Mendonça, J. Ricardo G.
2012-01-01
We define a new class of numbers based on the first occurrence of certain patterns of zeros and ones in the expansion of irracional numbers in a given basis and call them Sagan numbers, since they were first mentioned, in a special case, by the North-american astronomer Carl E. Sagan in his science-fiction novel "Contact." Sagan numbers hold connections with a wealth of mathematical ideas. We describe some properties of the newly defined numbers and indicate directions for further amusement.
Vorob'ev, Nikolai Nikolaevich
2011-01-01
Fibonacci numbers date back to an 800-year-old problem concerning the number of offspring born in a single year to a pair of rabbits. This book offers the solution and explores the occurrence of Fibonacci numbers in number theory, continued fractions, and geometry. A discussion of the ""golden section"" rectangle, in which the lengths of the sides can be expressed as a ration of two successive Fibonacci numbers, draws upon attempts by ancient and medieval thinkers to base aesthetic and philosophical principles on the beauty of these figures. Recreational readers as well as students and teacher
Number names and number understanding
DEFF Research Database (Denmark)
Ejersbo, Lisser Rye; Misfeldt, Morten
2014-01-01
through using mathematical names for the numbers such as one-ten-one for 11 and five-ten-six for 56. The project combines the renaming of numbers with supporting the teaching with the new number names. Our hypothesis is that Danish children have more difficulties learning and working with numbers, because...... the Danish number names are more complicated than in other languages. Keywords: A research project in grade 0 and 1th in a Danish school, Base-10 system, two-digit number names, semiotic, cognitive perspectives....
Petersen, T Kyle
2015-01-01
This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group. The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions. The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. There are four supplemental chapters throughout, ...
Institute of Scientific and Technical Information of China (English)
无
2004-01-01
THE last digit of my home phone number in Beijing is 4. “So what?” European readers might ask.This was my attitude when I first lived in China; I couldn't understand why Chinese friends were so shocked at my indifference to the number 4. But China brings new discoveries every day, and I have since seen the light. I know now that Chinese people have their own ways of preserving their well being, and that they see avoiding the number 4 as a good way to stay safe.
Andrews, George E
1994-01-01
Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic.In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simpl
Barnes, John
2016-01-01
In this intriguing book, John Barnes takes us on a journey through aspects of numbers much as he took us on a geometrical journey in Gems of Geometry. Similarly originating from a series of lectures for adult students at Reading and Oxford University, this book touches a variety of amusing and fascinating topics regarding numbers and their uses both ancient and modern. The author intrigues and challenges his audience with both fundamental number topics such as prime numbers and cryptography, and themes of daily needs and pleasures such as counting one's assets, keeping track of time, and enjoying music. Puzzles and exercises at the end of each lecture offer additional inspiration, and numerous illustrations accompany the reader. Furthermore, a number of appendices provides in-depth insights into diverse topics such as Pascal’s triangle, the Rubik cube, Mersenne’s curious keyboards, and many others. A theme running through is the thought of what is our favourite number. Written in an engaging and witty sty...
Murty, M Ram
2014-01-01
This book provides an introduction to the topic of transcendental numbers for upper-level undergraduate and graduate students. The text is constructed to support a full course on the subject, including descriptions of both relevant theorems and their applications. While the first part of the book focuses on introducing key concepts, the second part presents more complex material, including applications of Baker’s theorem, Schanuel’s conjecture, and Schneider’s theorem. These later chapters may be of interest to researchers interested in examining the relationship between transcendence and L-functions. Readers of this text should possess basic knowledge of complex analysis and elementary algebraic number theory.
Thelin, John R.
2013-01-01
What topic would you choose if you had the luxury of writing forever? In this article, John Thelin provides his response: He would opt to write about the history of higher education in a way that relies on quantitative data. "Numbers, please!" is his research request in taking on a longitudinal study of colleges and universities over…
Thelin, John R.
2013-01-01
What topic would you choose if you had the luxury of writing forever? In this article, John Thelin provides his response: He would opt to write about the history of higher education in a way that relies on quantitative data. "Numbers, please!" is his research request in taking on a longitudinal study of colleges and universities over…
Galbraith, Mary J.
1974-01-01
Examination of models for representing integers demonstrates that formal operational thought is required for establishing the operations on integers. Advocated is the use of many models for introducing negative numbers but, apart from addition, it is recommended that operations on integers be delayed until the formal operations stage. (JP)
Number names and number understanding
DEFF Research Database (Denmark)
Ejersbo, Lisser Rye; Misfeldt, Morten
2014-01-01
This paper concerns the results from the first year of a three-year research project involving the relationship between Danish number names and their corresponding digits in the canonical base 10 system. The project aims to develop a system to help the students’ understanding of the base 10 syste...
Number of Compositions and Convolved Fibonacci numbers
Janjic, Milan
2010-01-01
We consider two type of upper Hessenberg matrices which determinants are Fibonacci numbers. Calculating sums of principal minors of the fixed order of the first type leads us to convolved Fibonacci numbers. Some identities for these and for Fibonacci numbers are proved. We also show that numbers of compositions of a natural number with fixed number of ones appear as coefficients of characteristic polynomial of a Hessenberg matrix which determinant is a Fibonacci number. We derive the explicit...
Number of Compositions and Convolved Fibonacci numbers
Janjic, Milan
2010-01-01
We consider two type of upper Hessenberg matrices which determinants are Fibonacci numbers. Calculating sums of principal minors of the fixed order of the first type leads us to convolved Fibonacci numbers. Some identities for these and for Fibonacci numbers are proved. We also show that numbers of compositions of a natural number with fixed number of ones appear as coefficients of characteristic polynomial of a Hessenberg matrix which determinant is a Fibonacci number. We derive the explicit formula for the number of such compositions, in terms of convolutions of Fibonacci numbers.
Richardson, Thomas M.
2014-01-01
We introduce the super Patalan numbers, a generalization of the super Catalan numbers in the sense of Gessel, and prove a number of properties analagous to those of the super Catalan numbers. The super Patalan numbers generalize the super Catalan numbers similarly to how the Patalan numbers generalize the Catalan numbers.
On Number of Compositions of Natural Numbers
Janjic, Milan
2010-01-01
We first give a combinatorial interpretation of coefficients of Chebyshev polynomials, which allows us to connect them with compositions of natural numbers. Then we describe a relationship between the number of compositions of a natural number in which a certain number of parts are p-1, and other parts are not less than p with compositions in which all parts are not less than p. Then we find a relationship between principal minors of a type of Hessenberg matrices and compositions of natural numbers.
On Multiplying Negative Numbers.
Crowley, Mary L.; Dunn, Kenneth A.
1985-01-01
Comments on the history of negative numbers, some methods that can be used to introduce the multiplication of negative numbers to students, and an explanation of why the product of two negative numbers is a positive number are included. (MNS)
All Square Chiliagonal Numbers
A?iru, Muniru A.
2016-01-01
A square chiliagonal number is a number which is simultaneously a chiliagonal number and a perfect square (just as the well-known square triangular number is both triangular and square). In this work, we determine which of the chiliagonal numbers are perfect squares and provide the indices of the corresponding chiliagonal numbers and square…
Numbers Defy the Law of Large Numbers
Falk, Ruma; Lann, Avital Lavie
2015-01-01
As the number of independent tosses of a fair coin grows, the rates of heads and tails tend to equality. This is misinterpreted by many students as being true also for the absolute numbers of the two outcomes, which, conversely, depart unboundedly from each other in the process. Eradicating that misconception, as by coin-tossing experiments,…
Parameterizing by the Number of Numbers
Fellows, Michael R; Rosamond, Frances A
2010-01-01
The usefulness of parameterized algorithmics has often depended on what Niedermeier has called, "the art of problem parameterization". In this paper we introduce and explore a novel but general form of parameterization: the number of numbers. Several classic numerical problems, such as Subset Sum, Partition, 3-Partition, Numerical 3-Dimensional Matching, and Numerical Matching with Target Sums, have multisets of integers as input. We initiate the study of parameterizing these problems by the number of distinct integers in the input. We rely on an FPT result for ILPF to show that all the above-mentioned problems are fixed-parameter tractable when parameterized in this way. In various applied settings, problem inputs often consist in part of multisets of integers or multisets of weighted objects (such as edges in a graph, or jobs to be scheduled). Such number-of-numbers parameterized problems often reduce to subproblems about transition systems of various kinds, parameterized by the size of the system descripti...
Number words and number symbols a cultural history of numbers
Menninger, Karl
1992-01-01
Classic study discusses number sequence and language and explores written numerals and computations in many cultures. "The historian of mathematics will find much to interest him here both in the contents and viewpoint, while the casual reader is likely to be intrigued by the author's superior narrative ability.
On the number of special numbers
Indian Academy of Sciences (India)
KEVSER AKTAS; M RAM MURTY
2017-06-01
For lack of a better word, a number is called special if it has mutually distinct exponents in its canonical prime factorizaton for all exponents. Let $V (x)$ be the number of special numbers $\\leq x$. We will prove that there is a constant $c$ > 1 such that $V (x) \\sim \\frac{cx}{log x}$. We will make some remarks on determining the error term at the end. Using the explicit abc conjecture, we will study the existence of 23 consecutive special integers.
Smith, David Eugene; Ginsburg, Jekuthiel
Counting, naming numbers, numerals, computation, and fractions are the topics covered in this pamphlet. Number lore and interesting number properties are noted; the derivation of some arithmetic terms is briefly discussed. (DT)
Koninck, Jean-Marie De
2009-01-01
Who would have thought that listing the positive integers along with their most remarkable properties could end up being such an engaging and stimulating adventure? The author uses this approach to explore elementary and advanced topics in classical number theory. A large variety of numbers are contemplated: Fermat numbers, Mersenne primes, powerful numbers, sublime numbers, Wieferich primes, insolite numbers, Sastry numbers, voracious numbers, to name only a few. The author also presents short proofs of miscellaneous results and constantly challenges the reader with a variety of old and new n
Vazzana, Anthony; Garth, David
2007-01-01
One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topics.
Damian Slota; Roman Witula
2009-01-01
The scope of the paper is the definition and discussion of the polynomial generalizations of the {sc Fibonacci} numbers called here $delta$-{sc Fibonacci} numbers. Many special identities and interesting relations for these new numbers are presented. Also, different connections between $delta$-{sc Fibonacci} numbers and {sc Fibonacci} and {sc Lucas} numbersare proven in this paper.
Wilkie, James E. B.; Bodenhausen, Galen V.
2012-01-01
We examined the possibility that nonsocial, highly generic concepts are gendered. Specifically, we investigated the gender connotations of Arabic numerals. Across several experiments, we show that the number 1 and other odd numbers are associated with masculinity, whereas the number 2 and other even numbers are associated with femininity, in ways…
Wilkie, James E. B.; Bodenhausen, Galen V.
2012-01-01
We examined the possibility that nonsocial, highly generic concepts are gendered. Specifically, we investigated the gender connotations of Arabic numerals. Across several experiments, we show that the number 1 and other odd numbers are associated with masculinity, whereas the number 2 and other even numbers are associated with femininity, in ways…
Burkhart, Jerry
2009-01-01
Prime numbers are often described as the "building blocks" of natural numbers. This article shows how the author and his students took this idea literally by using prime factorizations to build numbers with blocks. In this activity, students explore many concepts of number theory, including the relationship between greatest common factors and…
Tan, Shanguang
2007-01-01
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.
Rips, Lance J; Thompson, Samantha
2014-03-01
Number systems-such as the natural numbers, integers, rationals, reals, or complex numbers-play a foundational role in mathematics, but these systems can present difficulties for students. In the studies reported here, we probed the boundaries of people's concept of a number system by asking them whether "number lines" of varying shapes qualify as possible number systems. In Experiment 1, participants rated each of a set of number lines as a possible number system, where the number lines differed in their structures (a single straight line, a step-shaped line, a double line, or two branching structures) and in their boundedness (unbounded, bounded below, bounded above, bounded above and below, or circular). Participants also rated each of a group of mathematical properties (e.g., associativity) for its importance to number systems. Relational properties, such as associativity, predicted whether participants believed that particular forms were number systems, as did the forms' ability to support arithmetic operations, such as addition. In Experiment 2, we asked participants to produce properties that were important for number systems. Relational, operation, and use-based properties from this set again predicted ratings of whether the number lines were possible number systems. In Experiment 3, we found similar results when the number lines indicated the positions of the individual numbers. The results suggest that people believe that number systems should be well-behaved with respect to basic arithmetic operations, and that they reject systems for which these operations produce ambiguous answers. People care much less about whether the systems have particular numbers (e.g., 0) or sets of numbers (e.g., the positives).
Jarvis, Frazer
2014-01-01
The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic. Algebraic Number Theory takes the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform. The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the fi...
All square chiliagonal numbers
Aṣiru, Muniru A.
2016-10-01
A square chiliagonal number is a number which is simultaneously a chiliagonal number and a perfect square (just as the well-known square triangular number is both triangular and square). In this work, we determine which of the chiliagonal numbers are perfect squares and provide the indices of the corresponding chiliagonal numbers and square numbers. The study revealed that the determination of square chiliagonal numbers naturally leads to a generalized Pell equation x2 - Dy2 = N with D = 1996 and N = 9962, and has six fundamental solutions out of which only three yielded integer values for use as indices of chiliagonal numbers. The crossing/independent recurrence relations satisfied by each class of indices of the corresponding chiliagonal numbers and square numbers are obtained. Finally, the generating functions serve as a clothesline to hang up the indices of the corresponding chiliagonal numbers and square numbers for easy display and this was used to obtain the first few sequence of square chiliagonal numbers.
DEFF Research Database (Denmark)
Elvik, Rune; Bjørnskau, Torkel
2017-01-01
Highlights •26 studies of the safety-in-numbers effect are reviewed. •The existence of a safety-in-numbers effect is confirmed. •Results are consistent. •Causes of the safety-in-numbers effect are incompletely known.......Highlights •26 studies of the safety-in-numbers effect are reviewed. •The existence of a safety-in-numbers effect is confirmed. •Results are consistent. •Causes of the safety-in-numbers effect are incompletely known....
Chen, Shi-Chao
2011-01-01
A natural number $n$ is called {\\it multiperfect} or {\\it$k$-perfect} for integer $k\\ge2$ if $\\sigma(n)=kn$, where $\\sigma(n)$ is the sum of the positive divisors of $n$. In this paper, we establish the structure theorem of odd multiperfect numbers analogous as Euler's theorem on odd perfect numbers. We prove the divisibility of the Euler part of odd multiperfect numbers and characterize the forms of odd perfect numbers $n=\\pi^\\alpha M^2$ such that $\\pi\\equiv\\alpha(\\text{mod}8)$. We also present some examples to show the nonexistence of odd perfect numbers as applications.
Matsumoto, Kohji
2002-01-01
The book includes several survey articles on prime numbers, divisor problems, and Diophantine equations, as well as research papers on various aspects of analytic number theory such as additive problems, Diophantine approximations and the theory of zeta and L-function Audience Researchers and graduate students interested in recent development of number theory
Xu, Junyan
2012-01-01
We point out that the recursive formula that appears in Erickson's presentation "Fusible Numbers" is incorrect, and pose an alternate conjecture about the structure of fusible numbers. Although we are unable to solve the conjecture, we succeed in establishing some basic properties of fusible numbers. We suggest some possible approaches to the conjecture, and list further problems in the final chapter.
Landy, David; Silbert, Noah; Goldin, Aleah
2013-01-01
Despite their importance in public discourse, numbers in the range of 1 million to 1 trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitical scenarios. Prior theoretical conceptions…
de Mestre, Neville
2008-01-01
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…
Niederreiter, Harald
2015-01-01
This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role, namely cryptography, coding theory, quasi-Monte Carlo methods, and pseudorandom number generation, allowing the authors to delineate the manifold links and interrelations between these areas. Number theory, which Carl-Friedrich Gauss famously dubbed the queen of mathematics, has always been considered a very beautiful field of mathematics, producing lovely results and elegant proofs. While only very few real-life applications were known in the past, today number theory can be found in everyday life: in supermarket bar code scanners, in our cars’ GPS systems, in online banking, etc. Starting with a brief introductory course on number theory in Chapter 1, which makes the book more accessible for undergraduates, the authors describe the four main application areas in Chapters...
DEFF Research Database (Denmark)
Jørgensen, Claus Bjørn; Suetens, Sigrid; Tyran, Jean-Robert
numbers based on recent drawings. While most players pick the same set of numbers week after week without regards of numbers drawn or anything else, we find that those who do change, act on average in the way predicted by the law of small numbers as formalized in recent behavioral theory. In particular......We investigate the “law of small numbers” using a unique panel data set on lotto gambling. Because we can track individual players over time, we can measure how they react to outcomes of recent lotto drawings. We can therefore test whether they behave as if they believe they can predict lotto......, on average they move away from numbers that have recently been drawn, as suggested by the “gambler’s fallacy”, and move toward numbers that are on streak, i.e. have been drawn several weeks in a row, consistent with the “hot hand fallacy”....
DEFF Research Database (Denmark)
Jørgensen, Claus Bjørn; Suetens, Sigrid; Tyran, Jean-Robert
We investigate the “law of small numbers” using a unique panel data set on lotto gambling. Because we can track individual players over time, we can measure how they react to outcomes of recent lotto drawings. We can therefore test whether they behave as if they believe they can predict lotto...... numbers based on recent drawings. While most players pick the same set of numbers week after week without regards of numbers drawn or anything else, we find that those who do change, act on average in the way predicted by the law of small numbers as formalized in recent behavioral theory. In particular......, on average they move away from numbers that have recently been drawn, as suggested by the “gambler’s fallacy”, and move toward numbers that are on streak, i.e. have been drawn several weeks in a row, consistent with the “hot hand fallacy”....
Cocos, Mihail
2011-01-01
In this paper we present a mathematical way of defining musical modes, we derive a formula for the total number of modes and define the musicality of a mode as the total number of harmonic chords whithin the mode. We also give an algorithm for the construction of a duet of melodic lines given a sequence of numbers and a mode. We attach the .mus files of the counterpoints obtained by using the sequence of primes and several musical modes.
Quantum Random Number Generators
Herrero-Collantes, Miguel; Garcia-Escartin, Juan Carlos
2016-01-01
Random numbers are a fundamental resource in science and engineering with important applications in simulation and cryptography. The inherent randomness at the core of quantum mechanics makes quantum systems a perfect source of entropy. Quantum random number generation is one of the most mature quantum technologies with many alternative generation methods. We discuss the different technologies in quantum random number generation from the early devices based on radioactive decay to the multipl...
1977-05-09
from one of the Moscow institutes. In childhood he played at hypnosis with his sister and hypnotized her. He studies In the 11th grade at night school...O R M I N G OR G. REPORT NUMBER 7. AUTHOR( s ) 8 C O N T R A C T OR GRANT NUMBER(e) Lev Kolodnyy 9. PERFORMING O R G A N I Z A T I O N NAME AND
Diamond, Harold G; Cheung, Man Ping
2016-01-01
"Generalized numbers" is a multiplicative structure introduced by A. Beurling to study how independent prime number theory is from the additivity of the natural numbers. The results and techniques of this theory apply to other systems having the character of prime numbers and integers; for example, it is used in the study of the prime number theorem (PNT) for ideals of algebraic number fields. Using both analytic and elementary methods, this book presents many old and new theorems, including several of the authors' results, and many examples of extremal behavior of g-number systems. Also, the authors give detailed accounts of the L^2 PNT theorem of J. P. Kahane and of the example created with H. L. Montgomery, showing that additive structure is needed for proving the Riemann hypothesis. Other interesting topics discussed are propositions "equivalent" to the PNT, the role of multiplicative convolution and Chebyshev's prime number formula for g-numbers, and how Beurling theory provides an interpretation of the ...
DEFF Research Database (Denmark)
Suetens, Sigrid; Galbo-Jørgensen, Claus B.; Tyran, Jean-Robert Karl
2016-01-01
as formalized in recent behavioral theory. In particular, players tend to bet less on numbers that have been drawn in the preceding week, as suggested by the ‘gambler’s fallacy’, and bet more on a number if it was frequently drawn in the recent past, consistent with the ‘hot-hand fallacy’.......We investigate the ‘law of small numbers’ using a data set on lotto gambling that allows us to measure players’ reactions to draws. While most players pick the same set of numbers week after week, we find that those who do change react on average as predicted by the law of small numbers...
Hirst, Keith
1994-01-01
Number and geometry are the foundations upon which mathematics has been built over some 3000 years. This book is concerned with the logical foundations of number systems from integers to complex numbers. The author has chosen to develop the ideas by illustrating the techniques used throughout mathematics rather than using a self-contained logical treatise. The idea of proof has been emphasised, as has the illustration of concepts from a graphical, numerical and algebraic point of view. Having laid the foundations of the number system, the author has then turned to the analysis of infinite proc
DEFF Research Database (Denmark)
Suetens, Sigrid; Galbo-Jørgensen, Claus B.; Tyran, Jean-Robert Karl
2016-01-01
We investigate the ‘law of small numbers’ using a data set on lotto gambling that allows us to measure players’ reactions to draws. While most players pick the same set of numbers week after week, we find that those who do change react on average as predicted by the law of small numbers...... as formalized in recent behavioral theory. In particular, players tend to bet less on numbers that have been drawn in the preceding week, as suggested by the ‘gambler’s fallacy’, and bet more on a number if it was frequently drawn in the recent past, consistent with the ‘hot-hand fallacy’....
Godefroy, Gilles
2004-01-01
Numbers are fascinating. The fascination begins in childhood, when we first learn to count. It continues as we learn arithmetic, algebra, geometry, and so on. Eventually, we learn that numbers not only help us to measure the world, but also to understand it and, to some extent, to control it. In The Adventure of Numbers, Gilles Godefroy follows the thread of our expanding understanding of numbers to lead us through the history of mathematics. His goal is to share the joy of discovering and understanding this great adventure of the mind. The development of mathematics has been punctuated by a n
Hyperquarks and generation number
Buchmann, Alfons J
2013-01-01
In a model in which quarks and leptons are built up from two spin 1/2 preons as fundamental entities, a new class of fermionic bound states (hyperquarks) arises. It turns out that these hyperquarks are necessary to fulfill the 't Hooft anomaly constraint, which then links the number of fermionic generations to the number of colors and hypercolors.
Multispecies quantum Hurwitz numbers
Harnad, J
2014-01-01
The construction of hypergeometric 2D Toda $\\tau$-functions as generating functions for quantum Hurwitz numbers is extended here to multispecies families. Both the enumerative geometrical significance of these multispecies quantum Hurwitz numbers as weighted enumerations of branched coverings of the Riemann sphere and their combinatorial significance in terms of weighted paths in the Cayley graph of $S_n$ are derived.
Onstad, Torgeir
1991-01-01
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)
DEFF Research Database (Denmark)
Levin, Bruce R; McCall, Ingrid C.; Perrot, Veronique
2017-01-01
We postulate that the inhibition of growth and low rates of mortality of bacteria exposed to ribosome-binding antibiotics deemed bacteriostatic can be attributed almost uniquely to these drugs reducing the number of ribosomes contributing to protein synthesis, i.e., the number of effective riboso...
Kolyada, Sergiy; Rybak, Oleksandr
2013-01-01
We introduce and study the Lyapunov numbers -- quantitative measures of the sensitivity of a dynamical system $(X,f)$ given by a compact metric space $X$ and a continuous map $f:X \\to X$. In particular, we prove that for a minimal topologically weakly mixing system all Lyapunov numbers are the same.
Rugani, Rosa; Sartori, Luisa
2016-01-01
Humans show a remarkable tendency to describe and think of numbers as being placed on a mental number line (MNL), with smaller numbers located on the left and larger ones on the right. Faster responses to small numbers are indeed performed on the left side of space, while responses to large numbers are facilitated on the right side of space (spatial-numerical association of response codes, SNARC effect). This phenomenon is considered the experimental demonstration of the MNL and has been extensively replicated throughout a variety of paradigms. Nevertheless, the majority of previous literature has mainly investigated this effect by means of response times and accuracy, whereas studies considering more subtle and automatic measures such as kinematic parameters are rare (e.g., in a reaching-to-grasp movement, the grip aperture is enlarged in responding to larger numbers than in responding to small numbers). In this brief review we suggest that numerical magnitude can also affect the what and how of action execution (i.e., temporal and spatial components of movement). This evidence could have large implications in the strongly debated issue concerning the effect of experience and culture on the orientation of MNL.
Dudley, Underwood
2008-01-01
Ideal for a first course in number theory, this lively, engaging text requires only a familiarity with elementary algebra and the properties of real numbers. Author Underwood Dudley, who has written a series of popular mathematics books, maintains that the best way to learn mathematics is by solving problems. In keeping with this philosophy, the text includes nearly 1,000 exercises and problems-some computational and some classical, many original, and some with complete solutions. The opening chapters offer sound explanations of the basics of elementary number theory and develop the fundamenta
Kneusel, Ronald T
2015-01-01
This is a book about numbers and how those numbers are represented in and operated on by computers. It is crucial that developers understand this area because the numerical operations allowed by computers, and the limitations of those operations, especially in the area of floating point math, affect virtually everything people try to do with computers. This book aims to fill this gap by exploring, in sufficient but not overwhelming detail, just what it is that computers do with numbers. Divided into two parts, the first deals with standard representations of integers and floating point numb
Morrison, Greg
2010-01-01
We propose a simple real-valued generalization of the well known integer-valued Erdos number as a topological, non-metric measure of the `closeness' felt between two nodes in an undirected, weighted graph. These real-valued Erdos numbers are asymmetric and are able to distinguish between network topologies that standard distance metrics view as identical. We use this measure to study some simple analytically tractable networks, and show the utility of our measure to devise a ratings scheme based on the generalized Erdos number that we deploy on the data from the NetFlix prize, and find a significant improvement in our ratings prediction over a baseline.
Professor Stewart's incredible numbers
Stewart, Ian
2015-01-01
Ian Stewart explores the astonishing properties of numbers from 1 to10 to zero and infinity, including one figure that, if you wrote it out, would span the universe. He looks at every kind of number you can think of - real, imaginary, rational, irrational, positive and negative - along with several you might have thought you couldn't think of. He explains the insights of the ancient mathematicians, shows how numbers have evolved through the ages, and reveals the way numerical theory enables everyday life. Under Professor Stewart's guidance you will discover the mathematics of codes,
Sierpinski, Waclaw
1988-01-01
Since the publication of the first edition of this work, considerable progress has been made in many of the questions examined. This edition has been updated and enlarged, and the bibliography has been revised.The variety of topics covered here includes divisibility, diophantine equations, prime numbers (especially Mersenne and Fermat primes), the basic arithmetic functions, congruences, the quadratic reciprocity law, expansion of real numbers into decimal fractions, decomposition of integers into sums of powers, some other problems of the additive theory of numbers and the theory of Gaussian
Crossley, John N
1987-01-01
This book presents detailed studies of the development of three kinds of number. In the first part the development of the natural numbers from Stone-Age times right up to the present day is examined not only from the point of view of pure history but also taking into account archaeological, anthropological and linguistic evidence. The dramatic change caused by the introduction of logical theories of number in the 19th century is also treated and this part ends with a non-technical account of the very latest developments in the area of Gödel's theorem. The second part is concerned with the deve
Corry, Leo
2015-01-01
The world around us is saturated with numbers. They are a fundamental pillar of our modern society, and accepted and used with hardly a second thought. But how did this state of affairs come to be? In this book, Leo Corry tells the story behind the idea of number from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through to the
LeVeque, William J
1996-01-01
This excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra. A knowledge of such algebraic concepts as group, ring, field, and domain is not assumed, however; all terms are defined and examples are given - making the book self-contained in this respect.The author begins with an introductory chapter on number theory and its early history. Subsequent chapters deal with unique factorization and the GCD, quadratic residues, number-theoretic functions and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diopha
Weiss, Edwin
1998-01-01
Careful organization and clear, detailed proofs characterize this methodical, self-contained exposition of basic results of classical algebraic number theory from a relatively modem point of view. This volume presents most of the number-theoretic prerequisites for a study of either class field theory (as formulated by Artin and Tate) or the contemporary treatment of analytical questions (as found, for example, in Tate's thesis).Although concerned exclusively with algebraic number fields, this treatment features axiomatic formulations with a considerable range of applications. Modem abstract te
Supersymmetric Displaced Number States
Directory of Open Access Journals (Sweden)
Fredy R. Zypman
2015-06-01
Full Text Available We introduce, generate and study a family of supersymmetric displaced number states (SDNS that can be considered generalized coherent states of the supersymmetric harmonic oscillator. The family is created from the seminal supersymmetric boson-fermion entangling annihilation operator introduced by Aragone and Zypman and later expanded by Kornbluth and Zypman. Using the momentum representation, the states are obtained analytically in compact form as displaced supersymmetric number states. We study their position-momentum uncertainties, and their bunchiness by classifying them according to their Mandel Q-parameter in phase space. We were also able to find closed form analytical representations in the space and number basis.
Cohn, Harvey
1980-01-01
""A very stimulating book ... in a class by itself."" - American Mathematical MonthlyAdvanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. Moreover, the book abounds with numerical examples and more concrete, specific theorems than are found in most contemporary treatments of the subject.The book is divided into three parts
Schwartz, Richard Evan
2014-01-01
In the American Mathematical Society's first-ever book for kids (and kids at heart), mathematician and author Richard Evan Schwartz leads math lovers of all ages on an innovative and strikingly illustrated journey through the infinite number system. By means of engaging, imaginative visuals and endearing narration, Schwartz manages the monumental task of presenting the complex concept of Big Numbers in fresh and relatable ways. The book begins with small, easily observable numbers before building up to truly gigantic ones, like a nonillion, a tredecillion, a googol, and even ones too huge for names! Any person, regardless of age, can benefit from reading this book. Readers will find themselves returning to its pages for a very long time, perpetually learning from and growing with the narrative as their knowledge deepens. Really Big Numbers is a wonderful enrichment for any math education program and is enthusiastically recommended to every teacher, parent and grandparent, student, child, or other individual i...
DEFF Research Database (Denmark)
Wanscher, Jørgen Bundgaard; Sørensen, Majken Vildrik
2006-01-01
highly uniform multidimensional draws, which are highly relevant for todays traffic models. This paper shows among others combined shuffling and scrambling seems needless, that scrambling gives the lowest correlation and that there are detectable differences between random numbers, dependent...
Strawn, Candace A.
1998-01-01
Describes LOGO's turtle graphics capabilities based on a sixth-grade classroom's activities with negative numbers and Logo programming. A sidebar explains LOGO and offers suggestions to teachers for using LOGO effectively. (LRW)
Quantum random number generator
Pooser, Raphael C.
2016-05-10
A quantum random number generator (QRNG) and a photon generator for a QRNG are provided. The photon generator may be operated in a spontaneous mode below a lasing threshold to emit photons. Photons emitted from the photon generator may have at least one random characteristic, which may be monitored by the QRNG to generate a random number. In one embodiment, the photon generator may include a photon emitter and an amplifier coupled to the photon emitter. The amplifier may enable the photon generator to be used in the QRNG without introducing significant bias in the random number and may enable multiplexing of multiple random numbers. The amplifier may also desensitize the photon generator to fluctuations in power supplied thereto while operating in the spontaneous mode. In one embodiment, the photon emitter and amplifier may be a tapered diode amplifier.
Quantum random number generators
Herrero-Collantes, Miguel; Garcia-Escartin, Juan Carlos
2017-01-01
Random numbers are a fundamental resource in science and engineering with important applications in simulation and cryptography. The inherent randomness at the core of quantum mechanics makes quantum systems a perfect source of entropy. Quantum random number generation is one of the most mature quantum technologies with many alternative generation methods. This review discusses the different technologies in quantum random number generation from the early devices based on radioactive decay to the multiple ways to use the quantum states of light to gather entropy from a quantum origin. Randomness extraction and amplification and the notable possibility of generating trusted random numbers even with untrusted hardware using device-independent generation protocols are also discussed.
Solar Indices - Sunspot Numbers
National Oceanic and Atmospheric Administration, Department of Commerce — Collection includes a variety of indices related to solar activity contributed by a number of national and private solar observatories located worldwide. This...
Brown, Ezra; Brunson, Cornelius
2008-01-01
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…
Energy Technology Data Exchange (ETDEWEB)
Nelson, R.N. (ed.)
1985-05-01
This publication lists all report number codes processed by the Office of Scientific and Technical Information. The report codes are substantially based on the American National Standards Institute, Standard Technical Report Number (STRN)-Format and Creation Z39.23-1983. The Standard Technical Report Number (STRN) provides one of the primary methods of identifying a specific technical report. The STRN consists of two parts: The report code and the sequential number. The report code identifies the issuing organization, a specific program, or a type of document. The sequential number, which is assigned in sequence by each report issuing entity, is not included in this publication. Part I of this compilation is alphabetized by report codes followed by issuing installations. Part II lists the issuing organization followed by the assigned report code(s). In both Parts I and II, the names of issuing organizations appear for the most part in the form used at the time the reports were issued. However, for some of the more prolific installations which have had name changes, all entries have been merged under the current name.
