THE CONGRUENT NUMBER PROBLEM KEITH CONRAD  

E-print Network

THE CONGRUENT NUMBER PROBLEM KEITH CONRAD 1. Introduction A right triangle is called rational when its legs and hypotenuse are all rational numbers. Examples of rational right triangles include) ratio- nal numbers can occur as the area of a rational right triangle. For instance, no rational right

Lozano-Robledo, Alvaro

296

Vector Rational Number Reconstruction Curtis Bright  

E-print Network

Vector Rational Number Reconstruction Curtis Bright cbright@uwaterloo.ca Arne Storjohann astorjoh and |ni| N for a given magnitude bound N. Applying elementwise rational number reconstruction requires. INTRODUCTION A rational number reconstruction of an integer a Z with respect to a positive modulus M Z>0

Storjohann, Arne

297

THE CONGRUENT NUMBER PROBLEM KEITH CONRAD  

E-print Network

THE CONGRUENT NUMBER PROBLEM KEITH CONRAD 1. Introduction A right triangle is called rational when its legs and hypotenuse are all rational numbers. Examples of rational right triangles include) rational numbers can occur as the area of a rational right triangle. For instance, no rational right

Lozano-Robledo, Alvaro

298

Vector Rational Number Reconstruction Curtis Bright  

E-print Network

Vector Rational Number Reconstruction By Curtis Bright A research paper presented to the University Bright 2009 #12;Vector Rational Number Reconstruction August 26, 2009 Abstract The final step of some algebraic algorithms is to reconstruct the common denominator d of a collection of rational numbers (ni/d)1

Storjohann, Arne

299

On Unit Sum Numbers of Rational Groups  

Microsoft Academic Search

The unit sum numbers of rational groups are investigated: the importance of the prime 2 being an automorphism of the rational group is discussed and other results are achieved by considering the number and distribution of rational primes which are, or are not, automorphisms of the group. Proof is given of the existence of rational groups with unit sum numbers

Brendan Goldsmith; C. Meehan; S. L. Wallutis

2002-01-01

300

Turing's normal numbers: towards randomness Veronica Becher  

E-print Network

Turing's normal numbers: towards randomness Ver´onica Becher Universidad de Buenos Aires & CONICET, Argentina vbecher@dc.uba.ar Abstract. In a manuscript entitled "A note on normal numbers" and written presumably in 1938 Alan Turing gave an algorithm that produces real numbers normal to every integer base

301

Levels of Number 1 Running head: LEVELS OF NUMBER KNOWLEDGE IN EARLY CHILDHOOD  

E-print Network

Levels of Number 1 Running head: LEVELS OF NUMBER KNOWLEDGE IN EARLY CHILDHOOD Levels of Number Knowledge in Early Childhood Barbara W. Sarnecka and Michael D. Lee University of California, Irvine Author of Number 3 Levels of Number Knowledge in Early Childhood Children learn to count (i.e., to recite

Stanford, Kyle

302

Sampling from the Mental Number Line Sampling from the Mental Number Line  

E-print Network

Sampling from the Mental Number Line 1 Sampling from the Mental Number Line: How are Approximate Kingdom m.j.inglis@lboro.ac.uk 3863 words #12;Sampling from the Mental Number Line 2 Abstract Nonsymbolic cognition research. #12;Sampling from the Mental Number Line 3 SAMPLING FROM THE MENTAL NUMBER LINE: HOW

Inglis, Matthew

303

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

304

Long-Wave Instability of Advective Flows in Inclined Layer with Solid Heat Conductive Boundaries  

E-print Network

We investigate the stability of the steady convective flow in a plane tilted layer with ideal thermal conductivity of solid boundaries in the presence of uniform longitudinal temperature gradient. Analytically found the stability boundary with respect to the long-wave perturbations, find the critical Grashof number for the most dangerous among them of even spiral perturbation.

R. V. Sagitov; A. N. Sharifulin

2011-01-07

305

Estimation of convective mass transfer in solar distillation systems  

Microsoft Academic Search

In this article a thermal model has been developed to determine the convective mass transfer for different Grashof Number range in solar distillatiOn process. The model is based on simple regression analysis. Based on the experimental data obtained from the rigorous outdoor experimentation on passive and active distillation systems for summer climatic conditions, the values of C and n have

Sanjay Kumar; G. N. Tiwari

1996-01-01

306

Effect of opposing buoyancy on the flow in free and wall jets  

Microsoft Academic Search

An experimental investigation of turbulent, downward-discharged heated air jets is described. The flow was visualized by introducing smoke into the jet upsteam of the discharge location. The downward penetration of the jets was measured over a wide range of Grashof and Reynolds numbers corresponding to mixed convection flows. The velocity and tempearture profiles of the jets were also obtained. It

D. Goldman; Y. Jaluria

1985-01-01

307

Components representation of negative numbers: evidence from auditory stimuli detection and number classification tasks.  

PubMed

Past research suggested that negative numbers could be represented in terms of their components in the visual modality. The present study examined the processing of negative numbers in the auditory modality and whether it is affected by context. Experiment 1 employed a stimuli detection task where only negative numbers were presented binaurally. Experiment 2 employed the same task, but both positive and negative numbers were mixed as cues. A reverse attentional spatial-numerical association of response codes (SNARC) effect for negative numbers was obtained in these two experiments. Experiment 3 employed a number classification task where only negative numbers were presented binaurally. Experiment 4 employed the same task, but both positive and negative numbers were mixed. A reverse SNARC effect for negative numbers was obtained in these two experiments. These findings suggest that negative numbers in the auditory modality are generated from the set of positive numbers, thus supporting a components representation. PMID:22133233

Kong, Feng; Zhao, Jingjing; You, Xuqun

2012-01-01

308

Fibonacci Numbers and the Golden Section  

NSDL National Science Digital Library

In 1202, the mathematician Fibonacci investigated the problem of how fast rabbits could breed under ideal circumstances. This problem and many more are detailed at the Fibonacci Numbers and the Golden Section Website, made available by Dr. Ron Knott of the University of Surrey (UK). A new addition to the site is a link to a reference page of over 100 formulas and equations demonstrating the properties of Fibonacci, Phi, and Lucus numbers series. The site's many links are categorized in the following sections: Fibonacci Numbers and Golden sections in Nature; The Intriguing Mathematical World of Fibonacci and Phi; The Puzzling World of Fibonacci Numbers; The Golden String; Fibonacci: the Man and His Times; and More Applications of Fibonacci Numbers and Phi. This site, through its extensive listings of links, contains a plethora of mathematical theories, equations, and proofs based on Fibonacci numbers.

Knott, Ron.

309

From Taub Numbers to the Bondi Mass  

E-print Network

Taub numbers are studied on asymptotically flat backgrounds with Killing symmetries. When the field equations are solved for a background spacetime and higher order functional derivatives (higher order variational derivatives of the Hilbert Lagrangean) are solved for perturbations from the background, such perturbed space-times admit zeroth, first, and second order Taub numbers. Zeroth order Taub numbers are Komar constants (upto numerical factors) or Penrose-Goldberg constants of the background. For a Killing symmetry of the background, first order Taub numbers give the contribution of the linearized perturbation to the associated backgound quantity, such as the perturbing mass. Second order Taub numbers give the contribution of second order perturbations to the background quantity. The Bondi mass is a sum of first and second order Taubs numbers on a Minkowski background.

E. N. Glass

1997-12-17

310

Relativistic theory of tidal Love numbers  

E-print Network

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.

Taylor Binnington; Eric Poisson

2009-09-16

311

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

312

HotBits: Genuine Random Numbers  

NSDL National Science Digital Library

HotBits is a genuine random number generator powered by radioactive decay. Simply click the "Request HotBits" link, and specify how many bytes you would like (up to 2048) and in what form you prefer them. Hexadecimal returns numbers and letters, while C language returns integers. Then click the "Get HotBits" button, and your random numbers will appear on the screen.

Walker, John

2009-10-21

313

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

314

Entropy of pseudo-random-number generators  

Microsoft Academic Search

Since the work of Ferrenberg et al. [Phys. Rev. Lett. 69, 3382 (1992)] some pseudo-random-number generators are known to yield wrong results in cluster Monte Carlo simulations. In this contribution the fundamental mechanism behind this failure is discussed. Almost all random-number generators calculate a new pseudo-random-number xi from preceding values, xi =f( xi-1 , xi-2 ,..., xi-q ) . Failure

Stephan Mertens; Heiko Bauke

2004-01-01

315

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

316

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 PMID:19364158

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

2013-01-01

317

Complex Rational Numbers in Quantum Mechanics  

E-print Network

A binary representation of complex rational numbers and their arithmetic is described that is not based on qubits. It takes account of the fact that $0s$ in a qubit string do not contribute to the value of a number. They serve only as place holders. The representation is based on the distribution of four types of systems, corresponding to $+1,-1,+i,-i,$ along an integer lattice. Complex rational numbers correspond to arbitrary products of four types of creation operators acting on the vacuum state. An occupation number representation is given for both bosons and fermions.

Paul Benioff

2005-08-03

318

CRC octane-number-requirement survey, 1990  

SciTech Connect

An annual statistical survey of octane number requirements of current model vehicles is conducted by the Coordinating Research Council, Inc. Test data have been obtained by seventeen companies on 356 1990 vehicles including passenger cars and light-duty trucks and vans, of which 169 were equipped with knock sensors. Octane number requirements were determined by testing at maximum-throttle conditions, as well as at part-throttle, with three unleaded fuel series of varying sensitivities. Requirements are expressed as the (R+M)/2 octane number, Research octane number, and Motor octane number of the reference fuel producing knock which was recurrent and repeatable at the lowest audible level. Estimated octane number requirements for the total vehicles are weighted in proportion to the 1990 vehicle model production and/or sales figures. The octane number requirements of 1990 models with average sensitivity unleaded fuels were 85.4 (R+M)/2 octane numbers at the 50 percent satisfaction level, and 89.2 (R+M)/2 octane numbers at the 90 percent satisfaction level.

Not Available

1991-07-01

319

CRC octane number requirement survey 1992  

SciTech Connect

An annual statistical survey of octane number requirements of current model vehicles is conducted by the Coordinating Research Council, Inc. Test data have been obtained by ten companies on 184 1992 vehicles including passenger cars and light-duty trucks and vans, of which 88 were equipped with knock sensors. Octane number requirements were determined by testing at maximum-throttle conditions, as well as at part-throttle, with four unleaded fuel series of varying sensitivities, one containing 15 percent methyl tertiary butyl ether. Requirements are expressed as the (R+M)/2 octane number, Research octane number, and Motor octane number of the reference fuel producing knock which was recurrent and repeatable at the lowest audible level. Estimated octane number requirements for the total vehicles are weighted in proportion to the 1992 vehicle model production and/or sales figures. The octane number requirements of 1992 models with average sensitivity unleaded fuels were 85.1 (R+M)/2 octane numbers at the 50 percent satisfaction level, and 92.0 (R+M)/2 octane numbers at the 90 percent satisfaction level. In order to make a more powerful test of statistical significance of the FBRUM fuel series, the 1991 ONRS was pooled with the 1992 ONRS and compared with the pooled data for the FBRU fuel series. There was no significant difference between the two fuel series up to about 90 percent satisfaction. Beyond 90 percent satisfaction, the variability in the data is high.

