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single compound cetane number data found in the scientific literature up until March 2014 as well as a number of unpublished values, most measured over the past decade at the National Renewable Energy Laboratory.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.
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.
Cetane numbers of biodiesel and its components
The cetane number is one of the prime fuel quality indicators of a petrodiesel or biodiesel fuel as it relates to the tendency of the fuel to ignite in the combustion chamber. It has been established that compound structure, including chain length, branching, and the presence of double bonds, is a m...
High cetane number paraffinic diesel fuel studies
Energy Technology Data Exchange (ETDEWEB)
Larmi, Martti; Sarjovaara, Teemu; Imperato, Matteo; Hulkkonen, Tuomo; Kaario, Ossi; Wehrfritz, Armin; Tilli, Aki; Brink, Anders [Aalto University (Finland)
2010-07-01
In the energy sector, stringent regulations have been implemented on combustion emissions in order to address health and environmental concerns and help improve air quality. High cetane number paraffinic fuels and their oxygenate blends have a good potential for reducing emissions. The aim of this collaborative study among several universities and industries is to develop optimum combustion technologies for those fuels and decrease their emissions by 70%. To do so, a literature review was undertaken as was the evaluation of reaction scheme, fuel spray studies, designs with CFD, engine tests with both high and medium speed research engines, and emissions measurement and analysis; all the tests and measurements were carried out using HVO, which is a typical high cetane number paraffinic fuel. Results from these studies are presented herein, further work will comprise the analysis of these results, CFD optimization, and tests with oxygenate blends.
A Group Contribution Method for Estimating Cetane and Octane Numbers
Energy Technology Data Exchange (ETDEWEB)
Kubic, William Louis [Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Process Modeling and Analysis Group
2016-07-28
Much of the research on advanced biofuels is devoted to the study of novel chemical pathways for converting nonfood biomass into liquid fuels that can be blended with existing transportation fuels. Many compounds under consideration are not found in the existing fuel supplies. Often, the physical properties needed to assess the viability of a potential biofuel are not available. The only reliable information available may be the molecular structure. Group contribution methods for estimating physical properties from molecular structure have been used for more than 60 years. The most common application is estimation of thermodynamic properties. More recently, group contribution methods have been developed for estimating rate dependent properties including cetane and octane numbers. Often, published group contribution methods are limited in terms of types of function groups and range of applicability. In this study, a new, broadly-applicable group contribution method based on an artificial neural network was developed to estimate cetane number research octane number, and motor octane numbers of hydrocarbons and oxygenated hydrocarbons. The new method is more accurate over a greater range molecular weights and structural complexity than existing group contribution methods for estimating cetane and octane numbers.
High cetane number paraffinic diesel fuels and emission reduction
Energy Technology Data Exchange (ETDEWEB)
Larmi, M.; Tilli, A.; Kaario, O.; Gong, Y.; Antila, E.; Sarjovaara, T.; Hillamo, H.; Hakkinen, K.; Lehto, K. [Helsinki Univ. of Technology, Helsinki (Finland); Brink, A. [Aalborg Univ., Aalborg (Finland); Aakko, P. [Saksa VTT, Espoo (Finland)
2009-07-01
This presentation discussed high cetane number (CN) paraffinic diesel fuels and emission reduction. The presentation outlined the synthetic and renewable fuels to be studied, including high CN paraffinic diesel fuels like hydrotreated vegetable oil (HVO) and FT-diesel fuel; high CN paraffinic diesel fuels with high concentration of oxygenates; biogas/NPG and dual fuel combustion in future projects; and neat oxygenates like dimethyl ether in future projects. Fatty acid methyl ester biodiesel and diesel fuel were used as reference fuels. The project objectives were to obtain a significant reduction of carbon dioxide, nitrogen oxide and particulate matter emissions of 70 per cent without drawbacks in efficiency or power output. The presentation also described combustion implementation; milestones at Aalto University School of Science and Technology (TKK); resources at TKK; the main research engine; LEO with EHVA; a literature study on previous research; fuel properties; HVO properties, density; high cetane number in the literature; and high CN effects. Previous studies that were discussed included direct comparisons with no calibrations; heavy duty engine performance; potential with engine calibration; exhaust gas recirculation; and room for new research. In general, standard test runs have been carried out with existing engines without considering the special properties of the fuels. tabs., figs.
Energy Technology Data Exchange (ETDEWEB)
Westbrook, C K; Pitz, W J; Mehl, M; Curran, H J
2010-03-03
For the first time, a detailed chemical kinetic reaction mechanism is developed for primary reference fuel mixtures of n-hexadecane and 2,2,4,4,6,8,8-heptamethyl nonane for diesel cetane ratings. The mechanisms are constructed using existing rules for reaction pathways and rate expressions developed previously for the primary reference fuels for gasoline octane ratings, n-heptane and iso-octane. These reaction mechanisms are validated by comparisons between computed and experimental results for shock tube ignition and for oxidation under jet-stirred reactor conditions. The combined kinetic reaction mechanism contains the submechanisms for the primary reference fuels for diesel cetane ratings and submechanisms for the primary reference fuels for gasoline octane ratings, all in one integrated large kinetic reaction mechanism. Representative applications of this mechanism to two test problems are presented, one describing fuel/air autoignition variations with changes in fuel cetane numbers, and the other describing fuel combustion in a jet-stirred reactor environment with the fuel varying from pure 2,2,4,4,6,8,8-heptamethyl nonane (Cetane number of 15) to pure n-hexadecane (Cetane number of 100). The final reaction mechanism for the primary reference fuels for diesel fuel and gasoline is available on the web.
Determination model for cetane number of biodiesel at different fatty acid composition: a review
Directory of Open Access Journals (Sweden)
Michal Angelovič
2014-05-01
Full Text Available The most accepted definition of biodiesel is stated at the EU technical regulation EN 14214 (2008 or in the USA in ASTM 6751-02. As a result of this highly strict description only methyl esters of fatty acids conform to these definitions, nevertheless the term ‘‘biodiesel’’ is spread out to other alkyl fatty esters. Some countries have adopted bioethanol for replacement of methanol in biodiesel transesterification and thus assuring a fully biological fuel. Of course, such position brings some problems in fulfilling technical requirements of EN 14214 or ASTM 6751-02. Biodiesel is actually a less complex mixture than petrodiesel, but different feedstock origins and the effect of seasonality may impose difficulties in fuel quality control. Since biodiesel is an alternative diesel fuel derived from the transesterification of triacylglycerol comprised materials, such as vegetable oils or animal fats, with simple alcohols to furnish the corresponding mono-alkyl esters, its composition depends on the raw material used, the cultivated area location, and harvest time. The choice of the raw material is usually the most important factor for fluctuations of biodiesel composition, because different vegetable oils and animal fats may contain different types of fatty acids. Important properties of this fuel vary significantly with the composition of the mixture. Cetane number, melting point, degree of saturation, density, cloud point, pour point, viscosity, and nitrogen oxides exhaust emission (NOx, for instance, deserve to be mentioned. One of the most important fuel quality indicators is the cetane number; however its experimental determination may be an expensive and lengthy task. To weaken situation concerning biodiesel, the availability of data in the literature is also scarce. In such scenario, the use of reliable models to predict the cetane number or any other essential characteristic may be of great utility. We reviewed available literature to
Directory of Open Access Journals (Sweden)
Miqdam Tariq Chaichan
2012-01-01
Full Text Available Due to the energy crisis and the stringent environmental regulations, diesel engines are offering good hope for automotive vehicles. However, a lot of work is needed to reduce the diesel exhaust emissions and give the way for full utilization of the diesel fuels excellent characteristics.A kind of cetane number improver has been proposed and tested to be used with diesel fuel as ameans of reducing exhaust emissions. The addition of (2-ethylhexyl nitrate was designed to raise fuel cetane number to three stages, 50, 52 and 55 compared to the used conventional diesel fuel whose CN was 48.5. The addition of CN improver results in the decrease brake specific fuel consumption by about 12.55%, and raise brake thermal efficiency to about 9%. Simultaneously, the emission characteristics of four fuels are determined in a diesel engine. At high loads, a little penalty on CO and HC emissions compared to baseline diesel fuel. NOx emissions of the higher CN fuels are decreased 6%, and CO of these fuels is reduced to about 30.7%. Engine noise reduced with increasing CN to about 10.95%. The results indicate the potential of diesel reformation for clean combustion in diesel engines.
International Nuclear Information System (INIS)
Highlights: • The effects of oxygenated fuels on diesel combustion are extensively investigated. • CO and soot emissions are reduced with the increase of oxygen concentration. • The C–O bond in the oxygenated fuels inhibits the formation of soot precursor C2H2. • Small intermediates such as C2H4 and C2H6 are significantly reduced. • Oxygen concentration seems to be the dominating factor affecting the emissions. - Abstract: The present modeling study aims to gain better insights on the effects of oxygenated fuels on the diesel oxidation and emission formation processes under realistic engine operating conditions. To do that, various blend fuels formulated from diesel, biodiesel, ethanol and DMC fuels were obtained with different oxygen concentrations, cetane numbers and C/H ratios. Simulations were conducted using the coupled KIVA–CHEMKIN code on a light duty diesel engine at a fixed engine speed of 2400 rpm under full load conditions. Constructed numerical simulation models integrated with detailed chemical kinetics were validated against the experimental results with reliable accuracies. Simulation results revealed that as the overall oxygen concentration of the blend fuel increased, significant beneficial effects were shown with reduced NOx, CO and soot emissions. Particularly, with the increase of oxygen concentration, the peak CO concentration and its final emission level were found to be remarkably reduced due to the fuel borne oxygen, reduced carbon influx as well as the possibility accelerated CO oxidation rate. More tangible reductions were shown on the soot emissions probably because the C–O bond in the oxygenated blend fuels had played an important role in inhibiting the carbon atoms from soot formation. Furthermore, as oxygenated fuels were added, the peak concentration of the soot precursor C2H2 species and small hydrocarbon intermediates such as C2H4 and C2H6 were also significantly reduced. In general, it was found that compared to the
Energy Technology Data Exchange (ETDEWEB)
Zotin, J.L.; Pacheco, M.E.; Souza, V.P.; Belato, D.; Silva, R.M.S. [PETROBRAS, Rio de Janeiro, RJ (Brazil). Centro de Pesquisas (CENPES)
2004-07-01
According to the Brazilian specifications for diesel, lower sulfur content and higher cetane number can be expected in the near future, leading to an increased capacity of hydrotreating processes. PETROBRAS has proved technology for hydrotreating processes with 8 high pressure single stage units in operation. However, the production of ultra low sulfur diesel with high cetane number may require two stages processes, with conventional hydrotreating in the first step and deep aromatic saturation (HDA), with increase in the cetane number, in the second one. In this approach, noble metal catalysts, which are more active for hydrogenation but more sensitive to sulfur and nitrogen poisoning, can be used in the second stage. In the present work, the 2 stages approach was studied for maximizing cetane number of Brazilian gasoils. The influence of operating variables and the inhibition effect by sulfur and nitrogen were analyzed. Diesel with sulfur content below 10 ppm and high aromatic conversions at relatively mild conditions were obtained with noble metal catalysts, with a cetane number increase up to 6 points in the second stage. Sulfur compounds have a stronger inhibition effect than basic nitrogen compounds on hydrogenation reaction rates, but a synergetic effect was observed when both contaminants were present in high concentrations. (author)
Directory of Open Access Journals (Sweden)
Yisel Sánchez-Borroto
2012-05-01
Full Text Available El número de cetano (CN es una de las propiedades más importantes para evaluar la calidad del proceso de combustión de un combustible tipo diesel. El CN de biocombustibles derivados de aceites vegetales está influenciado por su composición de ácidos grasos. El objetivo de esta investigación es obtener dos modelos físico-matemáticos que establezcan una relación entre el número de cetano de biocombustibles derivados de aceites vegetales y su composición de ácidos grasos esenciales. Para predecir el CN se desarrollaron dos modelos mediante un análisis de regresión múltiple, basado en datos experimentales extraídos de bases de datos referenciadas. El ajuste de los coeficientes del modelo se basa en la obtención de residuales mínimos. Se realiza una validación parcial del modelo y se establecen las pautas para la validación total del mismo. A partir de estos resultados queda establecida una herramienta muy útil para la determinación del número de cetano. Palabras claves: número de cetano, biodiesel, aceites vegetales, ácidos grasos.______________________________________________________________________________ Abstract The cetane number is one of the main properties for characterization of the ignition quality of a fuel for its use in a diesel engine. The cetane number of biofuels obtained from different vegetable oils is strongly considerably by their fatty acid composition. The scope of this research is to obtain two physical-mathematical models that establish a relationship between the cetane number and the composition of different biofuels derived from vegetable oils. The models were developed using an analysis of multiple regression, based on experimental data available in the literature. The coefficients adjustment of the model was based on the obtaining of lower residual in the capacity of prediction of the model. A partial validation of the model was developed. Starting from these results it a very useful tool for
Feasibility of using less viscous and lower cetane (LVLC) fuels in a diesel engine: A review
Vallinayagam, R.
2015-11-01
This review work focuses on biofuels with lower viscosity and cetane number and their mode of operation in a diesel engine. Though there were a number of review works describing the production, characterization and utilization of biodiesel, synthesized from vegetable oils, a comprehensive summary on other category of biofuels endowed with lower viscosity and cetane number has not come to light so far. In this backdrop, this review work would bring forth the existence of biofuels having lower viscosity and cetane number, classify them under one category and elucidate their operational feasibility in a diesel engine. Considerably, alcohol based fuels such as methanol, ethanol and butanol, and plant based light biofuels such as eucalyptus oil and pine oil have been chosen and classified as LVLC (less viscous and lower cetane) fuels in the current work. Besides describing the operation feasibility of these fuels, an extensive exploration of their physical, thermal and critical properties as well as their compositional attributes has been made. Despite their distinct properties, these fuels have found use in diesel engine by various strategies and apparently, they could be used in blends with diesel/biodiesel, dual fuel mode and as sole fuel. In this regard, herein, a detailed summary on operation of these fuels in the reported three different modes is clearly explained and their engine characteristics such as performance, combustion and emission are briefed. © 2015 Elsevier Ltd.
Energy Technology Data Exchange (ETDEWEB)
Souza, Tatiana Bittencourt de; Yamamoto, Carlos Itsuo; Cocco, Lilian Cristina [Universidade Federal do Parana (UFPR), Curitiba, PR (Brazil). Lab. de Analise de Combustiveis Automotivos (LACAUTets)
2008-07-01
This work presents the development of models for Calculated Cetane Index (CCI) determination with the purpose of tailor it to the diesel oil sold in Brazil, using optimization techniques. As the diesel is the main fuel on the Brazilian territory, their quality is of great importance. The CCI calculation is important to evaluate the diesel quality. The standard ASTM D 4737 does not take into account the presence of cetane booster additive and biodiesel, which creates the need to recast the equation of the CCI determination. About 300 representative samples were selected of diesel in Parana, during the 2006 to 2007 period, which had their physic-chemical properties determined using the methodology adopted by the ANP - the Brazilian petroleum, natural gas and biofuel agency. The Derived Cetane Number was obtained in the IQT apparatus and several models were proposed, all with better predictive capability than the equation of the standard ASTM D 4737. It is pointed out that biodiesel can act as cetane booster additive depending upon its origin, mostly in concentrations above 5%. The methodology can be expanded to generate a representative equation for the diesel sold in the whole Brazilian territory. (author)
Institute of Scientific and Technical Information of China (English)
赵阳; 吴佳; 王宣; 张晓昕; 孟祥堃
2007-01-01
介绍了植物油加氢制备柴油的主要化学反应、工艺方法以及该项技术的工业化状况,分析了植物油直接加氢、先加氢后异构、直接脱羧工艺以及植物油与矿物柴油掺炼工艺的特点,阐述了各工艺采用的催化剂类型、工艺条件以及产品属性.指出了该领域存在的问题和研究方向.
Yisel Sánchez-Borroto; Ramón Piloto-Rodríguez; Leonardo Goyos-Pérez; Nayvi Ferrer-Frontela
2012-01-01
El número de cetano (CN) es una de las propiedades más importantes para evaluar la calidad del proceso de combustión de un combustible tipo diesel. El CN de biocombustibles derivados de aceites vegetales está influenciado por su composición de ácidos grasos. El objetivo de esta investigación es obtener dos modelos físico-matemáticos que establezcan una relación entre el número de cetano de biocombustibles derivados de aceites vegetales y su composición de ácidos grasos esenciales. Para predec...
Khovanova, Tanya; Lewis, Joel Brewster
2013-01-01
We introduce numbers depending on three parameters which we call skyscraper numbers. We discuss properties of these numbers and their relationship with Stirling numbers of the first kind, and we also introduce a skyscraper sequence.
Hagen number versus Bejan number
Directory of Open Access Journals (Sweden)
Awad Mohamed M.
2013-01-01
Full Text Available This study presents Hagen number vs. Bejan number. Although their physical meaning is not the same because the former represents the dimensionless pressure gradient while the latter represents the dimensionless pressure drop, it will be shown that Hagen number coincides with Bejan number in cases where the characteristic length (l is equal to the flow length (L. Also, a new expression of Bejan number in the Hagen-Poiseuille flow will be introduced. At the end, extending the Hagen number to a general form will be presented. For the case of Reynolds analogy (Pr = Sc = 1, all these three definitions of Hagen number will be the same.