Alizée Dauvergne
2010-01-01
What makes the LHC the biggest particle accelerator in the world? Here are some of the numbers that characterise the LHC, and their equivalents in terms that are easier for us to imagine. Feature Number Equivalent Circumference ~ 27 km Distance covered by beam in 10 hours ~ 10 billion km a round trip to Neptune Number of times a single proton travels around the ring each second 11 245 Speed of protons first entering the LHC 299 732 500 m/s 99.9998 % of the speed of light Speed of protons when they collide 299 789 760 m/s 99.9999991 % of the speed of light Collision temperature ~ 1016 °C ove...
Chromosome numbers in Bromeliaceae
Directory of Open Access Journals (Sweden)
Cotias-de-Oliveira Ana Lúcia Pires
2000-01-01
Full Text Available The present study reports chromosome numbers of 17 species of Bromeliaceae, belonging to the genera Encholirium, Bromelia, Orthophytum, Hohenbergia, Billbergia, Neoglaziovia, Aechmea, Cryptanthus and Ananas. Most species present 2n = 50, however, Bromelia laciniosa, Orthophytum burle-marxii and O. maracasense are polyploids with 2n = 150, 2n = 100 and 2n = 150, respectively, while for Cryptanthus bahianus, 2n = 34 + 1-4B. B chromosomes were observed in Bromelia plumieri and Hohenbergia aff. utriculosa. The chromosome number of all species was determined for the first time, except for Billbergia chlorosticta and Cryptanthus bahianus. Our data supports the hypothesis of a basic number of x = 25 for the Bromeliaceae family and decreasing aneuploidy in the genus Cryptanthus.
Quantum random number generation
Ma, Xiongfeng; Yuan, Xiao; Cao, Zhu; Qi, Bing; Zhang, Zhen
2016-06-01
Quantum physics can be exploited to generate true random numbers, which have important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of quantumness—coherence, an important feature that differentiates quantum mechanics from classical physics. The generation of genuine randomness is generally considered impossible with only classical means. On the basis of the degree of trustworthiness on devices, quantum random number generators (QRNGs) can be grouped into three categories. The first category, practical QRNG, is built on fully trusted and calibrated devices and typically can generate randomness at a high speed by properly modelling the devices. The second category is self-testing QRNG, in which verifiable randomness can be generated without trusting the actual implementation. The third category, semi-self-testing QRNG, is an intermediate category that provides a tradeoff between the trustworthiness on the device and the random number generation speed.
CONFUSION WITH TELEPHONE NUMBERS
Telecom Service
2002-01-01
he area code is now required for all telephone calls within Switzerland. Unfortunately this is causing some confusion. CERN has received complaints that incoming calls intended for CERN mobile phones are being directed to private subscribers. This is caused by mistakenly dialing the WRONG code (e.g. 022) in front of the mobile number. In order to avoid these problems, please inform your correspondents that the correct numbers are: 079 201 XXXX from Switzerland; 0041 79 201 XXXX from other countries. Telecom Service
CONFUSION WITH TELEPHONE NUMBERS
Telecom Service
2002-01-01
The area code is now required for all telephone calls within Switzerland. Unfortunately this is causing some confusion. CERN has received complaints that incoming calls intended for CERN mobile phones are being directed to private subscribers. This is caused by mistakenly dialing the WRONG code (e.g. 022) in front of the mobile number. In order to avoid these problems, please inform your correspondents that the correct numbers are: 079 201 XXXX from Switzerland; 0041 79 201 XXXX from other countries. Telecom Service
Earthquake number forecasts testing
Kagan, Yan Y.
2017-10-01
We study the distributions of earthquake numbers in two global earthquake catalogues: Global Centroid-Moment Tensor and Preliminary Determinations of Epicenters. The properties of these distributions are especially required to develop the number test for our forecasts of future seismic activity rate, tested by the Collaboratory for Study of Earthquake Predictability (CSEP). A common assumption, as used in the CSEP tests, is that the numbers are described by the Poisson distribution. It is clear, however, that the Poisson assumption for the earthquake number distribution is incorrect, especially for the catalogues with a lower magnitude threshold. In contrast to the one-parameter Poisson distribution so widely used to describe earthquake occurrences, the negative-binomial distribution (NBD) has two parameters. The second parameter can be used to characterize the clustering or overdispersion of a process. We also introduce and study a more complex three-parameter beta negative-binomial distribution. We investigate the dependence of parameters for both Poisson and NBD distributions on the catalogue magnitude threshold and on temporal subdivision of catalogue duration. First, we study whether the Poisson law can be statistically rejected for various catalogue subdivisions. We find that for most cases of interest, the Poisson distribution can be shown to be rejected statistically at a high significance level in favour of the NBD. Thereafter, we investigate whether these distributions fit the observed distributions of seismicity. For this purpose, we study upper statistical moments of earthquake numbers (skewness and kurtosis) and compare them to the theoretical values for both distributions. Empirical values for the skewness and the kurtosis increase for the smaller magnitude threshold and increase with even greater intensity for small temporal subdivision of catalogues. The Poisson distribution for large rate values approaches the Gaussian law, therefore its skewness
Samuel, Pierre
2008-01-01
Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics - algebraic geometry, in particular.This book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Gal
Iwaniec, Henryk
2004-01-01
Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results, many of which belong to the mainstream of arithmetic. One of the main attractions of analytic number theory is the vast diversity of concepts and methods it includes. The main goal of the book is to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, its beautiful theorems and powerful techniques. The book is written with graduate students in mind, and the authors tried to balance between clarity, completeness, and generality. The exercis
2007-12-26
265–275. [7] H. G. Grundman, ‘ Sequences of consecutive Niven numbers’, Fibonacci Quart. 32 (1994), 174–175. [8] D. R. Heath-Brown and S. Konyagin...paper, we define a natural sequence in relation to q-Niven numbers. For a fixed but arbitrary k ∈ N and a base q ≥ 2, one may ask whether or not there...other words, ak is the smallest Niven number whose sum of the digits is a given positive integer k. We denote by ck the companion sequence ck = ak/k
Clette, Frédéric; Vaquero, José M; Cliver, Edward W
2014-01-01
Our knowledge of the long-term evolution of solar activity and of its primary modulation, the 11-year cycle, largely depends on a single direct observational record: the visual sunspot counts that retrace the last 4 centuries, since the invention of the astronomical telescope. Currently, this activity index is available in two main forms: the International Sunspot Number initiated by R. Wolf in 1849 and the Group Number constructed more recently by Hoyt and Schatten (1998a,b). Unfortunately, those two series do not match by various aspects, inducing confusions and contradictions when used in crucial contemporary studies of the solar dynamo or of the solar forcing on the Earth climate. Recently, new efforts have been undertaken to diagnose and correct flaws and biases affecting both sunspot series, in the framework of a series of dedicated Sunspot Number Workshops. Here, we present a global overview of our current understanding of the sunspot number calibration. While the early part of the sunspot record befor...
Babu, K S; Al-Binni, U; Banerjee, S; Baxter, D V; Berezhiani, Z; Bergevin, M; Bhattacharya, S; Brice, S; Brock, R; Burgess, T W; Castellanos, L; Chattopadhyay, S; Chen, M-C; Church, E; Coppola, C E; Cowen, D F; Cowsik, R; Crabtree, J A; Davoudiasl, H; Dermisek, R; Dolgov, A; Dutta, B; Dvali, G; Ferguson, P; Perez, P Fileviez; Gabriel, T; Gal, A; Gallmeier, F; Ganezer, K S; Gogoladze, I; Golubeva, E S; Graves, V B; Greene, G; Handler, T; Hartfiel, B; Hawari, A; Heilbronn, L; Hill, J; Jaffe, D; Johnson, C; Jung, C K; Kamyshkov, Y; Kerbikov, B; Kopeliovich, B Z; Kopeliovich, V B; Korsch, W; Lachenmaier, T; Langacker, P; Liu, C-Y; Marciano, W J; Mocko, M; Mohapatra, R N; Mokhov, N; Muhrer, G; Mumm, P; Nath, P; Obayashi, Y; Okun, L; Pati, J C; Pattie, R W; Phillips, D G; Quigg, C; Raaf, J L; Raby, S; Ramberg, E; Ray, A; Roy, A; Ruggles, A; Sarkar, U; Saunders, A; Serebrov, A; Shafi, Q; Shimizu, H; Shiozawa, M; Shrock, R; Sikdar, A K; Snow, W M; Soha, A; Spanier, S; Stavenga, G C; Striganov, S; Svoboda, R; Tang, Z; Tavartkiladze, Z; Townsend, L; Tulin, S; Vainshtein, A; Van Kooten, R; Wagner, C E M; Wang, Z; Wehring, B; Wilson, R J; Wise, M; Yokoyama, M; Young, A R
2013-01-01
This report, prepared for the Community Planning Study - Snowmass 2013 - summarizes the theoretical motivations and the experimental efforts to search for baryon number violation, focussing on nucleon decay and neutron-antineutron oscillations. Present and future nucleon decay search experiments using large underground detectors, as well as planned neutron-antineutron oscillation search experiments with free neutron beams are highlighted.
Alladi, Krishnaswami
2008-01-01
Contains chapters on number theory and related topics. This title covers topics that focus on multipartitions, congruences and identities, the formulas of Koshliakov and Guinand in Ramanujan's "Lost Notebook", alternating sign matrices and the Weyl character formulas, theta functions in complex analysis, and elliptic functions
Bell, Eric Temple
1991-01-01
From one of the foremost interpreters for lay readers of the history and meaning of mathematics: a stimulating account of the origins of mathematical thought and the development of numerical theory. It probes the work of Pythagoras, Galileo, Berkeley, Einstein, and others, exploring how ""number magic"" has influenced religion, philosophy, science, and mathematics
Schreuder, M.F.
2012-01-01
A low nephron number is, according to Brenner's hyperfiltration hypothesis, associated with hypertension, glomerular damage and proteinuria, and starts a vicious cycle that ends in renal failure over the long term. Nephron endowment is set during foetal life, and there is no formation of nephrons
Trudgian, Timothy
2009-01-01
One of the difficulties in any teaching of mathematics is to bridge the divide between the abstract and the intuitive. Throughout school one encounters increasingly abstract notions, which are more and more difficult to relate to everyday experiences. This article examines a familiar approach to thinking about negative numbers, that is an…
Haida Numbers and Calculation.
Cogo, Robert
Experienced traders in furs, blankets, and other goods, the Haidas of the 1700's had a well-developed decimal system for counting and calculating. Their units of linear measure included the foot, yard, and fathom, or six feet. This booklet lists the numbers from 1 to 20 in English and Haida; explains the Haida use of ten, hundred, and thousand…
Uniform random number generators
Farr, W. R.
1971-01-01
Methods are presented for the generation of random numbers with uniform and normal distributions. Subprogram listings of Fortran generators for the Univac 1108, SDS 930, and CDC 3200 digital computers are also included. The generators are of the mixed multiplicative type, and the mathematical method employed is that of Marsaglia and Bray.
Jorgensen, C.B.; Suetens, S.; Tyran, J.R.
2011-01-01
We investigate the "law of small numbers" using a unique panel data set on lotto gambling. Because we can track individual players over time, we can measure how they react to outcomes of recent lotto drawings. We can therefore test whether they behave as if they believe they can predict lotto
MacCarron, Pádraig; Dunbar, Robin
2016-01-01
The social brain hypothesis predicts that humans have an average of about 150 relationships at any given time. Within this 150, there are layers of friends of an ego, where the number of friends in a layer increases as the emotional closeness decreases. Here we analyse a mobile phone dataset, firstly, to ascertain whether layers of friends can be identified based on call frequency. We then apply different clustering algorithms to break the call frequency of egos into clusters and compare the number of alters in each cluster with the layer size predicted by the social brain hypothesis. In this dataset we find strong evidence for the existence of a layered structure. The clustering yields results that match well with previous studies for the innermost and outermost layers, but for layers in between we observe large variability.
Directory of Open Access Journals (Sweden)
Marco Ruffino
2001-12-01
Full Text Available In this paper I discuss the intuition behind Frege's and Russell's definitions of numbers as sets, as well as Benacerraf's criticism of it. I argue that Benacerraf's argument is not as strong as some philosophers tend to think. Moreover, I examine an alternative to the Fregean-Russellian definition of numbers proposed by Maddy, and point out some problems faced by it.Neste artigo discuto a intuição subjacente à definição de n∨meros como conjuntos proposta por Frege e Russell, assim como a crítica de Benacerraf a esta definição. Eu tento mostrar que o argumento de Benacerraf não é tão forte como alguns filósofos o tomaram. Adicionalmente, examino uma alternativa à definição de Frege e Russell proposta por Maddy, e indico algumas dificuldades encontrada pela mesma.
Sierpinski and Carmichael Numbers
2013-01-16
appear. 31 [21] E. M. Matveev, ‘An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers. II,’ Izv. Ross. Akad...Math. Comp. 37 (1981), 587–593. [23] C. Pontreau, ‘A Mordell- Lang plus Bogomolov type result for curves in G2m,’ Monatsh. Math. 157 (2009), 267–281. [24
Rocker, Graeme M; Verma, Jennifer Y; Demmons, Jillian; Mittmann, Nicole
2015-02-06
The 'Number Needed to Treat' (NNT) is a useful measure for estimating the number of patients that would need to receive a therapeutic intervention to avoid one of the adverse events that the treatment is designed to prevent. We explored the possibility of an adaption of NNT to estimate the 'Number Needed to $ave' (NN$) as a new, conceptual systems metric to estimate potential cost-savings to the health system from implementation of a treatment, or in this case, a program. We used the outcomes of the INSPIRED COPD Outreach ProgramTM to calculate that 26 patients would need to complete the program to avoid healthcare expenditures of $100,000, based on hospital bed days avoided. The NN$ does not translate into 'cost savings' per se, but redirection of resource expenditures for other purposes. We propose that the NN$ metric, if further developed, could help to inform system-level resource allocation decisions in a manner similar to the way that the NNT metric helps to inform individual-level treatment decisions.
Generalizations of Euler Numbers and Euler Numbers of Higher Order
Institute of Scientific and Technical Information of China (English)
LUOQiu-ming; QIFeng
2005-01-01
The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.
LeVeque, William J
2002-01-01
Classic two-part work now available in a single volume assumes no prior theoretical knowledge on reader's part and develops the subject fully. Volume I is a suitable first course text for advanced undergraduate and beginning graduate students. Volume II requires a much higher level of mathematical maturity, including a working knowledge of the theory of analytic functions. Contents range from chapters on binary quadratic forms to the Thue-Siegel-Roth Theorem and the Prime Number Theorem. Includes numerous problems and hints for their solutions. 1956 edition. Supplementary Reading. List of Symb
Thurston, H A
2007-01-01
The teaching of mathematics has undergone extensive changes in approach, with a shift in emphasis from rote memorization to acquiring an understanding of the logical foundations and methodology of problem solving. This book offers guidance in that direction, exploring arithmetic's underlying concepts and their logical development.This volume's great merit lies in its wealth of explanatory material, designed to promote an informal and intuitive understanding of the rigorous logical approach to the number system. The first part explains and comments on axioms and definitions, making their subseq
Pati, Jogesh C.; Salam, Abdus
We suggest that baryon-number conservation may not be absolute and that an integrally charged quark may disintegrate into two leptons and an antilepton with a coupling strength G Bmp2≲ 10-9. On the other hand, if quarks are much heavier than low-lying hadrons, the decay of a three-quark system like the proton is highly forbidden (proton lifetime ≳ 1028 y). Motivation for these ideas appears to arise within a unified theory of hadrons and leptons and their gauge interactions. We emphasize the consequences of such a possibility for real quark searches.
Neukirch, Jürgen; Wingberg, Kay
2013-01-01
The second edition is a corrected and extended version of the first. It is a textbook for students, as well as a reference book for the working mathematician, on cohomological topics in number theory. The first part provides algebraic background: cohomology of profinite groups, duality groups, free products, and homotopy theory of modules, with new sections on spectral sequences and on Tate cohomology of profinite groups. The second part deals with Galois groups of local and global fields: Tate duality, structure of absolute Galois groups of local fields, extensions with restricted ramificatio
Quantum random number generator
Stipcevic, M
2006-01-01
We report upon a novel principle for realization of a fast nondeterministic random number generator whose randomness relies on intrinsic randomness of the quantum physical processes of photonic emission in semiconductors and subsequent detection by the photoelectric effect. Timing information of detected photons is used to generate binary random digits-bits. The bit extraction method based on restartable clock theoretically eliminates both bias and autocorrelation while reaching efficiency of almost 0.5 bits per random event. A prototype has been built and statistically tested.
Beyond natural numbers: negative number representation in parietal cortex.
Blair, Kristen P; Rosenberg-Lee, Miriam; Tsang, Jessica M; Schwartz, Daniel L; Menon, Vinod
2012-01-01
Unlike natural numbers, negative numbers do not have natural physical referents. How does the brain represent such abstract mathematical concepts? Two competing hypotheses regarding representational systems for negative numbers are a rule-based model, in which symbolic rules are applied to negative numbers to translate them into positive numbers when assessing magnitudes, and an expanded magnitude model, in which negative numbers have a distinct magnitude representation. Using an event-related functional magnetic resonance imaging design, we examined brain responses in 22 adults while they performed magnitude comparisons of negative and positive numbers that were quantitatively near (difference 6). Reaction times (RTs) for negative numbers were slower than positive numbers, and both showed a distance effect whereby near pairs took longer to compare. A network of parietal, frontal, and occipital regions were differentially engaged by negative numbers. Specifically, compared to positive numbers, negative number processing resulted in greater activation bilaterally in intraparietal sulcus (IPS), middle frontal gyrus, and inferior lateral occipital cortex. Representational similarity analysis revealed that neural responses in the IPS were more differentiated among positive numbers than among negative numbers, and greater differentiation among negative numbers was associated with faster RTs. Our findings indicate that despite negative numbers engaging the IPS more strongly, the underlying neural representation are less distinct than that of positive numbers. We discuss our findings in the context of the two theoretical models of negative number processing and demonstrate how multivariate approaches can provide novel insights into abstract number representation.
Lepton family number violation
Energy Technology Data Exchange (ETDEWEB)
Herczeg, P.
1999-03-01
At present there is evidence from neutrino oscillation searches that the neutrinos are in fact massive particles and that they mix. If confirmed, this would imply that the conservation of LFN is not exact. Lepton family number violation (LFNV) has been searched for with impressive sensitivities in many processes involving charged leptons. The present experimental limits on some of them (those which the author shall consider here) are shown in Table 1. These stringent limits are not inconsistent with the neutrino oscillation results since, given the experimental bounds on the masses of the known neutrinos and the neutrino mass squared differences required by the oscillation results, the effects of LFNV from neutrino mixing would be too small to be seen elsewhere (see Section 2). The purpose of experiments searching for LFNV involving the charged leptons is to probe the existence of other sources of LFNV. Such sources are present in many extensions of the SM. In this lecture the author shall discuss some of the possibilities, focusing on processes that require muon beams. Other LFNV processes, such as the decays of the kaons and of the {tau}, provide complementary information. In the next Section he shall consider some sources of LFNV that do not require an extension of the gauge group of the SM (the added leptons or Higgs bosons may of course originate from models with extended gauge groups). In Section 3 he discusses LFNV in left-right symmetric models. In Section 4 he considers LFNV in supersymmetric models, first in R-parity conserving supersymmetric grand unified models, and then in the minimal supersymmetric standard model with R-parity violation. The last section is a brief summary of the author`s conclusions.
Beyond Natural Numbers: Negative Number Representation in Parietal Cortex
Blair, Kristen P.; Rosenberg-Lee, Miriam; Tsang, Jessica M.; Schwartz, Daniel L.; Menon, Vinod
2012-01-01
Unlike natural numbers, negative numbers do not have natural physical referents. How does the brain represent such abstract mathematical concepts? Two competing hypotheses regarding representational systems for negative numbers are a rule-based model, in which symbolic rules are applied to negative numbers to translate them into positive numbers when assessing magnitudes, and an expanded magnitude model, in which negative numbers have a distinct magnitude representation. Using an event-relate...
On Fibonacci Numbers Which Are Elliptic Korselt Numbers
2014-11-17
On Fibonacci numbers which are elliptic Korselt numbers Florian Luca School of Mathematics University of the Witwatersrand P. O. Box Wits 2050, South...is a CM elliptic curve with CM field Q( √ −d), then the set of n for which the nth Fibonacci number Fn satisfies an elliptic Korselt criterion for Q...SUBTITLE On Fibonacci Numbers Which Are Elliptic Korselt Numbers 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d
Percents Are Not Natural Numbers
Jacobs, Jennifer A.
2013-01-01
Adults are prone to treating percents, one representational format of rational numbers, as novel cases of natural number. This suggests that percent values are not differentiated from natural numbers; a conceptual shift from the natural numbers to the rational numbers has not yet occurred. This is most surprising, considering people are inundated…
Series of Reciprocal Triangular Numbers
Bruckman, Paul; Dence, Joseph B.; Dence, Thomas P.; Young, Justin
2013-01-01
Reciprocal triangular numbers have appeared in series since the very first infinite series were summed. Here we attack a number of subseries of the reciprocal triangular numbers by methodically expressing them as integrals.
Axiomatic of Fuzzy Complex Numbers
Angel Garrido
2012-01-01
Fuzzy numbers are fuzzy subsets of the set of real numbers satisfying some additional conditions. Fuzzy numbers allow us to model very difficult uncertainties in a very easy way. Arithmetic operations on fuzzy numbers have also been developed, and are based mainly on the crucial Extension Principle. When operating with fuzzy numbers, the results of our calculations strongly depend on the shape of the membership functions of these numbers. Logically, less regular membership functions may lead ...
Number Games, Magnitude Representation, and Basic Number Skills in Preschoolers
Whyte, Jemma Catherine; Bull, Rebecca
2008-01-01
The effect of 3 intervention board games (linear number, linear color, and nonlinear number) on young children's (mean age = 3.8 years) counting abilities, number naming, magnitude comprehension, accuracy in number-to-position estimation tasks, and best-fit numerical magnitude representations was examined. Pre- and posttest performance was…
Pauli Pascal Pyramids, Pauli Fibonacci Numbers, and Pauli Jacobsthal Numbers
Horn, Martin Erik
2007-01-01
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?
Number Games, Magnitude Representation, and Basic Number Skills in Preschoolers
Whyte, Jemma Catherine; Bull, Rebecca
2008-01-01
The effect of 3 intervention board games (linear number, linear color, and nonlinear number) on young children's (mean age = 3.8 years) counting abilities, number naming, magnitude comprehension, accuracy in number-to-position estimation tasks, and best-fit numerical magnitude representations was examined. Pre- and posttest performance was…
On Types of Distance Fibonacci Numbers Generated by Number Decompositions
Directory of Open Access Journals (Sweden)
Anetta Szynal-Liana
2014-01-01
Full Text Available We introduce new types of distance Fibonacci numbers which are closely related with number decompositions. Using special decompositions of the number n we give a sequence of identities for them. Moreover, we give matrix generators for distance Fibonacci numbers and their direct formulas.
[Intel random number generator-based true random number generator].
Huang, Feng; Shen, Hong
2004-09-01
To establish a true random number generator on the basis of certain Intel chips. The random numbers were acquired by programming using Microsoft Visual C++ 6.0 via register reading from the random number generator (RNG) unit of an Intel 815 chipset-based computer with Intel Security Driver (ISD). We tested the generator with 500 random numbers in NIST FIPS 140-1 and X(2) R-Squared test, and the result showed that the random number it generated satisfied the demand of independence and uniform distribution. We also compared the random numbers generated by Intel RNG-based true random number generator and those from the random number table statistically, by using the same amount of 7500 random numbers in the same value domain, which showed that the SD, SE and CV of Intel RNG-based random number generator were less than those of the random number table. The result of u test of two CVs revealed no significant difference between the two methods. Intel RNG-based random number generator can produce high-quality random numbers with good independence and uniform distribution, and solves some problems with random number table in acquisition of the random numbers.
Axiomatic of Fuzzy Complex Numbers
Directory of Open Access Journals (Sweden)
Angel Garrido
2012-04-01
Full Text Available Fuzzy numbers are fuzzy subsets of the set of real numbers satisfying some additional conditions. Fuzzy numbers allow us to model very difficult uncertainties in a very easy way. Arithmetic operations on fuzzy numbers have also been developed, and are based mainly on the crucial Extension Principle. When operating with fuzzy numbers, the results of our calculations strongly depend on the shape of the membership functions of these numbers. Logically, less regular membership functions may lead to very complicated calculi. Moreover, fuzzy numbers with a simpler shape of membership functions often have more intuitive and more natural interpretations. But not only must we apply the concept and the use of fuzzy sets, and its particular case of fuzzy number, but also the new and interesting mathematical construct designed by Fuzzy Complex Numbers, which is much more than a correlate of Complex Numbers in Mathematical Analysis. The selected perspective attempts here that of advancing through axiomatic descriptions.
Cosmic numbers the numbers that define our universe
Stein, James D
2011-01-01
Our fascination with numbers begins when we are children and continues throughout our lives. We start counting our fingers and toes and end up balancing checkbooks and calculating risk. So powerful is the appeal of numbers that many people ascribe to them a mystical significance. Other numbers go beyond the supernatural, working to explain our universe and how it behaves. In Cosmic Numbers , mathematics professor James D. Stein traces the discovery, evolution, and interrelationships of the numbers that define our world. Everyone knows about the speed of light and absolute zero, but numbers lik
On Bernoulli Numbers and Stirling Numbers%Bernoulli数与Stirling数
Institute of Scientific and Technical Information of China (English)
高泽图
2001-01-01
In this paper,using the method of formal power series, we study the Bernoulli numbers and the Stirling numbers,and point out the relation between Bernoulli numbers and Stirling numbers,and obtain several identities of including Bernoulli numbers and Stirling numbers.%应用形式幂级数的方法，研究Bernoulli数与Stirling数，指出它们之间的关系，获得几个包含Bernoulli数和Stirling数的恒等式.
Dettlaff, Magda; Yero, Ismael G
2012-01-01
The bondage number $b(G)$ of a nonempty graph $G$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with domination number greater than the domination number of $G$. Here we study the bondage number of some grid-like graphs. In this sense, we obtain some bounds or exact values of the bondage number of some Cartesian product, strong product or direct product of two paths.
Dettlaff, Magda; Lemanska, Magdalena; Yero, Ismael G.
2012-01-01
The bondage number $b(G)$ of a nonempty graph $G$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with domination number greater than the domination number of $G$. Here we study the bondage number of some grid-like graphs. In this sense, we obtain some bounds or exact values of the bondage number of some strong product and direct product of two paths.
Number sense as the bridge to number understanding
DEFF Research Database (Denmark)
Ejersbo, Lisser Rye
2016-01-01
In this article, I compare number sense, which is understood as an innate capacity to know about the magnitude and relations of numbers, with number understanding, which is understood as the ability to manipulate the symbolic arithmetic developed in a culture. My research focuses on the question...... of how number sense and number understanding can be used in a synergetic process in learning mathematics. Different research results have shown that consistent training in number sense (K-10) influences mathematical competencies in a positive manner, and that young children aged 5-6 years are able...... to solve symbolic problems that involve the approximate addition and subtraction of large two-digit numbers. Our experiment was conducted in a kindergarten class (age 5-6 years) and in a Grade 2 class (age 7-8 years) with students who had difficulties in number reading and symbolic arithmetic. Keywords...
Natural Number Bias in Operations with Missing Numbers
Christou, Konstantinos P.
2015-01-01
This study investigates the hypothesis that there is a natural number bias that influences how students understand the effects of arithmetical operations involving both Arabic numerals and numbers that are represented by symbols for missing numbers. It also investigates whether this bias correlates with other aspects of students' understanding of…
GRAPHS WHOSE CIRCULAR CLIQUE NUMBER EQUAL THE CLIQUE NUMBER
Institute of Scientific and Technical Information of China (English)
XU Baogang; ZHOU Xinghe
2005-01-01
The circular clique number of a graph G is the maximum fractional k/d such that Gkd admits a homomorphism to G. In this paper, we give some sufficient conditions for graphs whose circular clique number equal the clique number, we also characterize the K1,3-free graphs and planar graphs with the desired property.
Introducing Number and Arithmetic Concepts with Number Sticks.
Baroody, Arthur J.
1993-01-01
This article compares the relative merits of using Cuisenaire rods (unsegmented, unnumbered, and representing continuous quantities) and number sticks (segmented, numbered, and representing discrete quantities) to introduce number and arithmetic concepts to beginning students or students with learning difficulties or mental disabilities. (DB)
Multiple Bracket Function, Stirling Number, and Lah Number Identities
Coskun, Hasan
2012-01-01
The author has constructed multiple analogues of several families of combinatorial numbers in a recent article, including the bracket symbol, and the Stirling numbers of the first and second kind. In the present paper, a multiple analogue of another sequence, the Lah numbers, is developed, and certain associated identities and significant properties of all these sequences are constructed.
A Relation between Prime Numbers and Twin Prime Numbers
2001-01-01
Every mathematician has been concerned with prime numbers, and has metwith mysterious surprises about them. Besides intuition, using empirical methods has an important role to findrelations between prime numbers. A relation between any prime numberand any twin prime number has been obtained.
The concrete theory of numbers: initial numbers and wonderful properties of numbers repunit
Tarasov, Boris V
2007-01-01
In this work initial numbers and repunit numbers have been studied. All numbers have been considered in a decimal notation. The problem of simplicity of initial numbers has been studied. Interesting properties of numbers repunit are proved: $gcd(R_a, R_b) = R_{gcd(a,b)}$; $R_{ab}/(R_aR_b)$ is an integer only if $gcd(a,b) = 1$, where $a\\geq1$, $b\\geq1$ are integers. Dividers of numbers repunit, are researched by a degree of prime number.
THE RELATIONSHIP BETWEEN NUMBER NAMES AND NUMBER CONCEPTS
DEFF Research Database (Denmark)
Ejersbo, Lisser Rye; Misfeldt, Morten
2015-01-01
Different countries have different names for numbers. These names are often related in a regular way to the base-10 place value system used for writing numbers as digits. However, in several languages, this regularity breaks down (e.g., between 10 and 20), and there is limited knowledge of how...... the regularity or irregularity of number naming affects children’s formation of number concepts and arithmetic performance. We investigate this issue by reviewing relevant literature and undertaking a design research project addressing the specific irregularities of the Danish number names. In this project...
Bell Numbers, Determinants and Series
Indian Academy of Sciences (India)
P K Saikia; Deepak Subedi
2013-05-01
In this article, we study Bell numbers and Uppuluri Carpenter numbers. We obtain various expressions and relations between them. These include polynomial recurrences and expressions as determinants of certain matrices of binomial coefficients.
Distribution theory of algebraic numbers
Yang, Chung-Chun
2008-01-01
The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions Algebraic numbers Algebraic geometry Height functions The abc-conjecture Roth''s theorem Subspace theorems Vojta''s conjectures L-functions.
The theory of algebraic numbers
Pollard, Harry
1998-01-01
An excellent introduction to the basics of algebraic number theory, this concise, well-written volume examines Gaussian primes; polynomials over a field; algebraic number fields; and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture. 1975 edition. References. List of Symbols. Index.
Elementary number theory with programming
Lewinter, Marty
2015-01-01
A successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts in the fields of computer science and mathematics, the book features accessible coverage for readers with various levels of experience and explores number theory in the context of programming without relying on advanced prerequisite knowledge and con
The Mental Number Line in Dyscalculia: Impaired Number Sense or Access From Symbolic Numbers?
Lafay, Anne; St-Pierre, Marie-Catherine; Macoir, Joël
2016-03-25
Numbers may be manipulated and represented mentally over a compressible number line oriented from left to right. According to numerous studies, one of the primary reasons for dyscalculia is related to improper understanding of the mental number line. Children with dyscalculia usually show difficulty when they have to place Arabic numbers on a physical number line. However, it remains unclear whether they have a deficit with the mental number line per se or a deficit with accessing it from nonsymbolic and/or symbolic numbers. Quebec French-speaking 8- to 9-year-old children with (24) and without (37) dyscalculia were assessed with transcoding tasks (number-to-positionandposition-to-number) designed to assess the acuity of the mental number line with Arabic and spoken numbers as well as with analogic numerosities. Results showed that children with dyscalculia produced a larger percentage absolute error than children without mathematics difficulties in every task except the number-to-position transcoding task with analogic numerosities. Hence, these results suggested that children with dyscalculia do not have a general deficit of the mental number line but rather a deficit with accessing it from symbolic numbers.
Simple Remarks on Carmichael Numbers
Uchiyama, Shigenori
An odd composite number n for which an-1 ≡ 1 (mod n) for all integers a coprime to n is called a Carmichael number. This paper shows that some class of Carmichael numbers which have relatively large prime factors can be recognized in deterministic polynomial time under the assumption of the Extended Riemann Hypothesis (ERH). Also some related problems are discussed.
Jue, Brian
2010-01-01
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.)
Fletcher, Rodney
2008-01-01
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…
Betti Numbers of Gaussian Fields
Park, Changbom; Pranav, Pratyush; Chingangbam, Pravabati; van de Weygaert, Rien; Jones, Bernard; Vegter, Gert; Kim, Inkang; Hidding, Johan; Hellwing, Wojciech A.