Not Available

1993-08-01

320

CRC octane number requirement survey for 1989  

SciTech Connect

An annual statistical survey of octane number requirements of current model vehicles is conducted by the Coordinating Research Council, Inc. Test data have been obtained by eighteen companies on 391 1989 vehicles including passenger cars and light-duty trucks and vans, of which 179 were equipped with knock sensors. Maximum octane number requirements were determined by testing at maximum-throttle conditions, as well as at part-throttle, with three unleaded fuel series of varying sensitivities. Requirements are expressed as the (R+M)/2 octane number, Research octane number, and Motor octane number of the reference fuel producing knock which was recurrent and repeatable at the lowest audible level. Estimated octane number requirements for the total vehicles are weighted in proportion to the 1989 vehicle model production and/or sales figures. The maximum octane number requirements of 1989 models with average sensitivity unleaded fuels were 85.1 (R+M)/2 octane numbers at the 50 percent satisfaction level, and 89.2 (R+M)/2 octane numbers at the 90 percent satisfaction level. Comparison with previous Surveys are made in this report.

Not Available

1990-08-01

321

Mental Number Line, Number Line Estimation, and Mathematical Achievement: Their Interrelations in Grades 5 and 6  

ERIC Educational Resources Information Center

As indicated by the distance effect and the spatial-numerical association of response codes (SNARC) effect, natural numbers are mentally represented on a number line. Purportedly, this number line underlies children's number sense, which supports the acquisition of more advanced mathematical competencies. In 3 studies with a total of 429 fifth and…

Schneider, Michael; Grabner, Roland H.; Paetsch, Jennifer

2009-01-01

322

Deriving the number of jobs in proximity services from the number of inhabitants in French rural  

E-print Network

Deriving the number of jobs in proximity services from the number of inhabitants in French rural a minimum requirement approach to derive the number of jobs of proximity services per inhabitant observe that the minimum number of service jobs per inhabitant (interpreted as jobs of proximity services

Paris-Sud XI, Université de

323

Predicting landfalling hurricane numbers from basin hurricane numbers: basic statistical analysis  

E-print Network

One possible method for predicting landfalling hurricane numbers is to first predict the number of hurricanes in the basin and then convert that prediction to a prediction of landfalling hurricane numbers using an estimated proportion. Should this work better than just predicting landfalling hurricane numbers directly? We perform a basic statistical analysis of this question in the context of a simple abstract model.

Laepple, T; Penzer, J; Bellone, E; Nzerem, K; Laepple, Thomas; Jewson, Stephen; Penzer, Jeremy; Bellone, Enrica; Nzerem, Kechi

2007-01-01

324

From Whole Numbers to Invert and Multiply  

ERIC Educational Resources Information Center

Teachers report that engaging students in solving contextual problems is an important part of supporting student understanding of algorithms for fraction division. Meaning for whole-number operations is a crucial part of making sense of contextual problems involving rational numbers. The authors present a developed instructional sequence to…

Cavey, Laurie O.; Kinzel, Margaret T.

2014-01-01

325

SOCIAL SECURITY NUMBER AND NAME VERIFICATION  

E-print Network

SOCIAL SECURITY NUMBER AND NAME VERIFICATION Academic Year 2014­2015 *FA552-A* Please recycle. DIRECTIONS--You must verify your name and Social Security number for processing of your 2014­2015 Free Application for Federal Student Aid (FAFSA) to continue. Please attach a legible copy of your Social Security

Amin, S. Massoud

326

SOCIAL SECURITY NUMBER AND NAME VERIFICATION  

E-print Network

SOCIAL SECURITY NUMBER AND NAME VERIFICATION Academic Year 2013­2014 *FA552-A* Please recycle. DIRECTIONS--You must verify your name and Social Security number for processing of your 2013­2014 Free Application for Federal Student Aid (FAFSA) to continue. Please attach a legible copy of your Social Security

Amin, S. Massoud

327

Addition transducer for double base number system  

Microsoft Academic Search

Double base number system is proposed for performing the fast computational arithmetic. Two integers, two and three, are used to be the bases. Any number can have a representation as a binary array. In this paper, we consider an implementation model for addition which is one of fundamental arithmetic operations. The proposed addition model can be illustrated by a communication

Kriangyut Wangjitman; Athasit Surarerks

2006-01-01

328

Fostering Number Sense through Digits and Dice  

ERIC Educational Resources Information Center

Games are among the many types of activities that can be used to help promote number sense. Chosen and used wisely, games encourage learning and motivate many students to grasp concepts more quickly and fully. This article describes a popular and easy-to-implement number sense game--called Digits and Dice--most commonly used in conjunction with…

Wiest, Lynda R.

2006-01-01

329

14 CFR 47.15 - Registration number.  

Code of Federal Regulations, 2014 CFR

...number from the Registry by request in writing describing the aircraft by make, type, model, and serial number (or, if it is amateur-built, as provided in § 47.33(b)) and stating that the aircraft has not previously been registered anywhere....

2014-01-01

330

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

331

Predict octane number for gasoline blends  

Microsoft Academic Search

A model with five independent variables is used to predict the octane number of gasoline blends with more accuracy than any previous model. Often, it is useful to know the resulting octane number before the gasoline is blended. Clearly, such a model is useful because good predictive models have been few and far between. With high-powered and faster personal computers,

A. H. Zahed; S. A. Mullah; M. D. Bashir

1993-01-01

332

Reidentifying hardware after loss of serial number  

NASA Technical Reports Server (NTRS)

System traces fabrication and inspection records of special hardware back to the raw material. Reidentification of hardware, after loss of serial numbers, is established by X raying all parts again and comparing the new film with the original, whose numbers were previously recorded on serialized documents.

Wells, R. J.

1969-01-01

333

Demonstrations of the Enormity of Avogadro's Number  

Microsoft Academic Search

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

Damon Diemente

1998-01-01

334

When Symbolic Spatial Cues Go before Numbers  

ERIC Educational Resources Information Center

This work explores the effect of spatial cueing on number processing. Participants performed a parity judgment task. However, shortly before the target number, a cue (arrow pointing to left, arrow pointing to right or a cross) was centrally presented. In Experiment 1, in which responses were lateralized, the cue direction modulated the interaction…

Herrera, Amparo; Macizo, Pedro

2011-01-01

335

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

336

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

337

On Carmichael numbers in arithmetic progressions  

E-print Network

On Carmichael numbers in arithmetic progressions William D. Banks Department of Mathematics an analogue of Dirichlet's theorem on primes in an arithmetic progression holds for the set of Carmichael Carmichael numbers in the arithmetic progression 1 mod m, we use a straightforward variant of the Alford

Pomerance, Carl

338

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.

Ron Knott, Ph.D.

2007-12-12

339

182 MATHEMATICS MAGAZINE The Fibonacci Numbers--  

E-print Network

182 MATHEMATICS MAGAZINE The Fibonacci Numbers-- Exposed More Discretely ARTHUR T. BENJAMIN Harvey 90041 jquinn@oxy.edu In the previous article, Kalman and Mena [5] propose that Fibonacci and Lucas se generalize Fibonacci and Lucas numbers: Given nonnegative integers a and b, the generalized Fibonacci

Benjamin, Arthur T.

340

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

341

Predicting the required number of training samples  

NASA Technical Reports Server (NTRS)

A criterion which measures the quality of the estimate of the covariance matrix of a multivariate normal distribution is developed. Based on this criterion, the necessary number of training samples is predicted. Experimental results which are used as a guide for determining the number of training samples are included.

Kalayeh, H. M.; Landgrebe, D. A.

1982-01-01

342

Brandeis University Music current number of majors  

E-print Network

achievement. Leonard Bernstein fellowship each year, the music department awards fellowships to select internships in a music-related field for academic credit. rani Schloss '10, a music and education double majorBrandeis University Music fast facts current number of majors and minors: 44 Number of faculty: 14

Fraden, Seth

343

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

344

Power sums of Fibonacci and Lucas numbers  

Microsoft Academic Search

Polynomial representation formulae for power sums of the extended Fibonacci-Lucas numbers are established, which include, as special cases, four formulae for odd power sums of Melham type on Fibonacci and Lucas numbers, obtained recently by Ozeki and Prodinger (2009).

Wenchang Chu; Nadia N. Li

2011-01-01

345

Number Theory in Cryptography ! and its Application"  

E-print Network

Number Theory in Cryptography ! and its Application" http://www.math.jussieu.fr/~miw/! Michel, Kirtipur, Nepal ! Introduction to cryptography! 2! !Theoretical research in number theory has a long remain open. ! http://www.math.jussieu.fr/~miw/! Data transmission, Cryptography ! and Arithmetic! 3

Waldschmidt, Michel

346

Trees Associated with the Motzkin Numbers  

Microsoft Academic Search

. We consider plane rooted trees on n+1 vertices without branching pointson odd levels. The number of such trees in equal to the Motzkin number Mn . Wegive a bijective proof of this statement.1. Let Pn be the set of all plane rooted trees on n+1 unlabeled vertices withedges oriented from the root (see [1]). We say that a vertex

Alexander Kuznetsov; Igor Pak; Alexander Postnikov

1996-01-01

347

-P and T number -Residence Permit  

E-print Network

service options when opening bank account #12;Swedish Migration Board - Migrationsverket 2012- P and T number - Residence Permit - Banking Information - Insurance - Other... #12;P and T number or online. When you apply for an extension by post, you must use the form Application for residence permit

348

Fourier analysis in combinatorial number theory  

NASA Astrophysics Data System (ADS)

In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.

Shkredov, Il'ya D.

2010-09-01

349

Brandeis University Psychology current number of majors  

E-print Network

research in diverse areas including cognitive science; normal and abnormal psychology; health psychologyBrandeis University Psychology fast facts current number of majors and minors: 282 NumberBoUt the Program the Department of Psychology helps students establish a strong scientific and research foundation

Fraden, Seth

350

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 the…

Goldenhersh, Barbara, Ed.

351

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

352

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

353

Love numbers of the giant planets  

Microsoft Academic Search

The Love numbers for n = 2 to 10 were calculated for Jupiter, Saturn, and Uranus, and 'gravitational noise' from tides were determined. On the basis of these new Love numbers, the planetary dissipation functions are estimated to be greater than approximately 25,000, 14,000, and 5000 for Jupiter, Saturn, and Uranus, respectively.

S. V. Gavrilov; V. N. Zharkov

1977-01-01

354

Love numbers of the terrestrial planets  

Microsoft Academic Search

The latest geodetic parameters of the terrestrial planets are used to construct parametric models of the internal structure of the terrestrial planets. These models are then used to compute the static Love numbers from order 2 to 30. The influence of the outer core rigidity on the second-order Love numbers is discussed. The obtained results indicate that the probable ranges

Cheng-Zhi Zhang

1991-01-01

355

Love numbers of the terrestrial planets  

Microsoft Academic Search

Using the latest geodetic parameters of the terrestrial planets, the author constructed the parametric models of the internal structure of the terrestrial planets. By means of these models he computed their static Love numbers from order 2 to 30 and listed the results. Then he discussed the influence of the outer core rigidity on the second-order Love numbers.