Lužnik, Polona
2013-01-01
My graduate thesis contains a detailed examination of pentagonal nubers. In the beginning, I concentrate on figurate numbers and the mathematicians, who were the first to describe them. The work includes the basic characteristis of pentagonal numbers, how we can obtain them through calculating and counting of dots in graphic illustrtions and how we are able to check if a certain prime number is a pentagonal number or not.
Rich, Andrew
2008-01-01
The leftist number system consists of numbers with decimal digits arranged in strings to the left, instead of to the right. This system fails to be a field only because it contains zerodivisors. The same construction with prime base yields the p-adic numbers.
Directory of Open Access Journals (Sweden)
Schwarzweller Christoph
2015-02-01
Full Text Available In this article we introduce Proth numbers and prove two theorems on such numbers being prime [3]. We also give revised versions of Pocklington’s theorem and of the Legendre symbol. Finally, we prove Pepin’s theorem and that the fifth Fermat number is not prime.
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
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.
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, ...
河野, 雅文; 天谷, 賢児; 新井, 雅隆
2002-01-01
Effect of cetane number on ignition delay and ignition location of disesel spray was experimentally investigated. Five kinds of fuels, which had different cetane numbers of light fraction and heavy fraction of fuel, were used. As a result, the ignition delay was not so affected by the change of cetane number, however, the ignition location was strongly affected by a cetane number. When the light fraction cetane number was low, the ignition was not observed near the nozzle. And when the heavy ...
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 system...... 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....
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
Ji, Caleb; Khovanova, Tanya; Park, Robin; Song, Angela
2015-01-01
In this paper, we consider a game played on a rectangular $m \\times n$ gridded chocolate bar. Each move, a player breaks the bar along a grid line. Each move after that consists of taking any piece of chocolate and breaking it again along existing grid lines, until just $mn$ individual squares remain. This paper enumerates the number of ways to break an $m \\times n$ bar, which we call chocolate numbers, and introduces four new sequences related to these numbers. Using various techniques, we p...
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 system...... 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....
Sezin, Fatin
2009-01-01
It is instructive and interesting to find hidden numbers by using different positional numeration systems. Most of the present guessing techniques use the binary system expressed as less-than, greater-than or present-absent type information. This article describes how, by employing four cards having integers 1-64 written in different colours, one…
St-Amant, Patrick
2010-01-01
We will see that key concepts of number theory can be defined for arbitrary operations. We give a generalized distributivity for hyperoperations (usual arithmetic operations and operations going beyond exponentiation) and a generalization of the fundamental theorem of arithmetic for hyperoperations. We also give a generalized definition of the prime numbers that are associated to an arbitrary n-ary operation and take a few steps toward the development of its modulo arithmetic by investigating a generalized form of Fermat's little theorem. Those constructions give an interesting way to interpret diophantine equations and we will see that the uniqueness of factorization under an arbitrary operation can be linked with the Riemann zeta function. This language of generalized primes and composites can be used to restate and extend certain problems such as the Goldbach conjecture.
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...
T. Pathinathan; K. Ponnivalavan
2015-01-01
In this paper we define diamond fuzzy number with the help of triangular fuzzy number. We include basic arithmetic operations like addition, subtraction of diamond fuzzy numbers with examples. We define diamond fuzzy matrix with some matrix properties. We have defined Nested diamond fuzzy number and Linked diamond fuzzy number. We have further classified Right Linked Diamond Fuzzy number and Left Linked Diamond Fuzzy number. Finally we have verified the arithmetic operations for the above men...
Expansion of real numbers by algebraic numbers
Kaneko, Hajime
2008-01-01
In this paper we represent the fractional part of ξαn, where ξ is a nonzero real number and α is an algebraic number. By using this representation, we give new lower bounds for the distance from ξαn to the nearest integer.
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...
Directory of Open Access Journals (Sweden)
Paul W. Haggard
1985-01-01
Full Text Available The Legendre numbers, an infinite set of rational numbers are defined from the associated Legendre functions and several elementary properties are presented. A general formula for the Legendre numbers is given. Applications include summing certain series of Legendre numbers and evaluating certain integrals. Legendre numbers are used to obtain the derivatives of all orders of the Legendre polynomials at x=1.
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.
Institute of Scientific and Technical Information of China (English)
柳云骐; 陈为超; 周卫东; 薛颖; 张景成; 刘晨光
2009-01-01
在高压固定床微反装置上研究了豆油在加氢催化剂CoMo/γ-Al2O3,NiMoP/γ-Al2O3,NiMoP/γ-Al2O3-HUSY上的加氢反应规律,并研究了NiMoP/γ-Al2O3-HUSY催化剂对豆油和流化催化裂化(FCC)柴油耦合加氢产物性质的影响.实验结果表明,在压力3.0 MPa、温度320 ℃、液态空速2.0 h-1、氢气与原料油体积比(氢油比)500的条件下,CoMo/γ-Al2O3和NiMoP/γ-Al2O3催化剂上豆油加氢产物主要为n-C15～18,而添加酸性组分的NiMoP/γ-Al2O3-HUSY催化剂的裂化性能增强,产物中n-C15～18含量明显减少,C-15的含量增加;在压力4.0 MPa、温度370 ℃、液态空速1.0 h-1、氢油比500的条件下,豆油和FCC柴油的混合原料在NiMoP/γ-Al2O3-HUSY催化剂上的加氢脱硫率达97%左右,加氢脱氮率达80%以上,产物的十六烷值与未掺炼豆油的FCC柴油加氢产物相比,提高了1.8～6.5个单位.
Hanaki, Ryo
2014-01-01
We introduce a numerical invariant, called trivializing number, of knots and investigate it. The trivializing number gives an upper bound of unknotting number and canonical genus for knots. We present a table of trivializing numbers for up to 10 crossings knots. We conjecture that twice of the unknotting number of any positive knot is equal to the trivializing number of it and give a partial answer.
Octavian Cira; Florentin Smarandache
2015-01-01
The first prime number with the special property that its addition with reversal gives as result a prime number toois 229. The prime numbers with this property will be called Luhn prime numbers. In this article we intend to presenta performing algorithm for determining the Luhn prime numbers. Using the presented algorithm all the 50598 Luhnprime numbers have been, for p prime smaller than 2 · 107.
Directory of Open Access Journals (Sweden)
Octavian Cira
2015-04-01
Full Text Available The first prime number with the special property that its addition with reversal gives as result a prime number toois 229. The prime numbers with this property will be called Luhn prime numbers. In this article we intend to presenta performing algorithm for determining the Luhn prime numbers. Using the presented algorithm all the 50598 Luhnprime numbers have been, for p prime smaller than 2 · 107.
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
Mack, Nancy K.
2011-01-01
Exploring number systems of other cultures can be an enjoyable learning experience that enriches students' knowledge of numbers and number systems in important ways. It helps students deepen mental computation fluency, knowledge of place value, and equivalent representations for numbers. This article describes how the author designed her…
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…
Ouannas, Moussa
2011-01-01
In this paper I present the distribution of prime numbers which was treated in many researches by studying the function of Riemann; because it has a remarkable property; its non trivial zeros are prime numbers; but in this work I will show that we can find the distribution of prime numbers on remaining in natural numbers only.
Markwig, Hannah; Rau, Johannes
2014-01-01
In this paper, we define tropical analogues of real Hurwitz numbers, i.e. numbers of covers of surfaces with compatible involutions satisfying prescribed ramification properties. We prove a correspondence theorem stating the equality of the tropical numbers with their real counterparts. We apply this theorem to the case of double Hurwitz numbers (which generalizes our result from arXiv:1409.8095).
Directory of Open Access Journals (Sweden)
Damian Slota
2009-08-01
Full Text Available 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.
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.
Arthan, R. D.
2004-01-01
This note describes a representation of the real numbers due to Schanuel. The representation lets us construct the real numbers from first principles. Like the well-known construction of the real numbers using Dedekind cuts, the idea is inspired by the ancient Greek theory of proportion, due to Eudoxus. However, unlike the Dedekind construction, the construction proceeds directly from the integers to the real numbers bypassing the intermediate construction of the rational numbers. The constru...
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.
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.
Grešak, Rozalija
2015-01-01
The field of real numbers is usually constructed using Dedekind cuts. In these thesis we focus on the construction of the field of real numbers using metric completion of rational numbers using Cauchy sequences. In a similar manner we construct the field of p-adic numbers, describe some of their basic and topological properties. We follow by a construction of complex p-adic numbers and we compare them with the ordinary complex numbers. We conclude the thesis by giving a motivation for the int...
Pak, Igor
2014-01-01
We give a brief history of Catalan numbers, from their first discovery in the 18th century to modern times. This note will appear as an appendix in Richard Stanley's forthcoming book on Catalan numbers.
Bencze, Mihaly; Smarandache, Florentin
2008-01-01
In this article we present a simple proof of Borevich-Shafarevich's method to compute the sum of the first n natural numbers of the same power. We also prove several properties of Bernoulli's numbers.
Fibonacci Numbers and Identities
Lang, Cheng Lien; Lang, Mong Lung
2013-01-01
By investigating a recurrence relation about functions, we first give alternative proofs of various identities on Fibonacci numbers and Lucas numbers, and then, make certain well known identities visible via certain trivalent graph associated to the recurrence relation.
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.
Number Relationships in Preschool
Jung, Myoungwhon
2011-01-01
When a child understands number relationships, he or she comprehends the meaning of numbers by developing multiple, flexible ways of representing them. The importance of developing number relationships in the early years has been highlighted because it helps children build a good foundation for developing a more sophisticated understanding of…
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
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…
Shi, Yixun
2010-01-01
Starting with an interesting number game sometimes used by school teachers to demonstrate the factorization of integers, "sum-difference numbers" are defined. A positive integer n is a "sum-difference number" if there exist positive integers "x, y, w, z" such that n = xy = wz and x ? y = w + z. This paper characterizes all sum-difference numbers…
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…
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...
Directory of Open Access Journals (Sweden)
J.Vijayasekhar,
2011-02-01
Full Text Available Signed integers are normally represented using 2’s complement representation. Addition and subtraction of signed numbers is done in the same manner as for unsigned numbers. However carry (or borrow is simple ignored. Unlike unsigned number carry (or borrow does not mean overflow or error. Doubling of a signed number can be done by shift left. However, halving of a signed number can not be done by shift right. Hence special arithmetic instruction SAR (Shift arithmetic right is needed. We have defined an alternative representation for signed numbers. Here a positive number is represented by appended a zero (0 at right. Here a negative number is represented by inverting all bits in corresponding positive number. Two signed numbers are added by adding corresponding binary representation. After that carry is added to the result. Similarly two signed numbers are subtracted by subtracting corresponding binaryrepresentation. After that borrow is subtracted. Doubling and halving is done by ROL (Rotate left and ROR (Rotate right respectively. Following are drawbacks of our system. (A Addition is done in two stages. In the first stage the numbers are added. In the second stage carry is added. Carry can not be ignored as in 2’s complement representation. (B Same holds for subtraction. (C When an odd number is halved then error results. In 2’s complement representation approximate answer appears. The advantage of our system is that entire arithmetic can be carried using ordinary logical instructions. No special instruction is needed. In 2’s complement representation a special instruction SAR is needed. This instruction is not used for any other purpose.
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”....
Cantlon, Jessica F.; Platt, Michael L.; Brannon, Elizabeth M.
2009-01-01
In a world without numbers, we would be unable to build a skyscraper, hold a national election, plan a wedding, or pay for a chicken at the market. The numerical symbols used in all these behaviors build on the approximate number system (ANS) which represents the number of discrete objects or events as a continuous mental magnitude. In this review, we first discuss evidence that the ANS bears a set of behavioral and brain signatures that are universally displayed across animal species, human ...
Divisibility of characteristic numbers
Borghesi, Simone
2009-01-01
We use homotopy theory to define certain rational coefficients characteristic numbers with integral values, depending on a given prime number q and positive integer t. We prove the first nontrivial degree formula and use it to show that existence of morphisms between algebraic varieties for which these numbers are not divisible by q give information on the degree of such morphisms or on zero cycles of the target variety.
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...
Kruecken, R.
2010-01-01
The nuclear shell model is a benchmark for the description of the structure of atomic nuclei. The magic numbers associated with closed shells have long been assumed to be valid across the whole nuclear chart. Investigations in recent years of nuclei far away from nuclear stability at facilities for radioactive ion beams have revealed that the magic numbers may change locally in those exotic nuclei leading to the disappearance of classic shell gaps and the appearance of new magic numbers. Thes...
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...
DEFF Research Database (Denmark)
Suetens, Sigrid; Galbo-Jørgensen, Claus B.; Tyran, Jean-Robert Karl
2015-01-01
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 as...
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
Intuitive numbers guide decisions
Directory of Open Access Journals (Sweden)
Ellen Peters
2008-12-01
Full Text Available Measuring reaction times to number comparisons is thought to reveal a processing stage in elementary numerical cognition linked to internal, imprecise representations of number magnitudes. These intuitive representations of the mental number line have been demonstrated across species and human development but have been little explored in decision making. This paper develops and tests hypotheses about the influence of such evolutionarily ancient, intuitive numbers on human decisions. We demonstrate that individuals with more precise mental-number-line representations are higher in numeracy (number skills consistent with previous research with children. Individuals with more precise representations (compared to those with less precise representations also were more likely to choose larger, later amounts over smaller, immediate amounts, particularly with a larger proportional difference between the two monetary outcomes. In addition, they were more likely to choose an option with a larger proportional but smaller absolute difference compared to those with less precise representations. These results are consistent with intuitive number representations underlying: a perceived differences between numbers, b the extent to which proportional differences are weighed in decisions, and, ultimately, c the valuation of decision options. Human decision processes involving numbers important to health and financial matters may be rooted in elementary, biological processes shared with other species.
Vieru, Andrei
2012-01-01
We define and study a transform whose iterates bring to the fore interesting relations between Pisot numbers and primes. Although the relations we describe are general, they take a particular form in the Pisot limit points. We give three elegant formulae, which permit to locate on the whole semi-line all limit points that are not integer powers of other Pisot numbers.
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 number
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.
First Graders' Number Knowledge
Thomas, Jonathan N.; Tabor, Pamela D.; Wright, Robert J.
2010-01-01
As young children make sense of mathematics, they begin to see with new eyes. What once was uncertain may now be determined. Objects become countable; fingers become tools; and numbers become more than just names. Educators revel in such developments--which mark significant progress toward more sophisticated understanding of number--and work…
Oller-Marcén, Antonio M.
2012-01-01
An integer $n$ is said to be \\textit{arithmetic} if the arithmetic mean of its divisors is an integer. In this paper, using properties of the factorization of values of cyclotomic polynomials, we characterize arithmetic numbers. As an application, in Section 2, we give an interesting characterization of Mersenne numbers.
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)
Freitag, Herta Taussig; Freitag, Arthur H.
The development of number concepts from prehistoric time to the present day are presented. Section 1 presents the historical development, logical development, and the infinitude of numbers. Section 2 focuses on non-positional and positional numeration systems. Section 3 compares historical and modern techniques and devices for computation. Section…
DEFF Research Database (Denmark)
Elvik, Rune; Bjørnskau, Torkel
2016-01-01
been to determine if there is a safety-in-numbers effect. There is safety-in-numbers if the number of accidents increases less than proportionally to traffic volume (for motor vehicles, pedestrians and cyclists). All studies reviewed in the paper are multivariate accident prediction models, estimating...... of the safety-in-numbers effect is defensible. According to a random-effects inverse-variance meta-analysis, the summary estimates of the regression coefficients for traffic volume are 0.50 for motor vehicle volume, 0.43 for cycle volume and 0.51 for pedestrian volume. Estimates are highly consistent between...... studies. It is concluded that a safety-in-numbers effect exists. It is still not clear whether this effect is causal, nor, if causal, which mechanisms generate the effect....