2013-01-01
We present the relation between the genus in cosmology and the Betti numbers for excursion sets of three- and two-dimensional smooth Gaussian random fields, and numerically investigate the Betti numbers as a function of threshold level. Betti numbers are topological invariants of figures that can be
Linear or Exponential Number Lines
Stafford, Pat
2011-01-01
Having decided to spend some time looking at one's understanding of numbers, the author was inspired by "Alex's Adventures in Numberland," by Alex Bellos to look at one's innate appreciation of number. Bellos quotes research studies suggesting that an individual's natural appreciation of numbers is more likely to be exponential rather than linear,…
Goldbach numbers in short intervals
Institute of Scientific and Technical Information of China (English)
李红泽
1995-01-01
Suppose B is a sufficiently large positive constant, ε is a sufficiently small positive constant, N is a sufficiently large natural number, and A = N7/81+ε. It is proved that all even numbers in (N, N + A) with O(Alog-BN) exceptions are Goldbach numbers.
Kraaikamp, C.; Hartono, Y.
2002-01-01
In this note Hurwitzian numbers are defined for the nearest integer, and backward continued fraction expansions, and Nakada's $\\alpha$-expansions. It is shown that the set of Hurwitzian numbers for these continued fractions coincides with the classical set of such numbers.
Random Numbers and Quantum Computers
McCartney, Mark; Glass, David
2002-01-01
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…
Cognitive representation of negative numbers.
Fischer, Martin H
2003-05-01
To understand negative numbers, must we refer to positive number representations (the phylogenetic hypothesis), or do we acquire a negative mental number line (the ontogenetic hypothesis)? In the experiment reported here, participants made lateralized button responses to indicate the larger of two digits from the range -9 to 9. Digit pairs were displayed spatially congruent or incongruent with either a phylogenetic or an ontogenetic mental number line. The pattern of decision latencies suggests that negative numbers become associated with left space, thus supporting the ontogenetic view.
Quantum random number generator using photon-number path entanglement
Kwon, Osung; Cho, Young-Wook; Kim, Yoon-Ho
2010-08-01
We report an experimental implementation of quantum random number generator based on the photon-number-path entangled state. The photon-number-path entangled state is prepared by means of two-photon Hong-Ou-Mandel quantum interference at a beam splitter. The randomness in our scheme is of truly quantum mechanical origin as it comes from the projection measurement of the entangled two-photon state. The generated bit sequences satisfy the standard randomness test.
Pell Numbers, Pell-Lucas Numbers and Modular Group
Institute of Scientific and Technical Information of China (English)
Q. Mushtaq; U. Hayat
2007-01-01
We show that the matrix A(g), representing the element g = ((xy)2(xy2)2)m (m≥) of the modular group PSL(2,Z)=(x,y:x2=y3=1),where x:z →-1/z and y :z → -1/z, is a 2×2 symmetric matrix whose entries are Pell numbers and whose trace is a Pell-Lucas number. If g fixes elements of Q(√d), where d is a square-free positive number, on the circuit of the coset diagram, then d ＝ 2 and there are only four pairs of ambiguous numbers on the circuit.
Bernoulli numbers and zeta functions
Arakawa, Tsuneo; Kaneko, Masanobu
2014-01-01
Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausen–von Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of p-adic measures; the Euler–Maclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of ...
Compendium of Experimental Cetane Numbers
Energy Technology Data Exchange (ETDEWEB)
Yanowitz, Janet [Ecoengineering, Sharonville, OH (United States); Ratcliff, Matthew A. [National Renewable Energy Lab. (NREL), Golden, CO (United States); McCormick, Robert L. [National Renewable Energy Lab. (NREL), Golden, CO (United States); Taylor, J. D. [National Renewable Energy Lab. (NREL), Golden, CO (United States); Murphy, M. J. [Battelle, Columbus, OH (United States)
2017-02-22
This report is an updated version of the 2014 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 December 2016 as well as a number of previously unpublished values, most measured over the past decade at the National Renewable Energy Laboratory. This version of the compendium contains cetane values for 496 pure compounds, including 204 hydrocarbons and 292 oxygenates. 176 individual measurements are new to this version of the compendium, all of them collected using ASTM Method D6890, which utilizes an Ignition Quality Tester (IQT) a type of constant-volume combustion chamber. For many compounds, numerous measurements are included, often collected by different researchers using different methods. The text of this document is unchanged from the 2014 version, except for the numbers of compounds in Section 3.1, the Appendices, Table 1. Primary Cetane Number Data Sources and Table 2. Number of Measurements Included in Compendium. 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 number has been expanded, and the data have been annotated extensively to provide additional information that will help the reader judge the relative reliability of individual results.
Nieder, Andreas
2016-06-01
Humans and non-human primates share an elemental quantification system that resides in a dedicated neural network in the parietal and frontal lobes. In this cortical network, 'number neurons' encode the number of elements in a set, its cardinality or numerosity, irrespective of stimulus appearance across sensory motor systems, and from both spatial and temporal presentation arrays. After numbers have been extracted from sensory input, they need to be processed to support goal-directed behaviour. Studying number neurons provides insights into how information is maintained in working memory and transformed in tasks that require rule-based decisions. Beyond an understanding of how cardinal numbers are encoded, number processing provides a window into the neuronal mechanisms of high-level brain functions.
Number Comparison and Number Line Estimation Rely on Different Mechanisms
Directory of Open Access Journals (Sweden)
Delphine Sasanguie
2013-12-01
Full Text Available The performance in comparison and number line estimation is assumed to rely on the same underlying representation, similar to a compressed mental number line that becomes more linear with age. We tested this assumption explicitly by examining the relation between the linear/logarithmic fit in a non-symbolic number line estimation task and the size effect (SE in a non-symbolic comparison task in first-, second-, and third graders. In two experiments, a correlation between the estimation pattern in number line estimation and the SE in comparison was absent. An ANOVA showed no difference between the groups of children with a linear or a logarithmic representation considering their SE in comparison. This suggests that different mechanisms underlie both basic number processing tasks.
Iovane, Gerardo
2007-01-01
In this work we show that the prime distribution is deterministic. Indeed the set of prime numbers P can be expressed in terms of two subsets of N using three specific selection rules, acting on two sets of prime candidates. The prime candidates are obtained in terms of the first perfect number. The asymptotic behaviour is also considered. We obtain for the first time an explicit relation for generating the full set P of prime numbers smaller than n or equal to n.
Number line representations of fractions
Behr, Merlyn J.; Bright, George W.; Wachsmuth, Ipke; Wagner, Sigrid
1982-01-01
The study explored students' interpretations of representations of fractions on number lines and the effect of instruction on those interpretations. Subjects were five fourth-graders, and instruction was a four-day unit on the use of number lines. A 16-item, multiple-choice pre- and posttest was used along with videotaped interviews. Performance improved except when students had to associate a reduced fraction symbol with an equivalent, unreduced fraction representation on a number line. The ...
Brain representations of negative numbers.
Parnes, Michael; Berger, Andrea; Tzelgov, Joseph
2012-12-01
Participants performed a physical comparison task of pairs of positive and pairs of negative one-digit numbers while their electrophysiological brain activity was measured. The numerical value of the presented digits was either congruent or incongruent with the physical size of the digits. Analysis has shown that the earliest event-related potential (ERP) difference between positive and negative numbers was found in the P300 ERP component peak, where there was an inverse effect of congruity in the negative pairs, compared with the positive ones. This pattern of results supports the idea that natural numbers serve as primitives of the human cognitive system, whereas negative numbers are apparently generated if needed.
Directory of Open Access Journals (Sweden)
J. Y. Kang
2013-01-01
Full Text Available Recently, many mathematicians have studied different kinds of the Euler, Bernoulli, and Genocchi numbers and polynomials. In this paper, we give another definition of polynomials Ũn(x. We observe an interesting phenomenon of “scattering” of the zeros of the polynomials Ũn(x in complex plane. We find out some identities and properties related to polynomials Ũn(x. Finally, we also derive interesting relations between polynomials Ũn(x, Stirling numbers, central factorial numbers, and Euler numbers.
Prandtl number of toroidal plasmas
Energy Technology Data Exchange (ETDEWEB)
Itoh, Kimitaka (National Inst. for Fusion Science, Nagoya (Japan)); Itoh, Sanae; Fukuyama, Atsushi; Yagi, Masatoshi; Azumi, Masafumi
1993-12-01
Theory of the L-mode confinement in toroidal plasmas is developed. The Prandtl number, the ratio between the ion viscosity and the thermal conductivity is obtained for the anomalous transport process which is caused by the self-sustained turbulence in the toroidal plasma. It is found that the Prandtl number is of order unity both for the ballooning mode turbulence in tokamaks and for the interchange mode turbulence in helical system. The influence on the anomalous transport and fluctuation level is evaluated. Hartmann number and magnetic Prandtl number are also discussed. (author).
Indian Academy of Sciences (India)
MARK SHATTUCK
2016-10-01
In this paper, we consider a two-parameter polynomial generalization, denoted by ${\\mathcal G}_{a,b}(n, k; r)$, of the $r$-Lah numbers which reduces to these recently introduced numbers when $a = b = 1$. We present several identities for ${\\mathcal G}_{a,b}(n, k; r)$ that generalize earlier identities given for the $r$-Lah and $r$-Stirling numbers. We also provide combinatorial proofs of some earlier identities involving the $r$-Lah numbers by defining appropriate sign-changing involutions. Generalizing these arguments yields orthogonality-type relations that are satisfied by ${\\mathcal G}_{a,b}(n, k; r)$.
Compendium of Experimental Cetane Numbers
Energy Technology Data Exchange (ETDEWEB)
Yanowitz, J.; Ratcliff, M. A.; McCormick, R. L.; Taylor, J. D.; Murphy, M. J.
2014-08-01
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.
Wave Packets can Factorize Numbers
Mack, H; Haug, F; Freyberger, M; Schleich, W P; Mack, Holger; Bienert, Marc; Haug, Florian; Freyberger, Matthias; Schleich, Wolfgang P.
2002-01-01
We draw attention to various aspects of number theory emerging in the time evolution of elementary quantum systems with quadratic phases. Such model systems can be realized in actual experiments. Our analysis paves the way to a new, promising and effective method to factorize numbers.
Regular Numbers and Mathematical Worlds
Whitacre, Ian; Bouhjar, Khalid; Bishop, Jessica Pierson; Philipp, Randolph; Schappelle, Bonnie P.
2016-01-01
Rather than describing the challenges of integer learning in terms of a transition from positive to negative numbers, we have arrived at a different perspective: We view students as inhabiting distinct mathematical worlds consisting of particular types of numbers (as construed by the students). These worlds distinguish and illuminate students'…
Betti numbers of Gaussian fields
Park, Changbom; Chingangbam, Pravabati; van de Weygaert, Rien; Jones, Bernard; Vegter, Gert; Kim, Inkang; Hidding, Johan; Hellwing, Wojciech A
2013-01-01
We present the relation between the genus in cosmology and the Betti numbers for excursion sets of three- and two-dimensional smooth Gaussian random fields, and numerically investigate the Betti numbers as a function of threshold level. Betti numbers are topological invariants of figures that can be used to distinguish topological spaces. In the case of the excursion sets of a three-dimensional field there are three possibly non-zero Betti numbers; $\\beta_0$ is the number of connected regions, $\\beta_1$ is the number of circular holes, and $\\beta_2$ is the number of three-dimensional voids. Their sum with alternating signs is the genus of the surface of excursion regions. It is found that each Betti number has a dominant contribution to the genus in a specific threshold range. $\\beta_0$ dominates the high-threshold part of the genus curve measuring the abundance of high density regions (clusters). $\\beta_1$ dominates the genus near the median thresholds which measures the topology of negatively curved iso-den...
Ore, Oystein
1988-01-01
A prominent mathematician presents the principal ideas and methods of number theory within a historical and cultural framework. Oystein Ore's fascinating, accessible treatment requires only a basic knowledge of algebra. Topics include prime numbers, the Aliquot parts, linear indeterminate problems, congruences, Euler's theorem, classical construction problems, and many other subjects.
SICs and Algebraic Number Theory
Appleby, Marcus; Flammia, Steven; McConnell, Gary; Yard, Jon
2017-08-01
We give an overview of some remarkable connections between symmetric informationally complete measurements (SIC-POVMs, or SICs) and algebraic number theory, in particular, a connection with Hilbert's 12th problem. The paper is meant to be intelligible to a physicist who has no prior knowledge of either Galois theory or algebraic number theory.
Investigating the Randomness of Numbers
Pendleton, Kenn L.
2009-01-01
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…
Core Knowledge, Language, and Number
Spelke, Elizabeth S.
2017-01-01
The natural numbers may be our simplest, most useful, and best-studied abstract concepts, but their origins are debated. I consider this debate in the context of the proposal, by Gallistel and Gelman, that natural number system is a product of cognitive evolution and the proposal, by Carey, that it is a product of human cultural history. I offer a…
The Algebra of Complex Numbers.
LePage, Wilbur R.
This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…
On Counting the Rational Numbers
Almada, Carlos
2010-01-01
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…
Salman, M.; Broersma, Haitze J.
2007-01-01
For two given graphs $F$ and $H$, the Ramsey number $R(F,H)$ is the smallest positive integer $p$ such that for every graph $G$ on $p$ vertices the following holds: either $G$ contains $F$ as a subgraph or the complement of $G$ contains $H$ as a subgraph. In this paper, we study the Ramsey numbers $
Salman, M.; Broersma, Haitze J.
2004-01-01
For two given graphs $F$ and $H$, the Ramsey number $R(F,H)$ is the smallest positive integer $p$ such that for every graph $G$ on $p$ vertices the following holds: either $G$ contains $F$ as a subgraph or the complement of $G$ contains $H$ as a subgraph. In this paper, we study the Ramsey numbers $
Investigating the Randomness of Numbers
Pendleton, Kenn L.
2009-01-01
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…
Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers
Energy Technology Data Exchange (ETDEWEB)
Onishi, Yoshihiro [Faculty of Education Human Sciences, University of Yamanashi, Takeda, Kofu (Japan)
2011-10-31
The three fundamental properties of the Bernoulli numbers, namely, the von Staudt-Clausen theorem, von Staudt's second theorem, and Kummer's original congruence, are generalized to new numbers that we call generalized Bernoulli-Hurwitz numbers. These are coefficients in the power series expansion of a higher-genus algebraic function with respect to a suitable variable. Our generalization differs strongly from previous works. Indeed, the order of the power of the modulus prime in our Kummer-type congruences is exactly the same as in the trigonometric function case (namely, Kummer's own congruence for the original Bernoulli numbers), and as in the elliptic function case (namely, H. Lang's extension for the Hurwitz numbers). However, in other past results on higher-genus algebraic functions, the modulus was at most half of its value in these classical cases. This contrast is clarified by investigating the analogue of the three properties above for the universal Bernoulli numbers. Bibliography: 34 titles.
Urban aerosol number size distributions
Directory of Open Access Journals (Sweden)
T. Hussein
2004-01-01
Full Text Available Aerosol number size distributions have been measured since 5 May 1997 in Helsinki, Finland. The presented aerosol data represents size distributions within the particle diameter size range 8-400nm during the period from May 1997 to March 2003. The daily, monthly and annual patterns of the aerosol particle number concentrations were investigated. The temporal variation of the particle number concentration showed close correlations with traffic activities. The highest total number concentrations were observed during workdays; especially on Fridays, and the lowest concentrations occurred during weekends; especially Sundays. Seasonally, the highest total number concentrations were observed during winter and spring and lower concentrations were observed during June and July. More than 80% of the number size distributions had three modes: nucleation mode (30nm, Aitken mode (20-100nm and accumulation mode (}$'>90nm. Less than 20% of the number size distributions had either two modes or consisted of more than three modes. Two different measurement sites were used; in the first (Siltavuori, 5.5.1997-5.3.2001, the arithmetic means of the particle number concentrations were 7000cm, 6500cm, and 1000cm respectively for nucleation, Aitken, and accumulation modes. In the second site (Kumpula, 6.3.2001-28.2.2003 they were 5500cm, 4000cm, and 1000cm. The total number concentration in nucleation and Aitken modes were usually significantly higher during workdays than during weekends. The temporal variations in the accumulation mode were less pronounced. The lower concentrations at Kumpula were mainly due to building construction and also the slight overall decreasing trend during these years. During the site changing a period of simultaneous measurements over two weeks were performed showing nice correlation at both sites.
Graspable objects shape number processing
Directory of Open Access Journals (Sweden)
Mariagrazia eRanzini
2011-12-01
Full Text Available The field of numerical cognition represents an interesting case for action-based theories of cognition, since number is a special kind of abstract concept. Several studies have shown that within the parietal lobes adjacent neural regions code numerical magnitude and grasping-related information. This anatomical proximity between brain areas involved in number and sensorimotor processes may account for interactions between numerical magnitude and action. In particular, recent studies has demonstrated a causal role of action perception on numerical magnitude processing. If objects are represented in terms of actions (affordances, the causal role of action on number processing should extend to the case of objects affordances. This study investigates the relationship between numbers and objects affordances in two experiments, without (Experiment 1 or with (Experiment 2 a motor action execution (i.e., participants were asked to hold an object in their hands during the task. The task consisted in repeating aloud the odd or even digit within a pair depending on the type of the preceding or following object. Order of presentation (object-number vs. number-object, object type (graspable vs. ungraspable, object size (small vs. large, and Numerical magnitude (small vs. large were manipulated for each experiment. Experiment 1 showed a facilitation – in terms of quicker responses - for graspable over ungraspable objects preceded by numbers, and an effect of numerical magnitude after the presentation of graspable objects. Experiment 2 demonstrated that the action execution enhanced overall the sensitivity to numerical magnitude, however interfering with the effects of objects affordances on number processing. Overall, these findings demonstrate that numbers and graspable objects communicate with each other, supporting the view that abstract concepts may be grounded in motor experience.
Numbered nasal discs for waterfowl
Bartonek, J.C.; Dane, C.W.
1964-01-01
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.
CHANGE OF NUMBERING IN SWITZERLAND
Telephone Service
2002-01-01
Swiss telephone numbers are changing to ten-digit numbers. This means that the 0-022 area code will have to be used for calls to the Geneva region. From 29 March it will no longer be possible to make local calls without the 022 code. There will be no change in the procedure for dialling other destinations from CERN, including Zurich. Don't forget to change the numbers stored in your various memories (fax, telephone, modem, etc.). Please contact the switchboard (111) for any further information. Telephone Service IT/CS/TEL
CHANGE OF NUMBERING IN SWITZERLAND
Telephone Service
2002-01-01
Swiss telephone numbers are changing to ten-digit numbers. This means that the 0-022 area code will have to be used for calls to the Geneva region. From 29 March it will no longer be possible to make local calls without the 022 code. There will be no change in the procedure for dialling other destinations from CERN, including Zürich. Don't forget to change the numbers stored in your various memories (fax, telephone), and modems for ACB users. Please contact the switchboard (111) for any further information. Telephone Service IT/CS/TEL
Integral Presentations of Catalan Numbers
Dana-Picard, Thierry
2010-01-01
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.
Fibonacci Numbers and the Spreadsheet.
Verderber, Nadine L.
1991-01-01
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)
Spectral numbers in Floer theories
Usher, Michael
2007-01-01
The chain complexes underlying Floer homology theories typically carry a real-valued filtration, allowing one to associate to each Floer homology class a spectral number defined as the infimum of the filtration levels of chains representing that class. These spectral numbers have been studied extensively in the case of Hamiltonian Floer homology by Oh, Schwarz, and others. We prove that the spectral number associated to any nonzero Floer homology class is always finite, and that the infimum in the definition of the spectral number is always attained. In the Hamiltonian case, this implies that what is known as the "nondegenerate spectrality" axiom holds on all closed symplectic manifolds. Our proofs are entirely algebraic and rather elementary, and apply to any Floer-type theory (including Novikov homology) satisfying certain standard formal properties provided that one works with coefficients in a Novikov ring whose degree-zero part \\Lambda_0 is a field. The key ingredient is a theorem about linear transforma...
Department of Homeland Security — SEVIS by the Numbers is a quarterly report that highlights nonimmigrant student and exchange visitor trends, values and information using data from the Student and...
Women In Numbers - Europe workshop
Bucur, Alina; Feigon, Brooke; Schneps, Leila
2015-01-01
Covering topics in graph theory, L-functions, p-adic geometry, Galois representations, elliptic fibrations, genus 3 curves and bad reduction, harmonic analysis, symplectic groups and mould combinatorics, this volume presents a collection of papers covering a wide swath of number theory emerging from the third iteration of the international Women in Numbers conference, “Women in Numbers - Europe” (WINE), held on October 14–18, 2013 at the CIRM-Luminy mathematical conference center in France. While containing contributions covering a wide range of cutting-edge topics in number theory, the volume emphasizes those concrete approaches that make it possible for graduate students and postdocs to begin work immediately on research problems even in highly complex subjects.
Numbers their history and meaning
Flegg, Graham
2003-01-01
Readable, jargon-free book examines the earliest endeavors to count and record numbers, initial attempts to solve problems by using equations, and origins of infinite cardinal arithmetic. "Surprisingly exciting." - Choice.
Social Security Number (SSN) Verification
U.S. Department of Health & Human Services — This report presents the results of a validation study of Social Security numbers (SSNs) in Medicaid Statistical Information System (MSIS) records for the fourth...
Euclid's Number-Theoretical Work
Zhang, Shaohua
2009-01-01
The object of this paper is to affirm the number-theoretical role of Euclid and the historical significance of Euclid's algorithm. We give a brief introduction about Euclid's number-theoretical work. Our study is the first to show that Euclid's algorithm is essentially equivalent with Division algorithm which is the basis of Theory of Divisibility. Note also that Euclid's algorithm implies Euclid's first theorem and Euclid's second theorem. 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. It leads to the conclusion that Euclid's algorithm is the greatest number-theoretical achievement of the age.
Poison control center - emergency number
For a POISON EMERGENCY call: 1-800-222-1222 ANYWHERE IN THE UNITED STATES This national hotline number will let you ... is a free and confidential service. All local poison control centers in the United States use this ...
Department of Homeland Security — SEVIS by the Numbers is a quarterly report that highlights nonimmigrant student and exchange visitor trends, values and information using data from the Student and...
Integral Presentations of Catalan Numbers
Dana-Picard, Thierry
2010-01-01
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.
Boolean complexes and boolean numbers
Tenner, Bridget Eileen
2017-01-01
International audience; The Bruhat order gives a poset structure to any Coxeter group. The ideal of elements in this poset having boolean principal order ideals forms a simplicial poset. This simplicial poset defines the boolean complex for the group. In a Coxeter system of rank n, we show that the boolean complex is homotopy equivalent to a wedge of (n-1)-dimensional spheres. The number of these spheres is the boolean number, which can be computed inductively from the unlabeled Coxeter syste...
Urban aerosol number size distributions
Directory of Open Access Journals (Sweden)
T. Hussein
2003-10-01
Full Text Available Aerosol number size distributions were measured continuously in Helsinki, Finland from 5 May 1997 to 28 February 2003. The daily, monthly and annual patterns were investigated. The temporal variation of the particle number concentration was seen to follow the traffic density. The highest total particle number concentrations were usually observed during workdays; especially on Fridays, and the lower concentrations occurred during weekends; especially Sundays. Seasonally, the highest total number concentrations were usually observed during winter and spring and the lowest during June and July. More than 80\\% of the particle number size distributions were tri-modal: nucleation mode (Dp < 30 nm, Aitken mode (20–100 nm and accumulation mode (Dp > 90 nm. Less than 20% of the particle number size distributions have either two modes or consisted of more than three modes. Two different measurement sites are used; in the first place (Siltavuori, 5 May 1997–5 March 2001, the overall means of the integrated particle number concentrations were 7100 cm^{−3}, 6320 cm^{−3}, and 960 cm^{−3}, respectively, for nucleation, Aitken, and accumulation modes. In the second site (Kumpula, 6 March 2001–28 February 2003 they were 5670 cm^{−3}, 4050 cm^{−3}, and 900 cm^{−3}. The total number concentration in nucleation and Aitken modes were usually significantly higher during weekdays than during weekends. The variations in accumulation mode were less pronounced. The smaller concentrations in Kumpula were mainly due to building construction and also slight overall decreasing trend during these years. During the site changing a period of simultaneous measurements over two weeks were performed showing nice correlation in both sites.
Numbers for reducible cubic scrolls
Directory of Open Access Journals (Sweden)
Israel Vainsencher
2004-12-01
Full Text Available We show how to compute the number of reducible cubic scrolls of codimension 2 in (math blackboard symbol Pn incident to the appropriate number of linear spaces.Mostramos como calcular o número de rolos cúbicos redutíveis de codimensão 2 em (math blackboard symbol Pn incidentes a espaços lineares apropriados.
Random numbers from vacuum fluctuations
Shi, Yicheng; Chng, Brenda; Kurtsiefer, Christian
2016-07-01
We implement a quantum random number generator based on a balanced homodyne measurement of vacuum fluctuations of the electromagnetic field. The digitized signal is directly processed with a fast randomness extraction scheme based on a linear feedback shift register. The random bit stream is continuously read in a computer at a rate of about 480 Mbit/s and passes an extended test suite for random numbers.
Entropy estimation and Fibonacci numbers
Timofeev, Evgeniy A.; Kaltchenko, Alexei
2013-05-01
We introduce a new metric on a space of right-sided infinite sequences drawn from a finite alphabet. Emerging from a problem of entropy estimation of a discrete stationary ergodic process, the metric is important on its own part and exhibits some interesting properties. Notably, the number of distinct metric values for a set of sequences of length m is equal to Fm+3 - 1, where Fm is a Fibonacci number.
Dimensionless numbers in additive manufacturing
Mukherjee, T.; Manvatkar, V.; De, A.; DebRoy, T.
2017-02-01
The effects of many process variables and alloy properties on the structure and properties of additively manufactured parts are examined using four dimensionless numbers. The structure and properties of components made from 316 Stainless steel, Ti-6Al-4V, and Inconel 718 powders for various dimensionless heat inputs, Peclet numbers, Marangoni numbers, and Fourier numbers are studied. Temperature fields, cooling rates, solidification parameters, lack of fusion defects, and thermal strains are examined using a well-tested three-dimensional transient heat transfer and fluid flow model. The results show that lack of fusion defects in the fabricated parts can be minimized by strengthening interlayer bonding using high values of dimensionless heat input. The formation of harmful intermetallics such as laves phases in Inconel 718 can be suppressed using low heat input that results in a small molten pool, a steep temperature gradient, and a fast cooling rate. Improved interlayer bonding can be achieved at high Marangoni numbers, which results in vigorous circulation of liquid metal, larger pool dimensions, and greater depth of penetration. A high Fourier number ensures rapid cooling, low thermal distortion, and a high ratio of temperature gradient to the solidification growth rate with a greater tendency of plane front solidification.
Grammatical typology and frequency analysis: number availability and number use
Directory of Open Access Journals (Sweden)
Dunstan Brown
2013-12-01
Full Text Available The Smith-Stark hierarchy, a version of the Animacy Hierarchy, offers a typology of the cross-linguistic availability of number. The hierarchy predicts that the availability of number is not arbitrary. For any language, if the expression of plural is available to a noun, it is available to any noun of a semantic category further to the left of the hierarchy. In this article we move one step further by showing that the structure of the hierarchy can be observed in a statistical model of number use in Russian. We also investigate three co-variates: plural preference, pluralia tantum and irregularity effects; these account for an item's behaviour being different than that solely expected from its animacy position.
Number matters: control of mammalian mitochondrial DNA copy number.
Clay Montier, Laura L; Deng, Janice J; Bai, Yidong
2009-03-01
Regulation of mitochondrial biogenesis is essential for proper cellular functioning. Mitochondrial DNA (mtDNA) depletion and the resulting mitochondrial malfunction have been implicated in cancer, neurodegeneration, diabetes, aging, and many other human diseases. Although it is known that the dynamics of the mammalian mitochondrial genome are not linked with that of the nuclear genome, very little is known about the mechanism of mtDNA propagation. Nevertheless, our understanding of the mode of mtDNA replication has advanced in recent years, though not without some controversies. This review summarizes our current knowledge of mtDNA copy number control in mammalian cells, while focusing on both mtDNA replication and turnover. Although mtDNA copy number is seemingly in excess, we reason that mtDNA copy number control is an important aspect of mitochondrial genetics and biogenesis and is essential for normal cellular function.
Conversion of Number Systems using Xilinx.
Directory of Open Access Journals (Sweden)
Chinmay V. Deshpande
2015-08-01
Full Text Available There are different types of number systems. Binary number system, octal number system, decimal number system and hexadecimal number system. This paper demonstrates conversion of hexadecimal to binary number using Xilinx software.
The MIXMAX random number generator
Savvidy, Konstantin G.
2015-11-01
In this paper, we study the randomness properties of unimodular matrix random number generators. Under well-known conditions, these discrete-time dynamical systems have the highly desirable K-mixing properties which guarantee high quality random numbers. It is found that some widely used random number generators have poor Kolmogorov entropy and consequently fail in empirical tests of randomness. These tests show that the lowest acceptable value of the Kolmogorov entropy is around 50. Next, we provide a solution to the problem of determining the maximal period of unimodular matrix generators of pseudo-random numbers. We formulate the necessary and sufficient condition to attain the maximum period and present a family of specific generators in the MIXMAX family with superior performance and excellent statistical properties. Finally, we construct three efficient algorithms for operations with the MIXMAX matrix which is a multi-dimensional generalization of the famous cat-map. First, allowing to compute the multiplication by the MIXMAX matrix with O(N) operations. Second, to recursively compute its characteristic polynomial with O(N2) operations, and third, to apply skips of large number of steps S to the sequence in O(N2 log(S)) operations.
Transport numbers in transdermal iontophoresis.
Mudry, Blaise; Guy, Richard H; Delgado-Charro, M Begoña
2006-04-15
Parameters determining ionic transport numbers in transdermal iontophoresis have been characterized. The transport number of an ion (its ability to carry charge) is key to its iontophoretic delivery or extraction across the skin. Using small inorganic ions, the roles of molar fraction and mobility of the co- and counterions present have been demonstrated. A direct, constant current was applied across mammalian skin in vitro. Cations were anodally delivered from either simple M(+)Cl(-) solutions (single-ion case, M(+) = sodium, lithium, ammonium, potassium), or binary and quaternary mixtures thereof. Transport numbers were deduced from ion fluxes. In the single-ion case, maximum cationic fluxes directly related to the corresponding ionic aqueous mobilities were found. Addition of co-ions decreased the transport numbers of all cations relative to the single-ion case, the degree of effect depending upon the molar fraction and mobility of the species involved. With chloride as the principal counterion competing to carry current across the skin (the in vivo situation), a maximum limit on the single or collective cation transport number was 0.6-0.8. Overall, these results demonstrate how current flowing across the skin during transdermal iontophoresis is distributed between competing ions, and establish simple rules with which to optimize transdermal iontophoretic transport.
Hurwitz numbers and BKP hierarchy
Natanzon, S M
2015-01-01
We consider special series in ratios of the Schur functions which are defined by integers $\\textsc{f}\\ge 0$ and $\\textsc{e} \\le 2$, and also by the set of $3k$ parameters $n_i,q_i,t_i,\\,i=1,..., k$. These series may be presented in form of matrix integrals. In case $k=0$ these series generates Hurwitz numbers for the $d$-fold branched covering of connected surfaces with a given Euler characteristic $\\textsc{e}$ and arbitrary profiles at $\\textsc{f}$ ramification points. If $k>0$ they generate weighted sums of the Hurwitz numbers with additional ramification points which are distributed between color groups indexed by $i=1,...,k$, the weights being written in terms of parameters $n_i,q_i,t_i$. By specifying the parameters we get sums of all Hurwitz numbers with $\\textsc{f}$ arbitrary fixed profiles and the additional profiles provided the following condition: both, the sum of profile lengths and the number of ramification points in each color group are given numbers. In case $\\textsc{e}=\\textsc{f}=1,2$ the ser...
Quasiperpendicular high Mach number Shocks
Sulaiman, A H; Dougherty, M K; Burgess, D; Fujimoto, M; Hospodarsky, G B
2015-01-01
Shock waves exist throughout the universe and are fundamental to understanding the nature of collisionless plasmas. Reformation is a process, driven by microphysics, which typically occurs at high Mach number supercritical shocks. While ongoing studies have investigated this process extensively both theoretically and via simulations, their observations remain few and far between. In this letter we present a study of very high Mach number shocks in a parameter space that has been poorly explored and we identify reformation using in situ magnetic field observations from the Cassini spacecraft at 10 AU. This has given us an insight into quasi-perpendicular shocks across two orders of magnitude in Alfven Mach number (MA) which could potentially bridge the gap between modest terrestrial shocks and more exotic astrophysical shocks. For the first time, we show evidence for cyclic reformation controlled by specular ion reflection occurring at the predicted timescale of ~0.3 {\\tau}c, where {\\tau}c is the ion gyroperio...