Zhangzhi Cheng

1991-01-01

356

The Second Strong Law of Small Numbers.  

ERIC Educational Resources Information Center

Presented are 44 examples in which students are invited to guess what pattern of numbers is emerging and to decide whether the pattern will persist. Topics of examples include Pascal's triangle, integers, vertices, Fibonacci numbers, power series, partition functions, and Euler's theorem. The answers to all problems are included. (KR)

Guy, Richard K.

1990-01-01

357

National Resources [and] National Toll Free Numbers.  

ERIC Educational Resources Information Center

This resource list provides names, addresses, and telephone numbers of 13 information clearinghouses and 42 organizations providing information on children and youth with disabilities. Telephone numbers are designated as either voice or text telephone. Spanish-language resources are also indicated. A list of organizations that have national…

National Information Center for Children and Youth with Disabilities, Washington, DC.

358

Randomness as an Invariant for Number Representations  

Microsoft Academic Search

We show that the usual positional representations of a real number are either random, in the sense of Martin-Löf, for all bases or not so for any base. Thus, randomness is an invariant of number representations. All our proofs are constructive.

Cristian Calude; Helmut Jürgensen

1994-01-01

359

Writing about Numbers We Should Know  

NSDL National Science Digital Library

This opening assignment for an introductory quantitative reasoning course asks students to write about "Numbers We Should Know." Its goal is to help students begin to think quantitatively, evaluate the sources of quantitative information critically, and write using numbers precisely and thoughtfully.

Neil Lutsky

360

An invitation to additive prime number theory  

Microsoft Academic Search

The main purpose of this survey is to introduce an inexperienced reader to additive prime number theory and some related branches of analytic number theory. We state the main problems in the field, sketch their history and the basic machinery used to study them, and try to give a representative sample of the directions of current research.

A. V. Kumchev; D. I. Tolev

2004-01-01

361

Watersheds - Rounding of Numbers in Work Plans  

Microsoft Academic Search

This Technical Note provides a guide for rounding numbers used in the agreement, narrative and tables of Watershed Work Plans and River Basin Reports. Rounded numbers improve appearance and creditability, and reduces errors and conflicts. Ideas presented herein and in the attachments can serve as a guide. However, they will not rule out the necessity for prudent judgment in each

John T. Lewis; W. Richard Folsche; O. Wesley Hofstad; David Buland

1970-01-01

362

Smoothing ``Smooth'' Numbers John B. Friedlander *  

E-print Network

Smoothing ``Smooth'' Numbers John B. Friedlander * Scarborough College, University of Toronto. Partially supported by the NSF. #12; Smoothing ``Smooth'' Numbers John B. Friedlander and Andrew Granville is especially frustrating in view of the fact that there is a trivial argument (Friedlander and Lagarias, 1987

Bernstein, Daniel

363

New String Theories And Their Generation Number  

E-print Network

New heterotic string theories in four dimensions are constructed by tensoring a nonstandard SCFT along with some minimal SCFT's. All such theories are identified and their particle generation number is found. We prove that from the infinite number of new heterotic string theories only the {6} theory predicts three generations as seen in nature which makes it an interesting candidate for further study.

Arel Genish; Doron Gepner

2014-04-30

364

Good Morning, Numbers Day: Motivating for Mathematics  

ERIC Educational Resources Information Center

The aversion that many girls and boys experience towards mathematics has been one of the author's major concerns since he started teaching. In this article, he describes a project called "Numbers Day" that was designed to improve students' attitudes toward mathematics. There are many features of Numbers Day that teachers might incorporate into…

Ramentol, Salvador Vidal

2011-01-01

365

Lazy Computation with Exact Real Numbers  

Microsoft Academic Search

We provide a semantical framework for exact real arithmetic using linear fractional transformations on the extended real line. We present an extension of PCF with a real type which introduces an eventually breadth-first strategy for lazy evaluation of exact real numbers. In this language, we present the constant (pif), overcomes the problem of undecidability of comparison of real numbers in

Abbas Edalat; Peter John Potts; Philipp Sünderhauf

1998-01-01

366

GENERAL CHEMISTRY TEXTBOOK LIST ISBN Number  

E-print Network

FALL 2013 GENERAL CHEMISTRY TEXTBOOK LIST Course Number ISBN Number Title of Text and/or Material 12901 Lab Manual Fall 2012 Dept. of CHM Hayden-McNeil Revised 8/12/13 #12;FALL 2013 GENERAL CHEMISTRY Edition Author Publishers 11100 978-1-2591-9687-4 Introduction to Chemistry, 3rd ed. (packaged w

Jiang, Wen

367

Astronomy Basics Large and Small Numbers  

E-print Network

and 10 have exponents of 0 because 100=1. #12;Significant Figures 1.234 x 106 = 12.34 x 105 = 0.1234 x is preferred). The significant figures are the number of digits in the mantissa. This number (1.234 x 106 ) has 4 significant figures. For most purposes in this course, 2 or 3 significant figures suffice. #12

Walter, Frederick M.

368

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

369

Appendix 36 Number of KEFs by Biome  

E-print Network

Appendix 36 Number of KEFs by Biome Table 1. The number of Key Ecological Functions performed by the biomes pertinent to Sub basin planning Select Key Ecological Functions Eastside (Interior) Grasslands.1.2.1.3) freshwater or marine zooplankton 2 2 3 3 2 2 14 #12;Select Key Ecological Functions Eastside (Interior

370

Micelle aggregation numbers from colligative properties  

Microsoft Academic Search

An equilibrium model has been developed to derive micelle aggregation numbers n from colligative properties of surfactant solutions, with special regard to freezing point depression. The introduction of a mass action approach in the solute activity equation allows to get aggregation numbers close to those obtained from light scattering. The model can be applied with small formal changes to ionic

C. La Mesa

1990-01-01

371

Social Security Numbers Fermilab's International Services Office  

E-print Network

, such as banks, or to buy a car or house, or to get U.S. credit cards. To access certain state benefits are sure you have ever APPLIED or RECEIVED a Social Security Card or Social Security Number before SocialSocial Security Numbers Fermilab's International Services Office August 2011 #12;What is a Social

Quigg, Chris

372

Equal Opportunities Monitoring Job reference number  

E-print Network

Equal Opportunities Monitoring Name: Job reference number: (if applicable) Post applied for: Pay Number: (for internal candidates only): The Authority is committed to provide equal opportunity to any the effectiveness of our Equal Opportunities Policy please provide the following information. We have asked for your

373

Normal Numbers and Pseudorandom David H. Bailey  

E-print Network

Normal Numbers and Pseudorandom Generators David H. Bailey Jonathan M. Borwein December 4, 2011 Abstract For an integer b 2 a real number is b-normal if, for all m > 0, every m-long string of digits] are b-normal for every b, it has been rather difficult to exhibit explicit examples. No results

Bailey, David H.

374

FPGA Vendor Agnostic True Random Number Generator  

Microsoft Academic Search

This paper describes a solution for the generation of true random numbers in a purely digital fashion; making it suit- able for any FPGA type, because no FPGA vendor spe- cic features (e.g., like phase-locked loop) or external ana- log components are required. Our solution is based on a framework for a provable secure true random number gen- erator recently

Dries Schellekens; Bart Preneel; Ingrid Verbauwhede

2006-01-01

375

Estimating Avogadro's number from skylight and airlight  

NASA Astrophysics Data System (ADS)

Naked-eye determinations of the visual range yield order-of-magnitude estimates of Avogadro's number, using an argument of Rayleigh. Alternatively, by looking through a cardboard tube, we can compare airlight and skylight and give another estimate of this number using the law of atmospheres.

Pesic, Peter

2005-01-01

376

Visuospatial priming of the mental number line.  

PubMed

It has been argued that numbers are spatially organized along a "mental number line" that facilitates left-hand responses to small numbers, and right-hand responses to large numbers. We hypothesized that whenever the representations of visual and numerical space are concurrently activated, interactions can occur between them, before response selection. A spatial prime is processed faster than a numerical target, and consistent with our hypothesis, we found that such a spatial prime affects non-spatial, verbal responses more when the prime follows a numerical target (backward priming) then when it precedes it (forward priming). This finding emerged both in a number-comparison and a parity judgment task, and cannot be ascribed to a "Spatial-Numerical Association of Response Codes" (SNARC). Contrary to some earlier claims, we therefore conclude that visuospatial-numerical interactions do occur, even before response selection. PMID:17555739

Stoianov, Ivilin; Kramer, Peter; Umiltà, Carlo; Zorzi, Marco

2008-02-01

377

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

378

Relativistic theory of surficial Love numbers  

E-print Network

A relativistic theory of surficial Love numbers, which characterize the surface deformation of a body subjected to tidal forces, was initiated by Damour and Nagar. We revisit this effort in order to extend it, clarify some of its aspects, and simplify its computational implementation. First, we refine the definition of surficial Love numbers proposed by Damour and Nagar, and formulate it directly in terms of the deformed curvature of the body's surface, a meaningful geometrical quantity. Second, we develop a unified theory of surficial Love numbers that applies equally well to material bodies and black holes. Third, we derive a compactness-dependent relation between the surficial and (electric-type) gravitational Love numbers of a perfect-fluid body, and show that it reduces to the familiar Newtonian relation when the compactness is small. And fourth, we simplify the tasks associated with the practical computation of the surficial and gravitational Love numbers for a material body.

Philippe Landry; Eric Poisson

2014-04-27

379

Generating functions for weighted Hurwitz numbers  

E-print Network

Double Hurwitz numbers enumerating weighted $n$-sheeted branched coverings of the Riemann sphere or, equivalently, weighted paths in the Cayley graph of $S_n$ generated by transpositions are determined by an associated weight generating function. A uniquely determined $1$-parameter family of 2D Toda $\\tau$-functions of hypergeometric type is shown to consist of generating functions for such weighted Hurwitz numbers. Four classical cases are detailed, in which the weighting is uniform: Okounkov's double Hurwitz numbers, for which the ramification is simple at all but two specified branch points; the case of Belyi curves, with three branch points, two with specified profiles; the general case, with a specified number of branch points, two with fixed profiles, the rest constrained only by the genus; and the signed enumeration case, with sign determined by the parity of the number of branch points. Using the exponentiated quantum dilogarithm function as weight generator, three new types of weighted enumerations are introduced. These determine {\\em quantum} Hurwitz numbers depending on a deformation parameter $q$. By suitable interpretation of $q$, the statistical mechanics of quantum weighted branched covers may be related to that of Bosonic gases. The standard double Hurwitz numbers are recovered in the classical limit.

Mathieu Guay-Paquet; J. Harnad

2015-01-23

380

Skyrmions up to baryon number 108  

NASA Astrophysics Data System (ADS)

The Skyrme crystal is built up of repeating units similar to the cubic Skyrmion of baryon number 4. Using this as a guide, we construct new Skyrmion solutions in the massive-pion case, with various baryon numbers up to 108. Most of our solutions resemble chunks of the Skyrme crystal. They are constructed using a multilayer version of the rational map ansatz to create initial configurations, which are then relaxed numerically to find the energy minima. The coefficients of the rational maps are found by a geometrical construction related to the Skyrme crystal structure. We find some further solutions by numerical relaxation of clusters composed of baryon number 4 Skyrmions.

