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Sample records for cetane number

  1. 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single compound cetane number data found in the scientific literature up until March 2014 as well as a number of unpublished values, most measured over the past decade at the National Renewable Energy Laboratory.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.

  2. 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.

  3. Cetane numbers of biodiesel and its components

    Science.gov (United States)

    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...

  4. 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.

  5. 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.

  6. Prediction of the cetane number of biodiesel using artificial neural networks and multiple linear regression

    International Nuclear Information System (INIS)

    Highlights: ► We obtained models for estimation of cetane number of biodiesel. ► Twenty-four neural networks using two topologies were evaluated. ► The best neural network for predict the cetane number was selected. ► The best accuracy was obtained for the selected neural network. - Abstract: Models for estimation of cetane number of biodiesel from their fatty acid methyl ester composition using multiple linear regression and artificial neural networks were obtained in this work. For the obtaining of models to predict the cetane number, an experimental data from literature reports that covers 48 and 15 biodiesels in the modeling-training step and validation step respectively were taken. Twenty-four neural networks using two topologies and different algorithms for the second training step were evaluated. The model obtained using multiple regression was compared with two other models from literature and it was able to predict cetane number with 89% of accuracy, observing one outlier. A model to predict cetane number using artificial neural network was obtained with better accuracy than 92% except one outlier. The best neural network to predict the cetane number was a backpropagation network (11:5:1) using the Levenberg–Marquardt algorithm for the second step of the networks training and showing R = 0.9544 for the validation data.

  7. Detailed Chemical Kinetic Reaction Mechanisms for Primary Reference Fuels for Diesel Cetane Number and Spark-Ignition Octane Number

    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.

  8. 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

  9. Effect of Fuel Cetane Number on Multi-Cylinders Direct Injection Diesel Engine Performance and Exhaust Emissions

    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 fuel’s 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.

  10. Modeling study of oxygenated fuels on diesel combustion: Effects of oxygen concentration, cetane number and C/H ratio

    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

  11. Diesel with low sulfur content and high cetane number produced by two stages hydrotreating procedures; Diesel com baixos teores de enxofre e alto numero de cetano a partir de hidrotratamento em dois estagios

    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)

  12. Predicción del número de cetano de biocombustibles a partir de su composición de ácidos grasos//Cetane number estimation of biofuels from their fatty acid composition

    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

  13. Feasibility of using less viscous and lower cetane (LVLC) fuels in a diesel engine: A review

    KAUST Repository

    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.

  14. The Autoignition of iso-Cetane: Shock Tube Experiments and Kinetic Modeling

    Energy Technology Data Exchange (ETDEWEB)

    Oehlschlaeger, M A; Steinberg, J; Westbrook, C K; Pitz, W J

    2009-02-25

    Iso-cetane (2,2,4,4,6,8,8-heptamethylnonane, C{sub 16}H{sub 34}) is a highly branched alkane reference compound for determining cetane ratings. It is also a candidate branched alkane representative in surrogate mixtures for diesel and jet fuels. Here new experiments and kinetic modeling results are presented for the autoignition of iso-cetane at elevated temperatures and pressures relevant to combustion in internal combustion engines. Ignition delay time measurements were made in reflected shock experiments in a heated shock tube for {Phi} = 0.5 and 1.0 iso-cetane/air mixtures at temperatures ranging from 953 to 1347 K and pressures from 8 to 47 atm. Ignition delay times were measured using electronically excited OH emission, monitored through the shock tube end wall, and piezoelectric pressure transducer measurements, made at side wall locations. A new kinetic mechanism for the description of the oxidation of iso-cetane is presented that is developed based on a previous mechanism for iso-octane. Computed results from the mechanism are found in good agreement with the experimental measurements. To our knowledge, the ignition time measurements and detailed kinetic mechanism for isocetane presented here are the first of their kind.