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. PMID:27524965
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
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
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
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
Directory of Open Access Journals (Sweden)
R. A. Mollin
1986-01-01
Full Text Available A powerful number is a positive integer n satisfying the property that p2 divides n whenever the prime p divides n; i.e., in the canonical prime decomposition of n, no prime appears with exponent 1. In [1], S.W. Golomb introduced and studied such numbers. In particular, he asked whether (25,27 is the only pair of consecutive odd powerful numbers. This question was settled in [2] by W.A. Sentance who gave necessary and sufficient conditions for the existence of such pairs. The first result of this paper is to provide a generalization of Sentance's result by giving necessary and sufficient conditions for the existence of pairs of powerful numbers spaced evenly apart. This result leads us naturally to consider integers which are representable as a proper difference of two powerful numbers, i.e. n=p1−p2 where p1 and p2 are powerful numbers with g.c.d. (p1,p2=1. Golomb (op.cit. conjectured that 6 is not a proper difference of two powerful numbers, and that there are infinitely many numbers which cannot be represented as a proper difference of two powerful numbers. The antithesis of this conjecture was proved by W.L. McDaniel [3] who verified that every non-zero integer is in fact a proper difference of two powerful numbers in infinitely many ways. McDaniel's proof is essentially an existence proof. The second result of this paper is a simpler proof of McDaniel's result as well as an effective algorithm (in the proof for explicitly determining infinitely many such representations. However, in both our proof and McDaniel's proof one of the powerful numbers is almost always a perfect square (namely one is always a perfect square when n≢2(mod4. We provide in §2 a proof that all even integers are representable in infinitely many ways as a proper nonsquare difference; i.e., proper difference of two powerful numbers neither of which is a perfect square. This, in conjunction with the odd case in [4], shows that every integer is representable in
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
Forbes, Rod; Gardiner, Peter
2004-01-01
The Ministry of Agriculture and Forestry (MAF) undertakes forecasts and projections of livestock numbers as part of the twice yearly contribution to The Treasury’s economic and fiscal updates. MAF’s Pastoral Supply Response Model (PSRM) was recently re-developed and used for the first time in the Budget Economic and Fiscal Update round of 2004. The PSRM projects annual inventory numbers as at 30 June, births and livestock numbers for slaughter. The paper discusses the PSRM, the post-model adj...
A. Mironov; Morozov, A; Natanzon, S.
2012-01-01
The classical Hurwitz numbers of degree n together with the Hurwitz numbers of the seamed surfaces of degree n give rise to the Klein topological field theory. We extend this construction to the Hurwitz numbers of all degrees at once. The corresponding Cardy-Frobenius algebra is induced by arbitrary Young diagrams and arbitrary bipartite graphs. It turns out to be isomorphic to the algebra of differential operators from arXiv:1210.6955 which serves a model for open-closed string theory. The o...
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
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,
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
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.
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
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 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 th...
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...
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...
... View All Articles | Inside Life Science Home Page Genetics by the Numbers By Chelsea Toledo and Kirstie ... June 11, 2012 Scholars have been studying modern genetics since the mid-19th century, but even today ...
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...
Quantum random number generator
Energy Technology Data Exchange (ETDEWEB)
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.
Methods explained: Index numbers
Peter Goodridge
2007-01-01
Attempts to explain the subtle differences in the methodologies used to construct index numbers.Many of the statistics produced by the Office for National Statistics,particularly economic statistics, are published in the form ofindices. However, there are a number of different forms of indices and this article attempts to explain the subtle differences in themethodologies used to construct them, and also factors that feed into the choice of which type of index to use. Hypothetical examplesare...
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…
International Nuclear Information System (INIS)
The accuracy of CT number plots has been found lacking in several medical applications. This is of concern since the ability to compare and evaluate results on a reproducible and standard basis is essential to long term development. Apart from the technical limitations arising from the CT scanner and the data treatment, there are fundamental issues with the definition of the Hounsfield number, namely the absence of a standard photon energy and the need to specify the attenuation mechanism for standard measurements. This paper presents calculations to demonstrate the shortcomings of the present definition with a brief discussion. The remedy is straightforward, but probably of long duration as it would require an international agreement. - Highlights: ► The dependence of the CT number definition on photon energy is examined. ► Graphical examples of the CT number variation with photon energy are given. ► The influence of absorption edges and scattering on CT numbers is discussed. ► A proposal is made for an international standard devoted to CT number evaluation.
International Nuclear Information System (INIS)
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
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.
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.
DEFF Research Database (Denmark)
Wanscher, Jørgen Bundgaard; Sørensen, Majken Vildrik
2006-01-01
Random numbers are used for a great variety of applications in almost any field of computer and economic sciences today. Examples ranges from stock market forecasting in economics, through stochastic traffic modelling in operations research to photon and ray tracing in graphics. The construction...... of a model or a solution method requires certain characteristics of the random numbers used. This is usually a distribution classification, which the sequence of random numbers must fulfill; of these some are very hard to fulfill and others are next to impossible. Today mathematics allows us to transform...... distributions into others with most of the required characteristics. In essence, a uniform sequence which is transformed into a new sequence with the required distribution. The subject of this article is to consider the well known highly uniform Halton sequence and modifications to it. The intent is to generate...
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...
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
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
Gruber, Peter M
1987-01-01
This volume contains a fairly complete picture of the geometry of numbers, including relations to other branches of mathematics such as analytic number theory, diophantine approximation, coding and numerical analysis. It deals with convex or non-convex bodies and lattices in euclidean space, etc.This second edition was prepared jointly by P.M. Gruber and the author of the first edition. The authors have retained the existing text (with minor corrections) while adding to each chapter supplementary sections on the more recent developments. While this method may have drawbacks, it has the definit
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.
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 af
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
Are Occupation Numbers Observable?
Furnstahl, R. J.; Hammer, H. -W.
2001-01-01
The question of whether occupation numbers and momentum distributions of nucleons in nuclei are observables is considered from an effective field theory perspective. Field redefinitions lead to variations that imply the answer is negative, as illustrated in the interacting Fermi gas at low density. Implications for the interpretation of (e,e'p) experiments with nuclei are discussed.
International Nuclear Information System (INIS)
This document contains information dealing with the lessons learned from the experience of nuclear plants. In this issue the authors tried to avoid the 'tyranny' of numbers and concentrated on the main lessons learned. Topics include: filtration devices for air pollution abatement, crack repair and inspection, and remote handling equipment
Two Symmetric Properties of Mersenne Numbers and Fermat Numbers
Yongjin, Shi
2013-01-01
Mersenne numbers and Fermat numbers are two hot and difficult issues in number theory. This paper constructs a special group for every positive odd number other than 1, and discovers an algorithm for determining the multiplicative order of 2 modulo q for each positive odd number q. It is worth mentioning that this paper discovers two symmetric properties of Mersenne numbers and Fermat numbers.
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)
M. H. Hooshmand
2010-02-01
Full Text Available In this paper we first define homorooty between two integer numbers and study some of their properties. There after we shall state some applications of the homorooty in studying and solving some Diophantine equations and systems, as an interesting anduseful elementary method. Also by the homorooty, we state and prove the necessary and sufficient conditions for existence of finite solutions in a special case of the quartic equation and evaluate the bounds of its solutions.
Carlitz q-Bernoulli numbers and q-Stirling numbers
Kim, Taekyun
2007-01-01
In this paper we consider carlitz q-Bernoulli numbers and q-stirling numbers of the first and the second kind. From these numbers we derive many interesting formulae associated with q-Bernoulli numbers.
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.
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
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
Broadhurst, David
2010-01-01
This is an expansion of a talk for mathematics and physics students of the Manchester Grammar and Manchester High Schools. It deals with numbers such as the Riemann zeta value zeta(3)=sum_{n>0}1/n^3. Zeta values appear in the description of sunshine and of relics from the Big Bang. They also result from Feynman diagrams, which occur in the quantum field theory of fundamental particles such as photons, electrons and positrons. My talk included 7 reasonably simple problems, for which I here add solutions, with further details of their context.
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
Upreti, U. C.
1997-12-01
Nomogram construction using the parabolic relationship f0F2 = a0+a1R12+a2R122 between monthly median f0F2 and running average sunspot number (RASSN) R12 values has been described; here a0, a1 and a2 are the best fit coefficients. The nomogram can give the required local effective sunspot number (LESSN) values corresponding to any observed value of f0F2. Transforming the f0F2-RASSN relation to the form R122+pR12+q = 0 [where p = a1/a2 and q = (a0-f0F2)/a2], a practical method for the preparation of a single nomogram for f0F2-RASSN has been described and the problem of very high and very low values of the variables has also been dealt with successfully. A single nomogram for a large range of variables, namely, f0F2, a0, a1, and a2 has been obtained so that one can easily find LESSN values at any location, season, and time. The nomogram tends to minimize the errors in LESSN calculations at all levels of solar activity.
7 CFR 29.9205 - Identification number (farm serial number).
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Identification number (farm serial number). 29.9205 Section 29.9205 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE... number (farm serial number). The serial number assigned to an individual farm by the appropriate...
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.
Qubits from Number States and Bell Inequalities for Number Measurements
Larsson, Jan-Ake
2002-01-01
Bell inequalities for number measurements are derived via the observation that the bits of the number indexing a number state are proper qubits. Violations of these inequalities are obtained from the output state of the nondegenerate optical parametric amplifier.
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…
Furuya, Masako
2004-01-01
We show a lower estimate of the Milnor number of an isolated hypersurface singularity, via its Newton number. We also obtain analogous estimate of the Milnor number of an isolated singularity of a similar complete intersection variety.
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.
Neutrino number of the universe
International Nuclear Information System (INIS)
The influence of grand unified theories on the lepton number of the universe is reviewed. A scenario is presented for the generation of a large (>> 1) lepton number and a small (<< 1) baryon number. 15 references
Construction of the real numbers
Grešak, Rozalija
2013-01-01
In this thesis, there are described two standard constructions of the real numbers, these are the construction of real numbers via Dedekind cuts and the construction with metric fill of the rational numbers. Rational numbers are already a linearly ordered commutative field, so we first list the axioms of a linearly ordered commutative field. Then we take a look to the Dedekind's axiom, which only applies to real numbers and distinguishes between real and rational numbers. In thesis, there are...
Automatic Number Plate Recognition System
Rajshree Dhruw; Dharmendra Roy
2014-01-01
Automatic Number Plate Recognition (ANPR) is a mass surveillance system that captures the image of vehicles and recognizes their license number. The objective is to design an efficient automatic authorized vehicle identification system by using the Indian vehicle number plate. In this paper we discus different methodology for number plate localization, character segmentation & recognition of the number plate. The system is mainly applicable for non standard Indian number plates by recognizing...
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?
Generalized Lucas Numbers and Relations with Generalized Fibonacci Numbers
Kaygisiz, Kenan
2011-01-01
In this paper, we present a new generalization of the Lucas numbers by matrix representation using Genaralized Lucas Polynomials. We give some properties of this new generalization and some relations between the generalized order-k Lucas numbers and generalized order-k Fibonacci numbers. In addition, we obtain Binet formula and combinatorial representation for generalized order-k Lucas numbers by using properties of generalized Fibonacci numbers.
Representing Numbers: Prime and Irrational
Zazkis, Rina
2005-01-01
This article draws an analogy between prime and irrational numbers with respect to how these numbers are defined and how they are perceived by learners. Excerpts are presented from two research studies: a study on understanding prime numbers by pre-service elementary school teachers and a study on understanding irrational numbers by pre-service…
Cordial Languages and Cordial Numbers
J.Baskar Babujee; L. SHOBANA
2012-01-01
The concept of cordial labeling in graphs motivated us to introduce cordial words, cordial languages and cordial numbers. We interpret the notion of cordial labeling in Automata and thereby study the corresponding languages. In this paper we develop a new sequence of numbers called the cordial numbers in number theory using the labeling techniques in graph theory on automata theory.
Cordial Languages and Cordial Numbers
Directory of Open Access Journals (Sweden)
J. Baskar BABUJEE
2012-01-01
Full Text Available The concept of cordial labeling in graphs motivated us to introduce cordial words, cordial languages and cordial numbers. We interpret the notion of cordial labeling in Automata and thereby study the corresponding languages. In this paper we develop a new sequence of numbers called the cordial numbers in number theory using the labeling techniques in graph theory on automata theory.
Characteristic numbers of algebraic varieties
Kotschick, D
2011-01-01
A rational linear combination of Chern numbers is an oriented diffeomorphism invariant of smooth complex projective varieties if and only if it is a linear combination of the Euler and Pontryagin numbers. In dimension at least three only multiples of the top Chern number, which is the Euler characteristic, are invariant under diffeomorphisms that are not necessarily orientation-preserving. In the space of Chern numbers there are two distinguished subspaces, one spanned by the Euler and Pontryagin numbers, the other spanned by the Hirzebruch--Todd numbers. Their intersection is the span of the Euler number and the signature.
Identification numbers for chemical structures
International Nuclear Information System (INIS)
Several identification (ID) numbers for chemical structures (connectivity ID number, prime ID number, weighted ID number) are analyzed and tested until a counterexample (a pair of structures with the same ID number) is found. The analysis is carried out for acyclic structures with up to 20 atoms, trees with up to 20 points, benzenoid graphs and polyhexes with up to 10 hexagons, and all connected graphs with up to 6 points. Although all the (chemical) ID numbers studied are highly selective for many families of (molecular) graphs, none of them are unique; in all three cases the counterexamples are found. However, the greatest discriminative power is shown by the weighted ID number
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.
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
Prime numbers: periodicity, chaos, noise
Bershadskii, A.
2011-01-01
Logarithmic gaps have been used in order to find a periodic component of the sequence of prime numbers, hidden by a random noise (stochastic or chaotic). The recovered period for the sequence of the first 10000 prime numbers is equal to 8\\pm1 (subject to the prime number theorem). For small and moderate values of the prime numbers (first 2000 prime numbers) this result has been directly checked using the twin prime killing method.
Computational Complexity on Signed Numbers
Jaeger, Stefan
2011-01-01
This paper presents a new representation of natural numbers and discusses its consequences for computability and computational complexity. The paper argues that the introduction of the first Peano axiom in the traditional definition of natural numbers is not essential. It claims that natural numbers remain usable in traditional ways without assuming the existence of at least one natural number. However, the uncertainty about the existence of natural numbers translates into every computation a...
Countability of the Real Numbers
Vlahovic, Slavica; Vlahovic, Branislav
2004-01-01
The proofs that the real numbers are denumerable will be shown, i.e., that there exists one-to-one correspondence between the natural numbers $N$ and the real numbers $\\Re$. The general element of the sequence that contains all real numbers will be explicitly specified, and the first few elements of the sequence will be written. Remarks on the Cantor's nondenumerability proofs of 1873 and 1891 that the real numbers are noncountable will be given.
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.
Feeling Number: Grounding Number Sense in a Sense of Quantity
Wagner, David; Davis, Brent
2010-01-01
Drawing on results from psychology and from cultural and linguistic studies, we argue for an increased focus on developing quantity sense in school mathematics. We explore the notion of "feeling number", a phrase that we offer in a twofold sense--resisting tendencies to feel numb-er (more numb) by developing a feeling for numbers and the…
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.
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.
How Spencer Made Number: First Uses of the Number Words
Mix, Kelly S.
2009-01-01
This article describes the development of number concepts between infancy and early childhood. It is based on a diary study that tracked number word use in a child from 12 to 38 months of age. Number words appeared early in the child's vocabulary, but accurate reference to specific numerosities evolved gradually over the entire 27-month period.…
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…
A Relation between Prime Numbers and Twin Prime Numbers
Ergin, A.
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.
Chromatic number of graphs and edge Folkman numbers
Nenov, Nedyalko Dimov
2010-01-01
In the paper we give a lower bound for the number of vertices of a given graph using its chromatic number. We find the graphs for which this bound is exact. The results are applied in the theory of Foklman numbers.
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.
International Nuclear Information System (INIS)
One of the problems in creating of computers based on residue number system (RNS) is a problem of numbers translation from positional number system into the RNS and back. Accordingly, one approach to solve this problem is to choose the values of RNS bases. It is possible that this approach will help to compare the current value of numbers and determine the sign, without converting them to the positional number system
Poison control center - emergency number
... ANYWHERE IN THE UNITED STATES This national hotline number will let you talk to experts in poisoning. ... centers in the United States use this national number. You should call if you have any questions ...
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.
Butterflies and topological quantum numbers
Avron, J. E.; Osadchy, D.
2001-01-01
The Hofstadter model illustrates the notion of topological quantum numbers and how they account for the quantization of the Hall conductance. It gives rise to colorful fractal diagrams of butterflies where the colors represent the topological quantum numbers.
Saveliev Peter
2005-01-01
Suppose , are manifolds, are maps. The well-known coincidence problem studies the coincidence set . The number is called the codimension of the problem. More general is the preimage problem. For a map and a submanifold of , it studies the preimage set , and the codimension is . In case of codimension , the classical Nielsen number is a lower estimate of the number of points in changing under homotopies of , and for an arbitrary codimension, of the number of components of . We extend t...
The world of pentagonal numbers
Črep, Polona
2014-01-01
The master’s thesis accurately discusses the subject of the world of pentagonal numbers. First chapter generally describes what exactly power series are, when the power series converge and how do we calculate with power series. Further there is written what is generating function. Derivations of a generating function for pentagonal numbers have been made as well as for inverse pentagonal numbers etc. As the figurate numbers intertwine each other in some way the connection between pentagonal n...
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
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.
The status of Cantorian numbers
Frápolli, María J.
1992-01-01
A critical evaluation of Cantor's number conception is undertaken against which the interpretations by Wang and Hallett of Cantoran set theory are measured. Wang takes Cantor's theory to tend to be a theory of numbers rather than a theory of sets, while Hallett takes Cantor as proposing an ordinal theory of cardinal numbers which however permits Cantor to accept ordinal numbers as given without defining them. The evidence presented, however, shows that Cantor conceived numbe...
Periods and elementary real numbers
Yoshinaga, Masahiko
2008-01-01
The periods, introduced by Kontsevich and Zagier, form a class of complex numbers which contains all algebraic numbers and several transcendental quantities. Little has been known about qualitative properties of periods. In this paper, we compare the periods with hierarchy of real numbers induced from computational complexities. In particular we prove that periods can be effectively approximated by elementary rational Cauchy sequences. As an application, we exhibit a computable real number wh...