Feist, D. T. J.; Lau, P. H. C.; Manton, N. S.

2013-04-01

381

An Introduction to the Theory of Numbers  

NSDL National Science Digital Library

Written by Leo Moser and presented by the Trillia Group, this virtual text introduces visitors to the theory of numbers. After agreeing to the terms and conditions of use, users will be able to download the full document as an 87-page pdf file in either large or regular print. The chapters include: "Compositions and Partitions," "Irrational Numbers," "Diophantine Equations," and "Geometry of Numbers." The terms limit this free download to students in mathematic self-study or for instructors to consider this text for use in their classrooms.

Moser, Leo

2007-12-03

382

Critical points and number of master integrals  

NASA Astrophysics Data System (ADS)

We consider the question about the number of master integrals for a multiloop Feynman diagram. We show that, for a given set of denominators, this number is totally determined by the critical points of the polynomials entering either of the two representations: the parametric representation and the Baikov representation. In particular, for the parametric representation the corresponding polynomial is just the sum of Symanzik polynomials. The relevant topological invariant is the sum of the Milnor numbers of the proper critical points. We present a Mathematica package Mint to automatize the counting of the master integrals for the typical case, when all critical points are isolated.

Lee, Roman N.; Pomeransky, Andrei A.

2013-11-01

383

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

384

Nontopological Finite Temperature Induced Fermion Number  

E-print Network

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 temperature induced fermion number is temperature dependent but topological.

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

2001-02-20

385

47 CFR 52.111 - Toll free number assignment.  

Code of Federal Regulations, 2010 CFR

... 2010-10-01 2010-10-01 false Toll free number assignment. 52.111 Section 52.111...CARRIER SERVICES (CONTINUED) NUMBERING Toll Free Numbers § 52.111 Toll free number assignment. Toll free numbers...

2010-10-01

386

47 CFR 52.111 - Toll free number assignment.  

Code of Federal Regulations, 2012 CFR

... 2012-10-01 2012-10-01 false Toll free number assignment. 52.111 Section 52.111...CARRIER SERVICES (CONTINUED) NUMBERING Toll Free Numbers § 52.111 Toll free number assignment. Toll free numbers...

2012-10-01

387

47 CFR 52.111 - Toll free number assignment.  

Code of Federal Regulations, 2011 CFR

... 2011-10-01 2011-10-01 false Toll free number assignment. 52.111 Section 52.111...CARRIER SERVICES (CONTINUED) NUMBERING Toll Free Numbers § 52.111 Toll free number assignment. Toll free numbers...

2011-10-01

388

47 CFR 52.111 - Toll free number assignment.  

Code of Federal Regulations, 2013 CFR

... 2013-10-01 2013-10-01 false Toll free number assignment. 52.111 Section 52.111...CARRIER SERVICES (CONTINUED) NUMBERING Toll Free Numbers § 52.111 Toll free number assignment. Toll free numbers...

2013-10-01

389

33 CFR 62.43 - Numbers and letters.  

Code of Federal Regulations, 2011 CFR

...aids bearing even numbers and green aids bearing odd numbers. The numbers...sidemarks are numbered. However, aids other than those mentioned above...addition to numbers to identify the first aid to navigation in a waterway, or...

2011-07-01

390

33 CFR 62.43 - Numbers and letters.  

Code of Federal Regulations, 2010 CFR

...aids bearing even numbers and green aids bearing odd numbers. The numbers...sidemarks are numbered. However, aids other than those mentioned above...addition to numbers to identify the first aid to navigation in a waterway, or...

2010-07-01

391

47 CFR 52.111 - Toll free number assignment.  

Code of Federal Regulations, 2014 CFR

... 2014-10-01 2014-10-01 false Toll free number assignment. 52.111 Section 52.111...CARRIER SERVICES (CONTINUED) NUMBERING Toll Free Numbers § 52.111 Toll free number assignment. Toll free numbers...

2014-10-01

392

46 CFR 50.10-30 - Coast Guard number.  

Code of Federal Regulations, 2011 CFR

... Coast Guard number. (a) The Coast Guard number means that number assigned...tests and inspections. (b) The Coast Guard number shall be stamped on the...and pressure vessels. (c) The Coast Guard number is comprised of the...

2011-10-01

393

46 CFR 50.10-30 - Coast Guard number.  

Code of Federal Regulations, 2012 CFR

... Coast Guard number. (a) The Coast Guard number means that number assigned...tests and inspections. (b) The Coast Guard number shall be stamped on the...and pressure vessels. (c) The Coast Guard number is comprised of the...

2012-10-01

394

46 CFR 50.10-30 - Coast Guard number.  

Code of Federal Regulations, 2010 CFR

... Coast Guard number. (a) The Coast Guard number means that number assigned...tests and inspections. (b) The Coast Guard number shall be stamped on the...and pressure vessels. (c) The Coast Guard number is comprised of the...

2010-10-01

395

46 CFR 50.10-30 - Coast Guard number.  

Code of Federal Regulations, 2013 CFR

... Coast Guard number. (a) The Coast Guard number means that number assigned...tests and inspections. (b) The Coast Guard number shall be stamped on the...and pressure vessels. (c) The Coast Guard number is comprised of the...

2013-10-01

396

Department of Defense Worldwide Numbers for TBI  

MedlinePLUS

... and injury severity. The numbers are updated each quarter. Information posted here is collected from electronic medical ... updated previously reported data since the last reporting quarter. Refer to “Updates to Previously Reported Data” below. ** ...

397

Decay of Turbulence at High Reynolds Numbers  

NASA Astrophysics Data System (ADS)

Turbulent motions in a fluid decay at a certain rate once stirring has stopped. The role of the most basic parameter in fluid mechanics, the Reynolds number, in setting the decay rate is not generally known. This Letter concerns the high-Reynolds-number limit of the process. In a classical grid-turbulence wind-tunnel experiment that both reaches higher Reynolds numbers than ever before and covers a wide range of them (1 04number independent, which contradicts some models and supports others.

Sinhuber, Michael; Bodenschatz, Eberhard; Bewley, Gregory P.

2015-01-01

398

Simple continued fractions for some irrational numbers  

Microsoft Academic Search

Abstract: It is proved that the simple continued fractions for the irrational numbers denedand related quantities are predictable, that is, have a denite pattern. The proof usesonly elementary properties of continued fractions. The nature of the partial quotientsis discussed.1

Jeffrey Shallit

1979-01-01

399

User's Guide Part Number 34401-90004  

E-print Network

. Its combination of bench-top and system features makes this multimeter a versatile solution for your: Unless otherwise indicated, this manual applies to all Serial Numbers. #12;The Front Panel at a Glance 1

King, Roger

400

The Binary Representation of Rational Numbers.  

ERIC Educational Resources Information Center

Presented are the mathematical explanation of the algorithm for representing rational numbers in base two, paper-and-pencil methods for producing the representation, some patterns in these representations, and pseudocode for computer programs to explore these patterns. (MNS)

Schmalz, Rosemary

1987-01-01

401

Getting Help: Know the Numbers (For Parents)  

MedlinePLUS

... What to Expect Ebola: What to Know Getting Help: Know the Numbers KidsHealth > Parents > First Aid & Safety > ... country. Continue Teaching Kids How to Call for Help Even very young children can be taught how ...

402

The Gauss-Dirichlet Orbit Number  

E-print Network

Dirichlet computed in some particular cases the number of equivalence classes of representations of a nonzero integer by a representative system for the integral binary quadratic forms of a given discriminant. We complete this computation.

Pierre-Yves Gaillard

2008-09-20

403

Applicant Information B Number: Email: Phone  

E-print Network

Applicant Information B Number: Email: Phone: Last Name: First Name M.I.: Date Available: Expected earned: References (Please list three professional references) Full Name: Relationship: Company: Phone: Full Name: Relationship: Company: Phone: Full Name: Relationship: Company: Phone: Previous Employment

Suzuki, Masatsugu

404

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

405

LAB SAFETY MANUAL Phone Numbers ..............................................................................................5  

E-print Network

.............................................................................................88 Example of Safety Data Sheet (SDS) ­ Formerly Material Safety Data Sheets (MSDS) Appendix 3 Example........................................................................26 GHS Safety Data Sheets..............................................................27 IV1 LAB SAFETY MANUAL Phone Numbers

406

Elastic tail propulsion at low Reynolds number  

E-print Network

A simple way to generate propulsion at low Reynolds number is to periodically oscillate a passive flexible filament. Here we present a macroscopic experimental investigation of such a propulsive mechanism. A robotic swimmer ...

Yu, Tony S. (Tony Sheung)

2007-01-01

407

Decay of turbulence at high reynolds numbers.  

PubMed

Turbulent motions in a fluid decay at a certain rate once stirring has stopped. The role of the most basic parameter in fluid mechanics, the Reynolds number, in setting the decay rate is not generally known. This Letter concerns the high-Reynolds-number limit of the process. In a classical grid-turbulence wind-tunnel experiment that both reaches higher Reynolds numbers than ever before and covers a wide range of them (10^{4}number independent, which contradicts some models and supports others. PMID:25659002

Sinhuber, Michael; Bodenschatz, Eberhard; Bewley, Gregory P

2015-01-23

408

Chaotic behaviour of high Mach number flows  

NASA Technical Reports Server (NTRS)

The stability of the super-Alfvenic flow of a two-fluid plasma model with respect to the Mach number and the angle between the flow direction and the magnetic field is investigated. It is found that, in general, a large scale chaotic region develops around the initial equilibrium of the laminar flow when the Mach number exceeds a certain threshold value. After reaching a maximum the size of this region begins shrinking and goes to zero as the Mach number tends to infinity. As a result high Mach number flows in time independent astrophysical plasmas may lead to the formation of 'quasi-shocks' in the presence of little or no dissipation.

Varvoglis, H.; Ghosh, S.

1985-01-01

409

Ideal photon number amplifier and duplicator  

NASA Technical Reports Server (NTRS)

The photon number-amplification and number-duplication mechanism are analyzed in the ideal case. The search for unitary evolutions leads to consider also a number-deamplification mechanism, the symmetry between amplification and deamplification being broken by the integer-value nature of the number operator. Both transformations, amplification and duplication, need an auxiliary field which, in the case of amplification, turns out to be amplified in the inverse way. Input-output energy conservation is accounted for using a classical pump or through frequency-conversion of the fields. Ignoring one of the fields is equivalent to considering the amplifier as an open system involving entropy production. The Hamiltonians of the ideal devices are given and compared with those of realistic systems.

Dariano, G. M.

1992-01-01

410

Entropy of pseudo-random-number generators  

NASA Astrophysics Data System (ADS)

Since the work of

Ferrenberg et al. [Phys. Rev. Lett. 69, 3382 (1992)
] some pseudo-random-number generators are known to yield wrong results in cluster Monte Carlo simulations. In this contribution the fundamental mechanism behind this failure is discussed. Almost all random-number generators calculate a new pseudo-random-number xi from preceding values, xi =f( xi-1 , xi-2 ,…, xi-q ) . Failure of these generators in cluster Monte Carlo simulations and related experiments can be attributed to the low entropy of the production rule f() conditioned on the statistics of the input values xi-1 ,…, xi-q . Being a measure only of the arithmetic operations in the generator rule, the conditional entropy is independent of the lag in the recurrence or the period of the sequence. In that sense it measures a more profound quality of a random-number generator than empirical tests with their limited horizon.