  15. Revision of the equation Calculated Cetane Index for the characteristics of diesel commercialized in the Parana-Brazil; Revisao da equacao de Calculo do Indice de Cetano para as caracteristicas do diesel comercializado no Parana

    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)

  16. Models for the prediction of the cetane index of biofuels obtained from different vegetable oils using their fatty acid composition

    International Nuclear Information System (INIS)

    The objective of the present work is to obtain a physical-mathematical model that establishes a relationship between the cetane index of biofuels obtained from different vegetable oils and its composition of essential fatty acid. This model is based on experimental data obtained by the authors of the present work and an experimental data reported by different extracted authors of indexed databases. The adjustment of the coefficients of the model is based on the obtaining of residual minima in the capacity of prediction of the model. Starting from these results it is established a very useful tool for the determination of such an important parameter for the fuel diesel as it is the cetane index obtained from an analysis of chemical composition and not obtained from tests in engines banks, to save time and economic resources. (author)

  17. Advance in hydroprocessing technology of manufacturing diesel with high cetane number from vegetable oil%植物油加氢制备高十六烷值柴油组分研究进展

    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.

  18. Predicción del número de cetano de biocombustibles a partir de su composición de ácidos grasos//Cetane number estimation of biofuels from their fatty acid composition

    OpenAIRE

    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...

  19. Skyscraper Numbers

    OpenAIRE

    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.

  20. 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.

  1. Pentagonal numbers

    OpenAIRE

    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.

  2. Leftist Numbers

    Science.gov (United States)

    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.

  3. Proth 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.

  4. Sagan numbers

    OpenAIRE

    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.

  5. Fibonacci numbers

    CERN Document Server

    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

  6. Number names and number understanding

    DEFF Research Database (Denmark)

    Ejersbo, Lisser Rye; Misfeldt, Morten

    2014-01-01

    through using mathematical names for the numbers such as one-ten-one for 11 and five-ten-six for 56. The project combines the renaming of numbers with supporting the teaching with the new number names. Our hypothesis is that Danish children have more difficulties learning and working with numbers, because...... the Danish number names are more complicated than in other languages. Keywords: A research project in grade 0 and 1th in a Danish school, Base-10 system, two-digit number names, semiotic, cognitive perspectives....

  7. 燃料セタン価がディーゼル噴霧の着火に及ぼす影響

    OpenAIRE

    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 ...

  8. Eulerian numbers

    CERN Document Server

    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, ...

  9. Index Numbers

    OpenAIRE

    Diewert, Erwin

    2007-01-01

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

  10. 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....

  11. Chocolate Numbers

    OpenAIRE

    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...

  12. Number theory

    CERN Document Server

    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

  13. Magic Numbers

    Institute of Scientific and Technical Information of China (English)

    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.

  14. Number Guessing

    Science.gov (United States)

    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…

  15. Number Theories

    CERN Document Server

    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.

  16. Number of Compositions and Convolved Fibonacci numbers

    OpenAIRE

    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...

  17. Diamond Fuzzy Number

    OpenAIRE

    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...

  18. On Legendre numbers

    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.

  19. Trivializing number of knots

    OpenAIRE

    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.

  20. Luhn Prime Numbers

    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.

  1. LUHN PRIME NUMBERS

    OpenAIRE

    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.

  2. Co-Hydroprocessing of Soybean Oil and Fluid Catalytic Cracking Diesel Oil for Producing Clean Diesel Oil with High Cetane Number%流化催化裂化柴油和豆油耦合加氢生产高十六烷值清洁柴油

    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.

  3. Enriching Number Knowledge

    Science.gov (United States)

    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…

  4. Predicting Lotto Numbers

    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...

  5. δ-FIBONACCI NUMBERS

    OpenAIRE

    Damian Slota; Roman Witula

    2009-01-01

    The scope of the paper is the definition and discussion of the polynomial generalizations of the {sc Fibonacci} numbers called here $delta$-{sc Fibonacci} numbers. Many special identities and interesting relations for these new numbers are presented. Also, different connections between $delta$-{sc Fibonacci} numbers and {sc Fibonacci} and {sc Lucas} numbersare proven in this paper.

  6. Tropical Real Hurwitz numbers

    OpenAIRE

    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).

  7. δ-FIBONACCI NUMBERS

    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.

  8. Introduction to number theory

    CERN Document Server

    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.

  9. Building Numbers from Primes

    Science.gov (United States)

    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…

  10. Distribution of prime numbers

    OpenAIRE

    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.

  11. The Eudoxus Real Numbers

    OpenAIRE

    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...

  12. Algebraic number theory

    CERN Document Server

    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...

  13. p-adic numbers

    OpenAIRE

    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...

  14. History of Catalan numbers

    OpenAIRE

    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.