Triple crossing numbers of graphs
Tanaka, Hiroyuki; Teragaito, Masakazu
2010-01-01
We introduce the triple crossing number, a variation of crossing number, of a graph, which is the minimal number of crossing points in all drawings with only triple crossings of the graph. It is defined to be zero for a planar graph, and to be infinite unless a graph admits a drawing with only triple crossings. In this paper, we determine the triple crossing numbers for all complete multipartite graphs including all complete graphs.
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.
Data Compression with Prime Numbers
Chalmers, Gordon
2005-01-01
A compression algorithm is presented that uses the set of prime numbers. Sequences of numbers are correlated with the prime numbers, and labeled with the integers. The algorithm can be iterated on data sets, generating factors of doubles on the compression.
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…
Picard numbers of quintic surfaces
Schutt, M.
2014-01-01
We solve the Picard number problem for complex quintic surfaces by proving that every number between 1 and 45 occurs as Picard number of a quintic surface over the rationals. Our main technique consists in arithmetic deformations of Delsarte surfaces, but we also use K3 surfaces and wild automorphisms.
Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers
International Nuclear Information System (INIS)
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.
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.
Florentin Smarandache
2015-01-01
In this paper, we introduce for the first time the neutrosophic quadruple numbers (of the form + + + ) and the refined neutrosophic quadruple numbers. Then we define an absorbance law, based on a prevalence order, both of them in order to multiply the neutrosophic components ,, or their sub-components ,, and thus to construct the multiplication of neutrosophic quadruple numbers.
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 ...
Reprint Series: Prime Numbers and Perfect Numbers. RS-2.
Schaaf, William L., Ed.
This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series makes available expository articles which appeared in a variety of mathematical periodicals. Topics covered include: (1) the prime numbers; (2) mathematical sieves; (3) the factorgram; and (4) perfect numbers. (MP)
THE RELATIONSHIP BETWEEN NUMBER NAMES AND NUMBER CONCEPTS
DEFF Research Database (Denmark)
Ejersbo, Lisser Rye; Misfeldt, Morten
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...
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.
q-Bernoulli Numbers Associated with q-Stirling Numbers
Taekyun Kim
2008-01-01
We consider Carlitz q-Bernoulli numbers and q-Stirling numbers of the first and the second kinds. From the properties of q-Stirling numbers, we derive many interesting formulas associated with Carlitz q-Bernoulli numbers. Finally, we will prove ÃŽÂ²n,q=Ã¢ÂˆÂ‘m=0nÃ¢ÂˆÂ‘k=mn1/(1-q)n+m-kÃ¢ÂˆÂ‘d0+Ã¢Â‹Â¯+dk=n-kqÃ¢ÂˆÂ‘i=0kidis1,q(k,m)(-1)n-m((m+1)/[m+1]q), where ÃŽÂ²n,q are called Carlitz q-Bernoulli numbers.
An Introduction to Zoli Numbers
Zotos, Kostas; Litke, Andreas
2005-01-01
There have been many theories about the paradoxes of numbers, but this is far and away more paradoxical than most. In this paper we will present the Zoli Numbers which have some innovative characteristics. The basic concept of these numbers is that they don't follow strictly any Mathematical rule. They are called Zoli from the names of Zotos and Litke. We are going to see some examples with the Zoli Programming Language and reveal the connection with other mathematical topics.
Expected gaps between prime numbers
Holt, Fred B.
2007-01-01
We study the gaps between consecutive prime numbers directly through Eratosthenes sieve. Using elementary methods, we identify a recursive relation for these gaps and for specific sequences of consecutive gaps, known as constellations. Using this recursion we can estimate the numbers of a gap or of a constellation that occur between a prime and its square. This recursion also has explicit implications for open questions about gaps between prime numbers, including three questions posed by Erd\\...
Correlations between large prime numbers
Bershadskii, A.
2011-01-01
It is shown that short-range correlations between large prime numbers (~10^5 and larger) have a Poissonian nature. Correlation length \\zeta = 4.5 for the primes ~10^5 and it is increasing logarithmically according to the prime number theorem. For moderate prime numbers (~10^4) the Poissonian distribution is not applicable while the correlation length surprisingly continues to follow to the logarithmical law. A chaotic (deterministic) hypothesis has been suggested to explain the moderate prime...
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.
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 ${\\mathcal G}_{a,b}(n, k; r)$.
Euler Sums of Hyperharmonic Numbers
Dil, Ayhan; Khristo N. Boyadzhiev
2012-01-01
The hyperharmonic numbers h_{n}^{(r)} are defined by means of the classical harmonic numbers. We show that the Euler-type sums with hyperharmonic numbers: {\\sigma}(r,m)=\\sum_{n=1}^{\\infty}((h_{n}^{(r)})/(n^{m})) can be expressed in terms of series of Hurwitz zeta function values. This is a generalization of a result of Mez\\H{o} and Dil. We also provide an explicit evaluation of {\\sigma}(r,m) in a closed form in terms of zeta values and Stirling numbers of the first kind. Furthermore, we evalu...
Unsolved problems in number theory
Guy, Richard K
1994-01-01
Unsolved Problems in Number Theory contains discussions of hundreds of open questions, organized into 185 different topics. They represent numerous aspects of number theory and are organized into six categories: prime numbers, divisibility, additive number theory, Diophantine equations, sequences of integers, and miscellaneous. To prevent repetition of earlier efforts or duplication of previously known results, an extensive and up-to-date collection of references follows each problem. In the second edition, not only extensive new material has been added, but corrections and additions have been included throughout the book.
A generalization of Stirling numbers
Loeb, Daniel E.
1995-01-01
We generalize the Stirling numbers of the first kind $s(a,k)$ to the case where $a$ may be an arbitrary real number. In particular, we study the case in which $a$ is an integer. There, we discover new combinatorial properties held by the classical Stirling numbers, and analogous properties held by the Stirling numbers $s(n,k)$ with $n$ a negative integer. On g\\'{e}n\\'{e}ralise ici les nombres de Stirling du premier ordre $s(a,k)$ au cas o\\`u $a$ est un r\\'eel quelconque. On s'interesse en par...
On the Three Primordial Numbers
Gobbetti, Roberto; Pajer, Enrico; Roest, Diederik
2015-01-01
Cosmological observations have provided us with the measurement of just three numbers that characterize the very early universe: $ 1-n_{s} $, $ N $ and $\\ln\\Delta_R^2$. Although each of the three numbers individually carries limited information about the physics of inflation, one may hope to extract
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.
Generalized Ramsey numbers for graphs
Zhang, Yanbo
2015-01-01
This thesis contains new contributions to Ramsey theory, in particular results that establish exact values of graph Ramsey numbers that were unknown to date. Given two graphs F and H, the Ramsey number R(F,H) is the smallest integer N such that, for any graph G of order N, either G contains F as a s
Isomorphisms of Algebraic Number Fields
van Hoeij, Mark
2010-01-01
Let $\\mathbb{Q}(\\alpha)$ and $\\mathbb{Q}(\\beta)$ be algebraic number fields. We describe a new method to find (if they exist) all isomorphisms, $\\mathbb{Q}(\\beta) \\rightarrow \\mathbb{Q}(\\alpha)$. The algorithm is particularly efficient if the number of isomorphisms is one.
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…
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.
Jacobi and Kummer's Ideal Numbers
Lemmermeyer, Franz
2011-01-01
In this article we give a modern interpretation of Kummer's ideal numbers and show how they developed from Jacobi's work on cyclotomy, in particular the methods for studying "Jacobi sums" which he presented in his lectures on number theory and cyclotomy in the winter semester 1836/37.
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…
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.
Some applications of Legendre numbers
Directory of Open Access Journals (Sweden)
Paul W. Haggard
1988-01-01
Full Text Available The associated Legendre functions are defined using the Legendre numbers. From these the associated Legendre polynomials are obtained and the derivatives of these polynomials at x=0 are derived by using properties of the Legendre numbers. These derivatives are then used to expand the associated Legendre polynomials and xn in series of Legendre polynomials. Other applications include evaluating certain integrals, expressing polynomials as linear combinations of Legendre polynomials, and expressing linear combinations of Legendre polynomials as polynomials. A connection between Legendre and Pascal numbers is also given.
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.
Elliptic rook and file numbers
Schlosser, Michael J.; Yoo, Meesue
2015-01-01
Utilizing elliptic weights, we construct an elliptic analogue of rook numbers for Ferrers boards. Our elliptic rook numbers generalize Garsia and Remmel's q-rook numbers by two additional independent parameters a and b, and a nome p. These are shown to satisfy an elliptic extension of a factorization theorem which in the classical case was established by Goldman, Joichi and White and later was extended to the q-case by Garsia and Remmel. We obtain similar results for our elliptic analogues of...
Fundamental number theory with applications
Mollin, Richard A
2008-01-01
An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage. New to the Second Edition Removal of all advanced material to be even more accessible in scope New fundamental material, including partition theory, generating functions, and combinatorial number theory Expa
Louboutin, Stephane R.
2007-03-01
Let \\{K_m\\} be a parametrized family of simplest real cyclic cubic, quartic, quintic or sextic number fields of known regulators, e.g., the so-called simplest cubic and quartic fields associated with the polynomials P_m(x) Dx^3 -mx^2-(m+3)x+1 and P_m(x) Dx^4 -mx^3-6x^2+mx+1 . We give explicit formulas for powers of the Gaussian sums attached to the characters associated with these simplest number fields. We deduce a method for computing the exact values of these Gaussian sums. These values are then used to efficiently compute class numbers of simplest fields. Finally, such class number computations yield many examples of real cyclotomic fields Q(zeta_p)^+ of prime conductors pge 3 and class numbers h_p^+ greater than or equal to p . However, in accordance with Vandiver's conjecture, we found no example of p for which p divides h_p^+ .
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 ...
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...
Classical theory of algebraic numbers
Ribenboim, Paulo
2001-01-01
Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer invented ideals and the theory of cyclotomic fields in his attempt to prove Fermat's Last Theorem These were the starting points for the theory of algebraic numbers, developed in the classical papers of Dedekind, Dirichlet, Eisenstein, Hermite and many others This theory, enriched with more recent contributions, is of basic importance in the study of diophantine equations and arithmetic algebraic geometry, including methods in cryptography This book has a clear and thorough exposition of the classical theory of algebraic numbers, and contains a large number of exercises as well as worked out numerical examples The Introduction is a recapitulation of results about principal ideal domains, unique factorization domains and commutative fields Part One is devoted to residue classes and quadratic residues In Part Two one finds the study of algebraic integers, ideals, units, class numbers, the theory of decomposition, iner...
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.
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.
... Your Heart Alternate Language URL Español Know Your Blood Sugar Numbers: Use Them to Manage Your Diabetes Page Content Checking your blood sugar, also called blood glucose, is an important part ...
Some Remarkable Identities Involving Numbers
Directory of Open Access Journals (Sweden)
Ziobro Rafał
2014-09-01
Full Text Available The article focuses on simple identities found for binomials, their divisibility, and basic inequalities. A general formula allowing factorization of the sum of like powers is introduced and used to prove elementary theorems for natural numbers.
Some Remarkable Identities Involving Numbers
Ziobro Rafał
2014-01-01
The article focuses on simple identities found for binomials, their divisibility, and basic inequalities. A general formula allowing factorization of the sum of like powers is introduced and used to prove elementary theorems for natural numbers.
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...
Universal Algebras of Hurwitz Numbers
A. Mironov; Morozov, A; Natanzon, S.
2009-01-01
Infinite-dimensional universal Cardy-Frobenius algebra is constructed, which unifies all particular algebras of closed and open Hurwitz numbers and is closely related to the algebra of differential operators, familiar from the theory of Generalized Kontsevich Model.
Young Students Investigate Number Cubes.
Friedlander, Alex
1997-01-01
Describes a series of learning activities built around number cubes. Sample activities introduce elementary properties of the cube, the magic rule of seven, and basic concepts related to graphs in the plane coordinate system. (PVD)
Picard numbers of Delsarte surfaces
Bas Heijne
2014-01-01
We give a classification of all complex Delsarte surfaces with only isolated ADE singularities. This results in 83 types of surfaces. For each of these types, we give a closed formula for the Picard number depending only on the degree.
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)
R. Arrighi; I. Togoli; D. C. Burr
2014-01-01
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...
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.
Occupation numbers from functional integral
Wetterich, C.
2007-01-01
Occupation numbers for non-relativistic interacting particles are discussed within a functional integral formulation. We concentrate on zero temperature, where the Bogoliubov theory breaks down for strong couplings as well as for low dimensional models. We find that the leading behavior of the occupation numbers for small momentum is governed by a quadratic time derivative in the inverse propagator that is not contained in the Bogoliubov theory. We propose to use a functional renormalization ...
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.
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.
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.
Conversion of Number Systems using Xilinx.
Chinmay V. Deshpande; Prof. Chankya K. Jha
2015-01-01
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.
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.
Are Number Gestures Easier than Number Words for Preschoolers?
Nicoladis, Elena; Pika, Simone; Marentette, Paula
2010-01-01
Some researchers have argued that children's earliest symbols are based on their sensorimotor experience and that arbitrary symbol-referent mapping poses a challenge for them. If so, exposure to iconic symbols (such as one-finger-for-one-object manual gestures) might help children in a difficult domain such as number. We assessed 44 preschoolers'…
Number Meaning and Number Grammar in English and Spanish
Bock, Kathryn; Carreiras, Manuel; Meseguer, Enrique
2012-01-01
Grammatical agreement makes different demands on speakers of different languages. Being widespread in the languages of the world, the features of agreement systems offer valuable tests of how language affects deep-seated domains of human cognition and categorization. Number agreement is one such domain, with intriguing evidence that typological…
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.
Computing Bits of Algebraic Numbers
Datta, Samir
2011-01-01
We initiate the complexity theoretic study of the problem of computing the bits of (real) algebraic numbers. This extends the work of Yap on computing the bits of transcendental numbers like \\pi, in Logspace. Our main result is that computing a bit of a fixed real algebraic number is in C=NC1\\subseteq Logspace when the bit position has a verbose (unary) representation and in the counting hierarchy when it has a succinct (binary) representation. Our tools are drawn from elementary analysis and numerical analysis, and include the Newton-Raphson method. The proof of our main result is entirely elementary, preferring to use the elementary Liouville's theorem over the much deeper Roth's theorem for algebraic numbers. We leave the possibility of proving non-trivial lower bounds for the problem of computing the bits of an algebraic number given the bit position in binary, as our main open question. In this direction we show very limited progress by proving a lower bound for rationals.
Periodical plane puzzles with numbers
Rezende, Jorge
2011-01-01
Consider a periodical (in two independent directions) tiling of the plane with polygons (faces). In this article we shall only give examples using squares, regular hexagons, equilateral triangles and parallelograms ("unions" of two equilateral triangles). We shall call some "multiple" of the fundamental region "the board". We naturally identify pairs of corresponding edges of the the board. Figures 9 and 19-29, in this article, show different boards. The "border" of the board is represented by a yellow thick line, unless part of it or all of it is the edge of a face. The board is tiled by a finite number of polygons. Construct polygonal plates in the same number, shape and size as the polygons of the board. Adjacent to each side of each plate draw a number, or two numbers, like it is shown in Figures 1 and 18-29. Figure 1 shows the obvious possibility of having plates with simple drawings, coloured drawings, etc. Now the game is to put the plates over the board polygons in such a way that the numbers near eac...
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...
Super congruences and Euler numbers
Sun, Zhi-Wei
2010-01-01
Let $p>3$ be a prime. We prove that $$\\sum_{k=0}^{p-1}\\binom{2k}{k}/2^k=(-1)^{(p-1)/2}-p^2E_{p-3} (mod p^3),$$ $$\\sum_{k=1}^{(p-1)/2}\\binom{2k}{k}/k=(-1)^{(p+1)/2}8/3*pE_{p-3} (mod p^2),$$ $$\\sum_{k=0}^{(p-1)/2}\\binom{2k}{k}^2/16^k=(-1)^{(p-1)/2}+p^2E_{p-3} (mod p^3)$$, where E_0,E_1,E_2,... are Euler numbers. Our new approach is of combinatorial nature. We also formulate many conjectures concerning super congruences and relate most of them to Euler numbers or Bernoulli numbers. Motivated by ...
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.
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...
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...
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.
Square Partitions and Catalan Numbers
Bennett, Matthew; Chari, Vyjayanthi; Dolbin, R. J.; Manning, Nathan
2009-01-01
For each integer $k\\ge 1$, we define an algorithm which associates to a partition whose maximal value is at most $k$ a certain subset of all partitions. In the case when we begin with a partition $\\lambda$ which is square, i.e $\\lambda=\\lambda_1\\ge...\\ge\\lambda_k>0$, and $\\lambda_1=k,\\lambda_k=1$, then applying the algorithm $\\ell$ times gives rise to a set whose cardinality is either the Catalan number $c_{\\ell-k+1}$ (the self dual case) or twice the Catalan number. The algorithm defines a t...