Mertens, Stephan; Bauke, Heiko

2004-05-01

411

Five Little Ducks - Decomposing Number 5  

NSDL National Science Digital Library

This activity practices the decomposing of numbers one through five using a fuzzy stick with five yellow Pony beads on the stick. While manipulating the beads, the students will recite the poem "Five Little Ducks".

Mathis, Clara

2012-07-10

412

9 CFR 351.6 - Official number.  

Code of Federal Regulations, 2011 CFR

...CERTIFICATION CERTIFICATION OF TECHNICAL ANIMAL FATS FOR EXPORT Procedure for Obtaining Service...will assign a certified technical animal fat plant number to each plant granted service...to identify all certified technical animal fat prepared or stored by the...

2011-01-01

413

MARINE RESEARCH Volume 63, Number 6  

E-print Network

Journal of MARINE RESEARCH Volume 63, Number 6 Interfacial solitary wave run-up in the St. Lawrence Institute, Department of Fisheries and Oceans, Mont- Joli, QC, Canada, G5H 3ZA. Journal of Marine Research

Bourgault, Daniel

414

MARINE RESEARCH Volume 62, Number 1  

E-print Network

Journal of MARINE RESEARCH Volume 62, Number 1 Predictability of Lagrangian particle trajectories, University of Southern California, Los Angeles, California, 90089, U.S.A. Journal of Marine Research, 62, 1

Ozgökmen, Tamay M.

415

MARINE RESEARCH Volume 62, Number 6  

E-print Network

Journal of MARINE RESEARCH Volume 62, Number 6 Diffusivity and viscosity dependence in the linear. email: jlacasce@met.no Journal of Marine Research, 62, 743­769, 2004 743 #12;scales and parameterize

LaCasce, Joseph H.

416

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

417

21 CFR 207.35 - Notification of registrant; drug establishment registration number and drug listing number.  

Code of Federal Regulations, 2012 CFR

21 Food and Drugs 4 2012-04-01 2012-04-01 false Notification of registrant; drug establishment registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION,...

2012-04-01

418

21 CFR 207.35 - Notification of registrant; drug establishment registration number and drug listing number.  

Code of Federal Regulations, 2011 CFR

21 Food and Drugs 4 2011-04-01 2011-04-01 false Notification of registrant; drug establishment registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION,...

2011-04-01

419

21 CFR 207.35 - Notification of registrant; drug establishment registration number and drug listing number.  

Code of Federal Regulations, 2010 CFR

21 Food and Drugs 4 2010-04-01 2010-04-01 false Notification of registrant; drug establishment registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION,...

2010-04-01

420

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

421

21 CFR 207.35 - Notification of registrant; drug establishment registration number and drug listing number.  

Code of Federal Regulations, 2014 CFR

21 Food and Drugs 4 2014-04-01 2014-04-01 false Notification of registrant; drug establishment registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION,...

2014-04-01

422

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

Federal Register 2010, 2011, 2012, 2013, 2014

...COMMISSION 47 CFR Part 52 [WC Docket No. 07-244; CC Docket No. 95-116; DA 11-1954] Local Number Portability Porting Interval and Validation Requirements; Telephone Number Portability AGENCY: Federal Communications Commission. ACTION: Proposed...

2011-12-22

423

Lower Bounds for Measurable Chromatic Numbers  

Microsoft Academic Search

The Lovász theta function provides a lower bound for the chromatic number of finite graphs based on the solution of a semidefinite\\u000a program. In this paper we generalize it so that it gives a lower bound for the measurable chromatic number of distance graphs\\u000a on compact metric spaces.\\u000a \\u000a In particular we consider distance graphs on the unit sphere. There we

Christine Bachoc; Gabriele Nebe; FERNANDO M ´ ARIO DE OLIVEIRA FILHO; Frank Vallentin

2009-01-01

424

Fibonacci numbers in phyllotaxis : a simple model  

E-print Network

A simple model is presented which explains the occurrence of high order Fibonacci number parastichies in asteracae flowers by two distinct steps. First low order parastichies result from the fact that a new floret, at its appearance is repelled by two former ones, then, in order to accommodate for the increase of the radius, parastichies numbers have to evolve and can do it only by applying the Fibonacci recurrence formula.

Gilbert Zalczer

2012-03-28

425

On the Fibonacci k-numbers  

Microsoft Academic Search

We introduce a general Fibonacci sequence that generalizes, between others, both the classic Fibonacci sequence and the Pell sequence. These general kth Fibonacci numbers {Fk,n}n=0? were found by studying the recursive application of two geometrical transformations used in the well-known four-triangle longest-edge (4TLE) partition. Many properties of these numbers are deduce directly from elementary matrix algebra.

Sergio Falcón; Ángel Plaza

2007-01-01

426

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 increasing order, beginning with the least. 2400 \\ 4002 \\ 2040 \\ 420 \\ 2004 Arrange these numbers in decreasing order, beginni...

2012-05-01

427

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

428

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

429

Predicting apparent Sherwood numbers for fluidized beds  

SciTech Connect

Mass transfer data of bubbling fluidized beds have been reevaluated with a new model which is completely predictive. The model is based on a two-phase approach with active bypass, formally plug flow for the suspension gas and a consideration of backmixing in the main kinetic coefficient, i.e. in the apparent particle-to-fluid Sherwood number. A good agreement with experimental results of various authors with a broad range of Reynolds numbers and particle diameters is demonstrated.

Groenewold, H.; Tsotsas, E.

1999-09-01

430

Packing numbers of rational ruled 4-manifolds  

Microsoft Academic Search

We completely solve the symplectic packing problem with equally sized balls for any rational, ruled, symplectic 4-manifolds. We give explicit formulae for the packing numbers, the generalized Gromov widths, the stability numbers, and the corresponding obstructing exceptional classes. As a corollary, we give explicit values for when an ellipsoid of type $E(a, b)$, with $\\\\frac{b}{a} \\\\in \\\\N$, embeds in a

Olguta Buse; Martin Pinsonnault

2011-01-01

431

The prime number periodical cicada problem  

Microsoft Academic Search

Mathematical models are presented to argue for the signiflcance of prime number emergences of 13 year and 17 year periodical cicadas (Magi- cicada spp.). The prime number values arise as resonances of emergences with 2 and 3 year quasi-cycling predators. Predators with 2 and 3 year quasi-cycles are present due to their age dependent fecundity and mortality rates. Their quasi-cycles

G. F. Webb

2001-01-01

432

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

433

Effective condition number for finite difference method  

Microsoft Academic Search

For solving the linear algebraic equations Ax=b with the symmetric and positive definite matrix A, from elliptic equations, the traditional condition number in the 2-norm is defined by Cond.=?1\\/?n, where ?1 and ?n are the maximal and minimal eigenvalues of the matrix A, respectively. The condition number is used to provide the bounds of the relative errors from the perturbation

Zi-Cai Li; Cheng-Sheng Chien; Hung-Tsai Huang

2007-01-01

434

Of Colored Numbers and Numbered Colors: Interactive Processes in Grapheme-Color Synesthesia  

Microsoft Academic Search

Grapheme-color synesthetes experience a specific color when they see a grapheme but they do not report to perceive a grapheme when a color is presented. In this study, we investigate whether color can still evoke number-processes even when a vivid number experience is absent. We used color-number and number-color priming, both revealing faster responses in congruent compared to incongruent conditions.

Titia Gebuis; Tanja C. W. Nijboer; Maarten J. van der Smagt

2009-01-01

435

Mechanisms of Chromosome Number Evolution in Yeast  

PubMed Central

The whole-genome duplication (WGD) that occurred during yeast evolution changed the basal number of chromosomes from 8 to 16. However, the number of chromosomes in post-WGD species now ranges between 10 and 16, and the number in non-WGD species (Zygosaccharomyces, Kluyveromyces, Lachancea, and Ashbya) ranges between 6 and 8. To study the mechanism by which chromosome number changes, we traced the ancestry of centromeres and telomeres in each species. We observe only two mechanisms by which the number of chromosomes has decreased, as indicated by the loss of a centromere. The most frequent mechanism, seen 8 times, is telomere-to-telomere fusion between two chromosomes with the concomitant death of one centromere. The other mechanism, seen once, involves the breakage of a chromosome at its centromere, followed by the fusion of the two arms to the telomeres of two other chromosomes. The only mechanism by which chromosome number has increased in these species is WGD. Translocations and inversions have cycled telomere locations, internalizing some previously telomeric genes and creating novel telomeric locations. Comparison of centromere structures shows that the length of the CDEII region is variable between species but uniform within species. We trace the complete rearrangement history of the Lachancea kluyveri genome since its common ancestor with Saccharomyces and propose that its exceptionally low level of rearrangement is a consequence of the loss of the non-homologous end joining (NHEJ) DNA repair pathway in this species. PMID:21811419

Gordon, Jonathan L.; Byrne, Kevin P.; Wolfe, Kenneth H.

2011-01-01

436

Increased BRAF copy number in lung adenocarcinoma  

PubMed Central

Point mutation of the BRAF gene is a genetic event that occurs in a subset of lung adenocarcinoma cases. For example, BRAF V600E is a driver mutation that can be effectively targeted using selective BRAF and/or MEK inhibitors. The present study hypothesized that an increase in BRAF copy number may be correlated with certain clinicopathological features of lung adenocarcinoma in Japanese patients. The BRAF gene copy number was analyzed using quantitative polymerase chain reaction amplifications in 29 surgically treated lung adenocarcinoma cases without EGFR or Kras mutations from Nagoya City University Hospital (Nagoya, Japan). Seven BRAF-mutant cases were included. Increased BRAF gene copy number was identified in three lung adenocarcinoma patients (10.3%), all of which exhibited the V600E mutation. Using fluorescence in situ hybridization with BRAF-specific and chromosome 7 centromeric probes, increased copy number status was associated with gene amplification or gain of chromosome 7. Although increased BRAF copy number was correlated with BRAF V600E mutations, numerical changes in BRAF copy number were rare and mild in lung adenocarcinoma, resulting in no significant difference in pathological tumor status or tumor stage.