  15. About Bernoulli's Numbers

    OpenAIRE

    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.

  16. Fibonacci Numbers and Identities

    OpenAIRE

    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.

  17. Number Relationships in Preschool

    Science.gov (United States)

    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…

  18. Estimating Large Numbers

    Science.gov (United States)

    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…

  19. Survey on fusible numbers

    CERN Document Server

    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.

  20. Sum-Difference Numbers

    Science.gov (United States)

    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…

  1. Analytic number theory

    CERN Document Server

    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

  2. Discovery: Prime Numbers

    Science.gov (United States)

    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…

  3. Applied number theory

    CERN Document Server

    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...

  4. Number in Dinka

    DEFF Research Database (Denmark)

    Andersen, Torben

    In Dinka, a Western Nilotic language, nouns are inflected for number and distinguish between singular and plural. The number inflection is not expressed by affixation, but by phonological alternations in the root and in such a way that the number is not directly observable, but only detectable...... through agreement. With simple native nouns, which are typically monosyllables, the number inflection is unpredictable and irregular, but some fairly common singular-plural patterns can be established, as seen in the Agar dialect. There is strong internal and external evidence that originally, many nouns...... had a marked singular and an unmarked plural. Synchronically, however, the singular is arguably the basic member of the number category as revealed by the use of the two numbers. In addition, some nouns have a collective form, which is grammatically singular. Number also plays a role in the...

  5. CATALYSTS FOR HIGH CETANE ETHERS AS DIESEL FUELS

    Energy Technology Data Exchange (ETDEWEB)

    Kamil Klier; Richard G. Herman; Heock-Hoi Kwon; James G. C. Shen; Qisheng Ma; Robert A. Hunsicker; Andrew P. Butler; Scott J. Bollinger

    2003-03-01

    A tungstena-zirconia (WZ) catalyst has been investigated for coupling methanol and isobutanol to unsymmetrical ethers, i.e. methyl isobutyl ether (MIBE) and compared with earlier studied sulfated-zirconia (SZ) and Nafion-H catalysts. In all cases, the ether synthesis mechanism is a dual site S{sub N}2 process involving competitive adsorption of reactants on proximal acid sites. At low reaction temperatures, methylisobutylether (MIBE) is the predominant product. However, at temperatures >135 C the WZ catalyst is very good for dehydration of isobutanol to isobutene. The surface acid sites of the WZ catalyst and a Nafion-H catalyst were diagnosed by high resolution X-ray photoelectron spectroscopy (XPS) of N 1s shifts after adsorption of amines. Using pyridine, ethylenediamine, and triethylamine, it is shown that WZ has heterogeneous strong Broensted acid sites. Theoretical study located the transition state of the alcohol coupling reaction on proximal Broensted acid sites and accounted well for XPS core-level shifts upon surface acid-base interactions. While computations have not been carried out with WZ, it is shown that the SZ catalyst is a slightly stronger acid than CF{sub 3}SO{sub 3}H (a model for Nafion-H) by 1.3-1.4 kcal/mol. A novel sulfated zirconia catalyst having proximal strong Broensted acid sites was synthesized and shown to have significantly enhanced activity and high selectivity in producing MIBE or isobutene from methanol/isobutanol mixtures. The catalyst was prepared by anchoring 1,2-ethanediol bis(hydrogen sulfate) salt precursor onto zirconium hydroxide, followed by calcination to remove the -(CH{sub 2}CH{sub 2})- bridging residues.

  6. Signed Numbers Conversions

    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.

  7. Safety-in-numbers

    DEFF Research Database (Denmark)

    Elvik, Rune; Bjørnskau, Torkel

    2016-01-01

    This paper presents a systematic review and meta-analysis of studies that have estimated the relationship between the number of accidents involving motor vehicles and cyclists or pedestrians and the volume of motor vehicles, cyclists and pedestrians. A key objective of most of these studies has...... 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...... regression coefficients that show how the number of accidents depends on the conflicting flows (pedestrians, cyclists, motor vehicles), as well as (in some of the models) other factors that influence the number of accidents. Meta-analysis of regression coefficients involves methodological problems, which...

  8. Quantum Random Number Generators

    OpenAIRE

    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...

  9. New magic numbers

    OpenAIRE

    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...

  10. Beyond the Number Domain

    OpenAIRE

    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 ...