When a number is not only a number
DEFF Research Database (Denmark)
Christensen, Ken Ramshøj; Roepstorff, Andreas; Saddy, Douglas
). The control condition consists of simple x = x+1 strings (e.g. 1, 2, 3, 4, 5, 6…). The subjects have to press a button when they detect error to the general patterns, i.e., when a number does not conform to the numerical string. Using a block design to investigate the numerical processing, all three...... that such activation is dependent on the nature of the oddball, that is, the type of error or anomaly....
Cognitive Radio with Random Number of Secondary Number of Users
Zeng, Ruochen; Tepedelenlioglu, Cihan
2013-01-01
A single primary user cognitive radio system with multi-user diversity at the secondary users is considered where there is an interference constraint between secondary and primary users. The secondary user with the highest instantaneous SNR is selected for communication from a set of active users which also satisfies the interference constraint. The active number of secondary users is shown to be binomial, negative binomial, or Poisson-binomial distributed depending on various modes of operat...
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) "Youth Music"; (3) "Urban…
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…
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...
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...
Calculations of effective atomic number
Energy Technology Data Exchange (ETDEWEB)
Kaliman, Z. [Department of Physics, Faculty of Arts and Sciences, Omladinska 14, Rijeka (Croatia); Orlic, N. [Department of Physics, Faculty of Arts and Sciences, Omladinska 14, Rijeka (Croatia)], E-mail: norlic@ffri.hr; Jelovica, I. [Department of Physics, Faculty of Arts and Sciences, Omladinska 14, Rijeka (Croatia)
2007-09-21
We present and discuss effective atomic number (Z{sub eff}) obtained by different methods of calculations. There is no unique relation between the computed values. This observation led us to the conclusion that any Z{sub eff} is valid only for given process. We illustrate calculations for different subshells of atom Z=72 and for M3 subshell of several other atoms.
Effective interactions and magic numbers
International Nuclear Information System (INIS)
The magic numbers are the key concept of the shell model, and are shown to be different in exotic nuclei from those of stable nuclei. Its novel origin and robustness will be discussed, by referring to some basic but a sort of forgotten properties of the effective interaction. (author)
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).
Project Solo; Newsletter Number Eleven.
Pittsburgh Univ., PA. Project Solo.
An experimental 9th grade computer science syllabus is proposed. The syllabus would include the technical information needed for controlling and programing the computer in a number of modes and would preview some of the areas covered in the high school curriculum. A sample module of a topic not normally taught in high school--distance and…
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.)
Upper bounds on Nusselt number at finite Prandtl number
Choffrut, Antoine; Otto, Felix
2014-01-01
We study Rayleigh B\\'enard convection based on the Boussinesq approximation. We are interested in upper bounds on the Nusselt number $\\mathrm{Nu}$, the upwards heat transport, in terms of the Rayleigh number $\\mathrm{Ra}$, that characterizes the relative strength of the driving mechanism and the Prandtl number $\\mathrm{Pr}$, that characterizes the strength of the inertial effects. We show that, up to logarithmic corrections, the upper bound $\\mathrm{Nu}\\lesssim \\mathrm{Ra}^{\\frac{1}{3}}$ of Constantin and Doering in 1999 persists as long as $\\mathrm{Pr}\\gtrsim \\mathrm{Ra}^{\\frac{1}{3}}$ and then crosses over to $\\mathrm{Nu}\\lesssim\\mathrm{Pr}^{-\\frac{1}{2}}\\mathrm{Ra}^{\\frac{1}{2}}$. This result improves the one of Wang by going beyond the perturbative regime $\\mathrm{Pr} \\gg \\mathrm{Ra}$. The proof uses a new way to estimate the transport nonlinearity in the Navier-Stokes equations capitalizing on the no-slip boundary condition. It relies on a new Calder\\'on-Zygmund estimate for the non-stationary Stokes equ...
On Buffon Machines and Numbers
Flajolet, Philippe; Pelletier, Maryse; Soria, Michèle
2011-01-01
The well-know needle experiment of Buffon can be regarded as an analog (i.e., continuous) device that stochastically "computes" the number 2/pi ~ 0.63661, which is the experiment's probability of success. Generalizing the experiment and simplifying the computational framework, we consider probability distributions, which can be produced perfectly, from a discrete source of unbiased coin flips. We describe and analyse a few simple Buffon machines that generate geometric, Poisson, and logarithm...
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.
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.
Stum, Bernard Le; Quirós, Adolfo
2013-01-01
We introduce the notions of quantum characteristic and quantum flatness for arbitrary rings. More generally, we develop the theory of quantum integers in a ring and show that the hypothesis of quantum flatness together with positive quantum characteristic generalizes the usual notion of prime positive characteristic. We also explain how one can define quantum rational numbers in a ring and introduce the notion of twisted powers. These results play an important role in many different areas of ...
Large number discrimination by mosquitofish.
Directory of Open Access Journals (Sweden)
Christian Agrillo
Full Text Available BACKGROUND: Recent studies have demonstrated that fish display rudimentary numerical abilities similar to those observed in mammals and birds. The mechanisms underlying the discrimination of small quantities (<4 were recently investigated while, to date, no study has examined the discrimination of large numerosities in fish. METHODOLOGY/PRINCIPAL FINDINGS: Subjects were trained to discriminate between two sets of small geometric figures using social reinforcement. In the first experiment mosquitofish were required to discriminate 4 from 8 objects with or without experimental control of the continuous variables that co-vary with number (area, space, density, total luminance. Results showed that fish can use the sole numerical information to compare quantities but that they preferentially use cumulative surface area as a proxy of the number when this information is available. A second experiment investigated the influence of the total number of elements to discriminate large quantities. Fish proved to be able to discriminate up to 100 vs. 200 objects, without showing any significant decrease in accuracy compared with the 4 vs. 8 discrimination. The third experiment investigated the influence of the ratio between the numerosities. Performance was found to decrease when decreasing the numerical distance. Fish were able to discriminate numbers when ratios were 1:2 or 2:3 but not when the ratio was 3:4. The performance of a sample of undergraduate students, tested non-verbally using the same sets of stimuli, largely overlapped that of fish. CONCLUSIONS/SIGNIFICANCE: Fish are able to use pure numerical information when discriminating between quantities larger than 4 units. As observed in human and non-human primates, the numerical system of fish appears to have virtually no upper limit while the numerical ratio has a clear effect on performance. These similarities further reinforce the view of a common origin of non-verbal numerical systems in all
Lozenge Tilings and Hurwitz Numbers
Novak, Jonathan
2015-10-01
We give a new proof of the fact that, near a turning point of the frozen boundary, the vertical tiles in a uniformly random lozenge tiling of a large sawtooth domain are distributed like the eigenvalues of a GUE random matrix. Our argument uses none of the standard tools of integrable probability. In their place, it uses a combinatorial interpretation of the Harish-Chandra/Itzykson-Zuber integral as a generating function for desymmetrized Hurwitz numbers.
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.
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
Functional units for natural numbers
Bergstra, J A
2009-01-01
Interaction with services provided by an execution environment forms part of the behaviours exhibited by instruction sequences under execution. Mechanisms related to the kind of interaction in question have been proposed in the setting of thread algebra. Like thread, service is an abstract behavioural concept. The concept of a functional unit is similar to the concept of a service, but more concrete. A state space is inherent in the concept of a functional unit, whereas it is not inherent in the concept of a service. In this paper, we establish the existence of a universal computable functional unit for natural numbers and related results.
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 & 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
Propulsion at low Reynolds number
International Nuclear Information System (INIS)
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
Bridge Number and Conway Products
Blair, Ryan C.
2007-01-01
Schubert proved that, given a composite link $K$ with summands $K_{1}$ and $K_{2}$, the bridge number of $K$ satisfies the following equation: $$\\beta(K)=\\beta(K_{1})+\\beta(K_{2})-1.$$ In ``Conway Produts and Links with Multiple Bridge Surfaces", Scharlemann and Tomova proved that, given links $K_{1}$ and $K_{2}$, there is a Conway product $K_{1}\\times_{c}K_{2}$ such that $$\\beta(K_{1}\\times_{c} K_{2}) \\leq \\beta(K_{1}) + \\beta(K_{2}) - 1$$ In this paper, we define the generalized Conway prod...
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 ...
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. ...
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...
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 ...
Directory of Open Access Journals (Sweden)
Christian Agrillo
Full Text Available BACKGROUND: Research on human infants, mammals, birds and fish has demonstrated that rudimentary numerical abilities pre-date the evolution of human language. Yet there is controversy as to whether animals represent numbers mentally or rather base their judgments on non-numerical perceptual variables that co-vary with numerosity. To date, mental representation of number has been convincingly documented only for a few mammals. METHODOLOGY/PRINCIPAL FINDINGS: Here we used a training procedure to investigate whether mosquitofish could learn to discriminate between two and three objects even when denied access to non-numerical information. In the first experiment, fish were trained to discriminate between two sets of geometric figures. These varied in shape, size, brightness and distance, but no control for non-numerical variables was made. Subjects were then re-tested while controlling for one non-numerical variable at a time. Total luminance of the stimuli and the sum of perimeter of figures appeared irrelevant, but performance dropped to chance level when stimuli were matched for the cumulative surface area or for the overall space occupied by the arrays, indicating that these latter cues had been spontaneously used by the fish during the learning process. In a second experiment, where the task consisted of discriminating 2 vs 3 elements with all non-numerical variables simultaneously controlled for, all subjects proved able to learn the discrimination, and interestingly they did not make more errors than the fish in Experiment 1 that could access non-numerical information in order to accomplish the task. CONCLUSIONS/SIGNIFICANCE: Mosquitofish can learn to discriminate small quantities, even when non-numerical indicators of quantity are unavailable, hence providing the first evidence that fish, like primates, can use numbers. As in humans and non-human primates, genuine counting appears to be a 'last resort' strategy in fish, when no other
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.
Note on the Theory of Perfect Numbers
Carella, N. A.
2011-01-01
A perfect number is a number whose divisors add up to twice the number itself. The existence of odd perfect numbers is a millennia-old unsolved problem. This note proposes a proof of the nonexistence of odd perfect numbers. More generally, the same analysis seems to generalize to a proof of the nonexistence of odd multiperfect numbers.
Sun, Zhi-Hong
2014-01-01
Let $r(G_1, G_2)$ be the Ramsey number of the two graphs $G_1$ and $G_2$. For $n_1\\ge n_2\\ge 1$ let $S(n_1,n_2)$ be the double star given by $V(S(n_1,n_2))=\\{v_0,v_1,...,v_{n_1},w_0,w_1,...,w_{n_2}\\}$ and $E(S(n_1,n_2))=\\{v_0v_1,...,v_0v_{n_1},v_0w_0, w_0w_1,...,w_0w_{n_2}\\}$. In this paper we determine $r(K_{1,m-1},S(n_1,n_2))$ for $n_1\\ge m-2\\ge n_2$. For $n\\ge 6$ let $T_n^3=S(n-5,3)$, $T_n^{"}=(V,E_2)$ and $T_n^{'"} =(V,E_3)$, where $V=\\{v_0,v_1,...,v_{n-1}\\}$, $E_2=\\{v_0v_1,...,v_0v_{n-4}...
On Bernoulli Numbers and Its Properties
Cong, Lin
2004-01-01
In this survey paper, I first review the history of Bernoulli numbers, then examine the modern definition of Bernoulli numbers and the appearance of Bernoulli numbers in expansion of functions. I revisit some properties of Bernoulli numbers and the history of the computation of big Bernoulli numbers.
RIORDAN MATRICES AND SUMS OF HARMONIC NUMBERS
Directory of Open Access Journals (Sweden)
Emanuele Munarini
2011-10-01
Full Text Available We obtain a general identity involving the row-sums of a Riordan matrixand the harmonic numbers. From this identity, we deduce several particular identities involving numbers of combinatorial interest, such as generalized Fibonacci and Lucas numbers, Catalan numbers, binomial and trinomial coefficients and Stirling numbers.
Crosscap Numbers of Two-component Links
Zhang, Gengyu
2006-01-01
We define the crosscap number of a 2-component link as the minimum of the first Betti numbers of connected, non-orientable surfaces bounding the link. We discuss some properties of the crosscap numbers of 2-component links.
Some properties of θ-congruent numbers
Fujiwara, Masahiko
2002-01-01
The concept of θ-congruent numbers was first introduced by myself as a generalization of classical congruent numbers. Since then, several interesting properties have been found. This paper gives still further theorems related to θ-congruent numbers.
Some properties of fuzzy real numbers
Directory of Open Access Journals (Sweden)
Bayaz Daraby
2016-02-01
In this study, we try to prove Bernoulli's inequality in fuzzy real numbers with some of its applications. Also, we prove two other theorems in fuzzy real numbers which are proved before, for real numbers.
The generalized r-Whitney numbers
El-Desouky, B. S.; Shiha, F. A.; Shokr, Ethar M.
2016-01-01
In this paper, we define the generalized r-Whitney numbers of the first and second kind. Moreover, we drive the generalized Whitney numbers of the first and second kind. The recurrence relations and the generating functions of these numbers are derived. The relations between these numbers and generalized Stirling numbers of the first and second kind are deduced. Furthermore, some special cases are given. Finally, matrix representation of The relations between Whitney and Stirling numbers are ...
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
Fibonacci Numbers, Golden Section and Applications
Şen, Erdoğan
2013-01-01
In this thesis we examined mathematical properties of Fibonacci numbers and applications of this numbers in the nature,geometry and economy.We obtained Golden section and proved some mathematical identities using Golden section. Infinity of the prime numbers proved by using properties of Fibonacci numbers. Encounterings with Fibonacci numbers in the nature are examined with details. Also examples are given for relation about Fibonacci numbers and stock exchange and these are examined.
2010-01-01
... 7 Agriculture 8 2010-01-01 2010-01-01 false Lot number. 987.102 Section 987.102 Agriculture... RIVERSIDE COUNTY, CALIFORNIA Administrative Rules Definitions § 987.102 Lot number. Lot number is synonymous with code and means a combination of letters or numbers, or both, acceptable to the Committee,...
9 CFR 351.6 - Official number.
2010-01-01
... 9 Animals and Animal Products 2 2010-01-01 2010-01-01 false Official number. 351.6 Section 351.6... of Program § 351.6 Official number. The Administrator will assign a certified technical animal fat plant number to each plant granted service. Such number shall be preceded by the letter “C” and be...
2010-01-01
... 7 Agriculture 8 2010-01-01 2010-01-01 false Docket number. 900.5 Section 900.5 Agriculture... Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the proceeding may be referred to by such number....
7 CFR 29.32 - Identification number.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Identification number. 29.32 Section 29.32 Agriculture... INSPECTION Regulations Definitions § 29.32 Identification number. A number or a combination of letters and numbers in a design or mark approved by the Director, stamped, printed, or stenciled on a lot of...
14 CFR 47.15 - Identification number.
2010-01-01
... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Identification number. 47.15 Section 47.15... REGISTRATION General § 47.15 Identification number. (a) Number required. An applicant for Aircraft Registration must place a U.S. identification number (registration mark) on his Aircraft Registration...
9 CFR 355.8 - Official number.
2010-01-01
... 9 Animals and Animal Products 2 2010-01-01 2010-01-01 false Official number. 355.8 Section 355.8... IDENTIFICATION AS TO CLASS, QUALITY, QUANTITY, AND CONDITION Inauguration of Inspection § 355.8 Official number. To each plant granted inspection an official number shall be assigned. Such number shall be...
7 CFR 75.48 - Identification number.
2010-01-01
... 7 Agriculture 3 2010-01-01 2010-01-01 false Identification number. 75.48 Section 75.48 Agriculture... number. The Director may require the use of official identification numbers in connection with seed certificated or sampled under the Act. When identification numbers are required, they shall be specified by...
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.
Experimental Number Theory, Part I : Tower Arithmetic
Gnang, Edinah K.
2011-01-01
We introduce in this section an Algebraic and Combinatorial approach to the theory of Numbers. The approach rests on the observation that numbers can be identified with familiar combinatorial objects namely rooted trees, which we shall here refer to as towers. The bijection between numbers and towers provides some insights into unexpected connexions between Number theory, combinatorics and discrete probability theory.
On the Harmonic and Hyperharmonic Fibonacci Numbers
Tuglu, Naim; Kızılateş, Can; Kesim, Seyhun
2015-01-01
In this paper, we study the theory of the harmonic and the hyperharmonic Fibonacci numbers. Also, we get some combinatoric identities like as harmonic and hyperharmonic numbers and we obtain some useful formulas for $\\mathbb{F}_{n}$, which is finite sums of reciprocals of Fibonacci numbers. We obtain spectral and Euclidean norms of circulant matrices involving harmonic and hyperharmonic Fibonacci numbers.
The Irrationality Exponents of Computable Numbers
Becher, Verónica; Bugeaud, Yann; Slaman, Theodore A.
2014-01-01
We prove that a real number a greater than or equal to 2 is the irrationality exponent of some computable real number if and only if a is the upper limit of a computable sequence of rational numbers. Thus, there are computable real numbers whose irrationality exponent is not computable.
Girotondo dei Numeri (A Ring of Numbers).