Schellekens, A N
2016-01-01
This paper contains some personal reflections on several computational contributions to what is now known as the "String Theory Landscape". It consists of two parts. The first part concerns the origin of big numbers, and especially the number $10^{1500}$ that appeared in work on the covariant lattice construction (with W. Lerche and D. Luest). This part contains some new results. I correct a huge but inconsequential error, discuss some more accurate estimates, and compare with the counting for free fermion constructions. In particular I prove that the latter only provide an exponentially small fraction of all even self-dual lattices for large lattice dimensions. The second part of the paper concerns dealing with big numbers, and contains some lessons learned from various vacuum scanning projects.
Covering Numbers for Convex Functions
Guntuboyina, Adityanand
2012-01-01
In this paper we study the covering numbers of the space of convex and uniformly bounded functions in multi-dimension. We find optimal upper and lower bounds for the $\\epsilon$-covering number of $\\C([a, b]^d, B)$, in the $L_p$-metric, $1 \\le p 0$, and $\\C([a,b]^d, B)$ denotes the set of all convex functions on $[a, b]^d$ that are uniformly bounded by $B$. We summarize previously known results on covering numbers for convex functions and also provide alternate proofs of some known results. Our results have direct implications in the study of rates of convergence of empirical minimization procedures as well as optimal convergence rates in the numerous convexity constrained function estimation problems.
Negative numbers in simple arithmetic.
Das, Runa; LeFevre, Jo-Anne; Penner-Wilger, Marcie
2010-10-01
Are negative numbers processed differently from positive numbers in arithmetic problems? In two experiments, adults (N = 66) solved standard addition and subtraction problems such as 3 + 4 and 7 - 4 and recasted versions that included explicit negative signs-that is, 3 - (-4), 7 + (-4), and (-4) + 7. Solution times on the recasted problems were slower than those on standard problems, but the effect was much larger for addition than subtraction. The negative sign may prime subtraction in both kinds of recasted problem. Problem size effects were the same or smaller in recasted than in standard problems, suggesting that the recasted formats did not interfere with mental calculation. These results suggest that the underlying conceptual structure of the problem (i.e., addition vs. subtraction) is more important for solution processes than the presence of negative numbers.
Put numbers on the sustainability
DEFF Research Database (Denmark)
Hauschild, Michael Zwicky
2014-01-01
exposure of humans, to the local impacts associated with physical transformation of land and extraction of water. Chemicals can cause toxic impacts to humans and ecosystems on all scales. All these impacts need to be quantified if we want to put numbers on sustainability. The life cycle perspective...... on products and systems and the coverage of all relevant environmental impacts are combined in Life cycle assessment (LCA) which is introduced in the talk as the tool to put numbers on environmental sustainability. The basics of LCA are introduced, current applications are presented and a discussion of its...
Newborn infants perceive abstract numbers.
Izard, Véronique; Sann, Coralie; Spelke, Elizabeth S; Streri, Arlette
2009-06-23
Although infants and animals respond to the approximate number of elements in visual, auditory, and tactile arrays, only human children and adults have been shown to possess abstract numerical representations that apply to entities of all kinds (e.g., 7 samurai, seas, or sins). Do abstract numerical concepts depend on language or culture, or do they form a part of humans' innate, core knowledge? Here we show that newborn infants spontaneously associate stationary, visual-spatial arrays of 4-18 objects with auditory sequences of events on the basis of number. Their performance provides evidence for abstract numerical representations at the start of postnatal experience.
Geometric Number Systems and Spinors
Sobczyk, Garret
2015-01-01
The real number system is geometrically extended to include three new anticommuting square roots of plus one, each such root representing the direction of a unit vector along the orthonormal coordinate axes of Euclidean 3-space. The resulting geometric (Clifford) algebra provides a geometric basis for the famous Pauli matrices which, in turn, proves the consistency of the rules of geometric algebra. The flexibility of the concept of geometric numbers opens the door to new understanding of the nature of space-time, and of Pauli and Dirac spinors as points on the Riemann sphere, including Lorentz boosts.
Elementary Number Theory with Applications
Koshy, Thomas
2007-01-01
This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. Koshy has added a new chapter on continued fractions. The unique features of the first edition like news of recent discoveries, biographical sketches of mathematicians, and applications--like the use of congruence in scheduling of a round-robin tournament--are being refreshed with current information. More challenging exercises are included both in the t
Magic Numbers in Protein Structures
DEFF Research Database (Denmark)
Lindgård, Per-Anker; Bohr, Henrik
1996-01-01
A homology measure for protein fold classes has been constructed by locally projecting consecutive secondary structures onto a lattice. Taking into account hydrophobic forces we have found a mechanism for formation of domains containing magic numbers of secondary structures and multipla of these ......A homology measure for protein fold classes has been constructed by locally projecting consecutive secondary structures onto a lattice. Taking into account hydrophobic forces we have found a mechanism for formation of domains containing magic numbers of secondary structures and multipla...
Residual number processing in dyscalculia.
Cappelletti, Marinella; Price, Cathy J
2014-01-01
Developmental dyscalculia - a congenital learning disability in understanding numerical concepts - is typically associated with parietal lobe abnormality. However, people with dyscalculia often retain some residual numerical abilities, reported in studies that otherwise focused on abnormalities in the dyscalculic brain. Here we took a different perspective by focusing on brain regions that support residual number processing in dyscalculia. All participants accurately performed semantic and categorical colour-decision tasks with numerical and non-numerical stimuli, with adults with dyscalculia performing slower than controls in the number semantic tasks only. Structural imaging showed less grey-matter volume in the right parietal cortex in people with dyscalculia relative to controls. Functional MRI showed that accurate number semantic judgements were maintained by parietal and inferior frontal activations that were common to adults with dyscalculia and controls, with higher activation for participants with dyscalculia than controls in the right superior frontal cortex and the left inferior frontal sulcus. Enhanced activation in these frontal areas was driven by people with dyscalculia who made faster rather than slower numerical decisions; however, activation could not be accounted for by response times per se, because it was greater for fast relative to slow dyscalculics but not greater for fast controls relative to slow dyscalculics. In conclusion, our results reveal two frontal brain regions that support efficient number processing in dyscalculia.
Residual number processing in dyscalculia
Directory of Open Access Journals (Sweden)
Marinella Cappelletti
2014-01-01
Full Text Available Developmental dyscalculia – a congenital learning disability in understanding numerical concepts – is typically associated with parietal lobe abnormality. However, people with dyscalculia often retain some residual numerical abilities, reported in studies that otherwise focused on abnormalities in the dyscalculic brain. Here we took a different perspective by focusing on brain regions that support residual number processing in dyscalculia. All participants accurately performed semantic and categorical colour-decision tasks with numerical and non-numerical stimuli, with adults with dyscalculia performing slower than controls in the number semantic tasks only. Structural imaging showed less grey-matter volume in the right parietal cortex in people with dyscalculia relative to controls. Functional MRI showed that accurate number semantic judgements were maintained by parietal and inferior frontal activations that were common to adults with dyscalculia and controls, with higher activation for participants with dyscalculia than controls in the right superior frontal cortex and the left inferior frontal sulcus. Enhanced activation in these frontal areas was driven by people with dyscalculia who made faster rather than slower numerical decisions; however, activation could not be accounted for by response times per se, because it was greater for fast relative to slow dyscalculics but not greater for fast controls relative to slow dyscalculics. In conclusion, our results reveal two frontal brain regions that support efficient number processing in dyscalculia.
Residual number processing in dyscalculia.
Cappelletti, M.; Price, C.J.
2014-01-01
Developmental dyscalculia - a congenital learning disability in understanding numerical concepts - is typically associated with parietal lobe abnormality. However, people with dyscalculia often retain some residual numerical abilities, reported in studies that otherwise focused on abnormalities in the dyscalculic brain. Here we took a different perspective by focusing on brain regions that support residual number processing in dyscalculia. All participants accurately performed semantic and ca...
Surrena, Michelle
2011-01-01
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.)
Materiales, 1995
1995-01-01
Four booklets present articles on Spanish language and culture aimed at teachers of Spanish in the United States for student use in their classes. Number 17, "Los Jovenes Espanoles" (Spanish Youth), includes articles on Spanish youth sports, music, gangs, thoughts, and t-shirt slogans: (1) "Young Spanish Athletes"; (2)…
Materiales, 1997
1997-01-01
These three journals of contemporary cultural, historical, and social interest contain activities designed to enhance the awareness of students of Spanish as a foreign language regarding the entire panorama of daily life in Spain. Number 21 focuses on the role of modern Spanish women; their career status; female authors; and the changing place of…
Lenstra theorem in number fields
Indian Academy of Sciences (India)
S Subburam
2014-11-01
In this paper, we present a number field version of the celebrated result of Lenstra (Math. Comp. 42(165) (1984) 331–340) in 1984. Also, this result allows us to improve a result of Wikstrőm (On the -ary GCD-algorithm in rings of integers (2005) pp. 1189–1201).
An introduction to Catalan numbers
Roman, Steven
2015-01-01
This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics. Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more mathematically sophisticated topics. Each chapter focuses on a specific combinatorial object counted by these numbers, including paths, trees, tilings of a staircase, null sums in Zn+1, interval structures, partitions, permutations, semiorders, and more. Exercises are included at the end of book, along with hints and solutions, to help students obtain a better grasp of the material. The text is ideal for undergraduate students studying combinatorics, but will also appeal to anyone with a mathematical background who has an interest in learning about the Catalan numbers. “Roman does an admirable job of providing an introduction to Catalan numbers of a different nature from the previous ones. He has made an excellent choice o...
Questioning Zero and Negative Numbers
Wilcox, Virginia B.
2008-01-01
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…
On badly approximable complex numbers
DEFF Research Database (Denmark)
Esdahl-Schou, Rune; Kristensen, S.
We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably...
A generalized sense of number.
Arrighi, Roberto; Togoli, Irene; Burr, David C
2014-12-22
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.
Covering Numbers for Semicontinuous Functions
2016-04-29
di Matematica pura ed applicata, CLX:303–320, 1991. [3] H. Attouch and R. J-B Wets. A convergence theory for saddle functions. Transactions of the...P. L. Bartlett, J. Shawe-Taylor, and R. C. Williamson. Covering numbers for support vector machines. IEEE Transactions on Information Theory, 48(1
Learning Potentials in Number Blocks
DEFF Research Database (Denmark)
Majgaard, Gunver; Misfeldt, Morten; Nielsen, Jacob
2012-01-01
This paper describes an initial exploration of how an interactive cubic user-configurable modular robotic system can be used to support learning about numbers and how they are pronounced. The development is done in collaboration with a class of 7-8 year old children and their mathematics teacher....
On badly approximable complex numbers
DEFF Research Database (Denmark)
Esdahl-Schou, Rune; Kristensen, S.
We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably...
Counting problems for number rings
Brakenhoff, Johannes Franciscus
2009-01-01
In this thesis we look at three counting problems connected to orders in number fields. First we study the probability that for a random polynomial f in Z[X] the ring Z[X]/f is the maximal order in Q[X]/f. Connected to this is the probability that a random polynomial has a squarefree discriminant. T
Learning Potentials in Number Blocks
DEFF Research Database (Denmark)
Majgaard, Gunver; Misfeldt, Morten; Nielsen, Jacob
2012-01-01
This paper describes an initial exploration of how an interactive cubic user-configurable modular robotic system can be used to support learning about numbers and how they are pronounced. The development is done in collaboration with a class of 7-8 year old children and their mathematics teacher...
On Fixing number of Functigraphs
Fazil, Muhammad; Javaid, Imran; Murtaza, Muhammad
2016-01-01
The fixing number of a graph $G$ is the order of the smallest subset $S$ of its vertex set $V(G)$ such that stabilizer of $S$ in $G$, $\\Gamma_{S}(G)$ is trivial. Let $G_{1}$ and $G_{2}$ be disjoint copies of a graph $G$, and let $g:V(G_{1})\\rightarrow V(G_{2})$ be a function. A functigraph $F_{G}$ consists of the vertex set $V(G_{1})\\cup V(G_{2})$ and the edge set $E(G_{1})\\cup E(G_{2})\\cup \\{uv:v=g(u)\\}$. In this paper, we study the behavior of the fixing number in passing from $G$ to $F_{G}...
Ufnarovski, Victor; Ahlander, Bo
2003-09-01
We define the derivative of an integer to be the map sending every prime to 1 and satisfying the Leibnitz rule. The aim of the article is to consider the basic properties of this map and to show how to generalize the notion to the case of rational and arbitrary real numbers. We make some conjectures and find some connections with Goldbach's Conjecture and the Twin Prime Conjecture. Finally, we solve the easiest associated differential equations and calculate the generating function.
Bansal, N.; Pendavingh, R.; Pol, J.G. van der
2013-01-01
We consider the problem of determining mn, the number of matroids on n elements. The best known lower bound on mn is due to Knuth (1974) who showed that log log mn is at least n− 3 2 log n−O(1). On the other hand, Piﬀ (1973) showed that log log mn ≤ n − log n + log log n + O(1), and it has been conj
Complex numbers in quantum theory
Maynard, Glenn
In 1927, Nobel prize winning physicist, E. Schrodinger, in correspondence with Ehrenfest, wrote the following about the new theory: "What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers. Psi is surely fundamentally a real function." This seemingly simple issue remains unexplained almost ninety years later. In this dissertation I elucidate the physical and theoretical origins of the complex requirement. (Abstract shortened by ProQuest.).
Gyori, Ervin; Lovasz, Laszlo
2006-01-01
This volume honours the eminent mathematicians Vera Sos and Andras Hajnal. The book includes survey articles reviewing classical theorems, as well as new, state-of-the-art results. Also presented are cutting edge expository research papers with new theorems and proofs in the area of the classical Hungarian subjects, like extremal combinatorics, colorings, combinatorial number theory, etc. The open problems and the latest results in the papers are sure to inspire further research.
Brody, T. A.
1984-11-01
A new class of random-number generators is described, based on a combination of the logical exclusive-or operation and the McLaren-Marsaglia mechanism. It is suitable for any word length, requires no multiple-precision arithmetic, and contains no hard-to-determine constants. Though no theory is available, numerical tests have shown it to be very satisfactory. Execution time is less than twice that of standard congruential generators.
Sasanguie, Delphine; Göbel, Silke M; Moll, Kristina; Smets, Karolien; Reynvoet, Bert
2013-03-01
In this study, the performance of typically developing 6- to 8-year-old children on an approximate number discrimination task, a symbolic comparison task, and a symbolic and nonsymbolic number line estimation task was examined. For the first time, children's performances on these basic cognitive number processing tasks were explicitly contrasted to investigate which of them is the best predictor of their future mathematical abilities. Math achievement was measured with a timed arithmetic test and with a general curriculum-based math test to address the additional question of whether the predictive association between the basic numerical abilities and mathematics achievement is dependent on which math test is used. Results revealed that performance on both mathematics achievement tests was best predicted by how well childrencompared digits. In addition, an association between performance on the symbolic number line estimation task and math achievement scores for the general curriculum-based math test measuring a broader spectrum of skills was found. Together, these results emphasize the importance of learning experiences with symbols for later math abilities.
Quasiperpendicular High Mach Number Shocks
Sulaiman, A. H.; Masters, A.; Dougherty, M. K.; Burgess, D.; Fujimoto, M.; Hospodarsky, G. B.
2015-09-01
Shock waves exist throughout the Universe and are fundamental to understanding the nature of collisionless plasmas. Reformation is a process, driven by microphysics, which typically occurs at high Mach number supercritical shocks. While ongoing studies have investigated this process extensively both theoretically and via simulations, their observations remain few and far between. In this Letter we present a study of very high Mach number shocks in a parameter space that has been poorly explored and we identify reformation using in situ magnetic field observations from the Cassini spacecraft at 10 AU. This has given us an insight into quasiperpendicular shocks across 2 orders of magnitude in Alfvén Mach number (MA ) which could potentially bridge the gap between modest terrestrial shocks and more exotic astrophysical shocks. For the first time, we show evidence for cyclic reformation controlled by specular ion reflection occurring at the predicted time scale of ˜0.3 τc , where τc is the ion gyroperiod. In addition, we experimentally reveal the relationship between reformation and MA and focus on the magnetic structure of such shocks to further show that for the same MA , a reforming shock exhibits stronger magnetic field amplification than a shock that is not reforming.
A Pseudo-Random Number Generator Based on Normal Numbers
Energy Technology Data Exchange (ETDEWEB)
Bailey, David H.
2004-12-31
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.
Number Theory, Analysis and Geometry
Goldfeld, Dorian; Jones, Peter
2012-01-01
Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry, and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future. In the spirit of Lang's vast contribution to mathematics, th
Number & operations task & drill sheets
Reed, Nat
2011-01-01
For grades 6-8, our State Standards-based combined resource meets the number & operations concepts addressed by the NCTM standards and encourages the students to review the concepts in unique ways. The task sheets introduce the mathematical concepts to the students around a central problem taken from real-life experiences, while the drill sheets provide warm-up and timed practice questions for the students to strengthen their procedural proficiency skills. Included are problems involving place value, fractions, addition, subtraction and using money. The combined task & drill sheets offer spac
Topological Number of Edge States
Hashimoto, Koji
2016-01-01
We show that the edge states of the four-dimensional class A system can have topological charges, which are characterized by Abelian/non-Abelian monopoles. The edge topological charges are a new feature of relations among theories with different dimensions. From this novel viewpoint, we provide a non-Abelian analogue of the TKNN number as an edge topological charge, which is defined by an SU(2) 't Hooft-Polyakov BPS monopole through an equivalence to Nahm construction. Furthermore, putting a constant magnetic field yields an edge monopole in a non-commutative momentum space, where D-brane methods in string theory facilitate study of edge fermions.
Propulsion at low Reynolds number
Energy Technology Data Exchange (ETDEWEB)
Najafi, Ali [Institute for Advanced Studies in Basic Sciences, Zanjan 45195-159 (Iran, Islamic Republic of); Faculty of Science, Zanjan University, Zanjan 313 (Iran, Islamic Republic of); Golestanian, Ramin [Institute for Advanced Studies in Basic Sciences, Zanjan 45195-159 (Iran, Islamic Republic of)
2005-04-13
We study the propulsion of two model swimmers at low Reynolds number. Inspired by Purcell's model, we propose a very simple one-dimensional swimmer consisting of three spheres that are connected by two arms whose lengths can change between two values. The proposed swimmer can swim with a special type of motion, which breaks the time-reversal symmetry. We also show that an ellipsoidal membrane with tangential travelling wave on it can also propel itself in the direction preferred by the travelling wave. This system resembles the realistic biological animals like Paramecium.
Random number generators and causality
Energy Technology Data Exchange (ETDEWEB)
Larrondo, H.A. [Facultad de Ingenieria, Universidad Nacional de Mar del Plata, Juan B. Justo 4302, 7600 Mar del Plata (Argentina)]. E-mail: larrondo@fi.mdp.edu.ar; Martin, M.T. [Instituto de Fisica (IFLP), Facultad de Ciencias Exactas, Universidad Nacional de La Plata and Argentina' s National Council (CONICET), C.C. 727, 1900 La Plata (Argentina)]. E-mail: mtmartin@venus.unlp.edu.ar; Gonzalez, C.M. [Facultad de Ingenieria, Universidad Nacional de Mar del Plata, Juan B. Justo 4302, 7600 Mar del Plata (Argentina)]. E-mail: cmgonzal@fi.mdp.edu.ar; Plastino, A. [Instituto de Fisica (IFLP), Facultad de Ciencias Exactas, Universidad Nacional de La Plata and Argentina' s National Council (CONICET), C.C. 727, 1900 La Plata (Argentina)]. E-mail: plastino@venus.unlp.edu.ar; Rosso, O.A. [Chaos and Biology Group, Instituto de Calculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellon II, Ciudad Universitaria, 1428 Ciudad de Buenos Aires (Argentina)]. E-mail: oarosso@fibertel.com.ar
2006-04-03
We advance a prescription to randomize physical or algorithmic Random Number Generators (RNG's) that do not pass Marsaglia's DIEHARD test suite and discuss a special physical quantifier, based on an intensive statistical complexity measure, that is able to adequately assess the improvements produced thereby. Eight RNG's are evaluated and the associated results are compared to those obtained by recourse to Marsaglia's DIEHARD test suite. Our quantifier, which is evaluated using causality arguments, can forecast whether a given RNG will pass the above mentioned test.
Random number generators and causality
Larrondo, H. A.; Martín, M. T.; González, C. M.; Plastino, A.; Rosso, O. A.
2006-04-01
We advance a prescription to randomize physical or algorithmic Random Number Generators (RNG's) that do not pass Marsaglia's DIEHARD test suite and discuss a special physical quantifier, based on an intensive statistical complexity measure, that is able to adequately assess the improvements produced thereby. Eight RNG's are evaluated and the associated results are compared to those obtained by recourse to Marsaglia's DIEHARD test suite. Our quantifier, which is evaluated using causality arguments, can forecast whether a given RNG will pass the above mentioned test.
Nielsen number and differential equations
Directory of Open Access Journals (Sweden)
Andres Jan
2005-01-01
Full Text Available In reply to a problem of Jean Leray (application of the Nielsen theory to differential equations, two main approaches are presented. The first is via Poincaré's translation operator, while the second one is based on the Hammerstein-type solution operator. The applicability of various Nielsen theories is discussed with respect to several sorts of differential equations and inclusions. Links with the Sharkovskii-like theorems (a finite number of periodic solutions imply infinitely many subharmonics are indicated, jointly with some further consequences like the nontrivial -structure of solutions of initial value problems. Some illustrating examples are supplied and open problems are formulated.
Number theory III Diophantine geometry
1991-01-01
From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics ...
The MIXMAX random number generator
Savvidy, Konstantin G
2014-01-01
In this note, we give a practical solution to the problem of determining the maximal period of matrix generators of pseudo-random numbers which are based on an integer-valued unimodular matrix of size NxN known as MIXMAX and arithmetic defined on a Galois field GF[p] with large prime modulus p. The existing theory of Galois finite fields is adapted to the present case, and necessary and sufficient condition to attain the maximum period is formulated. Three efficient algorithms are presented. First, allowing to compute the multiplication by the MIXMAX matrix with O(N) operations. Second, to recursively compute the characteristic polynomial with O(N^2) operations, and third, to apply skips of large number of steps S to the sequence in O(N^2 log(S)) operations. It is demonstrated that the dynamical properties of this generator dramatically improve with the size of the matrix N, as compared to the classes of generators based on sparse matrices and/or sparse characteristic polynomials. Finally, we present the impl...
Formation number for vortex dipoles
Sadri, Vahid; Krueger, Paul S.
2016-11-01
This investigation considers the axisymmetric formation of two opposite sign concentric vortex rings from jet ejection between concentric cylinders. This arrangement is similar to planar flow in that the vortex rings will travel together when the gap between the cylinders is small, similar to a vortex dipole, but it has the advantage that the vortex motion is less constrained than the planar case (vortex stretching and vortex line curvature is allowed). The flow was simulated numerically at a jet Reynolds number of 1,000 (based on ΔR and the jet velocity), jet pulse length-to-gap ratio (L / ΔR) in the range 10-20, and gap-to-outer radius ratio (ΔR /Ro) in the range 0.01-0.1. Small gap ratios were chosen for comparison with 2D results. In contrast with 2D results, the closely paired vortices in this study exhibited pinch-off from the generating flow and finite formation numbers. The more complex flow evolution afforded by the axisymmetric model and its influence on the pinch-off process will be discussed. This material is based on work supported by the National Science Foundation under Grant No. 1133876 and SMU. This supports are gratefully acknowledged.
Banner prints social security numbers
Directory of Open Access Journals (Sweden)
Robbins RA
2014-02-01
Full Text Available No abstract available. Article truncated at 150 words. The Monday edition of the Arizona Republic contained a story with potential interest to our readers. On the most recent address labels of Banner Health's magazine, Smart & Healthy, the addressee's Social Security or Medicare identification numbers, which are often identical to their Social Security numbers (1. The magazine was mailed to more than 50,000 recipients in Arizona late last week. The recipients are members of the Medicare Pioneer Accountable Care Organization, a government health-care plan that Banner serves. Banner generated its mailing list from information it received from the U.S. Centers for Medicare & Medicaid Services, which is an agency within the U.S. Department of Health & Human Services (HHS responsible for administration of several federal health-care programs. Although medical information has been protected by the Health Insurance Portability and Accountability Act (HIPAA since 1996, penalties were recently increased. Civil monetary penalties were increased from a maximum of $100 ...
Topics in Number Theory Conference
Andrews, George; Ono, Ken
1999-01-01
From July 31 through August 3,1997, the Pennsylvania State University hosted the Topics in Number Theory Conference. The conference was organized by Ken Ono and myself. By writing the preface, I am afforded the opportunity to express my gratitude to Ken for beng the inspiring and driving force behind the whole conference. Without his energy, enthusiasm and skill the entire event would never have occurred. We are extremely grateful to the sponsors of the conference: The National Sci ence Foundation, The Penn State Conference Center and the Penn State Depart ment of Mathematics. The object in this conference was to provide a variety of presentations giving a current picture of recent, significant work in number theory. There were eight plenary lectures: H. Darmon (McGill University), "Non-vanishing of L-functions and their derivatives modulo p. " A. Granville (University of Georgia), "Mean values of multiplicative functions. " C. Pomerance (University of Georgia), "Recent results in primality testing. " C. ...
Signals of lepton number violation
Panella, O; Srivastava, Y N
1999-01-01
The production of like-sign-dileptons (LSD), in the high energy lepton number violating ( Delta L=+2) reaction, pp to 2jets+l/sup +/l /sup +/, (l=e, mu , tau ), of interest for the experiments to be performed at the forthcoming Large Hadron Collider (LHC), is reported, taking up a composite model scenario in which the exchanged virtual composite neutrino is assumed to be a Majorana particle. Numerical estimates of the corresponding signal cross-section that implement kinematical cuts needed to suppress the standard model background, are presented which show that in some regions of the parameter space the total number of LSD events is well above the background. Assuming non-observation of the LSD signal it is found that LHC would exclude a composite Majorana neutrino up to 700 GeV (if one requires 10 events for discovery). The sensitivity of LHC experiments to the parameter space is then compared to that of the next generation of neutrinoless double beta decay ( beta beta /sub 0 nu /) experiment, GENIUS, and i...
Cryptography and computational number theory
Shparlinski, Igor; Wang, Huaxiong; Xing, Chaoping; Workshop on Cryptography and Computational Number Theory, CCNT'99
2001-01-01
This volume contains the refereed proceedings of the Workshop on Cryptography and Computational Number Theory, CCNT'99, which has been held in Singapore during the week of November 22-26, 1999. The workshop was organized by the Centre for Systems Security of the Na tional University of Singapore. We gratefully acknowledge the financial support from the Singapore National Science and Technology Board under the grant num ber RP960668/M. The idea for this workshop grew out of the recognition of the recent, rapid development in various areas of cryptography and computational number the ory. The event followed the concept of the research programs at such well-known research institutions as the Newton Institute (UK), Oberwolfach and Dagstuhl (Germany), and Luminy (France). Accordingly, there were only invited lectures at the workshop with plenty of time for informal discussions. It was hoped and successfully achieved that the meeting would encourage and stimulate further research in information and computer s...
Nielsen number and differential equations
Directory of Open Access Journals (Sweden)
Jan Andres
2005-06-01
Full Text Available In reply to a problem of Jean Leray (application of the Nielsen theory to differential equations, two main approaches are presented. The first is via PoincarÃƒÂ©'s translation operator, while the second one is based on the Hammerstein-type solution operator. The applicability of various Nielsen theories is discussed with respect to several sorts of differential equations and inclusions. Links with the Sharkovskii-like theorems (a finite number of periodic solutions imply infinitely many subharmonics are indicated, jointly with some further consequences like the nontrivial RÃŽÂ´-structure of solutions of initial value problems. Some illustrating examples are supplied and open problems are formulated.
Generalized Compositions and Weighted Fibonacci Numbers
Janjic, Milan
2010-01-01
In this paper we consider particular generalized compositions of a natural number with a given number of parts. Its number is a weighted polynomial coefficient. The number of all generalized compositions of a natural number is a weighted $r$-generalized Fibonacci number. A relationship between these two numbers will be derived. We shall thus obtain a generalization of the well-known formula connecting Fibonacci numbers with the binomial coefficients.
Energy Technology Data Exchange (ETDEWEB)
Ekman, Lennart; Ekman, Mats [LE Geokonsult AB, Baelinge (Sweden)
2013-03-15
than those presented in Gustafson and Ljungberg (2010), which is in line with findings in Finland (Satakunta, Olkiluoto, Kivetty, Romuvaara) as well as with many of the baselines in the measurements at Oskarshamn (Aespoe/Laxemar). We recommend that the GPS measurements proceed for a number of years, preferably as continuous measurements rather than intermittent campaigns. The advantages with continuous measurements are that they enable identification of slow as well as rapid periodical changes, and also counteract the aliasing effect.
Access to emergency number services.
Harkins, Judith E; Strauss, Karen Peltz
2008-01-01
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.
Essays on the theory of numbers
Dedekind, Richard
1963-01-01
Two classic essays by great German mathematician: one provides an arithmetic, rigorous foundation for the irrational numbers, the other is an attempt to give the logical basis for transfinite numbers and properties of the natural numbers.
Arithmetic Algorithms for Hereditarily Binary Natural Numbers
Tarau, Paul
2013-01-01
We study some essential arithmetic properties of a new tree-based number representation, {\\em hereditarily binary numbers}, defined by applying recursively run-length encoding of bijective base-2 digits. Our representation expresses giant numbers like the largest known prime number and its related perfect number as well as the largest known Woodall, Cullen, Proth, Sophie Germain and twin primes as trees of small sizes. More importantly, our number representation supports novel algorithms that...
How to be Brilliant at Numbers
Webber, Beryl
2010-01-01
How to be Brilliant at Numbers will help students to develop an understanding of numbers, place value, fractions and decimals. They will develop the language of number, and of the relationships between numbers. They will also use mathematics to solve problems and will develop mathematical reasoning. Using the worksheets in this book, pupils will learn about: ancient Greek numbers; coins; digits; consecutive numbers; magic ladders; fractions; matching pairs; multiples of 10; rounding; decimal un
46 CFR Sec. 2 - Voyage numbers.
2010-10-01
... 46 Shipping 8 2010-10-01 2010-10-01 false Voyage numbers. Sec. 2 Section 2 Shipping MARITIME ADMINISTRATION, DEPARTMENT OF TRANSPORTATION A-NATIONAL SHIPPING AUTHORITY VOYAGE DATA Sec. 2 Voyage numbers. (a... designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change...
Some relations between entropy and approximation numbers
Institute of Scientific and Technical Information of China (English)
郑志明
1999-01-01
A general result is obtained which relates the entropy numbers of compact maps on Hilbert space to its approximation numbers. Compared with previous works in this area, it is particularly convenient for dealing with the cases where the approximation numbers decay rapidly. A nice estimation between entropy and approximation numbers for noncompact maps is given.
Using Quasigroups for Generating Pseudorandom Numbers
Godavarty, Vinod Kumar
2011-01-01
This paper presents an algorithm for generating pseudorandom numbers using quasigroups. Random numbers have several applications in the area of secure communication. The proposed algorithm uses a matrix of size n x n which is pre-generated and stored. The quality of random numbers generated is compared with other pseudorandom number generator using Marsaglia's Diehard battery of tests.
Mental number space in three dimensions.
Winter, Bodo; Matlock, Teenie; Shaki, Samuel; Fischer, Martin H
2015-10-01
A large number of experimental findings from neuroscience and experimental psychology demonstrated interactions between spatial cognition and numerical cognition. In particular, many researchers posited a horizontal mental number line, where small numbers are thought of as being to the left of larger numbers. This review synthesizes work on the mental association between space and number, indicating the existence of multiple spatial mappings: recent research has found associations between number and vertical space, as well as associations between number and near/far space. We discuss number space in three dimensions with an eye on potential origins of the different number mappings, and how these number mappings fit in with our current knowledge of brain organization and brain-culture interactions. We derive novel predictions and show how this research fits into a general view of cognition as embodied, grounded and situated.
A proof of image Euler Number formula
Institute of Scientific and Technical Information of China (English)
LIN Xiaozhu; SHA Yun; JI Junwei; WANG Yanmin
2006-01-01
Euler Number is one of the most important characteristics in topology. In two- dimension digital images, the Euler characteristic is locally computable. The form of Euler Number formula is different under 4-connected and 8-connected conditions. Based on the definition of the Foreground Segment and Neighbor Number, a formula of the Euler Number computing is proposed and is proved in this paper. It is a new idea to locally compute Euler Number of 2D image.
Quantum Mechanics interpreted in Quantum Real Numbers
Corbett, J V; Corbett, John V; Durt, Thomas
2002-01-01
The concept of number is fundamental to the formulation of any physical theory. We give a heuristic motivation for the reformulation of Quantum Mechanics in terms of non-standard real numbers called Quantum Real Numbers. The standard axioms of quantum mechanics are re-interpreted. Our aim is to show that, when formulated in the language of quantum real numbers, the laws of quantum mechanics appear more natural, less counterintuitive than when they are presented in terms of standard numbers.