SASAKI, HIDEFUMI; MAEKAWA, MASAHIKO; TATEMATSU, TSUTOMU; OKUDA, KATSUHIRO; MORIYAMA, SATORU; YANO, MOTOKI; FUJII, YOSHITAKA

2015-01-01

437

Chromosome number evolution in skippers (Lepidoptera, Hesperiidae)  

PubMed Central

Abstract Lepidoptera (butterflies and moths), as many other groups of animals and plants, simultaneously represent preservation of ancestral karyotype in the majority of families with a high degree of chromosome number instability in numerous independently evolved phylogenetic lineages. However, the pattern and trends of karyotype evolution in some Lepidoptera families are poorly studied. Here I provide a survey of chromosome numbers in skippers (family Hesperiidae) based on intensive search and analysis of published data. I demonstrate that the majority of skippers preserve the haploid chromosome number n=31 that seems to be an ancestral number for the Hesperiidae and the order Lepidoptera at whole. However, in the tribe Baorini the derived number n=16 is the most typical state which can be used as a (syn)apomorphic character in further phylogenetic investigations. Several groups of skippers display extreme chromosome number variations on within-species (e.g. the representatives of the genus Carcharodus Hübner, [1819]) and between-species (e.g. the genus Agathymus Freeman, 1959) levels. Thus, these groups can be used as model systems for future analysis of the phenomenon of chromosome instability. Interspecific chromosomal differences are also shown to be useful for discovering and describing new cryptic species of Hesperiidae representing in such a way a powerful tool in biodiversity research. Generally, the skipper butterflies promise to be an exciting group that will significantly contribute to the growing knowledge of patterns and processes of chromosome evolution. PMID:25610542

Lukhtanov, Vladimir A.

2014-01-01

438

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. PMID:20018695

Phillips, Rob; Milo, Ron

2009-01-01

439

The concrete theory of numbers : Problem of simplicity of Fermat number-twins  

E-print Network

The problem of simplicity of Fermat number-twins $f_{n}^{\\pm}=2^{2^n}\\pm3$ is studied. The question for what $n$ numbers $f_{n}^{\\pm}$ are composite is investigated. The factor-identities for numbers of a kind $x^2 \\pm k $ are found.

Boris V. Tarasov

2007-07-06

440

NEWSFOCUSNENEWSWSFOFOCUCUSS Cumulative number of PSI structures released Number of PSI technologies developed  

E-print Network

300 200 100 0 120 100 80 60 40 20 0 Cumulative number of PSI structures released Number of PSI-anglescattering Theoreticalmodeling Annotationandfunction DisseminationtoolsReagents PSI's History In Numbers Total per year CREDITS penicillin. Thanks to a long-running effort called the Protein Structure Initiative (PSI), Joachimiak had

Napp, Nils

441

II.2. Geometry 83 Menninger, K. 1992. Number Words and Number Symbols  

E-print Network

II.2. Geometry 83 Menninger, K. 1992. Number Words and Number Symbols: A Cultural History Zero to Infinity: What Makes Numbers Interesting. Natick, MA: A. K. Peters. II.2 Geometry Jeremy Gray 1 Introduction The modern view of geometry was inspired by the novel geometrical theories of hilbert [VI.63

Landweber, Laura

442

Fibonacci polynomials, generalized Stirling numbers, and Bernoulli, Genocchi and tangent numbers  

E-print Network

We study matrices which transform the sequence of Fibonacci or Lucas polynomials with even index to those with odd index and vice versa. They turn out to be intimately related to generalized Stirling numbers and to Bernoulli, Genocchi and tangent numbers and give rise to various identities between these numbers. There is also a close connection with the Akiyama-Tanigawa algorithm.

Cigler, Johann

2011-01-01

443

On the domination number and the 2-packing number of Fibonacci cubes and Lucas cubes  

Microsoft Academic Search

Let ?n and ?n be the n-dimensional Fibonacci cube and Lucas cube, respectively. The domination number ? of Fibonacci cubes and Lucas cubes is studied. In particular it is proved that ?(?n) is bounded below by ?Ln?2nn?3?, where Ln is the nth Lucas number. The 2-packing number ? of these cubes is also studied. It is proved that ?(?n) is

Aline Castro; Sandi Klavzar; Michel Mollard; Yoomi Rho

2011-01-01

444

PHONE / EXTENSION NUMBERS -External -4-digit phone numbers (DID -Direct Inward Dial)  

E-print Network

PHONE / EXTENSION NUMBERS - External - 4-digit phone numbers (DID - Direct Inward Dial) - 2500 - Dial 9 + telephone number - Emergency Calls - All phones are able to dial 911 or 9+911 ANSWER CALLS phone or another phone. - Both appearances can be used as a regular extension. - Place and receive calls

Olsen, Stephen L.

445

On the domination number and the 2-packing number of Fibonacci cubes and Lucas cubes  

E-print Network

On the domination number and the 2-packing number of Fibonacci cubes and Lucas cubes Aline Castro, Korea e-mail: rho@incheon.ac.kr Abstract Let n and n be the n-dimensional Fibonacci cube and Lucas cube, respectively. The domination number of Fibonacci cubes and Lucas cubes is studied. In particular it is proved

Paris-Sud XI, Université de

446

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

447

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

448

The concrete theory of numbers : Problem of simplicity of Fermat number-twins  

Microsoft Academic Search

The problem of simplicity of Fermat number-twins $f_{n}^{\\\\pm}=2^{2^n}\\\\pm3$ is studied. The question for what $n$ numbers $f_{n}^{\\\\pm}$ are composite is investigated. The factor-identities for numbers of a kind $x^2 \\\\pm k $ are found.

Boris V. Tarasov

2007-01-01

449

Department of Mathematics 1.1: Properties of Real Numbers  

E-print Network

to express the integers. (d) Rational Numbers: A rational number is any number that can be written in the form a b where a, b Z and b = 0. (The letter Q represents the set of all rational numbers) (e decimal. (f) Real Numbers: The rational and irrational numbers 2. Real Number Lines (a) There is a one

Ahmad, Sajjad

450

Neural correlates of numbers and mathematical terms.  

PubMed

Numerical processing has been demonstrated to be subserved typically by the brain regions around the bilateral intraparietal sulcus (IPS). The goal of the current study was to investigate whether the processing of mathematical terms shared the same brain regions with numerical processing. Healthy adult participants performed semantic distance judgment tasks on five types of materials, including geometric terms, algebraic terms, linguistic terms, words for tools and other common objects, and Arabic numbers. Brain activation was measured with functional magnetic resonance imaging (fMRI). The results showed that geometric terms had greater activation than algebraic terms, linguistic terms and tool words in the horizontal IPS, but algebraic terms did not have greater activation than linguistic terms and tool words in this region. Arabic numbers showed greater activation than non-number materials (including geometric terms, algebraic terms, linguistic terms and tool words) in the bilateral IPS, right inferior frontal gyrus and bilateral middle frontal gyrus, but the non-number materials showed stronger activation in the left inferior frontal gyrus and left middle temporal gyrus. These results suggest that the brain area for the processing of numbers (the left IPS) seems to be involved in semantic processing of geometric terms, but not that of other mathematical terms such as algebraic terms. Both algebraic and geometric terms share similar brain organization with basic semantic processing in the left temporal and frontal regions. PMID:22202882

Zhang, Han; Chen, Chuansheng; Zhou, Xinlin

2012-03-01

451

Language influences number processing - A quadrilingual study.  

PubMed

Reading/writing direction or number word formation influence performance even in basic numerical tasks such as magnitude comparison. However, so far the interaction of these language properties has not been evaluated systematically. In this study we tested English, German, Hebrew, and Arab participants realizing a natural 2×2 design of reading/writing direction (left-to-right vs. right-to-left) and number word formation (non-inverted vs. inverted, i.e., forty-seven vs. seven-and-forty). Symbolic number magnitude comparison was specifically influenced by the interaction of reading/writing direction and number word formation: participants from cultures where reading direction and the order of tens and units in number words are incongruent (i.e., German and Hebrew) exhibited more pronounced unit interference in place-value integration. A within-group comparison indicated that this effect was not due to differences in education. Thus, basic cultural differences in numerical cognition were driven by natural language variables and their specific combination. PMID:25497523

Moeller, Korbinian; Shaki, Samuel; Göbel, Silke M; Nuerk, Hans-Christoph

2015-03-01

452

Froude number corrections in anthropological studies.  

PubMed

The Froude number has been widely used in anthropology to adjust for size differences when comparing gait parameters or other nonmorphological locomotor variables (such as optimal walking speed or speed at gait transitions) among humans, nonhuman primates, and fossil hominins. However, the dynamic similarity hypothesis, which is the theoretical basis for Froude number corrections, was originally developed and tested at much higher taxonomic levels, for which the ranges of variation are much greater than in the intraspecific or intrageneric comparisons typical of anthropological studies. Here we present new experimental data on optimal walking speed and the mass-specific cost of transport at that speed from 19 adult humans walking on a treadmill, and evaluate the predictive power of the dynamic similarity hypothesis in this sample. Contrary to the predictions of the dynamic similarity hypothesis, we found that the mass-specific cost of transport at experimentally measured optimal walking speed and Froude number were not equal across individuals, but retained a significant correlation with body mass. Overall, the effect of lower limb length on optimal walking speed was weak. These results suggest that the Froude number may not be an effective way for anthropologists to correct for size differences across individuals, but more studies are needed. We suggest that researchers first determine whether geometric similarity characterizes their data before making inferences based on the dynamic similarity hypothesis, and then check the consistency of their results with and without Froude number corrections before drawing any firm conclusions. PMID:16485296

Steudel-Numbers, Karen; Weaver, Timothy D

2006-09-01

453

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. PMID:22558193

Núñez, Rafael; Cooperrider, Kensy; Wassmann, Jürg

2012-01-01

454

Grant Title: CHILDHOOD OBESITY PREVENTION Funding Opportunity Number: USDA-NIFA-AFRI-004156. CFDA Number(s): 10.310.  

E-print Network

Grant Title: CHILDHOOD OBESITY PREVENTION Funding Opportunity Number: USDA-NIFA-AFRI-004156. CFDA, including food environment, that influence childhood obesity and use this information to develop and obesity and promoting healthy behaviors in children and adolescents. Release and Expiration: Release Date

Farritor, Shane

455

Status of exotic-quantum-number mesons  

SciTech Connect

The search for mesons with non-quark-antiquark (exotic) quantum numbers has gone on for nearly 30 years. Currently there is experimental evidence of three isospin one states, the {pi}{sub 1}(1400), the {pi}{sub 1}(1600), and the {pi}{sub 1}(2015). For all of these states, there are questions about their identification and even if some of them exist. In this article, we will review both the theoretical work and the experimental evidence associated with these exotic quantum number states. We find that the {pi}{sub 1}(1600) could be the lightest exotic quantum number hybrid meson, but observations of other members of the nonet would be useful.

Meyer, C. A.; Van Haarlem, Y. [Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 (United States)

2010-08-15

456

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]. PMID:23213259

Tian, Ye

2012-01-01

457

A bias free true random number generator  

E-print Network

We propose a new approach to nondeterministic random number generation. In theory, the randomness originated from the uncorrelated nature of consecutive laser pulses with Poissonian photon number distribution and that of the consecutive single photon detections is used to generate random bit. In experiment, von Neumann correction method is applied to extract the final random bit. This method is proved to be bias free in randomness generation, provided that the single photon detections are mutually independent, and further, it has the advantage in generation efficiency of random bits since no postprocessing is needed. A true random number generator based on this new method is realized and its randomness is guaranteed using three batteries of statistical tests.