Palandra, Maria; And Others
This workbook in Italian for learning the numbers from one to ten is intended for use in a bilingual education setting. It is introduced and concluded by a song about playing "ring around the rosy" with numbers. Each paqe has a pen and ink drawing illustrating the number and a sentence about the picture and the number. (AMH)
Some properties of fuzzy real numbers
Bayaz Daraby; Javad Jafari
2016-01-01
In the mathematical analysis, there are some theorems and definitions that established for both real and fuzzy numbers. In this study, we try to prove Bernoulli's inequality in fuzzy real numbers with some of its applications. Also, we prove two other theorems in fuzzy real numbers which are proved before, for real numbers.
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.
On Legendre numbers of the second kind
Haggard, Paul W.
1988-01-01
The Legendre numbers of the second kind, an infinite set of rational numbers, are defined from the associated Legendre functions. An explicit formula and a partial table for these numbers are given and many elementary properties are presented. A connection is shown between Legendre numbers of the first and second kinds. Extended Legendre numbers of the first and second kind are defined in a natural way and these are expressed in terms of those of the second and first kind, respectively. Two o...
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.
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.
Prime number generation and factor elimination
Kumar, Vineet
2014-01-01
We have presented a multivariate polynomial function termed as factor elimination function,by which, we can generate prime numbers. This function's mapping behavior can explain the irregularities in the occurrence of prime numbers on the number line. Generally the different categories of prime numbers found till date, satisfy the form of this function. We present some absolute and probabilistic conditions for the primality of the number generated by this method. This function is capable of le...
Quantum Mechanics interpreted in Quantum Real Numbers
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.
Galois theory, motives and transcendental numbers
Andre, Yves
2008-01-01
From its early beginnings up to nowadays, algebraic number theory has evolved in symbiosis with Galois theory: indeed, one could hold that it consists in the very study of the absolute Galois group of the field of rational numbers. Nothing like that can be said of transcendental number theory. Nevertheless, couldn't one associate conjugates and a Galois group to transcendental numbers such as $\\pi$? Beyond, can't one envision an appropriate Galois theory in the field of transcendental number ...
h-analogue of Fibonacci Numbers
Benaoum, H. B.
2009-01-01
In this paper, we introduce the h-analogue of Fibonacci numbers for non-commutative h-plane. For h h'= 1 and h = 0, these are just the usual Fibonacci numbers as it should be. We also derive a collection of identities for these numbers. Furthermore, h-Binet's formula for the h-Fibonacci numbers is found and the generating function that generates these numbers is obtained.
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...
On q-deformed Stirling numbers
Simsek, Yilmaz
2007-01-01
The purpose of this article is to introduce q-deformed Stirling numbers of the first and second kinds. Relations between these numbers, Riemann zeta function and q-Bernoulli numbers of higher order are given. Some relations related to the classical Stirling numbers and Bernoulli numbers of higher order are found. By using derivative operator to the generating function of the q-deformed Stirling numbers of the second kinds, a new function is defined which interpolates the q-deformed Stirling n...
Two Kinds of Numbers and Their Applications
Institute of Scientific and Technical Information of China (English)
Zhi Zheng ZHANG; Hong FENG
2006-01-01
C. Radoux (J. Comput. Appl. Math., 115 (2000) 471-477) obtained a computational formula of Hankel determinants on some classical combinatorial sequences such as Catalan numbers and polynomials, Bell polynomials, Hermite polynomials, Derangement polynomials etc. From a pair of matrices this paper introduces two kinds of numbers. Using the first kind of numbers we give a unified treatment of Hankel determinants on those sequences, i.e., to consider a general representation of Hankel matrices on the first kind of numbers. It is interesting that the Hankel determinant of the first kind of numbers has a close relation that of the second kind of numbers.
Fibonacci number of the tadpole graph
Joe DeMaio; John Jacobson
2014-01-01
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 Fibon...
Poison control center - Emergency number (image)
... anywhere in the United States. This national hotline number will let you talk to experts in poisoning. ... control centers in the U.S. use this national number. You should call if you have any questions ...
Path count asymptotics and Stirling numbers
Petersen, K.; Varchenko, A.
2009-01-01
We obtain formulas for the growth rate of the numbers of certain paths in infinite graphs built on the two-dimensional Eulerian graph. Corollaries are identities relating Stirling numbers of the first and second kinds.
Power sum identities with generalized Stirling numbers
Khristo N. Boyadzhiev
2009-01-01
Several combinatorial identities are presented, involving Stirling functions of the second kind with a complex variable. The identities involve also Stirling numbers of the first kind, binomial coefficients and harmonic numbers.
Algebraic structures of sequences of numbers
Huang, I.-Chiau
2012-09-01
For certain sequences of numbers, commutative rings with a module structure over a non-commutative ring are constructed. Identities of these numbers are considered as realizations of algebraic relations.
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.
Number Theory in the High School Classroom.
Dence, Thomas
1999-01-01
Demonstrates some of the usefulness of number theory to students on the high school setting in four areas: Fibonacci numbers, Diophantine equations, continued fractions, and algorithms for computing pi. (ASK)
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.
Monotone Hurwitz numbers in genus zero
Goulden, I. P.; Guay-Paquet, Mathieu; 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...
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.
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.
Using Simulated Annealing to Factor Numbers
Altschuler, Eric Lewin; Williams, Timothy J.
2014-01-01
Almost all public secure communication relies on the inability to factor large numbers. There is no known analytic or classical numeric method to rapidly factor large numbers. Shor[1] has shown that a quantum computer can factor numbers in polynomial time but there is no practical quantum computer that can yet do such computations. We show that a simulated annealing[2] approach can be adapted to find factors of large numbers.
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...
M"Uller, Tom
2007-09-01
An odd prime number p is called anti-elite if only finitely many Fermat numbers are quadratic non-residues to p. This concept is the exact opposite to that of elite prime numbers. We study some fundamental properties of anti-elites and show that there are infinitely many of them. A computational search among all the numbers up to 100 billion yielded 84 anti-elite primes.
7 CFR 29.133 - Identification number.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Identification number. 29.133 Section 29.133... REGULATIONS TOBACCO INSPECTION Regulations Miscellaneous § 29.133 Identification number. The Director may require the use of official identification numbers in connection with tobacco certificated or...
2010-01-01
... 7 Agriculture 1 2010-01-01 2010-01-01 false Docket number. 1.414 Section 1.414 Agriculture Office... Conservation and Shortage Relief Act of 1990 (16 U.S.C. 620 et seq.) § 1.414 Docket number. Each proceeding, following its institution, shall be assigned a docket number by the Hearing Clerk, and thereafter...
27 CFR 24.115 - Registry number.
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Registry number. 24.115... OF THE TREASURY LIQUORS WINE Establishment and Operations Application § 24.115 Registry number. Upon approval of the application, the appropriate TTB officer will assign a registry number to the bonded...
40 CFR 264.11 - Identification number.
2010-07-01
... 40 Protection of Environment 25 2010-07-01 2010-07-01 false Identification number. 264.11 Section... Facility Standards § 264.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR 12746)....
2010-01-01
... 7 Agriculture 10 2010-01-01 2010-01-01 false Docket number. 1200.6 Section 1200.6 Agriculture... Governing Proceedings To Formulate and Amend an Order § 1200.6 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter...
21 CFR 1210.21 - Permit number.
2010-04-01
... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Permit number. 1210.21 Section 1210.21 Food and... IMPORT MILK ACT Permit Control § 1210.21 Permit number. Each permit issued under the Federal Import Milk Act, including each temporary permit, shall bear an individual number. The right to the use of...
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…
47 CFR 95.671 - Serial number.
2010-10-01
... 47 Telecommunication 5 2010-10-01 2010-10-01 false Serial number. 95.671 Section 95.671 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES PERSONAL RADIO... number. The serial number of each CB transmitter must be engraved on the transmitter chassis....
40 CFR 265.11 - Identification number.
2010-07-01
... 40 Protection of Environment 25 2010-07-01 2010-07-01 false Identification number. 265.11 Section... FACILITIES General Facility Standards § 265.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45...
2010-01-01
... 7 Agriculture 8 2010-01-01 2010-01-01 false Docket number. 900.54 Section 900.54 Agriculture... Governing Proceedings on Petitions To Modify or To Be Exempted From Marketing Orders § 900.54 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by...
24 CFR 3280.6 - Serial number.
2010-04-01
... 24 Housing and Urban Development 5 2010-04-01 2010-04-01 false Serial number. 3280.6 Section 3280... DEVELOPMENT MANUFACTURED HOME CONSTRUCTION AND SAFETY STANDARDS General § 3280.6 Serial number. (a) A manufactured home serial number which will identify the manufacturer and the state in which the...
46 CFR 10.207 - Identification number.
2010-10-01
... 46 Shipping 1 2010-10-01 2010-10-01 false Identification number. 10.207 Section 10.207 Shipping... CREDENTIAL General Requirements for All Merchant Mariner Credentials § 10.207 Identification number. For recordkeeping purposes only, a mariner's official MMC identification number is the individual's social...
2010-01-01
... 7 Agriculture 1 2010-01-01 2010-01-01 false Docket number. 1.134 Section 1.134 Agriculture Office... Adjudicatory Proceedings Instituted by the Secretary Under Various Statutes § 1.134 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the Hearing...
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.
Baxter Algebras, Stirling Numbers and Partitions
Guo, Li
2004-01-01
Recent developments of Baxter algebras have lead to applications to combinatorics, number theory and mathematical physics. We relate Baxter algebras to Stirling numbers of the first kind and the second kind, partitions and multinomial coefficients. This allows us to apply congruences from number theory to obtain congruences in Baxter algebras.
Linking numbers for handlebody-links
Mizusawa, Atsuhiko
2013-01-01
As a generalization of the linking number, we construct a set of invariant numbers for two-component handlebody-links. These numbers are elementary divisors associated with the natural homomorphism from the first homology group of a component to that of the complement of another component.
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…
47 CFR 32.20 - Numbering convention.
2010-10-01
... 47 Telecommunication 2 2010-10-01 2010-10-01 false Numbering convention. 32.20 Section 32.20 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES UNIFORM SYSTEM OF ACCOUNTS FOR TELECOMMUNICATIONS COMPANIES General Instructions § 32.20 Numbering convention. (a) The number...
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.
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.
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,….
Remarkable and Reversible Prime Number Patterns
Weber, H. J.
2012-01-01
Prime number multiplet classifications and patterns are extended to negative integers. The extension from prime numbers to single prime powers is also studied. Prime number septets at equal distance are given. It is also shown that each class of generalized twin primes of the classification contains a positive fraction of all prime pairs.
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.
The characteristic numbers of quartic plane curves
Vakil, Ravi
1998-01-01
The characteristic numbers of smooth plane quartics are computed using intersection theory on a component of the moduli space of stable maps. This completes the verification of Zeuthen's prediction of characteristic numbers of smooth plane curves. A short sketch of a computation of the characteristic numbers of plane cubics is also given as an illustration.
An Introduction to Conway's Games and Numbers
Schleicher, Dierk; Stoll, Michael
2004-01-01
This is an introduction into John Conway's beautiful Combinatorial Game Theory, providing precise statements and detailed proofs for the fundamental parts of his theory. (1) Combinatorial game theory, (2) the GROUP of games, (3) the FIELD of numbers, (4) ordinal numbers, (5) games and numbers, (6) infinitesimal games, (7) impartial games.
On a unified theory of numbers
Sinha, Nilotpal Kanti; Wolf, Marek
2010-01-01
We prove that several results in different areas of number theory such as the divergent series, summation of arithmetic functions, uniform distribution modulo one and summation over prime numbers which are currently considered to be independent results can be unified under a single equation. We apply our method to derive several new results in the above areas of number theory.
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…
49 CFR 230.47 - Boiler number.
2010-10-01
..., 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, shall... 49 Transportation 4 2010-10-01 2010-10-01 false Boiler number. 230.47 Section...
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....
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 Architecture"; (4) "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
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 $b_t(G_{n,4})$.
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
Bit recycling for scaling random number generators
Mennucci, Andrea C. G.
2010-01-01
Many Random Number Generators (RNG) are available nowadays; they are divided in two categories, hardware RNG, that provide "true" random numbers, and algorithmic RNG, that generate pseudo random numbers (PRNG). Both types usually generate random numbers (X_n) as independent uniform samples in a range 0...2^b-1, with b = 8, 16, 32 or b = 64. In applications, it is instead sometimes desirable to draw random numbers as independent uniform samples (Y_n) in a range 1, . . . M, where moreover M may...
Random Numbers in Scientific Computing: An Introduction
Katzgraber, Helmut G
2010-01-01
Random numbers play a crucial role in science and industry. Many numerical methods require the use of random numbers, in particular the Monte Carlo method. Therefore it is of paramount importance to have efficient random number generators. The differences, advantages and disadvantages of true and pseudo random number generators are discussed with an emphasis on the intrinsic details of modern and fast pseudo random number generators. Furthermore, standard tests to verify the quality of the random numbers produced by a given generator are outlined. Finally, standard scientific libraries with built-in generators are presented, as well as different approaches to generate nonuniform random numbers. Potential problems that one might encounter when using large parallel machines are discussed.
Certain number-theoretic episodes in algebra
Sivaramakrishnan, R
2006-01-01
Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important aspects of interconnections between number theory and commutative algebra. Using a pedagogical approach, the author presents the conceptual foundations of commutative algebra arising from number theory. Self-contained, the book examines situations where explicit algebraic analogues of theorems of number theory are available. Coverage is divided into four parts, beginning with elements of number theory and algebra such as theorems of Euler, Fermat, and Lagrange, Euclidean domains, and finite groups. In the second part, the book details ordered fields, fields with valuation, and other algebraic structures. This is followed by a review of fundamentals of algebraic number theory in the third part. The final part explores links with ring theory, finite dimensional algebras, and the Goldbach problem.
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
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.
27 CFR 20.179 - Package identification number or serial number.
2010-04-01
... number or serial number. 20.179 Section 20.179 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO... Package identification number or serial number. (a) Requirement. A dealer who fills packages with specially denatured spirits shall mark each package with a package identification number, in accordance...
An Evaluation of App-Based and Paper-Based Number Lines for Teaching Number Comparison
Weng, Pei-Lin; Bouck, Emily C.
2016-01-01
Number comparison is a fundamental skill required for academic and functional mathematics (e.g., time, money, purchasing) for students with disabilities. The most commonly used method to teach number comparison is number lines. Although historically paper number lines are used, app-based number lines may offer greater flexibility. This study…
On the binary expansions of algebraic numbers
Energy Technology Data Exchange (ETDEWEB)
Bailey, David H.; Borwein, Jonathan M.; Crandall, Richard E.; Pomerance, Carl
2003-07-01
Employing concepts from additive number theory, together with results on binary evaluations and partial series, we establish bounds on the density of 1's in the binary expansions of real algebraic numbers. A central result is that if a real y has algebraic degree D > 1, then the number {number_sign}(|y|, N) of 1-bits in the expansion of |y| through bit position N satisfies {number_sign}(|y|, N) > CN{sup 1/D} for a positive number C (depending on y) and sufficiently large N. This in itself establishes the transcendency of a class of reals {summation}{sub n{ge}0} 1/2{sup f(n)} where the integer-valued function f grows sufficiently fast; say, faster than any fixed power of n. By these methods we re-establish the transcendency of the Kempner--Mahler number {summation}{sub n{ge}0}1/2{sup 2{sup n}}, yet we can also handle numbers with a substantially denser occurrence of 1's. Though the number z = {summation}{sub n{ge}0}1/2{sup n{sup 2}} has too high a 1's density for application of our central result, we are able to invoke some rather intricate number-theoretical analysis and extended computations to reveal aspects of the binary structure of z{sup 2}.
Energy Technology Data Exchange (ETDEWEB)
Aalto, J.P.; Kiiski, U.; Mikkonen, S.; Nikkonen, J.; Piirainen, O. [Neste Oy, Porvoo (Finland)
1998-12-31
The target of the project was to research the use of biocomponent feed in oil refining processes. The target was also to produce high cetane number and low pour point diesel fuel. Tall oil fatty acid (TOFA) was studied as a feedstock to a mild hydrocracking and hydrodesulphurization processes. Also emission tests were performed. The cetane numbers of products were high but pour points were unsatisfactory. (orig.)
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.
Lockwood, Mike; Barnard, Luke A
2016-01-01
We use 5 test data series to quantify putative discontinuities around 1946 in 5 annual-mean sunspot number or group number sequences. The series tested are: the original and new versions of the Wolf/Zurich/International sunspot number composite [$R_{ISNv1}$ and $R_{ISNv2}$] ; the corrected version of $R_{ISNv1}$ [$R_C$]; the backbone group number [$R_{BB}$]; and the group number composite [$R_{UEA}$]. The test data are: the group number $N_G$ and total sunspot area $A_G$ from the RGO photoheliographic data; the CaK index from re-analysis of MWO CaII K spectroheliograms; the group number from the MWO sunspot drawings, $N_{MWO}$; and ionospheric critical frequencies at Slough [$foF2$]. The test data all vary with sunspot numbers, in some cases non-linearly. Tests use both before-and-after fit-residual comparison and correlation methods, applied to intervals iterated to minimise errors and eliminate the effect of the discontinuity date. It is not assumed that the correction required is by a constant factor, nor ...