The Bessel Numbers and Bessel Matrices
Institute of Scientific and Technical Information of China (English)
Sheng Liang YANG; Zhan Ke QIAO
2011-01-01
In this paper,using exponential Riordan arrays,we investigate the Bessel numbers and Bessel matrices.By exploring links between the Bessel matrices,the Stirling matrices and the degenerate Stirling matrices,we show that the Bessel numbers are special case of the degenerate Stirling numbers,and derive explicit formulas for the Bessel numbers in terms of the Stirling numbers and binomial coefficients.
The relational nature of rational numbers
Directory of Open Access Journals (Sweden)
Bruce Brown
2015-06-01
Full Text Available It is commonly accepted that the knowledge and learning of rational numbers is more complex than that of the whole number field. This complexity includes the broader range of application of rational numbers, the increased level of technical complexity in the mathematical structure and symbol systems of this field and the more complex nature of many conceptual properties of the rational number field. Research on rational number learning is divided as to whether children’s difficulties in learning rational numbers arise only from the increased complexity or also include elements of conceptual change. This article argues for a fundamental conceptual difference between whole and rational numbers. It develops the position that rational numbers are fundamentally relational in nature and that the move from absolute counts to relative comparisons leads to a further level of abstraction in our understanding of number and quantity. The argument is based on a number of qualitative, in-depth research projects with children and adults. These research projects indicated the importance of such a relational understanding in both the learning and teaching of rational numbers, as well as in adult representations of rational numbers on the number line. Acknowledgement of such a conceptual change could have important consequences for the teaching and learning of rational numbers.
New families of special numbers for computing negative order Euler numbers
Simsek, Yilmaz
2016-01-01
The main purpose of this paper is to construct new families of special numbers with their generating functions. These numbers are related to the many well-known numbers, which are the Bernoulli numbers, the Fibonacci numbers, the Lucas numbers, the Stirling numbers of the second kind and the central factorial numbers. Our other inspiration of this paper is related to the Golombek's problem \\cite{golombek} \\textquotedblleft Aufgabe 1088, El. Math. 49 (1994) 126-127\\textquotedblright . Our firs...
The Translated Dowling Polynomials and Numbers.
Mangontarum, Mahid M; Macodi-Ringia, Amila P; Abdulcarim, Normalah S
2014-01-01
More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such as exponential generating functions and explicit formula for the translated Dowling polynomials and numbers are obtained. Convexity, integral representation, and other interesting identities are also investigated and presented. We show that the properties obtained are generalizations of some of the known results involving the classical Bell polynomials and numbers. Lastly, we established the Hankel transform of the translated Dowling numbers.
A determinant of generalized Fibonacci numbers
Krattenthaler, Christian
2012-01-01
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.
Negative numbers are generated in the mind.
Ganor-Stern, Dana; Tzelgov, Joseph
2008-01-01
The goal of the present study was to disentangle two possible representations of negative numbers--the holistic representation, where absolute magnitude is integrated with polarity; and the components representation, where absolute magnitude is stored separately from polarity. Participants' performance was examined in two tasks involving numbers from--100 to 100. In the numerical comparison task, participants had to decide which number of a pair was numerically larger/smaller. In the number line task, participants were presented with a spatial number line on which they had to place a number. The results of both tasks support the components representation of negative numbers. The findings suggest that processing of negative numbers does not involve retrieval of their meaning from memory, but rather the integration of the polarity sign with the digits' magnitudes.
The Concept and Operations of Blind Number
Institute of Scientific and Technical Information of China (English)
PANG Yan-jun; LIU Kai-di; ZHANG Bo-wen
2001-01-01
This paper gives the definition and operations of blind number, and discusses its operationproperties. Blind number is a mathematical tool to express and deal with complex information with severalkinds of uncertainty.
Quantity Cognition: Numbers, Numerosity, Zero and Mathematics.
Harvey, Ben M
2016-05-23
Physical quantities differ from abstract numbers and mathematics, but recent results are revealing the neural representation of both: a new study demonstrates how an absence of quantity is transformed into a representation of zero as a number.
What Do Numbers Do in Transnational Governance?
DEFF Research Database (Denmark)
Krause Hansen, Hans; Porter, Tony
2012-01-01
This study examines how numbers in transnational governance constitute actors, objects, and relationships, including relationships of power. We review the existing literatures on numbers for insights relevant to their role in transnational governance, including the ontology of numbers, the history...... of numbers and their role in governance. On this basis, we set out the main distinctive ways that numbers are implicated in transnational governance. We conclude that studies of transnational governance would benefit from paying more attention to the much overlooked performative role of numbers in governance...... processes. Numbers have properties that differ from words, and shifts from one to the other in governance, for instance in the displacement of laws or norms with risk models or rankings based on numbers, have particular effects, including political effects on states, firms, individuals, and other actors...
The occurrence of prime numbers revisited
Ernesto Tapia Moore; José Tapia Yañez
2016-01-01
Based on an arithmetical and autocatalytic approach, the authors propose a solution for the occurrence of prime numbers. Exact arithmetical calculations are provided for: the closest prime to any given positive integer (or any number of bigger or smaller primes from that integer); the quantity of prime (and composite) numbers between 1 and any positive integer; the quantity of prime (and composite) numbers between any two positive integers.
The occurrence of prime numbers revisited
Directory of Open Access Journals (Sweden)
Ernesto Tapia Moore
2016-03-01
Full Text Available Based on an arithmetical and autocatalytic approach, the authors propose a solution for the occurrence of prime numbers. Exact arithmetical calculations are provided for: the closest prime to any given positive integer (or any number of bigger or smaller primes from that integer; the quantity of prime (and composite numbers between 1 and any positive integer; the quantity of prime (and composite numbers between any two positive integers.
A new definition of Bejan number
Directory of Open Access Journals (Sweden)
Awad Mohamed M.
2012-01-01
Full Text Available A new definition of Bejan number will be generated by replacing the thermal diffusivity with the mass diffusivity. For example, the Schmidt number is the mass transfer analog of the Prandtl number. For the case of Reynolds analogy (Sc = Pr = = 1, both current and new definitions of Bejan number are the same. This new definition is useful and needed for diffusion of mass (mass diffusion.
Caspar Wessel on representing complex numbers (1799)
DEFF Research Database (Denmark)
Branner, Bodil
1999-01-01
In celebration of the bicentenary of the publication of Wessel's paper on the geometric interpretation of complex numbers it is decsribed how Wessel used complex numbers to represent directions in surveying, at least as early as 1787.......In celebration of the bicentenary of the publication of Wessel's paper on the geometric interpretation of complex numbers it is decsribed how Wessel used complex numbers to represent directions in surveying, at least as early as 1787....
Some inequalities for the Bell numbers
Indian Academy of Sciences (India)
FENG QI
2017-09-01
In this paper, we present derivatives of the generating functions for the Bell numbers by induction and by the Faà di Bruno formula, recover an explicit formula in terms of the Stirling numbers of the second kind, find the (logarithmically) absolute and complete monotonicity of the generating functions, and construct some inequalities for the Bell numbers. From these inequalities, we derive the logarithmic convexity of the sequence of the Bell numbers.
Relativistic theory of tidal Love numbers
Binnington, Taylor; Poisson, Eric
2009-01-01
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 neut...
49 CFR 230.47 - Boiler number.
2010-10-01
... 49 Transportation 4 2010-10-01 2010-10-01 false Boiler number. 230.47 Section 230.47..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known,...
The numbering of Sarawak Forest Department collections
Ashton, P.S.
1966-01-01
Taxonomists working with material collected by the Sarawak Forest Department have often been hard put to decide how to quote numbers. Is the departmental series number preceeded by a letter S, or an F, or would it be best to quote only the collector and the number? I have tried to unravel the histor
2010-10-01
... 47 Telecommunication 1 2010-10-01 2010-10-01 false File numbers. 1.1405 Section 1.1405... Procedures § 1.1405 File numbers. Each complaint which appears to be essentially complete under § 1.1404 will be accepted and assigned a file number. Such assignment is for administrative purposes only and...
75 FR 18572 - Facility Control Numbers
2010-04-12
... Internal Revenue Service Facility Control Numbers AGENCY: Internal Revenue Service (IRS), Treasury. ACTION: Notice of planned use of Facility Control Numbers. SUMMARY: The IRS has developed and is publishing in this issue of the Federal Register, Facility Control Numbers to communicate to the motor fuel...
20 CFR 404.1220 - Identification numbers.
2010-04-01
... 20 Employees' Benefits 2 2010-04-01 2010-04-01 false Identification numbers. 404.1220 Section 404... § 404.1220 Identification numbers. (a) State and local governments. When a State submits a modification... will assign a special identification number to each political subdivision included in that...
2010-07-01
... 32 National Defense 6 2010-07-01 2010-07-01 false Numbers. 1602.19 Section 1602.19 National Defense Other Regulations Relating to National Defense SELECTIVE SERVICE SYSTEM DEFINITIONS § 1602.19 Numbers. Cardinal numbers may be expressed by Arabic or Roman symbols....
Developmental Changes in the Whole Number Bias
Braithwaite, David W.; Siegler, Robert S.
2017-01-01
Many students' knowledge of fractions is adversely affected by whole number bias, the tendency to focus on the separate whole number components (numerator and denominator) of a fraction rather than on the fraction's integrated magnitude (ratio of numerator to denominator). Although whole number bias appears early in the fraction learning process…
Combinatorial Interpretation of General Eulerian Numbers
Directory of Open Access Journals (Sweden)
Tingyao Xiong
2014-01-01
Full Text Available Since the 1950s, mathematicians have successfully interpreted the traditional Eulerian numbers and q-Eulerian numbers combinatorially. In this paper, the authors give a combinatorial interpretation to the general Eulerian numbers defined on general arithmetic progressions a,a+d,a+2d,….
General Eulerian Numbers and Eulerian Polynomials
Directory of Open Access Journals (Sweden)
Tingyao Xiong
2013-01-01
Full Text Available We will generalize the definitions of Eulerian numbers and Eulerian polynomials to general arithmetic progressions. Under the new definitions, we have been successful in extending several well-known properties of traditional Eulerian numbers and polynomials to the general Eulerian polynomials and numbers.
Fascinating Fibonaccis: Mystery and Magic in Numbers.
Garland, Trudi Hammel
This document presents activities and information related to Fibonacci numbers, which are based upon the Golden Ratio, in areas of the arts, sciences, and mathematics. The work is organized into eight chapters: (1) "Origins and Definitions"; (2) "Fibonacci Numbers in Nature"; (3) "Fibonacci Numbers in Art and…
A note on Quarks and numbers theory
Hage-Hassan, Mehdi
2013-01-01
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.
Evaluating Number Sense in Workforce Students
Steinke, Dorothea A.
2015-01-01
Earlier institution-sponsored research revealed that about 20% of students in community college basic math and pre-algebra programs lacked a sense of part-whole relationships with whole numbers. Using the same tool with a group of 86 workforce students, about 75% placed five whole numbers on an empty number line in a way that indicated lack of…
Graphing Powers and Roots of Complex Numbers.
Embse, Charles Vonder
1993-01-01
Using De Moivre's theorem and a parametric graphing utility, examines powers and roots of complex numbers and allows students to establish connections between the visual and numerical representations of complex numbers. Provides a program to numerically verify the roots of complex numbers. (MDH)
The Bezout Number of Piecewise Algebraic Curves
Institute of Scientific and Technical Information of China (English)
Dian Xuan GONG; Ren Hong WANG
2012-01-01
Based on the discussion of the number of roots of univariate spline and the common zero points of two piecewise algebraic curves,a lower upbound of Bezout number of two piecewise algebraic curves on any given non-obtuse-angled triangulation is found.Bezout number of two piecewise algebraic curves on two different partitions is also discussed in this paper.
The Decimal Representation of Real Numbers
Kalapodi, A.
2010-01-01
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…
Reading the World through Very Large Numbers
Greer, Brian; Mukhopadhyay, Swapna
2010-01-01
One original, and continuing, source of interest in large numbers is observation of the natural world, such as trying to count the stars on a clear night or contemplation of the number of grains of sand on the seashore. Indeed, a search of the internet quickly reveals many discussions of the relative numbers of stars and grains of sand. Big…
CIRCULAR CHROMATIC NUMBER AND MYCIELSKI GRAPHS
Institute of Scientific and Technical Information of China (English)
Liu Hongmei
2006-01-01
For a general graph G, M(G) denotes its Mycielski graph. This article gives a number of new sufficient conditions for G to have the circular chromatic number xc (M(G))equals to the chromatic number x(M(G)), which have improved some best sufficient conditions published up to date.
Identifying Fractions on a Number Line
Wong, Monica
2013-01-01
Fractions are generally introduced to students using the part--whole model. Yet the number line is another important representation which can be used to build fraction concepts (Australian Curriculum Assessment and Reporting Authority [ACARA], 2012). Number lines are recognised as key in students' number development not only of fractions, but…
Children's Use of Number Line Estimation Strategies
Peeters, Dominique; Degrande, Tine; Ebersbach, Mirjam; Verschaffel, Lieven; Luwel, Koen
2016-01-01
This study tested whether second graders use benchmark-based strategies when solving a number line estimation (NLE) task. Participants were assigned to one of three conditions based on the availability of benchmarks provided on the number line. In the bounded condition, number lines were only bounded at both sides by 0 and 200, while the midpoint…
Ordinality and the nature of symbolic numbers.
Lyons, Ian M; Beilock, Sian L
2013-10-23
The view that representations of symbolic and nonsymbolic numbers are closely tied to one another is widespread. However, the link between symbolic and nonsymbolic numbers is almost always inferred from cardinal processing tasks. In the current work, we show that considering ordinality instead points to striking differences between symbolic and nonsymbolic numbers. Human behavioral and neural data show that ordinal processing of symbolic numbers (Are three Indo-Arabic numerals in numerical order?) is distinct from symbolic cardinal processing (Which of two numerals represents the greater quantity?) and nonsymbolic number processing (ordinal and cardinal judgments of dot-arrays). Behaviorally, distance-effects were reversed when assessing ordinality in symbolic numbers, but canonical distance-effects were observed for cardinal judgments of symbolic numbers and all nonsymbolic judgments. At the neural level, symbolic number-ordering was the only numerical task that did not show number-specific activity (greater than control) in the intraparietal sulcus. Only activity in left premotor cortex was specifically associated with symbolic number-ordering. For nonsymbolic numbers, activation in cognitive-control areas during ordinal processing and a high degree of overlap between ordinal and cardinal processing networks indicate that nonsymbolic ordinality is assessed via iterative cardinality judgments. This contrasts with a striking lack of neural overlap between ordinal and cardinal judgments anywhere in the brain for symbolic numbers, suggesting that symbolic number processing varies substantially with computational context. Ordinal processing sheds light on key differences between symbolic and nonsymbolic number processing both behaviorally and in the brain. Ordinality may prove important for understanding the power of representing numbers symbolically.
The total bondage number of grid graphs
Hu, Fu-Tao; Xu, Jun-Ming
2011-01-01
The total domination number of a graph $G$ without isolated vertices is the minimum number of vertices that dominate all vertices in $G$. The total bondage number $b_t(G)$ of $G$ is the minimum number of edges whose removal enlarges the total domination number. This paper considers grid graphs. An $(n,m)$-grid graph $G_{n,m}$ is defined as the cartesian product of two paths $P_n$ and $P_m$. This paper determines the exact values of $b_t(G_{n,2})$ and $b_t(G_{n,3})$, and establishes some upper bounds of $b_t(G_{n,4})$.
Sparing of number words in oral production
Directory of Open Access Journals (Sweden)
Carlo Semenza
2014-04-01
In sentences only number words were spared; free standing function words and bound morphemes were as affected as other word categories. Discussion. These findings seem to set cardinal number words apart in the phonological output buffer from other possible building blocks of preassembled phonological units (like function words and bound morphemes. Building blocks constituted by numbers are more cohesive than the blocks constituted by function words and bound morphemes. Bencini et al. (2011 argued that numbers are recursive and consist of basic lexical units which are then combined following syntactic rules. This property would make number words resistant to damage in the phonological buffer.
Fibonacci and Catalan Numbers An Introduction
Grimaldi, Ralph
2012-01-01
In this one-of-a-kind book, Ralph Grimaldi uses his extensive experience from the classroom and as a leader of mini-courses to present an accessible, single resource on the topics of Fibonacci Numbers and Catalan Numbers . The book first embarks on a complete treatment of Fibonacci numbers. Starting with a historical background on the topic, the author goes on to present the properties of Fibonacci numbers, a slew of introductory-level examples, and in-depth discussion of related topics including compositions and palindromes; tiling and Fibonacci numbers
An adventurer's guide to number theory
Friedberg, Richard
1995-01-01
In this delightful guide, a noted mathematician and teacher offers a witty, historically oriented introduction to number theory, dealing with properties of numbers and with numbers as abstract concepts. Written for readers with an understanding of arithmetic and beginning algebra, the book presents the classical discoveries of number theory, including the work of Pythagoras, Euclid, Diophantus, Fermat, Euler, Lagrange and Gauss.Unlike many authors, however, Mr. Friedberg encourages students to think about the imaginative, playful qualities of numbers as they consider such subjects as primes
Percon8 Algorithm for Random Number Generation
Directory of Open Access Journals (Sweden)
Dr. Mrs. Saylee Gharge
2014-05-01
Full Text Available In today’s technology savvy world, computer security holds a prime importance. Most computer security algorithms require some amount of random data for generating public and private keys, session keys or for other purposes. Random numbers are those numbers that occur in a sequence such that the future value of the sequence cannot be predicted based on present or past values. Random numbers find application in statistical analysis and probability theory. The many applications of randomness have led to the development of random number generating algorithms. These algorithms generate a sequence of random numbers either computationally or physically. In our proposed technique, we have implemented a random number generation algorithm combining two existing random number generation techniques viz. Mid square method and Linear Congruential Generator
Neocortical glial cell numbers in human brains
DEFF Research Database (Denmark)
Pelvig, D.P.; Pakkenberg, H.; Stark, A.K.
2008-01-01
and neurons and counting were done in each of the four lobes. The study showed that the different subpopulations of glial cells behave differently as a function of age; the number of oligodendrocytes showed a significant 27% decrease over adult life and a strong correlation to the total number of neurons...... while the total astrocyte number is constant through life; finally males have a 28% higher number of neocortical glial cells and a 19% higher neocortical neuron number than females. The overall total number of neocortical neurons and glial cells was 49.3 billion in females and 65.2 billion in males......, a difference of 24% with a high biological variance. These numbers can serve as reference values in quantitative studies of the human neocortex. (C) 2007 Elsevier Inc. All rights reserved Udgivelsesdato: 2008/11...
Fibonacci number of the tadpole graph
Directory of Open Access Journals (Sweden)
Joe DeMaio
2014-10-01
Full Text Available In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2 and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph via algebraic and combinatorial methods.
Monotone Hurwitz numbers in genus zero
Goulden, I P; Novak, Jonathan
2012-01-01
Hurwitz numbers count branched covers of the Riemann sphere with specified ramification data, or equivalently, transitive permutation factorizations in the symmetric group with specified cycle types. Monotone Hurwitz numbers count a restricted subset of the branched covers counted by the Hurwitz numbers, and have arisen in recent work on the the asymptotic expansion of the Harish-Chandra-Itzykson-Zuber integral. In this paper we begin a detailed study of monotone Hurwitz numbers. We prove two results that are reminiscent of those for classical Hurwitz numbers. The first is the monotone join-cut equation, a partial differential equation with initial conditions that characterizes the generating function for monotone Hurwitz numbers in arbitrary genus. The second is our main result, in which we give an explicit formula for monotone Hurwitz numbers in genus zero.
Riemann equation for prime number diffusion.
Chen, Wen; Liang, Yingjie
2015-05-01
This study makes the first attempt to propose the Riemann diffusion equation to describe in a manner of partial differential equation and interpret in physics of diffusion the classical Riemann method for prime number distribution. The analytical solution of this equation is the well-known Riemann representation. The diffusion coefficient is dependent on natural number, a kind of position-dependent diffusivity diffusion. We find that the diffusion coefficient of the Riemann diffusion equation is nearly a straight line having a slope 0.99734 in the double-logarithmic axis. Consequently, an approximate solution of the Riemann diffusion equation is obtained, which agrees well with the Riemann representation in predicting the prime number distribution. Moreover, we interpret the scale-free property of prime number distribution via a power law function with 1.0169 the scale-free exponent in respect to logarithmic transform of the natural number, and then the fractal characteristic of prime number distribution is disclosed.
Self-correcting random number generator
Energy Technology Data Exchange (ETDEWEB)
Humble, Travis S.; Pooser, Raphael C.
2016-09-06
A system and method for generating random numbers. The system may include a random number generator (RNG), such as a quantum random number generator (QRNG) configured to self-correct or adapt in order to substantially achieve randomness from the output of the RNG. By adapting, the RNG may generate a random number that may be considered random regardless of whether the random number itself is tested as such. As an example, the RNG may include components to monitor one or more characteristics of the RNG during operation, and may use the monitored characteristics as a basis for adapting, or self-correcting, to provide a random number according to one or more performance criteria.
Cortical areas involved in Arabic number reading.
Roux, F-E; Lubrano, V; Lauwers-Cances, V; Giussani, C; Démonet, J-F
2008-01-15
Distinct functional pathways for processing words and numbers have been hypothesized from the observation of dissociated impairments of these categories in brain-damaged patients. We aimed to identify the cortical areas involved in Arabic number reading process in patients operated on for various brain lesions. Direct cortical electrostimulation was prospectively used in 60 brain mappings. We used object naming and two reading tasks: alphabetic script (sentences and number words) and Arabic number reading. Cortical areas involved in Arabic number reading were identified according to location, type of interference, and distinctness from areas associated with other language tasks. Arabic number reading was sustained by small cortical areas, often extremely well localized (area (Brodmann area 45), the anterior part of the dominant supramarginal gyrus (Brodmann area 40; p area (Brodmann area 37; p areas.
Waring’s Problem for Pyramidal Numbers
Institute of Scientific and Technical Information of China (English)
邓越凡; 杨振宁
1994-01-01
It has been proved that every positive integer is expressible as a sum of no more than eight pyramidal numbers P(m)=(m-1)m(m+1)/6.This paper reports on a computer calculation of the partition of integers from n=1 to 109 into pyramidal numbers.We find that no integer≤10°needs more than five pyramidal numbers for its partition,and only 241 of them do need five.We define J(n) as the least number of pyramidal numbers to partition n,and Nk(n) as the number of positive integers l less than or equal to n for which J(l)=k.Based on our numerical results we make conjectures about the asymptotic form of Nk(n) for n→∞
Relativistic theory of tidal Love numbers
Binnington, Taylor
2009-01-01
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.
Conferences on Combinatorial and Additive Number Theory
2014-01-01
This proceedings volume is based on papers presented at the Workshops on Combinatorial and Additive Number Theory (CANT), which were held at the Graduate Center of the City University of New York in 2011 and 2012. The goal of the workshops is to survey recent progress in combinatorial number theory and related parts of mathematics. The workshop attracts researchers and students who discuss the state-of-the-art, open problems, and future challenges in number theory.
On quark number susceptibilities at high temperatures
Bazavov, A; Hegde, P; Karsch, F; Miao, C; Mukherjee, Swagato; Petreczky, P; Schmidt, C; Velytsky, A
2013-01-01
We calculated second and fourth order quark number susceptibilities for 2+1 flavor QCD in the high temperature region using two improved staggered fermion formulations. The calculations are performed at several lattice spacing and we show that in the continuum limit the two formulations give consistent results. We compare our continuum extrapolated results on quark number susceptibilities with recent weak coupling calculations, and find that these cannot simultaneously explain the lattice results for second and fourth order quark number susceptibilities.
Physical tests for random numbers in simulations
Vattulainen, I.; Ala-Nissila, T.; Kankaala, K.
1994-11-01
We propose three physical tests to measure correlations in random numbers used in Monte Carlo simulations. The first test uses autocorrelation times of certain physical quantities when the Ising model is simulated with the Wolff algorithm. The second test is based on random walks, and the third on blocks of n successive numbers. We apply the tests to show that recent errors in high precision Ising simulations using generalized feedback shift register algorithms are due to short range correlations in random number sequences.
A note on generators of number fields
Vaaler, Jeffrey D
2012-01-01
We establish upper bounds for the smallest height of a generator of a number field $k$ over the rational field $\\Q$. Our first bound applies to all number fields $k$ having at least one real embedding. We also give a second conditional result for all number fields $k$ such that the Dedekind zeta-function associated to the Galois closure of $k/\\Q$ satisfies GRH. This provides a partial answer to a question of W. Ruppert.
High Atom Number in Microsized Atom Traps
2015-12-14
Final Performance Report on ONR Grant N00014-12-1-0608 High atom number in microsized atom traps for the period 15 May 2012 through 14 September...TYPE Final Technical Report 3. DATES COVERED (From - To) 05/15/2012-09/14/2012 4. TITLE AND SUBTITLE High atom number in microsized atom traps...forces for implementing a small-footprint, large-number atom -chip instrument. Bichromatic forces rely on absorption and stimulated emission to produce
High speed optical quantum random number generation.
Fürst, Martin; Weier, Henning; Nauerth, Sebastian; Marangon, Davide G; Kurtsiefer, Christian; Weinfurter, Harald
2010-06-07
We present a fully integrated, ready-for-use quantum random number generator (QRNG) whose stochastic model is based on the randomness of detecting single photons in attenuated light. We show that often annoying deadtime effects associated with photomultiplier tubes (PMT) can be utilized to avoid postprocessing for bias or correlations. The random numbers directly delivered to a PC, generated at a rate of up to 50 Mbit/s, clearly pass all tests relevant for (physical) random number generators.
Beyond natural numbers: Representation of negative numbers in the parietal cortex
Kristen Pilner Blair; Miriam eRosenberg-Lee; Tsang, Jessica M.; Schwartz, Daniel L.; Vinod eMenon
2012-01-01
Unlike natural numbers, negative numbers do not have natural physical referents. How does the brain represent such abstract mathematical concepts? Two competing hypotheses regarding representational systems for negative numbers are a rule-based model, in which symbolic rules are applied to negative numbers to translate them into positive numbers when assessing magnitudes, and an expanded magnitude model, in which negative numbers have a distinct magnitude representation. Using an event-relate...
Numbers and other math ideas come alive
Pappas, Theoni
2012-01-01
Most people don't think about numbers, or take them for granted. For the average person numbers are looked upon as cold, clinical, inanimate objects. Math ideas are viewed as something to get a job done or a problem solved. Get ready for a big surprise with Numbers and Other Math Ideas Come Alive. Pappas explores mathematical ideas by looking behind the scenes of what numbers, points, lines, and other concepts are saying and thinking. In each story, properties and characteristics of math ideas are entertainingly uncovered and explained through the dialogues and actions of its math
Caveney, Geoffrey; Sondow, Jonathan
2011-01-01
Gronwall's function $G$ is defined for $n>1$ by $G(n)=\\frac{\\sigma(n)}{n \\log\\log n}$ where $\\sigma(n)$ is the sum of the divisors of $n$. We call an integer $N>1$ a \\emph{GA1 number} if $N$ is composite and $G(N) \\ge G(N/p)$ for all prime factors $p$ of $N$. We say that $N$ is a \\emph{GA2 number} if $G(N) \\ge G(aN)$ for all multiples $aN$ of $N$. In arXiv 1110.5078, we used Robin's and Gronwall's theorems on $G$ to prove that the Riemann Hypothesis (RH) is true if and only if 4 is the only number that is both GA1 and GA2. Here, we study GA1 numbers and GA2 numbers separately. We compare them with superabundant (SA) and colossally abundant (CA) numbers (first studied by Ramanujan). We give algorithms for computing GA1 numbers; the smallest one with more than two prime factors is 183783600, while the smallest odd one is 1058462574572984015114271643676625. We find nineteen GA2 numbers $\\le 5040$, and prove that a GA2 number $N>5040$ exists if and only if RH is false, in which case $N$ is even and $>10^{8576}$.
Unique Physician Identification Number (UPIN) Directory
U.S. Department of Health & Human Services — The Unique Physician Identification Number (UPIN) Directory contains selected information on physicians, doctors of Osteopathy, limited licensed practitioners and...
Pegging Numbers For Various Tree Graphs
Levavi, Ariel
2011-01-01
In the game of pegging, each vertex of a graph is considered a hole into which a peg can be placed. A pegging move is performed by jumping one peg over another peg, and then removing the peg that has been jumped over from the graph. We define the pegging number as the smallest number of pegs needed to reach all the vertices in a graph no matter what the distribution. Similarly, the optimal-pegging number of a graph is defined as the smallest distribution of pegs for which all the vertices in the graph can be reached. We obtain tight bounds on the pegging numbers and optimal-pegging numbers of complete binary trees and compute the optimal-pegging numbers of complete infinitary trees. As a result of these computations, we deduce that there is a tree whose optimal-pegging number is strictly increased by removing a leaf. We also compute the optimal-pegging number of caterpillar graphs and the tightest upper bound on the optimal-pegging numbers of lobster graphs.
On Fibonacci Numbers Which Are Elliptic Carmichael
2014-12-27
On Fibonacci numbers which are elliptic Carmichael Florian Luca School of Mathematics University of the Witwatersrand P. O. Box Wits 2050, South...CM elliptic curve with CM field different from Q( √ −1), then the set of n for which the nth Fibonacci number Fn is elliptic Carmichael for E is of...number. 1. REPORT DATE 27 DEC 2014 2. REPORT TYPE 3. DATES COVERED 00-00-2014 to 00-00-2014 4. TITLE AND SUBTITLE On Fibonacci Numbers Which Are
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
@@ We have to find my friends Alice and Bill,who live in two different houses on Algebra Avenue. Each of the houses on Algebra Avenue is numbered with a two-digit number from 10 to 99. 1 can't remember where Alice and Bill live,but I remember that their house numbers are the reverse of each other (in the sense that "21" is the reverse of"12".) I also remember that the sum of their two house numbers is a perfect square.
Total dominator chromatic number of a graph
Directory of Open Access Journals (Sweden)
Adel P. Kazemi
2015-06-01
Full Text Available Given a graph $G$, the total dominator coloring problem seeks a proper coloring of $G$ with the additional property that every vertex in the graph is adjacent to all vertices of a color class. We seek to minimize the number of color classes. We initiate to study this problem on several classes of graphs, as well as finding general bounds and characterizations. We also compare the total dominator chromatic number of a graph with the chromatic number and the total domination number of it.
Numbers and prior knowledge in sentence comprehension
Directory of Open Access Journals (Sweden)
Pedro Macizo
2013-01-01
Full Text Available We evaluated whether the comprehension of sentences that contained numerical information could benefit from presenting numbers in Arabic format and from using prior knowledge. Participants read sentences including numbers (Arabic digits or number words while the comprehension accuracy was evaluated. In addition, the sentences were biased or unbiased by people's prior knowledge about quantities. The results showed better comprehension for sentences that contained Arabic digits as compared to number words. Moreover, biased sentences were understood more accurately than unbiased sentences. These results indicate that information about magnitude in sentence context is comprehended better when quantities are presented in Arabic format and when they are associated with participants' world knowledge.
Vector perturbations of galaxy number counts
Durrer, Ruth; Tansella, Vittorio
2016-07-01
We derive the contribution to relativistic galaxy number count fluctuations from vector and tensor perturbations within linear perturbation theory. Our result is consistent with the the relativistic corrections to number counts due to scalar perturbation, where the Bardeen potentials are replaced with line-of-sight projection of vector and tensor quantities. Since vector and tensor perturbations do not lead to density fluctuations the standard density term in the number counts is absent. We apply our results to vector perturbations which are induced from scalar perturbations at second order and give numerical estimates of their contributions to the power spectrum of relativistic galaxy number counts.
Vector perturbations of galaxy number counts
Durrer, Ruth
2016-01-01
We derive the contribution to relativistic galaxy number count fluctuations from vector and tensor perturbations within linear perturbation theory. Our result is consistent with the the relativistic corrections to number counts due to scalar perturbation, where the Bardeen potentials are replaced with line-of-sight projection of vector and tensor quantities. Since vector and tensor perturbations do not lead to density fluctuations the standard density term in the number counts is absent. We apply our results to vector perturbations which are induced from scalar perturbations at second order and give numerical estimates of their contributions to the power spectrum of relativistic galaxy number counts.
Generalized Ramsey numbers through adiabatic quantum optimization
Ranjbar, Mani; Macready, William G.; Clark, Lane; Gaitan, Frank
2016-09-01
Ramsey theory is an active research area in combinatorics whose central theme is the emergence of order in large disordered structures, with Ramsey numbers marking the threshold at which this order first appears. For generalized Ramsey numbers r( G, H), the emergent order is characterized by graphs G and H. In this paper we: (i) present a quantum algorithm for computing generalized Ramsey numbers by reformulating the computation as a combinatorial optimization problem which is solved using adiabatic quantum optimization; and (ii) determine the Ramsey numbers r({{T}}m,{{T}}n) for trees of order m,n = 6,7,8, most of which were previously unknown.
2013-06-19
... number administration more generally. The memorability, ubiquity, convenience, and universality of... judicious management of telephone numbers and promote further innovation and competition, the NPRM...
Effects of pitch on auditory number comparisons.