  11. Divisibility of characteristic numbers

    OpenAIRE

    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.

  12. Predicting Lotto 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...

  13. Multispecies quantum Hurwitz numbers

    OpenAIRE

    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.

  14. The Number Story.

    Science.gov (United States)

    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…

  15. The Fibonacci Numbers.

    Science.gov (United States)

    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)

  16. On arithmetic numbers

    OpenAIRE

    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.

  17. First Graders' Number Knowledge

    Science.gov (United States)

    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…

  18. Predicting Lotto Numbers

    NARCIS (Netherlands)

    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

  19. Predicting Lotto Numbers

    DEFF Research Database (Denmark)

    Suetens, Sigrid; Galbo-Jørgensen, Claus B.; Tyran, Jean-Robert Karl

    2016-01-01

    We investigate the ‘law of small numbers’ using a data set on lotto gambling that allows us to measure players’ reactions to draws. While most players pick the same set of numbers week after week, we find that those who do change react on average as predicted by the law of small numbers as...

  20. Avogadro's Number Ferromagnetically

    Science.gov (United States)

    Houari, Ahmed

    2010-01-01

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

  1. Pisot Numbers and Primes

    CERN Document Server

    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.

  2. Numbers in Action

    Science.gov (United States)

    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

  3. Numbers and computers

    CERN Document Server

    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

  4. Elementary theory of numbers

    CERN Document Server

    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

  5. Advanced number theory

    CERN Document Server

    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

  6. Mersenne Numbers: consolidated results

    OpenAIRE

    Haworth, Guy McCrossan; Holmes, Steve; Hunt, David; Lake, Tom; Reddaway, Stewart

    1986-01-01

    This document provides and comments on the results of the Lucas-Lehmer testing and/or partial factorisation of all Mersenne Numbers Mp = 2^p-1 where p is prime and less than 100,000. Previous computations have either been confirmed or corrected. The LLT computations on the ICL DAP is the first implementation of Fast-Fermat-Number-Transform multiplication in connection with Mersenne Number testing. This paper championed the disciplines of systematically testing the Mp, and of double-so...

  7. Fundamentals of number theory

    CERN Document Server

    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

  8. Asymptotic Hurwitz numbers

    OpenAIRE

    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...

  9. Brief history of numbers

    CERN Document Server

    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

  10. Professor Stewart's incredible numbers

    CERN Document Server

    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,

  11. Elementary number theory

    CERN Document Server

    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

  12. On powerful numbers

    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

  13. Projecting Livestock Numbers

    OpenAIRE

    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...

  14. The emergence of number

    CERN Document Server

    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

  15. Predicting Lotto Numbers

    OpenAIRE

    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...

  16. Algebraic number theory

    CERN Document Server

    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

  17. Drawing a random number

    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...... is to generate highly uniform multidimensional draws, which are highly relevant for todays traffic models. This paper shows among others combined shuffling and scrambling seems needless, that scrambling gives the lowest correlation and that there are detectable differences between random numbers...

  18. SEVIS By the Numbers

    Data.gov (United States)

    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...

  19. Genetics by the Numbers

    Science.gov (United States)

    ... 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 ...

  20. Basic analytic number theory

    OpenAIRE

    Farmer, David W.

    2004-01-01

    Comment: 11 pages, to appear in the proceedings of the school ``Recent Perspectives in Random Matrix Theory and Number Theory'' held at the Isaac Newton Institute, April 2004. Added appendix on big-O and

  1. 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.

  2. Logo and Negative Numbers.

    Science.gov (United States)

    Strawn, Candace A.

    1998-01-01

    Describes LOGO's turtle graphics capabilities based on a sixth-grade classroom's activities with negative numbers and Logo programming. A sidebar explains LOGO and offers suggestions to teachers for using LOGO effectively. (LRW)

  3. Solar Indices - Sunspot Numbers

    Data.gov (United States)

    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...

  4. Really big numbers

    CERN Document Server

    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...

  5. Detecting ''secret'' quantum numbers

    International Nuclear Information System (INIS)

    For a general quantum mechanical system undergoing a process, it is shown that one can tell from measurements on this system whether or not the system is characterized by quantum numbers the existence of which is unknown to the observer, even though the detection equipment used by the observer is unable to distinguish among the various possible values of the ''secret'' quantum number and hence always averages over them

  6. Methods explained: Index numbers

    OpenAIRE

    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...