Wei Wei; Hong Guo

2009-05-15

458

Electron heating in superhigh Mach number shocks  

NASA Astrophysics Data System (ADS)

Fluid and MHD models, as well as direct extrapolation of the earth's bow shock measurements in the high Mach number (HMN) range to the superhigh Mach number (SHMN) range predict that the downstream electron pressure is only a negligible fraction of the Rankine-Hugoniot downstream pressure. Following Alfven, plasma physics experimental-theoretical data combined with magnetospheric observations were used to probe the physics of the SHMN shocks. It is shown that inclusion of proper plasma physics considerations in the interaction of the reflected and transmitted ions and the electrons at the 'foot' of the shock leads to the surprising result that electron heating can dominate in the SHNM range. A stationary model of the shock structure is derived and shown to be the result of extrapolation of the high Mach number shock physics wiht incorporation of collective interactions at the foot.

Papadopoulos, K.

1988-05-01

459

Editorial Strengthening Psychiatry’s Numbers  

E-print Network

Atotal of 681 students graduating from allopathic medical schools in the United States matched into psychiatry residencies in 2013 (1). This number, small as it is, represents an increase in the percentage of U.S. medical student seniors entering psychiatry. Last year, only 3.9% of U.S. seniors—616 men and women—matchedinpsychiatry programs as PGY-1 residents, whereas, this year, the figure rose a tad to 4.2 % (1). When compared with the ever-increasing numbers of people living in the U.S., that is, the base population of individuals who may be affected by neuropsychiatric diseases and behavioral conditions, this slight increase does not nearly keep pace (Table 1). Also, the number of U.S. medical students matching into psychiatry presents only a part of the whole picture: 681 U.S. medical students filled just about half of the positions

Laura Weiss Roberts; Maurice Ohayon; D. Sc, Ph.D.; John Coverdale; Eugene V. Beresin; Alan K. Louie; Glendon R. Tait; M. Sc; Richard Balon

460

Autocorrelation peaks in congruential pseudorandom number generators  

NASA Technical Reports Server (NTRS)

The complete correlation structure of several congruential pseudorandom number generators (PRNG) of the same type and small cycle length was studied to deal with the problem of congruential PRNG almost repeating themselves at intervals smaller than their cycle lengths, during simulation of bandpass filtered normal random noise. Maximum period multiplicative and mixed congruential generators were studied, with inferences drawn from examination of several tractable members of a class of random number generators, and moduli from 2 to the 5th power to 2 to the 9th power. High correlation is shown to exist in mixed and multiplicative congruential random number generators and prime moduli Lehmer generators for shifts a fraction of their cycle length. The random noise sequences in question are required when simulating electrical noise, air turbulence, or time variation of wind parameters.

Neuman, F.; Merrick, R. B.

1976-01-01

461

High Reynolds Number Thermal Stability Experiments  

NASA Technical Reports Server (NTRS)

This work represents preliminary thermal stability results for liquid hydrocarbon fuels. High Reynolds Number Thermal Stability experiments with Jet A and RP-1 resulted in a quantitative measurement of the thermal stability. Each fuel flowed through a heated capillary tube that held the outlet temperature at 290 C. An optical pyrometer measured the surface temperature of the tube at 12 locations as a function of time. The High Reynolds Number Thermal Stability number was then determined using standards published by the American Society for Testing and Materials. The results for Jet A showed lower thermal stability than similar tests conducted at another facility. The RP-1 results are the first reported using this technique. Because the temperature rise on the capillary tube during testing for the RP-1 fuels was not significant, a new standard for the testing conditions should be developed for these types of fuels.

Emens, Jessica M.; Brown, Sarah P.; Frederick Robert A., Jr.; Wood, A. John

2004-01-01

462

Large numbers hypothesis. II - Electromagnetic radiation  

NASA Astrophysics Data System (ADS)

This paper develops the theory of electromagnetic radiation in the units covariant formalism incorporating Dirac's large numbers hypothesis (LNH). A direct field-to-particle technique is used to obtain the photon propagation equation which explicitly involves the photon replication rate. This replication rate is fixed uniquely by requiring that the form of a free-photon distribution function be preserved, as required by the 2.7 K cosmic radiation. One finds that with this particular photon replication rate the units covariant formalism developed in Paper I actually predicts that the ratio of photon number to proton number in the universe varies as t to the 1/4, precisely in accord with LNH. The cosmological red-shift law is also derived and it is shown to differ considerably from the standard form of (nu)(R) - const.

Adams, P. J.

1983-05-01

463

Large numbers hypothesis. II - Electromagnetic radiation  

NASA Technical Reports Server (NTRS)

This paper develops the theory of electromagnetic radiation in the units covariant formalism incorporating Dirac's large numbers hypothesis (LNH). A direct field-to-particle technique is used to obtain the photon propagation equation which explicitly involves the photon replication rate. This replication rate is fixed uniquely by requiring that the form of a free-photon distribution function be preserved, as required by the 2.7 K cosmic radiation. One finds that with this particular photon replication rate the units covariant formalism developed in Paper I actually predicts that the ratio of photon number to proton number in the universe varies as t to the 1/4, precisely in accord with LNH. The cosmological red-shift law is also derived and it is shown to differ considerably from the standard form of (nu)(R) - const.

Adams, P. J.

1983-01-01

464

Reynolds number effects on turbulent pipe flow  

NASA Astrophysics Data System (ADS)

The scaling of the mean velocities in turbulent wall-bounded flows is fairly well understood, but the scaling of the turbulence is not. This lack of understanding, particularly at high Reynolds number, limits our ability to predict important quantities such as drag on a vehicle, heat transfer from a hot surface or the melting of the ice caps. What makes the study of turbulence very complicated (numerically and experimentally) is that it is characterized by a large range of scales and this range increases with Reynolds number. At high Reynolds number, numerical investigations become extraordinarily difficult, and all previous experiments have been compromised by inadequate instrumentation and a lack of high quality facilities. In this thesis I report a set of measurements that give new insight into the behavior of pipe flow turbulence at high Reynolds number. To obtain reliable and accurate data, the limitations in current measurement techniques were investigated and quantified. To reduce the effects of these limitations, we developed a novel nano-scale velocity sensor that can resolve scales an order of magnitude smaller than conventional sensors. This, combined with facilities that can produce extreme Reynolds numbers, allows us to study flows never before possible. The results show that the scaling of the turbulence, in a pipe, is much more similar to the scaling of the mean velocities than previously believed. This behavior only becomes evident at high Reynolds numbers, much higher than previous experiments could attain. The results also reveal fundamental differences between the scaling of the turbulence in pipes and boundary layers, two canonical flows previously believed to behave similarly.

Hultmark, Marcus

465

Optokinetic Stimulation Modulates Neglect for the Number Space: Evidence from Mental Number Interval Bisection  

PubMed Central

Behavioral, neuropsychological, and neuroimaging data support the idea that numbers are represented along a mental number line (MNL), an analogical, visuospatial representation of number magnitude. The MNL is left-to-right oriented in Western cultures, with small numbers on the left and larger numbers on the right. Left neglect patients are impaired in the mental bisection of numerical intervals, with a bias toward larger numbers that are relatively to the right on the MNL. In the present study we investigated the effects of optokinetic stimulation (OKS) – a technique inducing visuospatial attention shifts by means of activation of the optokinetic nystagmus – on number interval bisection. One patient with left neglect following right-hemisphere stroke (BG) and four control patients with right-hemisphere damage, but without neglect, performed the number interval bisection task in three conditions of OKS: static, leftward, and rightward. In the static condition, BG misbisected to the right of the true midpoint. BG misbisected to the left following leftward OKS, and again to the right of the midpoint following rightward OKS. Moreover, the variability of BG’s performance was smaller following both leftward and rightward OKS, suggesting that the attentional bias induced by OKS reduced the “indifference zone” that is thought to underlie the length effect reported in bisection tasks. We argue that shifts of visuospatial attention, induced by OKS, may affect number interval bisection, thereby revealing an interaction between the processing of the perceptual space and the processing of the number space. PMID:22363280

Priftis, Konstantinos; Pitteri, Marco; Meneghello, Francesca; Umiltà, Carlo; Zorzi, Marco

2012-01-01

466

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

467

Distributed Search for Fermat Number Divisors  

NSDL National Science Digital Library

This distributed computing project hopes to add to the list of known Fermat number divisors. After downloading the required software, anyone willing to contribute their computer's idle time can take part in the project. Users that succeed in finding a divisor will be recognized on the site. There are further resources on this Web site than just the program. For instance, the main page offers an interesting historical account of Fermat numbers and their divisors, and the math section has graphs of results that are suitable for people with a decent understanding of the subject.

2000-01-01

468

Fibonacci Numbers and the Pascal Triangle  

NSDL National Science Digital Library

Offered in English, German, and Serbian, this site is a good introduction to the mathematical concepts of Pascal's Triangle, Fibonacci numbers, and the Golden Section. Because it is operated in Yugoslavia, there are occasional grammatical errors in the English version. Nevertheless, the information presented gives a valuable account of the significance of these topics. The content of the site includes historical perspectives (with brief profiles of the mathematicians who originated the ideas) and descriptions of the arithmetic and formulas involved in each concept. The close relationship of Pascal's Triangle, Fibonacci numbers, and the Golden Section is also outlined.

Jovanovic, Rasko.

469

Number Systems: Finger Counting (Session 1)  

NSDL National Science Digital Library

In this project you will examine number systems from various cultures around the world. Session 1: First let's begin by examining how other cultures finger count. First examine Image of Ancient Chinese finger counting system. 1.What do you notice about this counting system? 2.How are the fingers used in this system? Now watch the Youtube video finger counting to 10 in Chinese. Now Learn how to finger count to 10 in Chinese. What numbers are similar to our own finger counting system? At what point ...

Nunes-Bufford, Mrs.

2008-12-01

470

Reynolds number Scaling of Streamwise Structure Functions  

NASA Astrophysics Data System (ADS)

Turbulent velocity structure functions have been measured in the Princeton Superpipe facility using hot wire anemometry. In this facility, fully-developed turbulent pipe flow is developed over a very large range of Reynolds numbers, 31 × 10^3 to 35 × 10^6 (based on average velocity and diameter). The 1/4th through 3rd order structure functions were measured over a range of Reynolds Numbers from 120 × 10^3 to 16 × 10^6. Preliminary comparisons with theory by Yakhot [1996] are encouraging.

Schmanske, M.; Yakhot, V.; Smits, A. J.

1996-11-01

471

Probing lepton number violation on three frontiers  

SciTech Connect

Neutrinoless double beta decay constitutes the main probe for lepton number violation at low energies, motivated by the expected Majorana nature of the light but massive neutrinos. On the other hand, the theoretical interpretation of the (non-)observation of this process is not straightforward as the Majorana neutrinos can destructively interfere in their contribution and many other New Physics mechanisms can additionally mediate the process. We here highlight the potential of combining neutrinoless double beta decay with searches for Tritium decay, cosmological observations and LHC physics to improve the quantitative insight into the neutrino properties and to unravel potential sources of lepton number violation.

Deppisch, Frank F. [Department of Physics and Astronomy, University College London (United Kingdom)

2013-12-30

472

Multiplicative Conservation of Baryon Number and Baryogenesis  

E-print Network

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(6) particle content, and having an extra U(1)_N gauge symmetry. Within this framework, two-loop radiative neutrino masses are also possible, together with a new form of very long-lived matter.