Campbell, Jamie I D; Scheepers, Florence
2015-05-01
Three experiments investigated interactions between auditory pitch and the numerical quantities represented by spoken English number words. In Experiment 1, participants heard a pair of sequential auditory numbers in the range zero to ten. They pressed a left-side or right-side key to indicate if the second number was lower or higher in numerical value. The vocal pitches of the two numbers either ascended or descended so that pitch change was congruent or incongruent with number change. The error rate was higher when pitch and number were incongruent relative to congruent trials. The distance effect on RT (i.e., slower responses for numerically near than far number pairs) occurred with pitch ascending but not descending. In Experiment 2, to determine if these effects depended on the left/right spatial mapping of responses, participants responded "yes" if the second number was higher and "no" if it was lower. Again, participants made more number comparison errors when number and pitch were incongruent, but there was no distance × pitch order effect. To pursue the latter, in Experiment 3, participants were tested with response buttons assigned left-smaller and right-larger ("normal" spatial mapping) or the reverse mapping. Participants who received normal mapping first presented a distance effect with pitch ascending but not descending as in Experiment 1, whereas participants who received reverse mapping first presented a distance effect with pitch descending but not ascending. We propose that the number and pitch dimensions of stimuli both activated spatial representations and that strategy shifts from quantity comparison to order processing were induced by spatial incongruities.
Continental anthropogenic primary particle number emissions
Paasonen, Pauli; Kupiainen, Kaarle; Klimont, Zbigniew; Visschedijk, Antoon; Denier van der Gon, Hugo A. C.; Amann, Markus
2016-06-01
Atmospheric aerosol particle number concentrations impact our climate and health in ways different from those of aerosol mass concentrations. However, the global, current and future anthropogenic particle number emissions and their size distributions are so far poorly known. In this article, we present the implementation of particle number emission factors and the related size distributions in the GAINS (Greenhouse Gas-Air Pollution Interactions and Synergies) model. This implementation allows for global estimates of particle number emissions under different future scenarios, consistent with emissions of other pollutants and greenhouse gases. In addition to determining the general particulate number emissions, we also describe a method to estimate the number size distributions of the emitted black carbon particles. The first results show that the sources dominating the particle number emissions are different to those dominating the mass emissions. The major global number source is road traffic, followed by residential combustion of biofuels and coal (especially in China, India and Africa), coke production (Russia and China), and industrial combustion and processes. The size distributions of emitted particles differ across the world, depending on the main sources: in regions dominated by traffic and industry, the number size distribution of emissions peaks in diameters range from 20 to 50 nm, whereas in regions with intensive biofuel combustion and/or agricultural waste burning, the emissions of particles with diameters around 100 nm are dominant. In the baseline (current legislation) scenario, the particle number emissions in Europe, Northern and Southern Americas, Australia, and China decrease until 2030, whereas especially for India, a strong increase is estimated. The results of this study provide input for modelling of the future changes in aerosol-cloud interactions as well as particle number related adverse health effects, e.g. in response to tightening
Kong, Feng; Zhao, Jingjing; You, Xuqun
2012-01-01
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.
Analytic number theory an introductory course
Bateman, Paul T
2004-01-01
This valuable book focuses on a collection of powerful methods ofanalysis that yield deep number-theoretical estimates. Particularattention is given to counting functions of prime numbers andmultiplicative arithmetic functions. Both real variable ("elementary")and complex variable ("analytic") methods are employed.
Number & operations drill sheets : grades PK-2
Reed, Nat
2010-01-01
For grades PK-2, our Common Core State Standards-based resource meets the number & operations concepts addressed by the NCTM standards and encourages the students to review the concepts in unique ways. Each drill sheet contains warm-up and timed drill activities for the student to practice number & operations concepts.
A property of algebraic univoque numbers
De Vries, M.
2007-01-01
Consider the set U of real numbers q >= 1 for which only one sequence (c(i)) of integers 0 <= c(i) <= q satisfies the equality Sigma(infinity)(i= 1) ciq(-i) =1. We show that the set of algebraic numbers in U is dense in the closure (U) over bar of U.
Wigner function of the thermo number states
Institute of Scientific and Technical Information of China (English)
Hu Li-Yun; Fan Hong-Yi
2009-01-01
Based on thermo field dynamics (TFD) and using the thermo Wigner operator in the thermo entangled state representation we derive the Wigner function of number states at finite temperature (named thermo number states). The figure of Wigner function shows that its shape gets smoothed as the temperature rises, implying that the quantum noise becomes larger.
Beyond the Numbers Making Sense of Statistics
Christmann, Edwin
2011-01-01
Statistics is required coursework within most teacher certification programs. Beyond the Numbers presents a nonthreatening, practical approach to statistics, providing step-by-step instructions for understanding and implementing the essential components of the subject.The basic and understandable explanations in Beyond the Numbers break down complex statistical processes to simple arithmetic computations that can be applied with the confidence that accompanies understanding.
Baryon number violation in future accelerators
Energy Technology Data Exchange (ETDEWEB)
Tracas, N.D.; Zoupanos, G.
1989-03-30
As a demonstration of the possibility to observe baryon number violation in the next generation of accelerators we present a semirealistic GUT in which proton decay is forbidden and the unification scale is at approx. = 10/sup 3-4/ TeV, leading therefore to observable baryon number violating processes.
A supercongruence for generalized Domb numbers
Osburn, Robert
2012-01-01
Using techniques due to Coster, we prove a supercongruence for a generalization of the Domb numbers. This extends a recent result of Chan, Cooper and Sica and confirms a conjectural supercongruence for numbers which are coefficients in one of Zagier's seven "sporadic" solutions to second order Apery-like differential equations.
Motzkin numbers out of Random Domino Automaton
Białecki, Mariusz
2011-01-01
Motzkin numbers are derived from a special case of Random Domino Automaton - recently proposed toy model of earthquakes. An exact solution of the set of equations describing stationary state of Random Domino Automaton in "inverse-power" case is presented. A link with Motzkin numbers allows to present explicit form of asymptotic behaviour of the automaton.
Nonclassicality in phase-number uncertainty relations
Energy Technology Data Exchange (ETDEWEB)
Matia-Hernando, Paloma; Luis, Alfredo [Departamento de Optica, Facultad de Ciencias Fisicas, Universidad Complutense, 28040 Madrid (Spain)
2011-12-15
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.
Equations with Arithmetic Functions of Pell Numbers
2014-01-01
Postgraduate School in December, 2012. During the preparation of this paper, F. L. was supported in part by Project PAPIIT IN104512 ( UNAM ), VSP...Multiperfect numbers with identical digits, J. Number Theory 131 (2011), 260–284. Received: 10.01.2013 Accepted: 19.04.2014 1 Mathematical Institute, UNAM
Lepton number violation searches at the LHC
Salvucci, Antonio; The ATLAS collaboration
2017-01-01
Lepton number is conserved in the Standard Model, therefore, any evidence for its violation would indicate the existence of new physics. This talk presents a review of the latest searches performed at the LHC concerning Lepton Number Violation (LNV) processes in the context of Left-Right Symmetric theory and Seesaw mechanism.
Neural correlates of merging number words.
Hung, Yi-Hui; Pallier, Christophe; Dehaene, Stanislas; Lin, Yi-Chen; Chang, Acer; Tzeng, Ovid J-L; Wu, Denise H
2015-11-15
Complex number words (e.g., "twenty two") are formed by merging together several simple number words (e.g., "twenty" and "two"). In the present study, we explored the neural correlates of this operation and investigated to what extent it engages brain areas involved processing numerical quantity and linguistic syntactic structure. Participants speaking two typologically distinct languages, French and Chinese, were required to read aloud sequences of simple number words while their cerebral activity was recorded by functional magnetic resonance imaging. Each number word could either be merged with the previous ones (e.g., 'twenty three') or not (e.g., 'three twenty'), thus forming four levels ranging from lists of number words to complex numerals. When a number word could be merged with the preceding ones, it was named faster than when it could not. Neuroimaging results showed that the number of merges correlated with activation in the left inferior frontal gyrus and in the left inferior parietal lobule. Consistent findings across Chinese and French participants suggest that these regions serve as the neural bases for forming complex number words in different languages.
Keypad Geometry and Divisibility of Numbers
Van Dyke, Frances; Keynes, Michael
2010-01-01
In this article, the authors show how students can form familiar geometric figures on the calculator keypad and generate numbers that are all divisible by a common number. Students are intrigued by the results and want to know "why it works". The activities can be presented and students given an extended amount of time to think about…
On the Concept Image of Complex Numbers
Nordlander, Maria Cortas; Nordlander, Edvard
2012-01-01
A study of how Swedish students understand the concept of complex numbers was performed. A questionnaire was issued reflecting the student view of own perception. Obtained answers show a variety of concept images describing how students adopt the concept of complex numbers. These concept images are classified into four categories in order to…
Hello, I am not an NHS number.
Bates, Jane
2016-09-14
I was handed a request to return a patient's call and given a name, signs and symptoms and a number with ten digits, starting with a seven. There was no preceding zero, and assuming it must be a mistake I stuck one on, and dialled. The number was unobtainable.
Hacking DNA copy number for circuit engineering.
Wu, Feilun; You, Lingchong
2017-07-27
DNA copy number represents an essential parameter in the dynamics of synthetic gene circuits but typically is not explicitly considered. A new study demonstrates how dynamic control of DNA copy number can serve as an effective strategy to program robust oscillations in gene expression circuits.
When Symbolic Spatial Cues Go before Numbers
Herrera, Amparo; Macizo, Pedro
2011-01-01
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…
Comments on nonparametric predictions of sunspot numbers
DEFF Research Database (Denmark)
Jensen, J.L.
1993-01-01
Recent results of Cerrito (1990) are criticized, and the level of unexplainable noise in the observed series of sunspot numbers is discussed.......Recent results of Cerrito (1990) are criticized, and the level of unexplainable noise in the observed series of sunspot numbers is discussed....
On contact numbers in random rod packings
Wouterse, A.; Luding, Stefan; Philipse, A.P.
2009-01-01
Random packings of non-spherical granular particles are simulated by combining mechanical contraction and molecular dynamics, to determine contact numbers as a function of density. Particle shapes are varied from spheres to thin rods. The observed contact numbers (and packing densities) agree well
From Whole Numbers to Invert and Multiply
Cavey, Laurie O.; Kinzel, Margaret T.
2014-01-01
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…
Locating Fractions on a Number Line
Wong, Monica
2013-01-01
Understanding fractions remains problematic for many students. The use of the number line aids in this understanding, but requires students to recognise that a fraction represents the distance from zero to a dot or arrow marked on a number line which is a linear scale. This article continues the discussion from "Identifying Fractions on a…
On Ramsey numbers for paths versus wheels
Salman, M.; Broersma, Haitze J.
2004-01-01
For two given graphs $F$ and $H$, the Ramsey number $R(F,H)$ is the smallest positive integer $p$ such that for every graph $G$ on $p$ vertices the following holds: either $G$ contains $F$ as a subgraph or the complement of $G$ contains $H$ as a subgraph. In this paper, we study the Ramsey numbers $
On Ramsey numbers for paths versus wheels
Salman, M.; Broersma, Haitze J.
2007-01-01
For two given graphs $F$ and $H$, the Ramsey number $R(F,H)$ is the smallest positive integer $p$ such that for every graph $G$ on $p$ vertices the following holds: either $G$ contains $F$ as a subgraph or the complement of $G$ contains $H$ as a subgraph. In this paper, we study the Ramsey numbers $
Application of Chaotic Number Generators in Econophysics
Pellicer-Lostao, Carmen
2011-01-01
Agent-based models have demonstrated their power and flexibility in Econophysics. However their major challenge is still to devise more realistic simulation scenarios. The complexity of Economy makes appealing the idea of introducing chaotic number generators as simulation engines in these models. Chaos based number generators are easy to use and highly configurable. This makes them just perfect for this application.
Teach Kids about Numbers All around Us
Hudson, Hannah Trierweiler
2011-01-01
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…
Roman Bondage Numbers of Some Graphs
Hu, Fu-Tao
2011-01-01
A Roman dominating function on a graph $G=(V,E)$ is a function $f: V\\to \\{0,1,2\\}$ satisfying the condition that every vertex $u$ with $f(u)=0$ is adjacent to at least one vertex $v$ with $f(v)=2$. The weight of a Roman dominating function is the value $f(G)=\\sum_{u\\in V} f(u)$. The Roman domination number of $G$ is the minimum weight of a Roman dominating function on $G$. The Roman bondage number of a nonempty graph $G$ is the minimum number of edges whose removal results in a graph with the Roman domination number larger than that of $G$. This paper determines the exact value of the Roman bondage numbers of two classes of graphs, complete $t$-partite graphs and $(n-3)$-regular graphs with order $n$ for any $n\\ge 5$.
Topics from the theory of numbers
Grosswald, Emil
1984-01-01
Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. The publication of Emil Grosswald’s classic text presents an illuminating introduction to number theory. Combining the historical developments with the analytical approach, Topics from the Theory of Numbers offers the reader a diverse range of subjects to investigate, including: * divisibility * congruences * the Riemann zeta function * Diophantine equations and Fermat’s conjecture * the theory of partitions Comprehensive in nature, Topics from the Theory of Numbers is an ideal text for advanced undergraduates and graduate students alike. "In my opinion it is excellent. It is carefully written and represents clearly a work of a scholar who loves and understands his subject. One can only wish more authors would take such pains and would be as good and honest expositors as Grosswald." — Marc Kac "This book is designed for use in a first course in number theory at...
Ramsey numbers and adiabatic quantum computing.
Gaitan, Frank; Clark, Lane
2012-01-06
The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.
Wavelet analysis of sunspot relative numbers
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The time series of the monthly smoothed sunspot numbers in 1749-2000 is analyzed with the wavelet.The result shows that besides the known time-variation of the period about 11 years, other main periods of the sunspot numbers, such as the periods of about 100 years and so on,vary with time. We suggest that the time-variation of the main periods is the manifestation of the complex variation of sunspot numbers. It is significant to make a thorough study of the character and mechanism of the time-variation of the periods for proving prediction of sunspot numbers, especially for understanding the variation process of sunspot numbers.
The competition numbers of ternary Hamming graphs
Park, Boram
2010-01-01
The competition graph of a digraph D is a graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x,v) and (y,v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number k(G) of a graph G is defined to be the smallest number of such isolated vertices. In general, it is hard to compute the competition number k(G) for a graph G and it has been one of important research problems in the study of competition graphs to characterize a graph by its competition number. In this paper, we give the exact values of the competition numbers of ternary Hamming graphs.
Topological Numbers and the Weyl Semimetal
Elbistan, Mahmut
2016-01-01
Generalized Dirac monopoles in momentum space are constructed in even d+1 dimensions from the Weyl Hamiltonian in terms of Green's functions. In 3+1 spacetime dimensions, the (unit) charge of the monopole is equal to both the winding number and the Chern number, expressed as the integral of the Berry curvature. Based on the equivalence of the Chern and winding numbers, a chirally coupled field theory action is proposed for the Weyl semimetal phase. At the one loop order, the effective action yields both the chiral magnetic effect and the anomalous Hall effect. The Chern number appears as a coefficient in the conductivity, thus emphasizes the role of topology. The anomalous contribution of chiral fermions to transport phenomena is reflected as the gauge anomaly with the topological term $(\\bm{E}\\cdot\\bm{B})$. Relevance of monopoles and Chern numbers for the semiclassical chiral kinetic theory is also discussed.
Compendium of Experimental Cetane Number Data
Energy Technology Data Exchange (ETDEWEB)
Murphy, M. J.; Taylor, J. D.; McCormick, R. L.
2004-09-01
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.
True random numbers from amplified quantum vacuum
Jofre, M; Steinlechner, F; Anzolin, G; Torres, J P; Mitchell, M W; Pruneri, V; 10.1364/OE.19.020665
2011-01-01
Random numbers are essential for applications ranging from secure communications to numerical simulation and quantitative finance. Algorithms can rapidly produce pseudo-random outcomes, series of numbers that mimic most properties of true random numbers while quantum random number generators (QRNGs) exploit intrinsic quantum randomness to produce true random numbers. Single-photon QRNGs are conceptually simple but produce few random bits per detection. In contrast, vacuum fluctuations are a vast resource for QRNGs: they are broad-band and thus can encode many random bits per second. Direct recording of vacuum fluctuations is possible, but requires shot-noise-limited detectors, at the cost of bandwidth. We demonstrate efficient conversion of vacuum fluctuations to true random bits using optical amplification of vacuum and interferometry. Using commercially-available optical components we demonstrate a QRNG at a bit rate of 1.11 Gbps. The proposed scheme has the potential to be extended to 10 Gbps and even up t...
Andreescu, Titu
2014-01-01
It is impossible to imagine modern mathematics without complex numbers. The second edition of Complex Numbers from A to … Z introduces the reader to this fascinating subject that, from the time of L. Euler, has become one of the most utilized ideas in mathematics. The exposition concentrates on key concepts and then elementary results concerning these numbers. The reader learns how complex numbers can be used to solve algebraic equations and to understand the geometric interpretation of complex numbers and the operations involving them. The theoretical parts of the book are augmented with rich exercises and problems at various levels of difficulty. Many new problems and solutions have been added in this second edition. A special feature of the book is the last chapter, a selection of outstanding Olympiad and other important mathematical contest problems solved by employing the methods already presented. The book reflects the unique experience of the authors. It distills a vast mathematical literature, most ...
The lower bound on independence number
Institute of Scientific and Technical Information of China (English)
LI; Yusheng
2002-01-01
［1］Caro, Y., New Results on the Independence Number, Technical Report, Tel_Aviv: Tel_Aviv University, 1979.［2］Wei, V., A lower bound on the stability number of a simple graph, Bell Laboratories Technical Memorandum, 1981, 81_11217_11219.\\}［3］Alon, N., Spencer, J., The Probabilistic Method, New York: Wiley_Interscience, 1992.［4］Ajtai, M., Komls, J., Szemerédi E., A note on Ramsey numbers, J. Combin. Theory, Ser. A, 1980, 29: 354-360.［5］Shearer, J., A note on the independence number of triangle_free graphs, Discrete Math., 1983, 46: 83-87.［6］Kim, J., The Ramsey number R(3,t)has order of magnitude t\\+2／logt, Random Structures Algorithms, 1995, 7: 174-207.［7］Tardos, E., 1997 Fulkerson Prize, Notices of American Math. Soc., 1998, 45(8): 984.［8］Griggs, J., Lower bounds on the independence number in term of the degrees, J. Combin. Theory, Ser. B, 1983, 34: 22-29.［9］Li, Y., Rousseau, C., Fan_complete graph Ramsey numbers, J. Graph Theory, 1996, 23: 413-420.［10］Shearer, J., A note on the independence number of triangle_free graphs, II, J. Combin. Theory, Ser. B, 1991, 53: 300-307.［11］Li, Y., Rousseau, C., On book_complete Ramsey numbers, J. Combin. Theory, Ser. B, 1996, 68: 36-44.［12］Li, Y., Rousseau, C., Zang, W., Asymptotic upper bounds for Ramsey functions, Graphs Combin., 2001, 17: 123-128.［13］Caro, Y., Li, Y., Rousseau, C. et al., Asymptotic bounds for some bipartite graph: complete graph Ramsey numbers, Discrete Math., 2000, 220: 51-56.
Saxe, Geoffrey B.; Shaughnessy, Meghan M.; Gearhart, Maryl; Haldar, Lina Chopra
2013-01-01
Two investigations of fifth graders' strategies for locating whole numbers on number lines revealed patterns in students' coordination of numeric and linear units. In Study 1, we investigated the effects of context on students' placements of three numbers on an open number line. For one group ("n"?=?24), the line was presented in a…
Saxe, Geoffrey B.; Shaughnessy, Meghan M.; Gearhart, Maryl; Haldar, Lina Chopra
2013-01-01
Two investigations of fifth graders' strategies for locating whole numbers on number lines revealed patterns in students' coordination of numeric and linear units. In Study 1, we investigated the effects of context on students' placements of three numbers on an open number line. For one group ("n"?=?24), the line was presented in a…
Number Worlds: Visual and Experimental Access to Elementary Number Theory Concepts
Sinclair, Nathalie; Zazkis, Rina; Liljedahl, Peter
2004-01-01
Recent research demonstrates that many issues related to the structure of natural numbers and the relationship among numbers are not well grasped by students. In this article, we describe a computer-based learning environment called "Number Worlds" that was designed to support the exploration of elementary number theory concepts by making the…
Theory of analogous force on number sets
Canessa, Enrique
2003-10-01
A general statistical thermodynamic theory that considers given sequences of x-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability distributions px for natural numbers, we claim that they lead to a better understanding of probabilistic laws associated with number theory. Sequences of numbers are treated as the size measure of finite sets. By considering px to describe complex phenomena, the theory leads to derive a distinct analogous force fx on number sets proportional to (∂ px/∂ x) T at an analogous system temperature T. In particular, this leads to an understanding of the uneven distribution of integers of random sets in terms of analogous scale invariance and a screened inverse square force acting on the significant digits. The theory also allows to establish recursion relations to predict sequences of Fibonacci numbers and to give an answer to the interesting theoretical question of the appearance of the Benford's law in Fibonacci numbers. A possible relevance to prime numbers is also analyzed.
Effective condition number for finite difference method
Li, Zi-Cai; Chien, Cheng-Sheng; Huang, Hung-Tsai
2007-01-01
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.=[lambda]1/[lambda]n, where [lambda]1 and [lambda]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 of both A and b. Such a Cond. can only be reached by the worst situation of all rounding errors and all b. For the given b, the true relative errors may be smaller, or even much smaller than the Cond., which is called the effective condition number in Chan and Foulser [Effectively well-conditioned linear systems, SIAM J. Sci. Statist. Comput. 9 (1988) 963-969] and Christiansen and Hansen [The effective condition number applied to error analysis of certain boundary collocation methods, J. Comput. Appl. Math. 54(1) (1994) 15-36]. In this paper, we propose the new computational formulas for effective condition number Cond_eff, and define the new simplified effective condition number Cond_E. For the latter, we only need the eigenvector corresponding to the minimal eigenvalue of A, which can be easily obtained by the inverse power method. In this paper, we also apply the effective condition number for the finite difference method for Poisson's equation. The difference grids are not supposed to be quasiuniform. Under a non-orthogonality assumption, the effective condition number is proven to be O(1) for the homogeneous boundary conditions. Such a result is extraordinary, compared with the traditional , where hmin is the minimal meshspacing of the difference grids used. For the non-homogeneous Neumann and Dirichlet boundary conditions, the effective condition number is proven to be O(h-1/2) and , respectively, where h is the maximal meshspacing of the difference grids. Numerical experiments are carried out to verify the analysis made.
Low Nephron Number and Its Clinical Consequences
Directory of Open Access Journals (Sweden)
Valerie A. Luyckx
2011-10-01
Full Text Available decades ago, that developmental programming of the kidney impacts an individual’s risk for hypertension and renal disease in later life. Low birth weight is the strongest current clinical surrogate marker for an adverse intrauterine environment and, based on animal and human studies, is associated with a low nephron number. Other clinical correlates of low nephron number include female gender, short adult stature, small kidney size, and prematurity. Low nephron number in Caucasian and Australian Aboriginal subjects has been shown to be associated with higher blood pressures, and, conversely, hypertension is less prevalent in individuals with higher nephron numbers. In addition to nephron number, other programmed factors associated with the increased risk of hypertension include salt sensitivity, altered expression of renal sodium transporters, altered vascular reactivity, and sympathetic nervous system overactivity. Glomerular volume is universally found to vary inversely with nephron number, suggesting a degree of compensatory hypertrophy and hyperfunction in the setting of a low nephron number. This adaptation may become overwhelmed in the setting of superimposed renal insults, e.g. diabetes mellitus or rapid catch-up growth, leading to the vicious cycle of on-going hyperfiltration, proteinuria, nephron loss and progressive renal functional decline. Many millions of babies are born with low birth weight every year, and hypertension and renal disease prevalences are increasing around the globe. At present, little can be done clinically to augment nephron number; therefore adequate prenatal care and careful postnatal nutrition are crucial to optimize an individual’s nephron number during development and potentially to stem the tide of the growing cardiovascular and renal disease epidemics worldwide.
The Bondage Number of Mesh Networks
Hu, Fu-Tao; Xu, Jun-Ming
2011-01-01
The bondage number $b(G)$ of a nonempty graph $G$ is the smallest number of edges whose removal from $G$ results in a graph with domination number greater than that of $G$. Denote $P_n\\times P_m$ be the Cartesian product of two paths $P_n$ and $P_m$. This paper determines that the exact value of $b(P_n\\times P_2)$, $b(P_n\\times P_3)$ and $b(P_n\\times P_4)$ for $n\\ge 2$.
Acceleration Detection of Large (Probably Prime Numbers
Directory of Open Access Journals (Sweden)
Dragan Vidakovic
2013-02-01
Full Text Available In order to avoid unnecessary applications of Miller-Rabin algorithm to the number in question, we resortto trial division by a few initial prime numbers, since such a division take less time. How far we should gowith such a division is the that we are trying to answer in this paper?For the theory of the matter is fullyresolved. However, that in practice we do not have much use.Therefore, we present a solution that isprobably irrelevant to theorists, but it is very useful to people who have spent many nights to producelarge (probably prime numbers using its own software.
Algebraic Geometry and Number Theory Summer School
Sarıoğlu, Celal; Soulé, Christophe; Zeytin, Ayberk
2017-01-01
This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.
The covering number of $M_{24}$
Directory of Open Access Journals (Sweden)
Michael Epstein
2016-09-01
Full Text Available A finite cover $\\mathcal{C}$ of a group $G$ is a finite collection of proper subgroups of $G$ such that $G$ is equal to the union of all of the members of $\\mathcal{C}$. Such a cover is called {\\em minimal} if it has the smallest cardinality among all finite covers of $G$. The covering number of $G$, denoted by $\\sigma(G$, is the number of subgroups in a minimal cover of $G$. In this paper the covering number of the Mathieu group $M_{24}$ is shown to be 3336.
Quantum numbers and band topology of nanotubes
Damnjanovic, M; Vukovic, T; Maultzsch, J
2003-01-01
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.
Physical tests for random numbers in simulations
Energy Technology Data Exchange (ETDEWEB)
Vattulainen, I.; Ala-Nissila, T.; Kankaala, K. (Research Institute for Theoretical Physics, P.O. Box 9 (Siltavuorenpenger 20 C), FIN-00014 University of Helsinki (Finland) Department of Electrical Engineering, Tampere University of Technology, P.O. Box 692, FIN-3310, Tampere (Finland) Center for Scientific Computing, P.O. Box 405, FIN-02101 Espoo (Finland))
1994-11-07
We propose three physical tests to measure correlations in random numbers used in Monte Carlo simulations. The first test uses autocorrelation times of certain physical quantities when the Ising model is simulated with the Wolff algorithm. The second test is based on random walks, and the third on blocks of [ital n] successive numbers. We apply the tests to show that recent errors in high precision Ising simulations using generalized feedback shift register algorithms are due to short range correlations in random number sequences.
Modal Wave Number Spectrum for Mesoscale Eddies
Institute of Scientific and Technical Information of China (English)
KANG Ying; PENG Linhui
2003-01-01
The variations of ocean environmental parameters invariably result in variations of local modal wave numbers of a sound pressure field. The asymptotic Hankel transform with a short sliding window is applied to the complex sound pressure field in the water containing a mesoscale eddy to examine the variation of local modal wave numbers in such a range-dependent environment. The numerical simulation results show that modal wave number spectra obtained by this method can reflect the location and strength of a mesoscale eddy, therefore it can be used to monitor the strength and spatial scale of ocean mesoscale eddies.
VLSI binary multiplier using residue number systems
Energy Technology Data Exchange (ETDEWEB)
Barsi, F.; Di Cola, A.
1982-01-01
The idea of performing multiplication of n-bit binary numbers using a hardware based on residue number systems is considered. This paper develops the design of a VLSI chip deriving area and time upper bounds of a n-bit multiplier. To perform multiplication using residue arithmetic, numbers are converted from binary to residue representation and, after residue multiplication, the result is reconverted to the original notation. It is shown that the proposed design requires an area a=o(n/sup 2/ log n) and an execution time t=o(log/sup 2/n). 7 references.
Baryon Number Violation and String Topologies
Sjöstrand, Torbjörn
2003-01-01
In supersymmetric scenarios with broken R-parity, baryon number violating sparticle decays become possible. In order to search for such decays, a good understanding of expected event properties is essential. We here develop a complete framework that allows detailed studies. Special attention is given to the hadronization phase, wherein the baryon number violating vertex is associated with the appearance of a junction in the colour confinement field. This allows us to tell where to look for the extra (anti)baryon directly associated with the baryon number violating decay.
On the number of finite topological spaces
Directory of Open Access Journals (Sweden)
Lucio R. Berrone
1993-05-01
Full Text Available In this paper we deal with the problem of enumerating the finite topological spaces, studying the enumeration of a restrictive class of them. By employing simple techniques, we obtain a recursive lower bound for the number of topological spaces on a set of n elements. Besides we prove some collateral results, among which we can bring a new proof (Cor. 1.5 of the fact that p(n – the number of partitions of the integer n – is the number of non-isomorphic Boolean algebras on a set of n elements.
Hyperimmunity and A-computable universal numberings
Issakhov, Assylbek
2016-08-01
Whether there exists a computable universal numbering for a computable family is the key question in theory of numberings. In a very general setting, this problem was explored in [Yu. L. Ershov, Theory of Numberings, Handbook of Computability Theory, North-Holland; Amsterdam: Stud. Log. Found. Math., Vol. 140, pp. 473-503, 1999]. For sets A that are Turing jumps of the empty set, the problem was treated in [S. A. Badaev, S. S. Goncharov, and A. Sorbi, Computability and Models, 11-44 (2003)] and other papers. In this work, we investigate families of total functions computable relative to hyperimmune and hyperimmune-free oracles.
The Modified Negative Decision Number in Graphs
Directory of Open Access Journals (Sweden)
Changping Wang
2011-01-01
Full Text Available A mapping x:V→{-1,1} is called negative if ∑u∈N[v]x(u≤1 for every v∈V. The maximum of the values of ∑v∈Vx(v taken over all negative mappings x, is called the modified negative decision number and is denoted by βD′(G. In this paper, several sharp upper bounds of this number for a general graph are presented. Exact values of these numbers for cycles, paths, cliques and bicliques are found.
Numbers at work a cultural perspective
Taschner , Rudolf
2007-01-01
Drawing primarily from historical examples, this book explains the tremendous role that numbers and, in particular, mathematics play in all aspects of our civilization and culture. The lively style and illustrative examples will engage the reader who wants to understand the many ways in which mathematics enables science, technology, art, music, politics, and rational foundations of human thought. Each chapter focuses on the influence of mathematics in a specific field and on a specific historical figure, such as ""Pythagoras: Numbers and Symbol""; ""Bach: Numbers and Music""; ""Descartes: Numb
Unpredictability and the transmission of numbers
Myers, John M
2015-01-01
Curiously overlooked in physics is its dependence on the transmission of numbers. For example the transmission of numerical clock readings is implicit in the concept of a coordinate system. The transmission of numbers and other logical distinctions is often achieved over a computer-mediated communications network in the face of an unpredictable environment. By unpredictable we mean something stronger than the spread of probabilities over given possible outcomes, namely an opening to unforeseeable possibilities. Unpredictability, until now overlooked in theoretical physics, makes the transmission of numbers interesting. Based on recent proofs within quantum theory that provide a theoretical foundation to unpredictability, here we show how regularities in physics rest on a background of channels over which numbers are transmitted. As is known to engineers of digital communications, numerical transmissions depend on coordination reminiscent of the cycle of throwing and catching by players tossing a ball back and...
Opening the Door on Triangular Numbers
McMartin, Kimberley; McMaster, Heather
2016-01-01
As an alternative to looking solely at linear functions, a three-lesson learning progression developed for Year 6 students that incorporates triangular numbers to develop children's algebraic thinking is described and evaluated.
Introduction to the geometry of complex numbers
Deaux, Roland
2008-01-01
Geared toward readers unfamiliar with complex numbers, this text explains how to solve problems that frequently arise in the applied sciences and emphasizes constructions related to algebraic operations. 1956 edition.
Arabic Alphabet and Numbers Sign Language Recognition
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Mahmoud Zaki Abdo
2015-11-01
Full Text Available This paper introduces an Arabic Alphabet and Numbers Sign Language Recognition (ArANSLR. It facilitates the communication between the deaf and normal people by recognizing the alphabet and numbers signs of Arabic sign language to text or speech. To achieve this target, the system able to visually recognize gestures from hand image input. The proposed algorithm uses hand geometry and the different shape of a hand in each sign for classifying letters shape by using Hidden Markov Model (HMM. Experiments on real-world datasets showed that the proposed algorithm for Arabic alphabet and numbers sign language recognition is suitability and reliability compared with other competitive algorithms. The experiment results show that the increasing of the gesture recognition rate depends on the increasing of the number of zones by dividing the rectangle surrounding the hand.
Large Numbers and Calculators: A Classroom Activity.