Notes on the Theory of Algebraic Numbers
Wright, Steve
2015-01-01
A series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required. Based primarily on the texts of E. Hecke, Lectures on the Theory of Algebraic Numbers, Springer-Verlag, 1981 (English translation by G. Brauer and J. Goldman) and D. Marcus, Number Fields, Springer, 1977.
From Taub Numbers to the Bondi Mass
Glass, E. N.
1997-01-01
Taub numbers are studied on asymptotically flat backgrounds with Killing symmetries. When the field equations are solved for a background spacetime and higher order functional derivatives (higher order variational derivatives of the Hilbert Lagrangean) are solved for perturbations from the background, such perturbed space-times admit zeroth, first, and second order Taub numbers. Zeroth order Taub numbers are Komar constants (upto numerical factors) or Penrose-Goldberg constants of the backgro...
Continental anthropogenic primary particle number emissions
Paasonen, Pauli; Kupiainen, Kaarle; Klimont, Zbigniew; Visschedijk, Antoon; Denier van der Gon, Hugo A. C.; Amann, Markus
2016-01-01
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 im...
Measuring human salivary amylase copy number variation
Dhar, Sugandha
2010-01-01
Copy number variations represent large scale genomic alterations varying from 1kb to 3Mb and are proposed as a driving force for genome evolution and variation. One such locus exhibiting copy number variation and genome evolution is salivary amylase, which is responsible for the digestion of starch in the human parotid glands. It was reported that since human salivary amylase gene (AMY1) copy numbers are correlated positively with protein levels, and also due to the correlation of high gene c...
Generalized Ramsey numbers through adiabatic quantum optimization
Ranjbar, Mani; Macready, William G.; Clark, Lane; Gaitan, Frank
2016-01-01
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 usin...
Dimensions, nodes and phases in quantum numbers
Rau, A. R. P.
2009-01-01
Students of quantum mechanics encounter discrete quantum numbers in a somewhat incoherent and bewildering number of ways. For each physical system studied, quantum numbers seem to be introduced in its own specific way, some enumerating from 1 and others from 0, without a common uniting thread. This essay presents a point of view that builds on dimensions, boundary conditions and various inputs that, while known, are often not brought together to present a simple, consistent picture. At the sa...
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.
Generation of large prime numbers from a sequence of previous prime numbers
Samir, Brahim Belhaouari; Rezk, Youssef A. Y.
2012-09-01
A prime number is co-prime with all the primes as well. This paper utilizes this fact by generating larger prime numbers based on a set of smaller prime numbers. The prime numbers are ordered and each two consecutive primes are coupled to generate their co-prime number formula extending this process larger prime sequence is established. Will the process help us produce larger prime numbers faster and more efficiently? This paper investigates the described process.
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
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.
Algebra and Number Theory An Integrated Approach
Dixon, Martyn; Subbotin, Igor
2011-01-01
Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications. Based on the authors' extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines-linear algebra, abstract algebra, and number theory-into one compr
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.
On the Turan number of forests
Lidický, Bernard; Palmer, Cory
2012-01-01
The Turan number of a graph H, ex(n,H), is the maximum number of edges in a graph on n vertices which does not have H as a subgraph. We determine the Turan number and find the unique extremal graph for forests consisting of paths when n is sufficiently large. This generalizes a result of Bushaw and Kettle [ Combinatorics, Probability and Computing 20:837--853, 2011]. We also determine the Turan number and extremal graphs for forests consisting of stars of arbitrary order.
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.
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.
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.
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.
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...
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
2010-07-01
... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false Numbering. 105-1.109 Section 105-1.109 Public Contracts and Property Management Federal Property Management Regulations System (Continued) GENERAL SERVICES ADMINISTRATION 1-INTRODUCTION 1.1-Regulations System § 105-1.109 Numbering....
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.
Cellular Automata Rules and Linear Numbers
Nayak, Birendra Kumar; Sahoo, Sudhakar; Biswal, Sagarika
2012-01-01
In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at "0". Some mathematical results on linear as well as non-linear CA rules are derived. Integers associated with linear CA rules are defined as linear numbers and the properties of these linear numbers are studied.
Finite groups in Axiomatic Index Number Theory
Marco Fattore
2006-01-01
In this paper we adopt Group Theory to investigate the symmetry and invariance properties of price index numbers. An alternative treatment is given to the study of the reversibilty axioms, that clarifies their meaning and allows for a conceptual unification of this topic, within the framework of Axiomatic Index Number Theory.
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.
Queneau numbers - recent results and a bibliography
Asveld, Peter R.J.
2013-01-01
Publications dealing with Queneau numbers can be divided roughly into two categories. In the first one the relation to poetry and, more generally, to literature is the central issue. The second one consists of papers that investigate the mathematical properties of the Queneau numbers and of integer
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.
Tunnel number one, genus one fibered knots
Baker, Kenneth L.; Johnson, Jesse E.; Klodginski, Elizabeth A.
2006-01-01
We determine the genus one fibered knots in lens spaces that have tunnel number one. We also show that every tunnel number one, once-punctured torus bundle is the result of Dehn filling a component of the Whitehead link in the 3-sphere.
Hodge Numbers for All CICY Quotients
Constantin, Andrei; Lukas, Andre
2016-01-01
We present a general method for computing Hodge numbers for Calabi-Yau manifolds realised as discrete quotients of complete intersections in products of projective spaces. The method relies on the computation of equivariant cohomologies and is illustrated for several explicit examples. In this way, we compute the Hodge numbers for all discrete quotients obtained in Braun's classification arXiv:1003.3235.
A Generalization of the Prime Number Theorem
Bruckman, Paul S.
2008-01-01
In this article, the author begins with the prime number theorem (PNT), and then develops this into a more general theorem, of which many well-known number theoretic results are special cases, including PNT. He arrives at an asymptotic relation that allows the replacement of certain discrete sums involving primes into corresponding differentiable…
Toward a dynamical model for prime numbers
Bonanno, Claudio; Mega, Mirko S.
2003-01-01
We show one possible dynamical approach to the study of the distribution of prime numbers. Our approach is based on two complexity methods, the Computable Information Content and the Entropy Information Gain, looking for analogies between the prime numbers and intermittency.
Carmichael Numbers on a Quantum Computer
Carlini, A.; Hosoya, A.
1999-01-01
We present a quantum probabilistic algorithm which tests with a polynomial computational complexity whether a given composite number is of the Carmichael type. We also suggest a quantum algorithm which could verify a conjecture by Pomerance, Selfridge and Wagstaff concerning the asymptotic distribution of Carmichael numbers smaller than a given integer.
Topological quantum numbers in the Hall effect
Avron, J. E.; Osadchy, D.; Seiler, R.
2003-01-01
Topological quantum numbers account for the precise quantization that occurs in the integer Hall effect. In this theory, Kubo's formula for the conductance acquires a topological interpretation in terms of Chern numbers and their non-commutative analog, the Fredholm Indices.
Quantum chromatic numbers via operator systems
Paulsen, Vern I.; Todorov, Ivan G.
2013-01-01
We define several new types of quantum chromatic numbers of a graph and characterise them in terms of operator system tensor products. We establish inequalities between these chromatic numbers and other parameters of graphs studied in the literature and exhibit a link between them and non-signalling correlation boxes.
On the abundance of the irrational numbers
Mueckenheim, W.
2003-01-01
Based upon the axiom of choice it is proved that the cardinality of the rational numbers is not less than the cardinality of the irrational numbers. This contradicts a main result of transfinite set theory and shows that the axiom of choice is invalid.
s-Numbers sequences for homogeneous polynomials
Caliskan, Erhan; Rueda, Pilar
2015-01-01
We extend the well known theory of $s$-numbers of linear operators to homogeneous polynomials defined between Banach spaces. Approximation, Kolmogorov and Gelfand numbers of polynomials are introduced and some well-known results of the linear and multilinear settings are obtained for homogeneous polynomials.
Generalized Fibonacci Numbers and Blackwell's Renewal Theorem
Christensen, Sören
2010-01-01
We investigate a connection between generalized Fibonacci numbers and renewal theory for stochastic processes. Using Blackwell's renewal theorem we find an approximation to the generalized Fibonacci numbers. With the help of error estimates in the renewal theorem we figure out an explicit representation.
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.
A Thermodynamic Classification of Real Numbers
Garrity, Thomas
2008-01-01
A new classification scheme for real numbers is given, motivated by ideas from statistical mechanics in general and work of Knauf and of Fiala and Kleban in particular. Critical for this classification of a real number will be the Diophantine properties of its continued fraction expansion.
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 them. As…
Search for lepton-family-number nonconservation
International Nuclear Information System (INIS)
A review of the status of lepton-family-number nonconservation is given. After a brief historical and theoretical discussion, a description of how experimental searches for lepton-family-number nonconservation are performed is presented. Finally, a summary of the results from past experiments and prospects for future experiments is given
Ground state number fluctuations of trapped particles
Tran, Muoi N.
This thesis encompasses a number of problems related to the number fluctuations from the ground state of ideal particles in different statistical ensembles. In the microcanonical ensemble most of these problems may be solved using number theory. Given an energy E, the well-known problem of finding the number of ways of distributing N bosons over the excited levels of a one-dimensional harmonic spectrum, for instance, is equivalent to the number of restricted partitions of E. As a result, the number fluctuation from the ground state in the microcanonical ensemble for this system may be found analytically. When the particles are fermions instead of bosons, however, it is difficult to calculate the exact ground state number fluctuation because the fermionic ground state consists of many levels. By breaking up the energy spectrum into particle and hole sectors, and mapping the problem onto the classic number partitioning theory, we formulate a method of calculating the particle number fluctuation from the ground state in the microcanonical ensemble for fermions. The same quantity is calculated for particles interacting via an inverse-square pairwise interaction in one dimension. In the canonical ensemble, an analytical formula for the ground state number fluctuation is obtained by using the mapping of this system onto a system of noninteracting particles obeying the Haldane-Wu exclusion statistics. In the microcanonical ensemble, however, the result can be obtained only for a limited set of values of the interacting strength parameter. Usually, for a discrete set of a mean-field single-particle quantum spectrum and in the microcanonical ensemble, there are many combinations of exciting particles from the ground state. The spectrum given by the logarithms of the prime number sequence, however, is a counterexample to this rule. Here, as a consequence of the fundamental theorem of arithmetic, there is a one-to-one correspondence between the microstate and the macrostate
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 ...
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.
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.
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...
A small world network of prime numbers
Chandra, Anjan Kumar; Dasgupta, Subinay
2005-11-01
According to Goldbach conjecture, any even number can be broken up as the sum of two prime numbers: n=p+q. We construct a network where each node is a prime number and corresponding to every even number n, we put a link between the component primes p and q. In most cases, an even number can be broken up in many ways, and then we chose one decomposition with a probability |p-q|α. Through computation of average shortest distance and clustering coefficient, we conclude that for α>-1.8 the network is of small world type and for α<-1.8 it is of regular type. We also present a theoretical justification for such behaviour.
Planar complex numbers in even n dimensions
Olariu, Silviu
2000-01-01
Planar commutative n-complex numbers of the form u=x_0+h_1x_1+h_2x_2+...+h_{n-1}x_{n-1} are introduced in an even number n of dimensions, the variables x_0,...,x_{n-1} being real numbers. The planar n-complex numbers can be described by the modulus d, by the amplitude \\rho, by n/2 azimuthal angles \\phi_k, and by n/2-1 planar angles \\psi_{k-1}. The exponential function of a planar n-complex number can be expanded in terms of the planar n-dimensional cosexponential functions f_{nk}, k=0,1,...,n...
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...
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 $n\\ge 5$.
Instanton number calculus on noncommutative R4
International Nuclear Information System (INIS)
In noncommutative spaces, it is unknown whether the Pontrjagin class gives integer, as well as, the relation between the instanton number and Pontrjagin class is not clear. Here we define 'Instanton number' by the size of Bα in the ADHM construction. We show the analytical derivation of the noncommutative U(1) instanton number as an integral of Pontrjagin class (instanton charge) with the Fock space representation. Our approach is for the arbitrary converge noncommutative U(1) instanton solution, and is based on the converge condition and the anti-self-dual (ASD) equation itself. We give the Stokes' theorem for the number operator representation. The Stokes' theorem on the noncommutative space shows that instanton charge is given by some boundary sum. Using the ASD conditions, we conclude that the instanton charge is equivalent to the instanton number. (author)
Ramsey numbers and adiabatic quantum computing.
Gaitan, Frank; Clark, Lane
2012-01-01
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.
Bit recycling for scaling random number generators
Mennucci, Andrea C G
2010-01-01
Many Random Number Generators (RNG) are available nowadays; they are divided in two categories, hardware RNG, that provide "true" random numbers, and algorithmic RNG, that generate pseudo random numbers (PRNG). Both types usually generate random numbers (X_n) as independent uniform samples in a range 0...2^b-1, with b = 8, 16, 32 or b = 64. In applications, it is instead sometimes desirable to draw random numbers as independent uniform samples (Y_n) in a range 1, . . . M, where moreover M may change between drawings. Transforming the sequence (X_n) to (Y_n) is sometimes known as scaling. We discuss different methods for scaling the RNG, both in term of mathematical efficiency and of computational speed.
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.
Schneider, Michael; Grabner, Roland H.; Paetsch, Jennifer
2009-01-01
As indicated by the distance effect and the spatial-numerical association of response codes (SNARC) effect, natural numbers are mentally represented on a number line. Purportedly, this number line underlies children's number sense, which supports the acquisition of more advanced mathematical competencies. In 3 studies with a total of 429 fifth and…
Zooming in and out from the Mental Number Line: Evidence for a Number Range Effect
Pinhas, Michal; Pothos, Emmanuel M.; Tzelgov, Joseph
2013-01-01
The representation of numbers is commonly viewed as an ordered continuum of magnitudes, referred to as the "mental number line." Previous work has repeatedly shown that number representations evoked by a given task can be easily altered, yielding an ongoing discussion about the basic properties of the mental number line and how malleable…
Xu, Jing; Fan, Yi-Zheng; Tan, Ying-Ying
2014-01-01
In this paper we characterize the unique graph whose algebraic connectivity is minimum among all connected graphs with given order and fixed matching number or edge covering number, and present two lower bounds for the algebraic connectivity in terms of the matching number or edge covering number.
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…
Predicting landfalling hurricane numbers from basin hurricane numbers: basic statistical analysis
Laepple, T; Penzer, J; Bellone, E; Nzerem, K; Laepple, Thomas; Jewson, Stephen; Penzer, Jeremy; Bellone, Enrica; Nzerem, Kechi
2007-01-01
One possible method for predicting landfalling hurricane numbers is to first predict the number of hurricanes in the basin and then convert that prediction to a prediction of landfalling hurricane numbers using an estimated proportion. Should this work better than just predicting landfalling hurricane numbers directly? We perform a basic statistical analysis of this question in the context of a simple abstract model.
Theory of analogous force on number sets
International Nuclear Information System (INIS)
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 yields 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. (author)
Jewson, Stephen; Laepple, Thomas; O'Shay, Adam; Penzer, Jeremy; Bellone, Enrica; Nzerem, Kechi
2007-01-01
One possible method for predicting landfalling hurricane numbers is to first predict the number of hurricanes in the basin and then convert that prediction to a prediction of landfalling hurricane numbers using an estimated proportion. Should this work better than just predicting landfalling hurricane numbers directly? We perform a basic statistical analysis of this question in the context of a simple abstract model, and convert some previous predictions of basin numbers into landfalling numb...
Carmichael number variable relations: three-prime Carmichael numbers up to 10^24
Chick, J. M.
2007-01-01
Bounds and other relations involving variables connected with Carmichael numbers are reviewed and extended. Families of numbers or individual numbers attaining or approaching these bounds are given. A new algorithm for finding three-prime Carmichael numbers is described, with its implementation up to $10^{24}$. Statistics relevant to the distribution of three-prime Carmichael numbers are given, with particular reference to the conjecture of Granville and Pomerance in [A.Granville and C.Pomera...
DISTRIBUTION OF PRIME NUMBERS. ALGORITHM OF TWINS NUMBERS AND THEIR INFINITE
Chermidov S. I.
2015-01-01
In the article on the basis of numbers of the specific form, where the parameter elements, which form a semigroup under multiplication we have presented a method for determination and distribution of composite numbers and the prime numbers, and accurate calculation of the values of pi in the interval from 1 to N. We present a new algorithm for the distribution of primes. We have reached the law of distribution parameters of composite numbers and prime numbers (Distribution of the parameters o...
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.
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.
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.
The Power of Numbers in Global Governance
DEFF Research Database (Denmark)
Krause Hansen, Hans; Mühlen-Schulte, Arthur
2012-01-01
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...
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.
Critical points and number of master integrals
Lee, Roman N
2013-01-01
We consider the question about the number of master integrals for a multiloop Feynman diagram. We show that, for a given set of denominators, this number is totally determined by the critical points of the polynomials entering either of the two representations: the parametric representation and the Baikov representation. In particular, for the parametric representation the corresponding polynomial is just the sum of Symanzik polynomials. The relevant topological invariant is the sum of the Milnor numbers of the proper critical points. We present a Mathematica package Mint to automatize the counting of the master integrals.