Ernest Ma

2007-10-04

473

Approximate resolution of hard numbering problems  

SciTech Connect

We present a new method for estimating the number of solutions of constraint satisfaction problems. We use a stochastic forward checking algorithm for drawing a sample of paths from a search tree. With this sample, we compute two values related to the number of solutions of a CSP instance. First, an unbiased estimate, second, a lower bound with an arbitrary low error probability. We will describe applications to the Boolean Satisfiability problem and the Queens problem. We shall give some experimental results for these problems.

Bailleux, O.; Chabrier, J.J. [CRID Universite de Bourgogne, Dijon (France)

1996-12-31

474

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...

475

Number fluctuation spectroscopy of motile microorganisms.  

PubMed Central

A random-walk model of motility is used to predict the dynamics of fluctuations in the number of particles in a small observation volume. The results show that number fluctuations provide a measure of the mean swimming speed as well as the persistence length. Experimental light-scattering results are presented for three strains of Escherichia coli whose motion appears random-walk in nature. For the strain with th elongest persistence length, excellent agreement is found that theoretical predictions. For the more erratic strains, however, the shape of the measured scattered light intensity correlation functions indicates the presence of a contribution due to orientational fluctuations. PMID:1096972

Schaefer, D W; Berne, B J

1975-01-01

476

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

477

Detection of Chern numbers and entanglement in topological two-species systems through subsystem winding numbers  

E-print Network

Topological invariants, such as the Chern number, characterise topological phases of matter. Here we provide a method to detect Chern numbers in systems with two distinct species of fermion, such as spins, orbitals or several atomic states. We analytically show that the Chern number can be decomposed as a sum of component specific winding numbers, which are themselves physically observable. We apply this method to two systems, the quantum spin Hall insulator and a staggered topological superconductor, and show that (spin) Chern numbers are accurately reproduced. The measurements required for constructing the component winding numbers also enable one to probe the entanglement spectrum with respect to component partitions. Our method is particularly suited to experiments with cold atoms in optical lattices where time-of-flight images can give direct access to the relevant observables.

James de Lisle; Suvabrata De; Emilio Alba; Alex Bullivant; Juan J. Garcia-Ripoll; Ville Lahtinen; Jiannis K. Pachos

2014-07-15

478

Courant Number and Mach Number Insensitive CE/SE Euler Solvers  

NASA Technical Reports Server (NTRS)

It has been known that the space-time CE/SE method can be used to obtain ID, 2D, and 3D steady and unsteady flow solutions with Mach numbers ranging from 0.0028 to 10. However, it is also known that a CE/SE solution may become overly dissipative when the Mach number is very small. As an initial attempt to remedy this weakness, new 1D Courant number and Mach number insensitive CE/SE Euler solvers are developed using several key concepts underlying the recent successful development of Courant number insensitive CE/SE schemes. Numerical results indicate that the new solvers are capable of resolving crisply a contact discontinuity embedded in a flow with the maximum Mach number = 0.01.

Chang, Sin-Chung

2005-01-01

479

COURSE DESCRIPTION Dept., Number CS 4351  

E-print Network

COURSE DESCRIPTION Dept., Number CS 4351 Selected Elective Course Title Computer Security Semester; identification and authentication; protection against external and internal threats; communication protocols: Synthesis and Evaluation: Level 3 outcomes are those in which the student can apply the material in new

Kreinovich, Vladik

480

REAL NUMBERS WITH POLYNOMIAL CONTINUED FRACTION EXPANSIONS  

E-print Network

continued fraction expan- sion does not have a predictable pattern can be expressed as polynomial continued fractions (so that the partial quotients do have a predictable pattern). For example the first continued LAUGHLIN AND NANCY J. WYSHINSKI be used to decide if a number is irrational. For example

Mc Laughlin, James

481

REAL NUMBERS WITH POLYNOMIAL CONTINUED FRACTION EXPANSIONS  

E-print Network

whose regular continued fraction expan­ sion does not have a predictable pattern can be expressed as polynomial continued fractions (so that the partial quotients do have a predictable pattern). For example Fractions. 1 #12; 2 J. MC LAUGHLIN AND NANCY J. WYSHINSKI be used to decide if a number is irrational

Mc Laughlin, James

482

CIMAS Research Associate II Position Number 047938  

E-print Network

Number: 047938 Pay Grade: 7 Department / Hospital: COOP INST FOR MARINE AND ATMOS STUDIES Pay Band Min for Marine and Atmospheric Studies (CIMAS) of the University of Miami, Rosenstiel School of Marine will assist scientists, engineers, and technicians in the evaluation of all related instruments and systems

483

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...

484

Micellar Aggregation Numbers - A Fluorescence Study  

NASA Astrophysics Data System (ADS)

This two-day laboratory experiment describes how the influence of the hydrocarbon chain length and added salt on the micellar aggregation number of ionic surfactants can be investigated by steady-state fluorescence measurements. Emphasis is put on the necessity to validate the models used to evaluate the data, and examples are given when a given model does not work. For the effect of added salt, sodium dodecylsulphate with and without added sodium chloride was investigated. Both quenchers used, i.e., dodecylpyridinium chloride (DoPyrCl) and 1,3-dicyanobenzene (DCB), yield aggregation numbers in agreement with literature values. For the effect of surfactant chain length, however, the used model failed under certain circumstances. Three alkyltrimethylammonium halides were investigated (CnTA+; n=12, 14, and 16). For the shortest one, DoPyrCl yields a good aggregation number while DCB fails due to electrostatic interactions. For the tetradecyl surfactant, DoPyrCl does not work well, as the difference between the tail-lengths of the quencher and surfactant causes problems in the determination of the amount of micelle-bound quencher. Tetradecylpyridinium chloride circumvents this problem and a consistent aggregation number is obtained. Finally, for the longest surfactant, not even a quencher with a tail of equal length of the surfactant's worked out well, due to the slow diffusion of the quencher in the micellar aggregate.

van Stam, Jan; Depaemelaere, Sigrid; de Schryver, Frans C.

1998-01-01

485

University Admissions. Policy Note. Number 3  

ERIC Educational Resources Information Center

University admissions, like many other aspects of the higher education sector, are going through a time of significant change. From 2012, universities will receive full funding under the Commonwealth Grants Scheme (CGS) for as many places as they offer. Previously, the Government limited the number of funded places, with a tolerance band for…

Group of Eight (NJ1), 2012

2012-01-01

486

RIKENRESEARCH FEBRUARY2014 VOLUME 9 NUMBER 2  

E-print Network

focused laser beam can generate high-energy radiation and accelerate particles up to gigaelectron- volt in a number of different directions: high-energy photonics, quantum metrology, nanophotonics and terahertz photonics. The earliest lasers emitted photons with the energy of about 1 electronvolt, but today a strongly

Fukai, Tomoki

487

Number Line Tightrope-Pursue the Patterns  

NSDL National Science Digital Library

This page introduces the tightrope which allows learners to explore families of numbers in the range -10 to 100. A link is provided to a guide that explains the family symbols used, and another link provides information about the families and questions about extending the set beyond 100.

2009-06-14

488

How Do Students Misunderstand Number Representations?  

ERIC Educational Resources Information Center

We used both student interviews and diagnostic testing to reveal students' misconceptions about number representations in computing systems. This article reveals that students who have passed an undergraduate level computer organization course still possess surprising misconceptions about positional notations, two's complement representation, and…

Herman, Geoffrey L.; Zilles, Craig; Loui, Michael C.

2011-01-01

489

Policy Title: Policy Number: Real Estate  

E-print Network

Policy Title: Policy Number: Real Estate Transactions and Management 2.3.4 Category: Financial(s): Planning + Design + Construction University of Cincinnati Real Estate Transactions and Management Policy aspects of real estate transactions and management, including the delegation of responsibility for all

Papautsky, Ian

490

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

491

Very high Mach number shocks: theory  

SciTech Connect

The theory and simulation of collisionless perpendicular supercritical shock structure is reviewed, with major emphasis on recent research results. The primary tool of investigation is the hybrid simulation method, in which the Newtonian orbits of a large number of ion macroparticles are followed numerically, and in which the electrons are treated as a charge neutralizing fluid. The principal results to be presented are (1) electron resistivity is not required to explain the observed quasi-stationarity of the earth's bow shock, (2) the structure of the perpendicular shock at very high Mach numbers (M/sub A/ approx. = 15 - 20 and ..beta.. approx. = 1, where M/sub A/ is the Alfven Mach number of the shock and ..beta.. is the ratio of the thermal to magnetic pressure) depends sensitively on the upstream ..beta.. and electron resistivity, (3) two-dimensional turbulence will become increasingly important as the Mach number is increased, and (4) non-adiabatic bulk electron heating will result when a thermal electron cannot complete a gyro-orbit while transiting the shock. 32 refs., 13 figs.

Quest, K.B.

1986-01-01

492

ISSN 0962-8436 number 1539  

E-print Network

ISSN 0962-8436 volume 365 number 1539 pages 345­543 Darwin and the evolution of flowers Papers, Toronto, Ontario M5S 3B2, Canada Charles Darwin studied floral biology for over 40 years and wrote three research on floral function and the evolution of mating systems. Here I review Darwin's seminal

Barrett, C.H.

493

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

494

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

495

Plant Ecology VOLUME 5, NUMBER 1,  

E-print Network

of species in a larger sample (multinomial model), a larger area (Poisson model) or a larger number species accumulation curve for empirical examples. We provide new, unconditional variance estimators of species counted in a biodiversity study is a key metric but is usually a biased underestimate of total

Gotelli, Nicholas J.

496

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

497

Chinese Number Words, Culture, and Mathematics Learning  

ERIC Educational Resources Information Center

This review evaluates the role of language--specifically, the Chinese-based system of number words and the simplicity of Chinese mathematical terms--in explaining the relatively superior performance of Chinese and other East Asian students in cross-national studies of mathematics achievement. Relevant research is critically reviewed focusing on…

Ng, Sharon Sui Ngan; Rao, Nirmala

2010-01-01

498

WASHINGTON UNIVERSITY SUBJECT INITIALS________ DERMATOLOGY SUBJECT NUMBER________  

E-print Network

________ CHRONIC ITCH BIOBANK PATIENT QUESTIONNAIRE 2 of 4 Do you have kidney disease? No Yes - If yes, do you receive or have you ever received dialysis? No Yes Do you suffer from liver disease? No Yes - If yes, whatWASHINGTON UNIVERSITY SUBJECT INITIALS________ DERMATOLOGY SUBJECT NUMBER________ CHRONIC ITCH

Gereau, Robert W. IV

499

Effective Atomic Numbers of Heterogeneous Materials  

Microsoft Academic Search

FOR a single element, the three gamma-ray processes-photoelectric, Compton and pair production, can be expressed as a function of photon energy hnu and the atomic number Z of the element. At a given photon energy, the interaction is proportional to Zn where n is between 4 and 5 for the photoelectric effect, 1 for the Compton effect, and 2 for

R. C. Murty

1965-01-01

500

Fill the Bus (Exploring 2-digit Numbers)  

NSDL National Science Digital Library

Students will practice and explore base ten concepts and 2-digit numbers by filling ten frame buses with counters and then describing the totals in terms of tens and ones. After initial guided practice, they will play a game to fill ten buses.

Elizabeth Gehron

2012-09-22