Arcavi, Abraham; Hadas, Nurit
1989-01-01
Described is an activity demonstrating how a scientific calculator can be used in a mathematics classroom to introduce new content while studying a conventional topic. Examples of reading and writing large numbers, and reading hidden results are provided. (YP)
The disentangling number for phylogenetic mixtures
Sullivant, Seth
2011-01-01
We provide a logarithmic upper bound for the disentangling number on unordered lists of leaf labeled trees. This results is useful for analyzing phylogenetic mixture models. The proof depends on interpreting multisets of trees as high dimensional contingency tables.
Multiplex congruence network of natural numbers
National Research Council Canada - National Science Library
Yan, Xiao-Yong; Wang, Wen-Xu; Chen, Guan-Rong; Shi, Ding-Hua
2016-01-01
.... Congruence arithmetic has been a fundamental tool for data security and computer algebra. However, much less attention was devoted to the topological features of congruence relations among natural numbers...
Chaotic behaviour of high Mach number flows
Varvoglis, H.; Ghosh, S.
1985-01-01
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.
Means of Staff Number Reduction and Outplacement
National Research Council Canada - National Science Library
H. Urbancová
2014-01-01
.... The objective is to present the ways of staff number reduction in Czech organizations and outplacement for the laid-off workers and a partial objective is to compare the results with those in the Slovak Republic...
A brief introduction to particle number estimation
DEFF Research Database (Denmark)
Dorph-Petersen, Karl-Anton; Nyengaard, Jens Randel; Gundersen, Hans Jørgen Gottlieb
1998-01-01
The principle of particle number estimation using the disector is described emphasising the practical similarities and differences in the application of the principle in biomedicine and non-biological sciences....
Copy number variation across European populations.
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Wanting Chen
Full Text Available Genome analysis provides a powerful approach to test for evidence of genetic variation within and between geographical regions and local populations. Copy number variants which comprise insertions, deletions and duplications of genomic sequence provide one such convenient and informative source. Here, we investigate copy number variants from genome wide scans of single nucleotide polymorphisms in three European population isolates, the island of Vis in Croatia, the islands of Orkney in Scotland and the South Tyrol in Italy. We show that whereas the overall copy number variant frequencies are similar between populations, their distribution is highly specific to the population of origin, a finding which is supported by evidence for increased kinship correlation for specific copy number variants within populations.
Complex Binary Number System Algorithms and Circuits
Jamil, Tariq
2013-01-01
This book is a compilation of the entire research work on the topic of Complex Binary Number System (CBNS) carried out by the author as the principal investigator and members of his research groups at various universities during the years 1992-2012. Pursuant to these efforts spanning several years, the realization of CBNS as a viable alternative to represent complex numbers in an 'all-in-one' binary number format has become possible and efforts are underway to build computer hardware based on this unique number system. It is hoped that this work will be of interest to anyone involved in computer arithmetic and digital logic design and kindle renewed enthusiasm among the engineers working in the areas of digital signal and image processing for developing newer and efficient algorithms and techniques incorporating CBNS.
The Power of Numbers in Global Governance
DEFF Research Database (Denmark)
Krause Hansen, Hans; Mühlen-Schulte, Arthur
2012-01-01
The deployment of numbers have become a sine qua non in governance practices worldwide in recent decades. But the reasons behind this development and its implications for governance practices have not been systematically researched and theorised. This introductory article provides a short overview...... of the historical and contemporary role of numbers in different governance settings. It includes a discussion of the capacity of numbers to foster social identities, relations and truths across national boundaries, to construct issue areas and to enable various modes of surveillance, communication and action...... at a distance in the global political economy. It argues that the use of numbers in global governance should not be regarded only as a platform for knowledge sharing and learning. More than this, it needs to be understood in broader terms as a mechanism of inclusion and exclusion from complex social hierarchies...
Arithmetic Operations Beyond Floating Point Number Precision
Wang, Chih-Yueh; Chen, Hong-Yu; Chen, Yung-Ko
2010-01-01
In basic computational physics classes, students often raise the question of how to compute a number that exceeds the numerical limit of the machine. While technique of avoiding overflow/underflow has practical application in the electrical and electronics engineering industries, it is not commonly utilized in scientific computing, because scientific notation is adequate in most cases. We present an undergraduate project that deals with such calculations beyond a machine's numerical limit, known as arbitrary precision arithmetic. The assignment asks students to investigate the validity of floating point number precision and the approach of calculating the exact value of a large number, using the basic scientific programming language Fortran. Examples of the successive multiplication of even number and the multiplication and division of two overflowing floats are presented. The application of the scheme to hardware and firmware design which requires the allocation of finite memory, as in a digital signal proce...
Genetic Algorithms, Floating Point Numbers and Applications
Hardy, Yorick; Steeb, Willi-Hans; Stoop, Ruedi
The core in most genetic algorithms is the bitwise manipulations of bit strings. We show that one can directly manipulate the bits in floating point numbers. This means the main bitwise operations in genetic algorithm mutations and crossings are directly done inside the floating point number. Thus the interval under consideration does not need to be known in advance. For applications, we consider the roots of polynomials and finding solutions of linear equations.
A number-phase Wigner function
Energy Technology Data Exchange (ETDEWEB)
Moya-Cessa, Hector [INAOE, Coordinacion de Optica, Apartado Postal 51 y 216, 72000 Puebla, Puebla (Mexico)
2003-06-01
One of the most prominent quasiprobability functions in quantum mechanics is the Wigner function, which gives the correct marginal probability functions if integrated over position or momentum. Here we depart from the definition of the position-momentum Wigner function to, by analogy, construct a number-phase Wigner function that, if summed over photon numbers, gives the correct phase distribution and, if integrated over phase, gives the correct photon distribution.
The chromatic number of comparability 3-hypergraphs
2014-01-01
Beginning with the concepts of orientation for a 3-hypergraph and transitivity for an oriented 3-hypergraph, it is natural to study the class of comparability 3-hypergraphs (those that can be transitively oriented). In this work we show three different behaviors in respect to the relationship between the chromatic number and the clique number of a comparability 3-hypergraph, this is in contrast with the fact that a comparability simple graph is a perfect graph.
Bethe's quantum numbers and rigged configurations
Directory of Open Access Journals (Sweden)
Anatol N. Kirillov
2016-04-01
Full Text Available We propose a method to determine the quantum numbers, which we call the rigged configurations, for the solutions to the Bethe ansatz equations for the spin-1/2 isotropic Heisenberg model under the periodic boundary condition. Our method is based on the observation that the sums of Bethe's quantum numbers within each string behave particularly nicely. We confirm our procedure for all solutions for length 12 chain (totally 923 solutions.
Teacher education students' number sense: initial explorations
Kaminski, Eugene
1997-09-01
Use of number sense can assist learners in their understanding of, and calculating in, mathematics. This paper reports on these aspects which were investigated with six primary pre-service teacher education students at the commencement of a semester unit in mathematics education. Various mathematical examples were completed by each student in individual sessions which suggested that the students had at least a limited development of number sense.
Fibonacci and Lucas numbers with applications
Koshy, Thomas
2011-01-01
[Koshy's] book is without doubt the most comprehensive and scholarly work on Fibonacci numbers to date and I am sure that it will quickly signal its presence and impose itself as an authoritative reference manual on Fibonacci numbers. -Napoleon Gauthier, Royal Military College of Canada, Kingston, ON What a gem this is! [...] My only regrest about the book is that it wasn't around years ago. It fills such a void. -Monte Zerger, Adams State College, Alamosa, CO
Some properties of deformed q-numbers
Lobão, Thierry C. Petit; Cardoso, Pedro G. S.; Pinho, Suani T. R.; Borges, Ernesto P.
2009-01-01
p. 402/407 Nonextensive statistical mechanics has been a source of investigation in mathematical structures such as deformed algebraic structures. In this work, we present some consequences of q-operations on the construction of q-numbers for all numerical sets. Based on such a construction, we present a new product that distributes over the q-sum. Finally, we present different patterns of q-Pascal’s triangles, based on q-sum, whose elements are q-numbers.
Some properties of deformed $q$-numbers
Lobão, Thierry C. Petit; Cardoso, Pedro G. S.; Pinho, Suani T. R.; Borges, Ernesto P.
2009-01-01
Nonextensive statistical mechanics has been a source of investigation in mathematical structures such as deformed algebraic structures. In this work, we present some consequences of $q$-operations on the construction of $q$-numbers for all numerical sets. Based on such a construction, we present a new product that distributes over the $q$-sum. Finally, we present different patterns of $q$-Pascal's triangles, based on $q$-sum, whose elements are $q$-numbers.
All-optical fast random number generator.
Li, Pu; Wang, Yun-Cai; Zhang, Jian-Zhong
2010-09-13
We propose a scheme of all-optical random number generator (RNG), which consists of an ultra-wide bandwidth (UWB) chaotic laser, an all-optical sampler and an all-optical comparator. Free from the electric-device bandwidth, it can generate 10Gbit/s random numbers in our simulation. The high-speed bit sequences can pass standard statistical tests for randomness after all-optical exclusive-or (XOR) operation.
Large number discrimination in newborn fish.
Directory of Open Access Journals (Sweden)
Laura Piffer
Full Text Available Quantitative abilities have been reported in a wide range of species, including fish. Recent studies have shown that adult guppies (Poecilia reticulata can spontaneously select the larger number of conspecifics. In particular the evidence collected in literature suggest the existence of two distinct systems of number representation: a precise system up to 4 units, and an approximate system for larger numbers. Spontaneous numerical abilities, however, seem to be limited to 4 units at birth and it is currently unclear whether or not the large number system is absent during the first days of life. In the present study, we investigated whether newborn guppies can be trained to discriminate between large quantities. Subjects were required to discriminate between groups of dots with a 0.50 ratio (e.g., 7 vs. 14 in order to obtain a food reward. To dissociate the roles of number and continuous quantities that co-vary with numerical information (such as cumulative surface area, space and density, three different experiments were set up: in Exp. 1 number and continuous quantities were simultaneously available. In Exp. 2 we controlled for continuous quantities and only numerical information was available; in Exp. 3 numerical information was made irrelevant and only continuous quantities were available. Subjects successfully solved the tasks in Exp. 1 and 2, providing the first evidence of large number discrimination in newborn fish. No discrimination was found in experiment 3, meaning that number acuity is better than spatial acuity. A comparison with the onset of numerical abilities observed in shoal-choice tests suggests that training procedures can promote the development of numerical abilities in guppies.
Energy Technology Data Exchange (ETDEWEB)
Falcon, Sergio [Department of Mathematics, University of Las Palmas de Gran Canaria (ULPGC), 35017-Las Palmas de Gran Canaria (Spain)]. E-mail: sfalcon@dma.ulpgc.es; Plaza, Angel [Department of Mathematics, University of Las Palmas de Gran Canaria (ULPGC), 35017-Las Palmas de Gran Canaria (Spain)
2007-06-15
We introduce a general Fibonacci sequence that generalizes, between others, both the classic Fibonacci sequence and the Pell sequence. These general kth Fibonacci numbers {l_brace}F{sub k,n}{r_brace}{sub n=0}{sup {approx}} 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.
Analysis of Additive Random Number Generators.
1977-03-01
linear congruential generators yn*\\* ayn+bmo,iPa- The simplest example of a sequence satisfying (1.1) with *> I is the Fibonacci sequence with p - 2...However, the Fibonacci sequence is not a suitable random number generator because successive triples are very poorly distributed in three...number generator should have small discrepancy. Definition 2.1 can be extended naturally to define discrepancy for sequences of points yn lying in
Random Number Generation for High Performance Computing
2015-01-01
TOTAL: PERCENT_SUPPORTEDNAME FTE Equivalent: Total Number: Discipline Robin Schulze 0.43 0.43 1 Names of Post Doctorates Names of Faculty Supported...Agent, or Firm- Meyertons, Hood , Kivlin, Kowert & Goetze!, P.C.; Eric B. Meyertons (57) ABSTRACT A method of assessing parallel random number...Meyertons, Hood , Kivlin, Kowert & Goetzel, P.C. P.O. Box 398 Austin, TX 78767-0398 Ph: (512) 853-8800 PATENT 5660-14400
Fractions but not negative numbers are represented on the mental number line.
Ganor-Stern, Dana
2012-02-01
The present study is the first to directly compare numerical representations of positive numbers, negative numbers and unit fractions. The results show that negative numbers and unit fractions were not represented in the same way. Distance effects were found when positive numbers were compared with fractions but not when they were compared with negative numbers, thus suggesting that unit fractions but not negative numbers were represented on the number line with positive numbers. As indicated by the semantic congruity effect, negative numbers were perceived to be small, positive numbers were perceived as large, while unit fractions were perceived neither as large nor small. Comparisons between negative numbers were faster than between unit fractions, possibly due to the smaller differences between the holistic magnitudes of the unit fractions. Finally, comparing unit fractions to 1 was faster than comparing them to 0, consistent with the idea that unit fractions are perceived as entities smaller than 1 (Kallai & Tzelgov, 2009). The results are consistent with the idea of a mental division between numbers that represent a quantity (positive numbers and unit fractions) and those that do not (negative numbers).
Persistent consequences of atypical early number concepts
Directory of Open Access Journals (Sweden)
Michèle M. M. Mazzocco
2013-09-01
Full Text Available How does symbolic number knowledge performance help identify young children at risk for poor mathematics achievement outcomes? In research and practice, classification of mathematics learning disability (MLD, or dyscalculia is typically based on composite scores from broad measures of mathematics achievement. These scores do predict later math achievement levels, but do not specify the nature of math difficulties likely to emerge among students at greatest risk for long-term mathematics failure. Here we report that gaps in 2nd and 3rd graders’ number knowledge predict specific types of errors made on math assessments at Grade 8. Specifically, we show that early whole number misconceptions predict slower and less accurate performance, and atypical computational errors, on Grade 8 arithmetic tests. We demonstrate that basic number misconceptions can be detected by idiosyncratic responses to number knowledge items, and that when such misconceptions are evident during primary school they persist throughout the school age years, with variable manifestation throughout development. We conclude that including specific qualitative assessments of symbolic number knowledge in primary school may provide greater specificity of the types of difficulties likely to emerge among students at risk for poor mathematics outcomes.
Patterns in rational base number systems
Morgenbesser, Johannes F; Thuswaldner, Jörg
2012-01-01
Number systems with a rational number $a/b > 1$ as base have gained interest in recent years. In particular, relations to Mahler's 3/2-problem as well as the Josephus problem have been established. In the present paper we show that the patterns of digits in the representations of positive integers in such a number system are uniformly distributed. We study the sum-of-digits function of number systems with rational base $a/b$ and use representations w.r.t. this base to construct normal numbers in base $a$ in the spirit of Champernowne. The main challenge in our proofs comes from the fact that the language of the representations of integers in these number systems is not context-free. The intricacy of this language makes it impossible to prove our results along classical lines. In particular, we use self-affine tiles that are defined in certain subrings of the ad\\'ele ring $\\mathbb{A}_\\mathbb{Q}$ and Fourier analysis in $\\mathbb{A}_\\mathbb{Q}$. With help of these tools we are able to reformulate our results as ...
QSPR Models for Octane Number Prediction
Directory of Open Access Journals (Sweden)
Jabir H. Al-Fahemi
2014-01-01
Full Text Available Quantitative structure-property relationship (QSPR is performed as a means to predict octane number of hydrocarbons via correlating properties to parameters calculated from molecular structure; such parameters are molecular mass M, hydration energy EH, boiling point BP, octanol/water distribution coefficient logP, molar refractivity MR, critical pressure CP, critical volume CV, and critical temperature CT. Principal component analysis (PCA and multiple linear regression technique (MLR were performed to examine the relationship between multiple variables of the above parameters and the octane number of hydrocarbons. The results of PCA explain the interrelationships between octane number and different variables. Correlation coefficients were calculated using M.S. Excel to examine the relationship between multiple variables of the above parameters and the octane number of hydrocarbons. The data set was split into training of 40 hydrocarbons and validation set of 25 hydrocarbons. The linear relationship between the selected descriptors and the octane number has coefficient of determination (R2=0.932, statistical significance (F=53.21, and standard errors (s =7.7. The obtained QSPR model was applied on the validation set of octane number for hydrocarbons giving RCV2=0.942 and s=6.328.
Complex architecture of primes and natural numbers.
García-Pérez, Guillermo; Serrano, M Ángeles; Boguñá, Marián
2014-08-01
Natural numbers can be divided in two nonoverlapping infinite sets, primes and composites, with composites factorizing into primes. Despite their apparent simplicity, the elucidation of the architecture of natural numbers with primes as building blocks remains elusive. Here, we propose a new approach to decoding the architecture of natural numbers based on complex networks and stochastic processes theory. We introduce a parameter-free non-Markovian dynamical model that naturally generates random primes and their relation with composite numbers with remarkable accuracy. Our model satisfies the prime number theorem as an emerging property and a refined version of Cramér's conjecture about the statistics of gaps between consecutive primes that seems closer to reality than the original Cramér's version. Regarding composites, the model helps us to derive the prime factors counting function, giving the probability of distinct prime factors for any integer. Probabilistic models like ours can help to get deeper insights about primes and the complex architecture of natural numbers.
Ion stopping powers and CT numbers.
Moyers, Michael F; Sardesai, Milind; Sun, Sean; Miller, Daniel W
2010-01-01
One of the advantages of ion beam therapy is the steep dose gradient produced near the ion's range. Use of this advantage makes knowledge of the stopping powers for all materials through which the beam passes critical. Most treatment planning systems calculate dose distributions using depth dose data measured in water and an algorithm that converts the kilovoltage X-ray computed tomography (CT) number of a given material to its linear stopping power relative to water. Some materials present in kilovoltage scans of patients and simulation phantoms do not lie on the standard tissue conversion curve. The relative linear stopping powers (RLSPs) of 21 different tissue substitutes and positioning, registration, immobilization, and beamline materials were measured in beams of protons accelerated to energies of 155, 200, and 250 MeV; carbon ions accelerated to 290 MeV/n; and iron ions accelerated to 970 MeV/n. These same materials were scanned with both kilovoltage and megavoltage CT scanners to obtain their CT numbers. Measured RLSPs and CT numbers were compared with calculated and/or literature values. Relationships of RLSPs to physical densities, electronic densities, kilovoltage CT numbers, megavoltage CT numbers, and water equivalence values converted by a treatment planning system are given. Usage of CT numbers and substitution of measured values into treatment plans to provide accurate patient and phantom simulations are discussed. 2010 American Association of Medical Dosimetrists. Published by Elsevier Inc. All rights reserved.
Relations between Multi-Poly-Bernoulli numbers and Poly-Bernoulli numbers of negative index
Komaki, Hiroyuki
2015-01-01
Poly-Bernoulli numbers $B_n^{(k)}\\in\\mathbb{Q}$\\,($n \\geq 0$,\\,$k \\in \\mathbb{Z}$) are defined by Kaneko in 1997. Multi-Poly-Bernoulli numbers\\,$B_n^{(k_1,k_2,\\ldots, k_r)}$, defined by using multiple polylogarithms, are generations of Kaneko's Poly-Bernoulli numbers\\,$B_n^{(k)}$. We researched relations between Multi-Poly-Bernoulli numbers and Poly-Bernoulli numbers of negative index in particular. In section 2, we introduce a identity for Multi-Poly-Bernoulli numbers of negative index which...
Courant number and unsteady flow computation
Lai, Chintu; ,
1993-01-01
The Courant number C, the key to unsteady flow computation, is a ratio of physical wave velocity, ??, to computational signal-transmission velocity, ??, i.e., C = ??/??. In this way, it uniquely relates a physical quantity to a mathematical quantity. Because most unsteady open-channel flows are describable by a set of n characteristic equations along n characteristic paths, each represented by velocity ??i, i = 1,2,....,n, there exist as many as n components for the numerator of C. To develop a numerical model, a numerical integration must be made on each characteristic curve from an earlier point to a later point on the curve. Different numerical methods are available in unsteady flow computation due to the different paths along which the numerical integration is actually performed. For the denominator of C, the ?? defined as ?? = ?? 0 = ??x/??t has been customarily used; thus, the Courant number has the familiar form of C?? = ??/??0. This form will be referred to as ???common Courant number??? in this paper. The commonly used numerical criteria C?? for stability, neutral stability and instability, are imprecise or not universal in the sense that r0 does not always reflect the true maximum computational data-transmission speed of the scheme at hand, i.e., Ctau is no indication for the Courant constraint. In view of this , a new Courant number, called the ???natural Courant number???, Cn, that truly reflects the Courant constraint, has been defined. However, considering the numerous advantages inherent in the traditional C??, a useful and meaningful composite Courant number, denoted by C??* has been formulated from C??. It is hoped that the new aspects of the Courant number discussed herein afford the hydraulician a broader perspective, consistent criteria, and unified guidelines, with which to model various unsteady flows.
Extending the mental number line--how do negative numbers contribute?
Zhang, Yu; You, Xuqun
2012-01-01
Previous studies suggest that there is an association between positive numbers and space; however, there is less agreement for negative numbers. The main purpose of the present study was to investigate the nature of the processing and representation of negative numbers, and the association between negative numbers and space. Results of the two experiments show that low-level processing (perception) of negative numbers can induce spatial shifts of attention. Whether this is caused by their numerical value or absolute value depends on the numerical context and task requirements, indicating that there are both components and holistic processing, and representation for negative numbers. The representation is automatically associated with leftward space; the coding and representation of the mental number line is adaptable to the specific numerical context and task requirements. The mental number line, therefore, can extend to the left side of zero, thus supporting the context-dependent view.
True random numbers from amplified quantum vacuum.
Jofre, M; Curty, M; Steinlechner, F; Anzolin, G; Torres, J P; Mitchell, M W; Pruneri, V
2011-10-10
Random numbers are essential for applications ranging from secure communications to numerical simulation and quantitative finance. Algorithms can rapidly produce pseudo-random outcomes, series of numbers that mimic most properties of true random numbers while quantum random number generators (QRNGs) exploit intrinsic quantum randomness to produce true random numbers. Single-photon QRNGs are conceptually simple but produce few random bits per detection. In contrast, vacuum fluctuations are a vast resource for QRNGs: they are broad-band and thus can encode many random bits per second. Direct recording of vacuum fluctuations is possible, but requires shot-noise-limited detectors, at the cost of bandwidth. We demonstrate efficient conversion of vacuum fluctuations to true random bits using optical amplification of vacuum and interferometry. Using commercially-available optical components we demonstrate a QRNG at a bit rate of 1.11 Gbps. The proposed scheme has the potential to be extended to 10 Gbps and even up to 100 Gbps by taking advantage of high speed modulation sources and detectors for optical fiber telecommunication devices.
The geodetic numbers of graphs and digraphs
Institute of Scientific and Technical Information of China (English)
Chang-hong LU
2007-01-01
For every two vertices u and v in a graph G, a u-v geodesic is a shortest path between u and v. Let I(u, v) denote the set of all vertices lying on a u-v geodesic. For a vertex subset S, let I(S)denote the union of all I(u, v) for u, v ∈ S. The geodetic number g(G) of a graph G is the minimum cardinality of a set S with I(S) = V(G). For a digraph D, there is analogous terminology for the geodetic number g(D). The geodetic spectrum of a graph G, denoted by S(G), is the set of geodetic numbers of all orientations of graph G. The lower geodetic number is g-(G) = minS(G) and the upper geodetic number is g+ (G) = maxS(G). The main purpose of this paper is to study the relations among g(G), g-(G) and g+ (G) for connected graphs G. In addition, a sufficient and necessary condition for the equality of g(G) and g(G × K2) is presented, which improves a result of Chartrand, Harary and Zhang.
The geodetic numbers of graphs and digraphs
Institute of Scientific and Technical Information of China (English)
2007-01-01
For every two vertices u and v in a graph G,a u-v geodesic is a shortest path between u and v.Let I（u,v）denote the set of all vertices lying on a u-v geodesic.For a vertex subset S,let I（S） denote the union of all I（u,v）for u,v∈S.The geodetic number g（G）of a graph G is the minimum cardinality of a set S with I（S）=V（G）.For a digraph D,there is analogous terminology for the geodetic number g（D）.The geodetic spectrum of a graph G,denoted by S（G）,is the set of geodetic numbers of all orientations of graph G.The lower geodetic number is g-（G）=minS（G）and the upper geodetic number is g+（G）=maxS（G）.The main purpose of this paper is to study the relations among g（G）,g-（G）and g+（G）for connected graphs G.In addition,a sufficient and necessary condition for the equality of g（G）and g（G×K2）is presented,which improves a result of Chartrand,Harary and Zhang.
Means of Staff Number Reduction and Outplacement
Directory of Open Access Journals (Sweden)
Urbancová H.
2014-09-01
Full Text Available The paper focuses on staff number reducing in Czech organizations because it is an important issue due to adaptation to changing economic conditions and ongoing financial crisis. The number of organizations reducing their staff number goes up in all sectors of economy including agriculture and the problem is associated with financial costs. The objective is to present the ways of staff number reduction in Czech organizations and outplacement for the laid-off workers and a partial objective is to compare the results with those in the Slovak Republic. Moreover, the paper discusses the recommendation in the sphere of knowledge continuity for organizations and it also examines the cost level of employees’ turnover. The results were obtained by implementing quantitative research with the help of questionnaire data collection (n = 109 which were analyzed by the tools of descriptive statistics. Results show that 52.3% of organizations have reduced their staff number. However, outplacement was used by only 10.1% of the addressed Czech organizations, out of which 28.6% were agricultural.
Hunhold, Laslo
2017-01-01
This thesis examines a modern concept for machine numbers based on interval arithmetic called 'Unums' and compares it to IEEE 754 floating-point arithmetic, evaluating possible uses of this format where floating-point numbers are inadequate. In the course of this examination, this thesis builds theoretical foundations for IEEE 754 floating-point numbers, interval arithmetic based on the projectively extended real numbers and Unums.
An Exploratory Study of a Number Sense Program to Develop Kindergarten Students' Number Proficiency
Sood, Sheetal; Jitendra, Asha K.
2013-01-01
This study examined the effectiveness of a number sense program on kindergarten students' number proficiency and responsiveness to treatment as a function of students' risk for mathematics difficulties. The program targeted development of relationships among numbers (e.g., spatial, more and less). A total of 101 kindergarten students (not at risk:…
Krause, F.; Lindemann, O.; Toni, I.; Bekkering, H.
2014-01-01
A dominant hypothesis on how the brain processes numerical size proposes a spatial representation of numbers as positions on a "mental number line." An alternative hypothesis considers numbers as elements of a generalized representation of sensorimotor-related magnitude, which is not obligatorily
Fibonacci polynomials, generalized Stirling numbers, and Bernoulli, Genocchi and tangent numbers
Cigler, Johann
2011-01-01
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.
J. Lisle, de; De, S.; Alba, E.; Bullivant, A.; Garcia-Ripoll, J.J.; Lahtinen, V.; Pachos, J.K.
2014-01-01
Topological invariants, such as the Chern number, characterize 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
Quantum Field Theories and Prime Numbers Spectrum
Menezes, G
2012-01-01
The Riemann hypothesis states that all nontrivial zeros of the zeta function lie on the critical line $\\Re(s)=1/2$. Hilbert and P\\'olya suggested a possible approach to prove it, based on spectral theory. Within this context, some authors formulated the question: is there a quantum mechanical system related to the sequence of prime numbers? In this Letter we assume that there is a class of hypothetical physical systems described by self-adjoint operators with countable infinite number of degrees of freedom with spectra given by the sequence of primes numbers. We prove a no-go theorem. We show that the generating functional of connected Schwinger functions of such theories cannot be constructed.
Symbolic representation of number in chimpanzees.
Matsuzawa, Tetsuro
2009-02-01
This paper aims to summarize the existing evidence for the symbolic representation of number in chimpanzees. Chimpanzees can represent, to some extent, both the cardinal and the ordinal aspect of number. Through the medium of Arabic numerals we compared working memory in humans and chimpanzees using the same apparatus and following the same procedure. Three young chimpanzees outperformed human adults in memorizing briefly presented numerals. However, we found that chimpanzees were less proficient at a variety of other cognitive tasks including imitation, cross-modal matching, symmetry of symbols and referents, and one-to-one correspondence. In sum, chimpanzees do not possess human-like capabilities for representation at an abstract level. The present paper will discuss the constraints of the number concept in chimpanzees, and illuminate some unique features of human cognition.
Droplet Number Concentration Value-Added Product
Energy Technology Data Exchange (ETDEWEB)
Riihimaki, L. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); McFarlane, S. [DOE ARM Climate Research Facility, Washington, DC (United States); Sivaraman, C. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2014-06-01
The ndrop_mfrsr value-added product (VAP) provides an estimate of the cloud droplet number concentration of overcast water clouds retrieved from cloud optical depth from the multi-filter rotating shadowband radiometer (MFRSR) instrument and liquid water path (LWP) retrieved from the microwave radiometer (MWR). When cloud layer information is available from vertically pointing lidar and radars in the Active Remote Sensing of Clouds (ARSCL) product, the VAP also provides estimates of the adiabatic LWP and an adiabatic parameter (beta) that indicates how divergent the LWP is from the adiabatic case. quality control (QC) flags (qc_drop_number_conc), an uncertainty estimate (drop_number_conc_toterr), and a cloud layer type flag (cloud_base_type) are useful indicators of the quality and accuracy of any given value of the retrieval. Examples of these major input and output variables are given in sample plots in section 6.0.
Arithmetic Operations on Trapezoidal Fuzzy Numbers
Directory of Open Access Journals (Sweden)
J. Vahidi
2013-10-01
Full Text Available In this paper, several new algebraic mathematics for positive fuzzy numbers of type $(\\overline{a}, \\overline{\\overline{a}}, \\overline{\\overline{\\overline{a}}}, \\overline{\\overline{\\overline{\\overline{a}}}}$ are devised and do not need the computation of $\\alpha$-cut of the fuzzy number. Direct mathematical expressions to evaluate exponential, square root, logarithms, inverse exponential etc. of positive fuzzy numbers of type $(\\overline{a}, \\overline{\\overline{a}}, \\overline{\\overline{\\overline{a}}}, \\overline{\\overline{\\overline{\\overline{a}}}}$ are obtained using the basic analytical principles of algebraic mathematics and Taylor series expansion. At the end, Various numerical examples are also solved to demonstrate the use of contrived expressions.
Elliptic Carmichael Numbers and Elliptic Korselt Criteria
Silverman, Joseph H
2011-01-01
Let E/Q be an elliptic curve, let L(E,s)=\\sum a_n/n^s be the L-series of E/Q, and let P be a point in E(Q). An integer n > 2 having at least two distinct prime factors will be be called an elliptic pseudoprime for (E,P) if E has good reduction at all primes dividing n and (n+1-a_n)P = 0 (mod n). Then n is an elliptic Carmichael number for E if n is an elliptic pseudoprime for every P in E(Z/nZ). In this note we describe two elliptic analogues of Korselt's criterion for Carmichael numbers, and we analyze elliptic Carmichael numbers of the form pq.
Seniority Number in Valence Bond Theory.
Chen, Zhenhua; Zhou, Chen; Wu, Wei
2015-09-01
In this work, a hierarchy of valence bond (VB) methods based on the concept of seniority number, defined as the number of singly occupied orbitals in a determinant or an orbital configuration, is proposed and applied to the studies of the potential energy curves (PECs) of H8, N2, and C2 molecules. It is found that the seniority-based VB expansion converges more rapidly toward the full configuration interaction (FCI) or complete active space self-consistent field (CASSCF) limit and produces more accurate PECs with smaller nonparallelity errors than its molecular orbital (MO) theory-based analogue. Test results reveal that the nonorthogonal orbital-based VB theory provides a reverse but more efficient way to truncate the complete active Hilbert space by seniority numbers.
Two results on the digraph chromatic number
Harutyunyan, Ararat
2011-01-01
It is known (Bollob\\'{a}s (1978); Kostochka and Mazurova (1977)) that there exist graphs of maximum degree $\\Delta$ and of arbitrarily large girth whose chromatic number is at least $c \\Delta / \\log \\Delta$. We show an analogous result for digraphs where the chromatic number of a digraph $D$ is defined as the minimum integer $k$ so that $V(D)$ can be partitioned into $k$ acyclic sets, and the girth is the length of the shortest cycle in the corresponding undirected graph. It is also shown, in the same vein as an old result of Erdos (1962), that there are digraphs with arbitrarily large chromatic number where every large subset of vertices is 2-colorable.
National transonic facility Mach number system
Kern, F. A.; Knight, C. W.; Zasimowich, R. F.
1985-01-01
The Mach number system for the Langley Research Center's National Transonic Facility was designed to measure pressures to determine Mach number to within + or - 0.002. Nine calibration laboratory type fused quartz gages, four different range gages for the total pressure measurement, and five different range gages for the static pressure measurement were used to satisfy the accuracy requirement over the 103,000-890,000 Pa total pressure range of the tunnel. The system which has been in operation for over 1 year is controlled by a programmable data process controller to select, through the operation of solenoid valves, the proper range fused quartz gage to maximize the measurement accuracy. The pressure gage's analog outputs are digitized by the process controller and transmitted to the main computer for Mach number computation. An automatic two-point on-line calibration of the nine quartz gages is provided using a high accuracy mercury manometer.