Ramsey numbers and adiabatic quantum computing
Gaitan, Frank; Clark, Lane
2011-01-01
The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers $R(m,n)$ with $m,n\\geq 3$, 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 correctl...
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.
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 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 $n\\ge 2$.
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
Chapter 7. Morphology: Numbers and Numerals
Nesset, Tore
2015-01-01
Numbers are very often rendered as letters in medieval texts. Only occasionally you encounter numbers written out, so that we can see how they were pronounced and inflected. It is nevertheless worthwhile to explore the Common Slavic and Old Rusian number systems, because they provide historical explanations of many idiosyncracies and exceptions you have struggled with in Modern Russian. Have you ever wondered why два, три and четыре combine with nouns in the genitive singular? And did you kno...
New feature for an old large number
International Nuclear Information System (INIS)
A new context for the appearance of the Eddington number (1039), which is due to the examination of elastic scattering of scalar particles (ΠK → ΠK) non-minimally coupled to gravity, is presented. (author)
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......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 combines physical interaction, learning, and immediate feedback. Speakmath supports the children’s understanding of place value in the sense that it allows them to experiment and create large numbers. Surprisingly the children found it very fun to express very large numbers, and also made smalls contests...
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.
Medicare Managed Care: Numbers and Trends
Zarabozo, Carlos; Taylor, Charles(8 Cherryl House, Seymour Gardens, Sutton Coldfield, West Midlands, B74 4ST, U.K.); Hicks, Jarret
1996-01-01
This article captures some key trends in Medicare managed care. The figures which accompany this article explore, among other issues: enrollment; numbers of participating plans; demographic characteristics such as geographic location, age, and income; and premium and benefit comparisons.
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)
Copy number variation across European populations.
Directory of Open Access Journals (Sweden)
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.
The abc-conjecture for Algebraic Numbers
Institute of Scientific and Technical Information of China (English)
Jerzy BROWKIN
2006-01-01
The abc-conjecture for the ring of integers states that, for every ε＞ 0 and every triple of relatively prime nonzero integers (a, b, c) satisfying a + b = c, we have max(|a|, |b|, |c|) ≤ rad(abc)1+ε with a finite number of exceptions. Here the radical rad(m) is the product of all distinct prime factors of m.In the present paper we propose an abc-conjecture for the field of all algebraic numbers. It is based on the definition of the radical (in Section 1) and of the height (in Section 2) of an algebraic number.From this abc-conjecture we deduce some versions of Fermat's last theorem for the field of all algebraic numbers, and we discuss from this point of view known results on solutions of Fermat's equation in fields of small degrees over Q.
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...
Arabic Alphabet and Numbers Sign Language Recognition
Directory of Open Access Journals (Sweden)
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.
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.
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....
Rhizobial gibberellin negatively regulates host nodule number.
Tatsukami, Yohei; Ueda, Mitsuyoshi
2016-01-01
In legume-rhizobia symbiosis, the nodule number is controlled to ensure optimal growth of the host. In Lotus japonicus, the nodule number has been considered to be tightly regulated by host-derived phytohormones and glycopeptides. However, we have discovered a symbiont-derived phytohormonal regulation of nodule number in Mesorhizobium loti. In this study, we found that M. loti synthesized gibberellic acid (GA) under symbiosis. Hosts inoculated with a GA-synthesis-deficient M. loti mutant formed more nodules than those inoculated with the wild-type form at four weeks post inoculation, indicating that GA from already-incorporated rhizobia prevents new nodule formation. Interestingly, the genes for GA synthesis are only found in rhizobial species that inhabit determinate nodules. Our findings suggest that the already-incorporated rhizobia perform GA-associated negative regulation of nodule number to prevent delayed infection by other rhizobia. PMID:27307029
Factorization numbers of finite abelian groups
Mohammad Farrokhi Derakhshandeh Ghouchan
2013-01-01
The number of factorizations of a finite abelian group as the product of two subgroups is computed in two different ways and a combinatorial identity involving Gaussian binomial coefficients is presented.
Factorization numbers of finite abelian groups
Directory of Open Access Journals (Sweden)
Mohammad Farrokhi Derakhshandeh Ghouchan
2013-06-01
Full Text Available The number of factorizations of a finite abelian group as the product of two subgroups is computed in two different ways and a combinatorial identity involving Gaussian binomial coefficients is presented.
Character Sums Over The Prime Numbers
Carella, N. A.
2012-01-01
A few elementary estimates of a basic character sum over the prime numbers are derived here. These estimates are nontrivial for character sums modulo large q. In addition, an omega result for character sums over the primes is also included.
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.
Positional codes of complex numbers and vectors
Solomon, I.
2008-01-01
A little-known theory of positional coding of complex numbers and vectors is described this theory may be used for the development of specialized processors. The theory is supplemented by numerous examples.
Bone Mass Measurement: What the Numbers Mean
... supported by your browser. Home Bone Basics Bone Mass Measurement: What the Numbers Mean Publication available in: ... been one or more osteoporotic fractures. Low Bone Mass Versus Osteoporosis The information provided by a BMD ...
Generation of Random Numbers by Micromechanism
Mita, Makoto; Toshiyoshi, Hiroshi; Ataka, Manabu; Fujita, Hiroyuki
We have successfully developed a novel micromechanism of random number generator (RNG) by using the silicon micromachining technique. The MEM(Micro Electro Mechanical)RNG produce a series of random numbers by using the pull-in instability of electrostatic actuation operated with a typical dc 150 volt. The MEM RNG is made by the deep reactive ion etching of a silicon-on-insulator(SOI) wafer, and is very small compared with the conventional RNG hardware based on the randomness of thermal noise or isotope radiation. Quality of randomness has been experimentally confirmed by the self-correlation study of the generated series of numbers. The MEM RNG proposed here would be a true random number generation, which is needed for the highly secured encryption system of today’s information technology.
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.
Colton, Simon; Dennis, Louise Abigail
2002-01-01
We present the NumbersWithNames program which performs data-mining on the Encyclopedia of Integer Sequences to find interesting conjectures in number theory. The program forms conjectures by finding empirical relationships between a sequence chosen by the user and those in the Encyclopedia. Furthermore, it transforms the chosen sequence into another set of sequences about which conjectures can also be formed. Finally, the program prunes and sorts the conjectures so that themost plausible o...
Characteristic Numbers of Matrix Lie Algebras
Zhang, Yu-Feng; Fan, En-Gui
2008-04-01
A notion of characteristic number of matrix Lie algebras is defined, which is devoted to distinguishing various Lie algebras that are used to generate integrable couplings of soliton equations. That is, the exact classification of the matrix Lie algebras by using computational formulas is given. Here the characteristic numbers also describe the relations between soliton solutions of the stationary zero curvature equations expressed by various Lie algebras.
Characteristic Numbers of Matrix Lie Algebras
Institute of Scientific and Technical Information of China (English)
QU Chang-Zheng; ZHANG Yu-Feng; LI Yan-Yan; FAN En-Gui
2008-01-01
A notion of characteristic number of matrix Lie algebras is defined, which is devoted to distinguishing various Lie Mgebras that ～re used to generate integrable couplings of soliton equations. That is, the exact classification of the matrix Lie algebras by using computational formulas is given. Here the characteristic numbers also describe the relations between soliton solutions of the stationary zero curvature equations expressed by various Lie algebras.
Algebraic independence of p-adic numbers
Nesterenko, Yu V.
2008-06-01
We prove lower bounds for the transcendence degree of fields generated by values of the p-adic exponential function. In particular, we estimate the transcendence degree of the field \\mathbb Q(e^{\\alpha_1},\\dots,e^{\\alpha_d}), where \\alpha_1,\\dots,\\alpha_d are algebraic (over the field of rational numbers) p-adic numbers that form a basis of a finite extension of \\mathbb Q.
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 ...
Factorization of numbers with physical systems
Merkel, Wolfgang
2007-01-01
In the present thesis we approach the factorization problem with a combination of quantum physics and aspects of number theory. The key to our approach is based on Gauss sums which are central to number theory. We take advantage of the cyclic properties of Gauss sums. The main idea consists in regarding a Gauss sum to arise from the superposition of quantum paths which are weighted by quadratic phase factors. Thus our schemes solely base on interference. We present three quantum optical rea...
Virtual Betti numbers of real algebraic varieties
McCrory, Clint; Parusinski, Adam
2002-01-01
The weak factorization theorem for birational maps is used to prove that for all nonnegative i the ith mod 2 Betti number of compact nonsingular real algebraic varieties has a unique extension to a "virtual Betti number" beta_i defined for all real algebraic varieties, such that if Y is a closed subvariety of X, then beta_i(X) = beta_i(X\\Y) + beta_i(Y).
Hyperbolic complex numbers in two dimensions
Olariu, Silviu
2000-01-01
A system of commutative hyperbolic complex numbers in 2 dimensions is studied in this paper. Exponential and trigonometric forms are obtained for these hyperbolic twocomplex numbers. Expressions are given for the elementary functions of hyperbolic twocomplex variable. The functions of a hyperbolic twocomplex variable which are defined by power series are analytic. Relations of equality exist between partial derivatives of the real components a function of a hyperbolic twocomplex variable. The...
Multiperfect Numbers in Certain Quadratic Rings
Defant, Colin
2015-01-01
Using an extension of the abundancy index to imaginary quadratic rings that are unique factorization domains, we investigate what we call $n$-powerfully $t$-perfect numbers in these rings. This definition serves to extend the concept of multiperfect numbers that have been defined and studied in the integers. At the end of the paper, as well as at various points throughout the paper, we point to some potential areas for further research.
The number and probability of canalizing functions
Just, Winfried; Shmulevich, Ilya; Konvalina, John
2003-01-01
Canalizing functions have important applications in physics and biology. For example, they represent a mechanism capable of stabilizing chaotic behavior in Boolean network models of discrete dynamical systems. When comparing the class of canalizing functions to other classes of functions with respect to their evolutionary plausibility as emergent control rules in genetic regulatory systems, it is informative to know the number of canalizing functions with a given number of input variables. Th...
Bethe's quantum numbers and rigged configurations
Kirillov, Anatol N.; Sakamoto, Reiho
2016-01-01
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).
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
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.
On the Number of 2-SAT Functions
Ilinca, Liviu; 10.1017/S096354830900995X
2010-01-01
We give an alternative proof of a conjecture of Bollob\\'as, Brightwell and Leader, first proved by Peter Allen, stating that the number of boolean functions definable by 2-SAT formulae is $(1+o(1))2^{\\binom{n+1}{2}}$. One step in the proof determines the asymptotics of the number of "odd-blue-triangle-free" graphs on $n$ vertices.
An algorithm for multipication of Kaluza numbers
Cariow, Aleksandr; Cariowa, Galina; Łentek, Rafał
2015-01-01
This paper presents the derivation of a new algorithm for multiplying of two Kaluza numbers. Performing this operation directly requires 1024 real multiplications and 992 real additions. The proposed algorithm can compute the same result with only 512 real multiplications and 576 real additions. The derivation of our algorithm is based on utilizing the fact that multiplication of two Kaluza numbers can be expressed as a matrixvector product. The matrix multiplicand that participates in the pr...
An algorithm for multiplication of Dirac numbers
Aleksandr Cariow; Galina Cariowa
2013-01-01
In this work a rationalized algorithm for Dirac numbers multiplication is presented. This algorithm has a low computational complexity feature and is well suited to parallelization of computations. The computation of two Dirac numbers product using the naïve method takes 256 real multiplications and 240 real additions, while the proposed algorithm can compute the same result in only 128 real multiplications and 160 real additions. During synthesis of the discussed algorithm we use the fact th...
Generalizations of Bernoulli numbers and polynomials
Qiu-Ming Luo; Bai-Ni Guo; Feng Qi; Lokenath Debnath
2003-01-01
The concepts of Bernoulli numbers Bn, Bernoulli polynomials Bn(x), and the generalized Bernoulli numbers Bn(a,b) are generalized to the one Bn(x;a,b,c) which is called the generalized Bernoulli polynomials depending on three positive real parameters. Numerous properties of these polynomials and some relationships between Bn, Bn(x), Bn(a,b), and Bn(x;a,b,c) are established.
Diophantine approximation and special Liouville numbers
Schleischitz, Johannes
2013-01-01
This paper introduces some methods to determine the simultaneous approximation constants of a class of well approximable numbers $\\zeta_{1},\\zeta_{2},...,\\zeta_{k}$. The approach relies on results on the connection between the set of all $s$-adic expansions ($s\\geq 2$) of $\\zeta_{1},\\zeta_{2},...,\\zeta_{k}$ and their associated approximation constants. As an application, explicit construction of real numbers $\\zeta_{1},\\zeta_{2},...,\\zeta_{k}$ with prescribed approximation properties are dedu...
Two-dimensional Einstein numbers and associativity
Gregor, Tomáš; Haluška, Ján
2013-01-01
In this paper, we deal with generalizations of real Einstein numbers to various spaces and dimensions. We search operations and their properties in generalized settings. Especially, we are interested in the generalized operation of hyperbolic addition to more-dimensional spaces, which is associative and commutative. We extend the theory to some abstract spaces, especially to Hilbert-like ones. Further, we bring two different two-dimensional generalizations of Einstein numbers and study proper...
ON CONJUGATES AND MODULII OF BICOMPLEX NUMBERS
Directory of Open Access Journals (Sweden)
JAISHREE
2012-06-01
Full Text Available The paper presents extensive use of complex pairs to develop the algebraic properties of bicomplex numbers and contains various aspects of finding the conjugates and modulii of bicomplex numbers.We discuss three types of conjugations and some specific modulii with complex and hyperbolic ranges. We also examine the impact of different conjugations on the principal ideals I1 and I2.
A monadic, functional implementation of real numbers
O'Connor, Russell
2006-01-01
Large scale real number computation is an essential ingredient in several modern mathematical proofs. Because such lengthy computations cannot be verified by hand, some mathematicians want to use software proof assistants to verify the correctness of these proofs. This paper develops a new implementation of the constructive real numbers and elementary functions for such proofs by using the monad properties of the completion operation on metric spaces. Bishop and Bridges's notion of regular se...
Factorization of the tenth Fermat number
Brent, Richard P.
We describe the complete factorization of the tenth Fermat number F_{10} by the elliptic curve method (ECM). F_{10} is a product of four prime factors with 8, 10, 40 and 252 decimal digits. The 40-digit factor was found after about 140 Mflop-years of computation. We also discuss the complete factorization of other Fermat numbers by ECM, and summarize the factorizations of F_5, ..., F_{11}.
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.
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 ...
40 CFR 86.113-07 - Fuel specifications.
2010-07-01
... Heavy-Duty Vehicles; Test Procedures § 86.113-07 Fuel specifications. Section 86.113-07 includes text... ASTM test method No. Type 2-D (i) Cetane Number D613 40-50 (ii) Cetane Index D976 40-50 (iii...) (293.3-332.2) (E) EP °F D86 610-690 ( °C) (321.1-365.6) (iv) Gravity °API D287 32-37 (v) Total...
Mining for Numbers. A Heuristic Approach to Some Prime Number Work
Tapson, Frank
1973-01-01
Whole numbers written in spiral or triangular patterns with spaces occupied by prime numbers blocked in produces interesting visual patterns. Described is a game based on these patterns that may be played at many different levels. (JP)
The distribution of prime numbers and associated problems in number theory
International Nuclear Information System (INIS)
Some problems in number theory, namely the gaps between consecutive primes, the distribution of primes in arithmetic progressions, Brun-Titchmarsh theorem, Fermat's last theorem, The Thue equation, the gaps between square-free numbers are discussed
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.
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.
Unpredictability and the transmission of numbers
Myers, John M.; Madjid, F. Hadi
2016-03-01
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 forth. In digital communications, the players are computers, and the required coordination involves unpredictably adjusting "live clocks" that step these computers through phases of a cycle. We show how this phasing, which we call logical synchronization, constrains number-carrying networks, and, if a spacetime manifold in invoked, put "stripes" on spacetime. Via its logically synchronized channels, a network of live clocks serves as a reference against which to locate events. Such a network in any case underpins a coordinate frame, and in some cases the direct use of a network can be tailored to investigate an unpredictable environment. Examples include explorations of gravitational variations near Earth.
2014-01-01
A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics, and theoretical physics. Here we show how one can obtain further interesting and (almost) serendipitous identities about certain finite or infinite series involving binomial coefficients, harmonic numbers...
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:…
de J. Lisle; S. De; E. Alba; A. Bullivant; J.J. Garcia-Ripoll; V. Lahtinen; J.K. Pachos
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 decompose
The concrete theory of numbers : Problem of simplicity of Fermat number-twins
Tarasov, Boris V.
2007-01-01
The problem of simplicity of Fermat number-twins $f_{n}^{\\pm}=2^{2^n}\\pm3$ is studied. The question for what $n$ numbers $f_{n}^{\\pm}$ are composite is investigated. The factor-identities for numbers of a kind $x^2 \\pm k $ are found.
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.
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.
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.