Some Exact Ramsey-Tur\\'an Numbers
Balogh, József
2011-01-01
Let r be an integer, f(n) a function, and H a graph. Introduced by Erd\\H{o}s, Hajnal, S\\'{o}s, and Szemer\\'edi, the r-Ramsey-Tur\\'{a}n number of H, RT_r(n, H, f(n)), is defined to be the maximum number of edges in an n-vertex, H-free graph G with \\alpha_r(G) <= f(n) where \\alpha_r(G) denotes the K_r-independence number of G. In this note, using isoperimetric properties of the high dimensional unit sphere, we construct graphs providing lower bounds for RT_r(n,K_{r+s},o(n)) for every 2 <= s <= r. These constructions are sharp for an infinite family of pairs of r and s. The only previous sharp construction was by Bollob\\'as and Erd\\Hos for r = s = 2.
Optimal Strouhal number for swimming animals
Eloy, Christophe
2011-01-01
To evaluate the swimming performances of aquatic animals, an important dimensionless quantity is the Strouhal number, St = fA/U, with f the tail-beat frequency, A the peak-to-peak tail amplitude, and U the swimming velocity. Experiments with flapping foils have exhibited maximum propulsive efficiency in the interval 0.25 < St < 0.35 and it has been argued that animals likely evolved to swim in the same narrow interval. Using Lighthill's elongated-body theory to address undulatory propulsion, it is demonstrated here that the optimal Strouhal number increases from 0.15 to 0.8 for animals spanning from the largest cetaceans to the smallest tadpoles. To assess the validity of this model, the swimming kinematics of 53 different species of aquatic animals have been compiled from the literature and it shows that their Strouhal numbers are consistently near the predicted optimum.
Upper Locating-Domination Numbers of Cycles
Institute of Scientific and Technical Information of China (English)
Yan Cai ZHAO; Er Fang SHAN; Ru Zhao GAO
2011-01-01
A set D of vertices in a graph G＝(V,E) is a locating-dominating set (LDS) if for every two vertices u,v of V\\D the sets N(u)∩ D and N(v)∩ D are non-empty and different.The locating-domination number γL(G) is the minimum cardinality of an LDS of G,and the upper-locating domination number ΓL(G) is the maximum cardinality of a minimal LDS of G.In the present paper,methods for determining the exact values of the upper locating-domination numbers of cycles are provided.
Large numbers hypothesis. II - Electromagnetic radiation
Adams, P. J.
1983-01-01
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.
Random Numbers Certified by Bell's Theorem
Pironio, S; Massar, S; de la Giroday, A Boyer; Matsukevich, D N; Maunz, P; Olmschenk, S; Hayes, D; Luo, L; Manning, T A; Monroe, C
2009-01-01
Randomness is difficult to characterize mathematically, and its generation must rely on an unpredictable physical process. Inaccuracies in the theoretical modelling of such processes or failures of the devices, possibly due to adversarial attacks, limit the reliability of random number generators in ways that are difficult to control and detect. Here, we show that the nonlocal correlations of entangled quantum particles can be used to design a new type of cryptographically secure random number generator without the need for any assumptions on the internal working of the devices. This strong form of randomness generation is impossible classically and possible in quantum systems only if certified by a Bell inequality violation. We demonstrate this proposal in a system of two entangled atoms separated by approximately 1 meter. The observed Bell inequality violation, featuring near-perfect detection efficiency, guarantees that 42 new random numbers are generated with 99% confidence. Our results lay the groundwork...
Random Numbers from a Delay Equation
Self, Julian; Mackey, Michael C.
2016-10-01
Delay differential equations can have "chaotic" solutions that can be used to mimic Brownian motion. Since a Brownian motion is random in its velocity, it is reasonable to think that a random number generator might be constructed from such a model. In this preliminary study, we consider one specific example of this and show that it satisfies criteria commonly employed in the testing of random number generators (from TestU01's very stringent "Big Crush" battery of tests). A technique termed digit discarding, commonly used in both this generator and physical RNGs using laser feedback systems, is discussed with regard to the maximal Lyapunov exponent. Also, we benchmark the generator to a contemporary common method: the multiple recursive generator, MRG32k3a. Although our method is about 7 times slower than MRG32k3a, there is in principle no apparent limit on the number of possible values that can be generated from the scheme we present here.
Number systems and the Chinese Remainder Theorem
van de Woestijne, Christiaan E
2011-01-01
A well-known generalisation of positional numeration systems is the case where the base is the residue class of $x$ modulo a given polynomial $f(x)$ with coefficients in (for example) the integers, and where we try to construct finite expansions for all residue classes modulo $f(x)$, using a suitably chosen digit set. We give precise conditions under which direct or fibred products of two such polynomial number systems are again of the same form. The main tool is a general form of the Chinese Remainder Theorem. We give applications to simultaneous number systems in the integers.
Number sense how the mind creates mathematics
Dehaene, Stanislas
2011-01-01
Our understanding of how the human brain performs mathematical calculations is far from complete, but in recent years there have been many exciting breakthroughs by scientists all over the world. Now, in The Number Sense, Stanislas Dehaene offers a fascinating look at this recent research, in an enlightening exploration of the mathematical mind. Dehaene begins with the eye-opening discovery that animals--including rats, pigeons, raccoons, and chimpanzees--can perform simple mathematical calculations, and that human infants also have a rudimentary number sense. Dehaene suggests that this rudime
The nine numbers of the cosmos
Rowan-Robinson, Michael
1999-01-01
How old is the universe? How far away are the galaxies and how fast are they travelling away from us? What is dark matter and why do astronomers think it pervades the universe? How heavy is the vacuum? How do galaxies form?Michael Rowan-Robinson answers these and many more questions in a highly original and intriguing way. He encapsulates our current knowledge (both what we do and don't know) of the origin and the nature of the universe into nine numbers. These cosmic numbers appear to be independent characteristics of our universe and include its age, the Hubble constant (a measure of its rat
Flexagons yield a curious Catalan number identity
Callan, David
2010-01-01
Hexaflexagons were popularized by the late Martin Gardner in his first Scientific American column in 1956. Oakley and Wisner showed that they can be represented abstractly by certain recursively defined permutations called pats, and deduced that they are counted by the Catalan numbers. Counting pats by number of descents yields the curious identity Sum[1/(2n-2k+1)binom{2n-2k+1}{k}binom{2k}{n-k},k=0..n] = C(n), where only the middle third of the summands are nonzero.
Cantor-Type Sets in Hyperbolic Numbers
Balankin, A. S.; Bory-Reyes, J.; Luna-Elizarrarás, M. E.; Shapiro, M.
2016-12-01
The construction of the ternary Cantor set is generalized into the context of hyperbolic numbers. The partial order structure of hyperbolic numbers is revealed and the notion of hyperbolic interval is defined. This allows us to define a general framework of the fractal geometry on the hyperbolic plane. Three types of the hyperbolic analogues of the real Cantor set are identified. The complementary nature of the real Cantor dust and the real Sierpinski carpet on the hyperbolic plane are outlined. The relevance of these findings in the context of modern physics are briefly discussed.
L^2-Betti numbers of hypersurface complements
Maxim, Laurentiu
2012-01-01
In \\cite{DJL07} it was shown that if $\\scra$ is an affine hyperplane arrangement in $\\C^n$, then at most one of the $L^2$--Betti numbers $b_i^{(2)}(\\C^n\\sm \\scra,\\id)$ is non--zero. In this note we prove an analogous statement for complements of complex affine hyperurfaces in general position at infinity. Furthermore, we recast and extend to this higher-dimensional setting results of \\cite{FLM,LM06} about $L^2$--Betti numbers of plane curve complements.
Number theory meets high energy physics
Todorov, Ivan
2017-03-01
Feynman amplitudes in perturbative quantum field theory are being expressed in terms of an algebra of functions, extending the familiar logarithms, and associated numbers— periods. The study of these functions (including hyperlogarithms) and numbers (like the multiple zeta values), that dates back to Leibniz and Euler, has attracted anew the interest of algebraic geometers and number theorists during the last decades. The two originally independent developments are recently coming together in an unlikely collaboration between particle physics and what were regarded as the most abstruse branches of mathematics.
10 conjectures in additive number theory
Cloitre, Benoit
2011-01-01
Following an idea of Rowland we give a conjectural way to generate increasing sequences of primes using algorithms involving the gcd. These algorithms seem not so useless for searching primes since it appears we found sometime primes much more greater than the number of required iterations. In an other hand we propose new formulations of famous conjectures from the additive theory of numbers (the weak twin prime conjecture, the Polignac conjecture, the Goldbach conjecture or the very general Schinzel's hypothesis H). For the moment these are experimental results obtained using pari-gp.
History of the theory of numbers
Dickson, Leonard Eugene
2005-01-01
The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This second volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to the subject of diophantine analysis. It can be read independently of the preceding volume, which explores divisibility and primality, and volume III, which examines quadratic and higher forms.Featured topics include
Energy information data base: report number codes
Energy Technology Data Exchange (ETDEWEB)
None
1979-09-01
Each report processed by the US DOE Technical Information Center is identified by a unique report number consisting of a code plus a sequential number. In most cases, the code identifies the originating installation. In some cases, it identifies a specific program or a type of publication. Listed in this publication are all codes that have been used by DOE in cataloging reports. This compilation consists of two parts. Part I is an alphabetical listing of report codes identified with the issuing installations that have used the codes. Part II is an alphabetical listing of installations identified with codes each has used. (RWR)
Number theory and the periodicity of matter
Boeyens, Jan C A
2008-01-01
Presents a fully scientific account of the use of the golden ratio and explores the observation that stable nucleides obey a number theory based general lawThe interest in number theory is worldwide and covers the entire spectrum of human knowledge. Those aspects covered here will not be immediately accessible to the general lay readership, but, scientists of all pursuations immediately appreciate the importance of the applications described hereThe well-known interest of engineers, medical practitioners and information technologists in popular scientific matters, should make this an attractive buy for such individuals. Undergraduate students in these disciplines should be equally interested.
Directory of Open Access Journals (Sweden)
Shetnikov, Andrey
2009-06-01
Full Text Available The paper concerns the concept of number (arithmos, important for dialectical method of later Plato. It becomes clear that the arithmos in Plato’s dialectics should be understood as a concrete operation, a sort of tekhne, such as counting, enumeration, compilation of a comprehensive and systematic list, etc., rather then the theoretical number of abstract arithmetic. The author analyses a series of grammatical, musical and rhetorical examples, supplied by Plato in the Philebus and other dialogues, and traces the usage of arithmos and similar words in the earlier tradition, particularly, in Homer, Hesiod, the classical tragedy, and Herodotus.
Metric propositional neighborhood logics on natural numbers
DEFF Research Database (Denmark)
Bresolin, Davide; Della Monica, Dario; Goranko, Valentin
2013-01-01
Metric Propositional Neighborhood Logic (MPNL) over natural numbers. MPNL features two modalities referring, respectively, to an interval that is “met by” the current one and to an interval that “meets” the current one, plus an infinite set of length constraints, regarded as atomic propositions...... is decidable in double exponential time and expressively complete with respect to a well-defined sub-fragment of the two-variable fragment FO2[N,=,numbers. Moreover, we show that MPNL can be extended in a natural way...
On the arrowhead-Fibonacci numbers
Directory of Open Access Journals (Sweden)
Gültekin Inci
2016-01-01
Full Text Available In this paper, we define the arrowhead-Fibonacci numbers by using the arrowhead matrix of the characteristic polynomial of the k-step Fibonacci sequence and then we give some of their properties. Also, we study the arrowhead-Fibonacci sequence modulo m and we obtain the cyclic groups from the generating matrix of the arrowhead-Fibonacci numbers when read modulo m. Then we derive the relationships between the orders of the cyclic groups obtained and the periods of the arrowhead-Fibonacci sequence modulo m.
Lepton number violation in 331 models
Fonseca, Renato M
2016-01-01
Different models based on the extended $SU(3)_{C}\\times SU(3)_{L}\\times U(1)_{X}$ (331) gauge group have been proposed over the past four decades. Yet, despite being an active research topic, the status of lepton number in 331 models has not been fully addressed in the literature, and furthermore many of the original proposals can not explain the observed neutrino masses. In this paper we review the basic features of various 331 models, focusing on potential sources of lepton number violation. We then describe different modifications which can be made to the original models in order to accommodate neutrino (and charged lepton) masses.
Lepton number violation in 331 models
Fonseca, Renato M.; Hirsch, Martin
2016-12-01
Different models based on the extended S U (3 )C×S U (3 )L×U (1 )X (331) gauge group have been proposed over the past four decades. Yet, despite being an active research topic, the status of lepton number in 331 models has not been fully addressed in the literature, and furthermore many of the original proposals can not explain the observed neutrino masses. In this paper we review the basic features of various 331 models, focusing on potential sources of lepton number violation. We then describe different modifications which can be made to the original models in order to accommodate neutrino (and charged lepton) masses.
Lockwood, M.; Owens, M. J.; Barnard, L.
2016-11-01
We use five test data series to search for, and quantify, putative discontinuities around 1946 in five different annual-mean sunspot-number or sunspot-group-number data sequences. The data series tested are the original and new versions of the Wolf/Zürich/International sunspot number composite [R_{{ISNv1}} and R_{{ISNv2}}] (respectively Clette et al. in Adv. Space Res. 40, 919, 2007 and Clette et al. in The Solar Activity Cycle 35, Springer, New York, 2015); the corrected version of R ISNv1 proposed by Lockwood, Owens, and Barnard ( J. Geophys. Res. 119, 5193, 2014a) [R C]; the new "backbone" group-number composite proposed by Svalgaard and Schatten ( Solar Phys. 291, 2016) [R_{{BB}}]; and the new group-number composite derived by Usoskin et al. ( Solar Phys. 291, 2016) [R_{{UEA}}]. The test data series used are the group-number [NG] and total sunspot area [A G] from the Royal Observatory, Greenwich/Royal Greenwich Observatory (RGO) photoheliographic data; the Ca K index from the recent re-analysis of Mount Wilson Observatory (MWO) spectroheliograms in the Calcium ii K ion line; the sunspot-group-number from the MWO sunspot drawings [N_{{MWO}}]; and the dayside ionospheric F2-region critical frequencies measured by the Slough ionosonde [foF2]. These test data all vary in close association with sunspot numbers, in some cases non-linearly. The tests are carried out using both the before-and-after fit-residual comparison method and the correlation method of Lockwood, Owens, and Barnard, applied to annual mean data for intervals iterated to minimise errors and to eliminate uncertainties associated with the precise date of the putative discontinuity. It is not assumed that the correction required is by a constant factor, nor even linear in sunspot number. It is shown that a non-linear correction is required by RC, R_{BB}, and R_{{ISNv1}}, but not by R_{{ISNv2}} or R_{{UEA}}. The five test datasets give very similar results in all cases. By multiplying the probability
High Prandtl number effect on Rayleigh-Bénard convection heat transfer at high Rayleigh number
Ma, Li; Li, Jing; Ji, Shui; Chang, Huajian
2017-02-01
This paper represents results of the Rayleigh-Bénard convection heat transfer in silicon oil confined by two horizontal plates, heated from below, and cooled from above. The Prandtl numbers considered as 100-10,000 corresponding to three types of silicon oil. The experiments covered a range of Rayleigh numbers from 2.14·109 to 2.27·1013. The data points that the Nusselt number dependents on the Rayleigh number, which is asymptotic to a 0.248 power. Furthermore, the experiment results can fit the data in low Rayleigh number well.
Two-bit quantum random number generator based on photon-number-resolving detection
Jian, Yi; Ren, Min; Wu, E.; Wu, Guang; Zeng, Heping
2011-07-01
Here we present a new fast two-bit quantum random number generator based on the intrinsic randomness of the quantum physical phenomenon of photon statistics of coherent light source. Two-bit random numbers were generated according to the number of detected photons in each light pulse by a photon-number-resolving detector. Poissonian photon statistics of the coherent light source guaranteed the complete randomness of the bit sequences. Multi-bit true random numbers were generated for the first time based on the multi-photon events from a coherent light source.
Wave packet dynamics and factorization of numbers
Mack, H; Haug, F; Straub, F S; Freyberger, M; Schleich, W P; Mack, Holger; Bienert, Marc; Haug, Florian; Straub, Frank S.; Freyberger, Matthias; Schleich, Wolfgang P.
2002-01-01
We connect three phenomena of wave packet dynamics: Talbot images, revivals of a particle in a box and fractional revivals. The physical origin of these effects is deeply rooted in phase factors which are quadratic in the quantum number. We show that the characteristic structures in the time evolution of these systems allow us to factorize large integers.
Boundary induced nonlinearities at small Reynolds numbers
Sbragaglia, M.; Sugiyama, K.
2007-01-01
We investigate the importance of boundary slip at finite Reynolds numbers for mixed boundary conditions. Nonlinear effects are induced by the non-homogeneity of the boundary condition and change the symmetry properties of the flow with an overall mean flow reduction. To explain the observed drag
Number of bidders and the winner's curse
Peeters, Ronald; Tenev, Anastas
2016-01-01
The second-price sealed-bid common-value auction exhibits lower winner's curse probability compared to the rst-price auction for any number of bidders. For both auction types, above a certain threshold adding more bidders increases the chances of the winner's curse only marginally while it decreases
Did Hypatia Know about Negative Numbers?
Abramowicz, Marek
2012-01-01
In this Letter we comment on one particular aspect of Hypatia's enigmatic biography by translating into English a short poem that appeared in a recent review of the third revised Polish edition of Maria Dzielska's book about Hypatia. It poses a simple and specifc question: did Hypatia know about the negative numbers?
The Ronkin number of an exponential sum
Silipo, James
2011-01-01
We give an intrinsic estimate of the number of connected components of the complementary set to the amoeba of an exponential sum with real spectrum improving the result of Forsberg, Passare and Tsikh in the polynomial case and that of Ronkin in the exponential one.
On the Ramanujan conjecture over number fields
Blomer, Valentin
2010-01-01
We extend to an arbitrary number field the best known bounds towards the Ramanujan conjecture for the groups GL(n), n=2, 3, 4. In particular, we present a technique allowing to overcome the analytic obstacles posed by the presence of an infinite group of units.
The heterogeneous nature of number space interactions
Directory of Open Access Journals (Sweden)
Jean-Philippe evan Dijck
2012-01-01
Full Text Available It is generally accepted that the mental representation of numerical magnitude consists of a spatial ‘mental number line’ with smaller quantities on the left and larger quantities on the right. However, the amount of dissociations between tasks that were believed to tap onto this representational medium is accumulating, questioning the universality of this model. The aim of the present study was to unravel the functional relationship between the different tasks and effects that are typically used as evidence for the mental number line. For this purpose, a group of right brain damaged patients (with and without neglect and healthy controls were subjected to physical line bisection, number interval bisection, parity judgment and magnitude comparison. Using principal component analysis, different orthogonal components were extracted. We discuss how this component structure captures the dissociations reported in the literature and how it can be considered as a first step towards a new unitary framework for understanding the relation between numbers and space.
DEFF Research Database (Denmark)
Elmasry, Amr Ahmed Abd Elmoneim; Jensen, Claus; Katajainen, Jyrki
2010-01-01
is 2 i-1, and hence we can implement a priority queue as a forest of heap-ordered complete binary trees. The resulting data structure guarantees O(1) worst-case cost per insert and O(lg n) worst-case cost per delete, where n is the number of elements stored. © 2010 Springer-Verlag Berlin Heidelberg....
Robot technology and numbers in the classroom
DEFF Research Database (Denmark)
Majgaard, Gunver; Nielsen, Jacob; Misfeldt, Morten
2010-01-01
This paper explores how a cubic user-configurable modular robotic system can be used to support learning about numbers and how they are pronounced. The development is done in collaboration with a class of 7-8 year old children and their mathematics teacher. The tool is called Speakmath and it com...
Radical Software. Number Two. The Electromagnetic Spectrum.
Korot, Beryl, Ed.; Gershuny, Phyllis, Ed.
1970-01-01
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…
The number of expats is rather stable
DEFF Research Database (Denmark)
Andersen, Torben
2008-01-01
aggregate data from the Danish economist’s and the engineer’s trade unions show that during the last decade there has been stagnation in the number of expatriates. Taking into consideration that the three trade unions cover the very large majority of Danish knowledge workers occupying foreign job...
Critical Number of Fields in Stochastic Inflation
Vennin, Vincent; Assadullahi, Hooshyar; Firouzjahi, Hassan; Noorbala, Mahdiyar; Wands, David
2017-01-01
Stochastic effects in generic scenarios of inflation with multiple fields are investigated. First passage time techniques are employed to calculate the statistical moments of the number of inflationary e -folds, which give rise to all correlation functions of primordial curvature perturbations through the stochastic δ N formalism. The number of fields is a critical parameter. The probability of exploring arbitrarily large-field regions of the potential becomes nonvanishing when more than two fields are driving inflation. The mean number of e -folds can be infinite, depending on the number of fields; for plateau potentials, this occurs even with one field. In such cases, correlation functions of curvature perturbations are infinite. They can, however, be regularized if a reflecting (or absorbing) wall is added at large energy or field value. The results are found to be independent of the exact location of the wall and this procedure is, therefore, well defined for a wide range of cutoffs, above or below the Planck scale. Finally, we show that, contrary to single-field setups, multifield models can yield large stochastic corrections even at sub-Planckian energy, opening interesting prospects for probing quantum effects on cosmological fluctuations.
Workjobs II: Number Activities for Early Childhood.
Baratta-Lorton, Mary
This curriculum guide presents a program of 20 open-ended math activities to be used to supplement the math programs in kindergarten, first, or second grade classrooms. The program consists of child-oriented counters and gameboards used to explore the concept of number from counting to making up and solving addition and subtraction equations. Each…
Arithmetic for First Graders Lacking Number Concepts
Kamii, Constance; Rummelsburg, Judith
2008-01-01
To build cognitive foundation for number, twenty-six low-performing, low-SES first graders did mathematical physical-knowledge activities, such as "bowling," during the first half of the year. As their arithmetic readiness developed, they tried more word problems and games. At the end of the year, these children did better in mental arithmetic and…
Hardware Random number Generator for cryptography
Soorat, Ram; Vudayagiri, Ashok
2015-01-01
One of the key requirement of many schemes is that of random numbers. Sequence of random numbers are used at several stages of a standard cryptographic protocol. A simple example is of a Vernam cipher, where a string of random numbers is added to massage string to generate the encrypted code. It is represented as $C=M \\oplus K $ where $M$ is the message, $K$ is the key and $C$ is the ciphertext. It has been mathematically shown that this simple scheme is unbreakable is key K as long as M and is used only once. For a good cryptosystem, the security of the cryptosystem is not be based on keeping the algorithm secret but solely on keeping the key secret. The quality and unpredictability of secret data is critical to securing communication by modern cryptographic techniques. Generation of such data for cryptographic purposes typically requires an unpredictable physical source of random data. In this manuscript, we present studies of three different methods for producing random number. We have tested them by study...
RICE CONDITION NUMBERS OF CERTAIN CHARACTERISTIC SUBSPACES
Institute of Scientific and Technical Information of China (English)
生汉芳; 刘新国
2002-01-01
This paper proposes the Rice condition numbers for invariant subspace, singular subspaces of a matrix and deflating subspaces of a regular matrix pair. The first-order perturbation estimations for these subspaces are derived by applying perturbation expansions of orthogonal projection operators.
A Geometrical Application of Number Theory
Srinivasan, V. K.
2013-01-01
Any quadruple of natural numbers {a, b, c, d} is called a "Pythagorean quadruple" if it satisfies the relationship "a[superscript 2] + b[superscript 2] + c[superscript 2]". This "Pythagorean quadruple" can always be identified with a rectangular box of dimensions "a greater than 0," "b greater than…
Proofs in Number Theory: History and Heresy.
Rowland, Tim
The domain of number theory lends itself particularly well to generic argument, presented with the intention of conveying the force and structure of a conventional generalized argument through the medium of a particular case. The potential of generic examples as a didactic tool is virtually unrecognized. Although the use of such examples has good…
Synesthesia and Number Cognition in Children
Green, Jennifer A. K.; Goswami, Usha
2008-01-01
Grapheme-color synesthesia, when achromatic digits evoke an experience of a specific color (photisms), has been shown to be consistent, involuntary, and linked with number concept in adults, yet there have been no comparable investigations with children. We present a systematic study of grapheme-color synesthesia in children aged between 7 and 15…
Synesthesia and Number Cognition in Children
Green, Jennifer A. K.; Goswami, Usha
2008-01-01
Grapheme-color synesthesia, when achromatic digits evoke an experience of a specific color (photisms), has been shown to be consistent, involuntary, and linked with number concept in adults, yet there have been no comparable investigations with children. We present a systematic study of grapheme-color synesthesia in children aged between 7 and 15…
Toward a Coherent Treatment of Negative Numbers
Kreith, Kurt; Mendle, Al
2013-01-01
The transition from whole numbers to integers involves challenges for both students and teachers. Leadership in mathematics education calls for an ability to translate depth of understanding into effective teaching methods, and this landscape includes alternative treatments of familiar topics. Noting the multiple meanings associated with the…
Continued fractions constructed from prime numbers
Wolf, Marek
2010-01-01
We give 50 digits values of the simple continued fractions whose denominators are formed from a) prime numbers, b) twin primes, c) primes of the form m^2+1 and Mersenne primes. All these continued fractions belong to the set of measure zero of exceptions to the Khinchin Theorem.
Authenticating "Number the Stars" Using Nonfiction Resources
Groce, Robin D.
2009-01-01
"Number the Stars" by Lois Lowry is a popular historical novel for adolescent readers about the Nazi occupation of Copenhagen, Denmark during World War II and the efforts of Danish resisters who successfully rescued 98% of that nation's Jewish population. While this 1998 book is considered to be a fictional account, most of the events in…
Room Airflows with Low Reynolds Number Effects
DEFF Research Database (Denmark)
Topp, Claus; Nielsen, Peter V.; Davidson, Lars
The behaviour of room airflows under fully turbulent conditions is well known both in terms of experiments and, numerical calculations by computational fluid dynamics (CFD). For room airflows where turbulence is not fully developed though, i.e. flows at low Reynolds numbers, the existing knowledge...
Visualizing the Arithmetic of Complex Numbers
Soto-Johnson, Hortensia
2014-01-01
The Common Core State Standards Initiative stresses the importance of developing a geometric and algebraic understanding of complex numbers in their different forms (i.e., Cartesian, polar and exponential). Unfortunately, most high school textbooks do not offer such explanations much less exercises that encourage students to bridge geometric and…
Binomial Squares in Pure Cubic Number Fields
Lemmermeyer, Franz
2011-01-01
Let K = Q(\\omega) with \\omega^3 = m be a pure cubic number field. We show that the elements\\alpha \\in K^\\times whose squares have the form a - \\omega form a group isomorphic to the group of rational points on the elliptic curve E_m: y^2= x^3 - m.
Understanding Quantum Numbers in General Chemistry Textbooks
Niaz, Mansoor; Fernandez, Ramon
2008-01-01
Quantum numbers and electron configurations form an important part of the general chemistry curriculum and textbooks. The objectives of this study are: (1) Elaboration of a framework based on the following aspects: (a) Origin of the quantum hypothesis, (b) Alternative interpretations of quantum mechanics, (c) Differentiation between an orbital and…
Some Functional Equations Originating from Number Theory
Indian Academy of Sciences (India)
Soon-Mo Jung; Jae-Hyeong Bae
2003-05-01
We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.
Multiinstanton ladders in baryon number violating processes
Lazarides, G
1995-01-01
We estimate the contribution of a class of multiinstanton ladder graphs to baryon and lepton number violating processes in the standard model. We find that this contribution is negligible and does not alter the high energy behavior of the leading semiclassical approximation.
Forecasting distribution of numbers of large fires
Haiganoush K. Preisler; Jeff Eidenshink; Stephen Howard; Robert E. Burgan
2015-01-01
Systems to estimate forest fire potential commonly utilize one or more indexes that relate to expected fire behavior; however they indicate neither the chance that a large fire will occur, nor the expected number of large fires. That is, they do not quantify the probabilistic nature of fire danger. In this work we use large fire occurrence information from the...
Highest Weight Categories For Number Rings
Pilkington, Annette
2011-01-01
This paper examines the concept of a stratified exact category in the context of number rings and corresponding Galois groups. BGG reciprocity and duality are proven for these categories making them highest weight categories. The strong connections between the structure of the category and ramification in the ring are explored.
A mathematical history of the golden number
Herz-Fischler, Roger
1998-01-01
A comprehensive study of the historic development of division in extreme and mean ratio (""the golden number""), this text traces the concept's development from its first appearance in Euclid's Elements through the 18th century. The coherent but rigorous presentation offers clear explanations of DEMR's historical transmission and features numerous illustrations.
Understanding Quantum Numbers in General Chemistry Textbooks
Niaz, Mansoor; Fernandez, Ramon
2008-01-01
Quantum numbers and electron configurations form an important part of the general chemistry curriculum and textbooks. The objectives of this study are: (1) Elaboration of a framework based on the following aspects: (a) Origin of the quantum hypothesis, (b) Alternative interpretations of quantum mechanics, (c) Differentiation between an orbital and…
The Learning Potentials of Number Blocks
DEFF Research Database (Denmark)
Majgaard, Gunver; Nielsen, Jacob; Misfeldt, Morten
2012-01-01
This paper describes an initial exploration of how an interactive cubic user-configurable modular robotic system can be used to support learning about numbers and how they are pronounced. The development is done in collaboration with a class of 7-8 year old children and their mathematics teacher....
Asymptotic estimates for generalized Stirling numbers
Chelluri, R.; Richmond, L.B.; Temme, N.M.
1999-01-01
Uniform asymptotic expansions are given for the Stirling numbers of the first kind for integral arguments and for the second kind as defined for real arguments by Flajolet and Prodinger. The logconcavity of the resulting real valued function of Flajolet and Prodinger is established for a range inclu
EXPERIMENTAL RETRIEVAL SYSTEMS STUDIES, REPORT NUMBER 3.
ANDERSON, RONALD R.; AND OTHERS
CONTENTS--(1) AN ASSOCIATIVITY TECHNIQUE FOR AUTOMATICALLY OPTIMIZING RETRIEVAL RESULTS BY RONALD R. ANDERSON. AN ASSOCIATIVE TECHNIQUE BY WHICH IT IS POSSIBLE TO AUTOMATICALLY EXPAND AND NARROW THE NUMBER OF DOCUMENTS RETRIEVED AND TO RETRIEVE DOCUMENTS RELATED TO A REQUEST EVEN THOUGH THEY MAY NOT BE INDEXED BY THE EXACT TERMS OF THE REQUEST IS…
Poison control center - Emergency number (image)
For a poison emergency call 1-800-222-1222 anywhere in the United States. This national hotline number will let you ... is a free and confidential service. All local poison control centers in the U.S. use this national ...
European Science Notes. Volume 40, Number 6.
1986-06-01
of a number of ma- determining androgens, estrogens, and lignant blood diseases (such as leuke- prolactin in blood plasma, and androgen mia) the use...RehabilitatioConcern for the situation of dis- that lactobacilli in foods such as a olen inr the stheatonofds h yogurt, cheese , sausage, and sauerkraut
Production of Numbers about the Future
DEFF Research Database (Denmark)
Huikku, Jari; Mouritsen, Jan; Silvola, Hanna
of prominent Finnish business managers, auditors, analysts, investors, financial supervisory authority, academics and media, the paper extends prior research which has used large data. The paper analyses impairment testing as a process where network of human and non-human actors produce numbers about...
Ultra-fast Quantum Random Number Generator
Yicheng, Shi
We describe a series of Randomness Extractors for removing bias and residual correlations in random numbers generated from measurements on noisy physical systems. The structures of the randomness extractors are based on Linear Feedback Shift Registers (LFSR). This leads to a significant simplification in the implementation of randomness extractors.
Random numbers certified by Bell's theorem.
Pironio, S; Acín, A; Massar, S; de la Giroday, A Boyer; Matsukevich, D N; Maunz, P; Olmschenk, S; Hayes, D; Luo, L; Manning, T A; Monroe, C
2010-04-15
Randomness is a fundamental feature of nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulation of physical and biological systems. Random numbers, however, are difficult to characterize mathematically, and their generation must rely on an unpredictable physical process. Inaccuracies in the theoretical modelling of such processes or failures of the devices, possibly due to adversarial attacks, limit the reliability of random number generators in ways that are difficult to control and detect. Here, inspired by earlier work on non-locality-based and device-independent quantum information processing, we show that the non-local correlations of entangled quantum particles can be used to certify the presence of genuine randomness. It is thereby possible to design a cryptographically secure random number generator that does not require any assumption about the internal working of the device. Such a strong form of randomness generation is impossible classically and possible in quantum systems only if certified by a Bell inequality violation. We carry out a proof-of-concept demonstration of this proposal in a system of two entangled atoms separated by approximately one metre. The observed Bell inequality violation, featuring near perfect detection efficiency, guarantees that 42 new random numbers are generated with 99 per cent confidence. Our results lay the groundwork for future device-independent quantum information experiments and for addressing fundamental issues raised by the intrinsic randomness of quantum theory.