  7. Fibonacci's Forgotten Number

    Science.gov (United States)

    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…

  8. CT number definition

    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.

  9. Report number codes

    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

  10. Report number codes

    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.

  11. 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.

  12. The LHC in numbers

    CERN Multimedia

    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...

  13. CONFUSION WITH TELEPHONE NUMBERS

    CERN Document Server

    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

  14. CONFUSION WITH TELEPHONE NUMBERS

    CERN Document Server

    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  

  15. Geometry of numbers

    CERN Document Server

    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

  16. Algebraic theory of numbers

    CERN Document Server

    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

  17. Perfect numbers and groups

    OpenAIRE

    Leinster, Tom

    2001-01-01

    A number is perfect if it is the sum of its proper divisors; here we call a finite group `perfect' if its order is the sum of the orders of its proper normal subgroups. (This conflicts with standard terminology but confusion should not arise.) The notion of perfect group generalizes that of perfect number, since a cyclic group is perfect exactly when its order is perfect. We show that, in fact, the only abelian perfect groups are the cyclic ones, and exhibit some non-abelian perfect groups of...

  18. Baryon Number Violation

    CERN Document Server

    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.

  19. Playing the Numbers

    Science.gov (United States)

    Doyle, William R.

    2010-01-01

    Some say that the educators now have a gender-stratified system of higher education, with nearly 60 percent of all undergraduates being women and fewer men attending each year. The battle for gender equity for women in higher education has been a long and contentious one. In the decades since, increasing numbers of women have gone to college, to…

  20. Introducing Complex Numbers

    Science.gov (United States)

    Trudgian, Timothy

    2009-01-01

    One of the difficulties in any teaching of mathematics is to bridge the divide between the abstract and the intuitive. Throughout school one encounters increasingly abstract notions, which are more and more difficult to relate to everyday experiences. This article examines a familiar approach to thinking about negative numbers, that is an…

  1. The magic of numbers

    CERN Document Server

    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

  2. Safety in glomerular numbers.

    NARCIS (Netherlands)

    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

  3. Are Occupation Numbers Observable?

    OpenAIRE

    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.

  4. The Net by Numbers.

    Science.gov (United States)

    McMurdo, George

    1996-01-01

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

  5. The numbers game

    Directory of Open Access Journals (Sweden)

    Oli Brown

    2008-10-01

    Full Text Available Estimates of the potential number of ‘climate changemigrants’ vary hugely. In order to persuade policymakers ofthe need to act and to provide a sound basis for appropriateresponses, there is an urgent need for better analysis, betterdata and better predictions.

  6. ALARA notes, Number 8

    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

  7. Two Symmetric Properties of Mersenne Numbers and Fermat Numbers

    OpenAIRE

    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.

  8. Calling Dunbar's Numbers

    CERN Document Server

    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.

  9. Numbers and sets

    Directory of Open Access Journals (Sweden)

    Marco Ruffino

    2001-12-01

    Full Text Available In this paper I discuss the intuition behind Frege's and Russell's definitions of numbers as sets, as well as Benacerraf's criticism of it. I argue that Benacerraf's argument is not as strong as some philosophers tend to think. Moreover, I examine an alternative to the Fregean-Russellian definition of numbers proposed by Maddy, and point out some problems faced by it.Neste artigo discuto a intuição subjacente à definição de n∨meros como conjuntos proposta por Frege e Russell, assim como a crítica de Benacerraf a esta definição. Eu tento mostrar que o argumento de Benacerraf não é tão forte como alguns filósofos o tomaram. Adicionalmente, examino uma alternativa à definição de Frege e Russell proposta por Maddy, e indico algumas dificuldades encontrada pela mesma.

  10. Calling Dunbar's Numbers

    OpenAIRE

    MacCarron, Pádraig; Kaski, Kimmo; 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 ...

  11. Chromosome numbers in Bromeliaceae

    OpenAIRE

    2000-01-01

    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. u...

  12. Homoroot integer numbers

    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.

  13. Prime numbers -- your gems

    OpenAIRE

    Motohashi, Yoichi

    2005-01-01

    Prime numbers or primes are man's eternal treasures that have been cherished for several millennia, until today. As their academic ancestors in ancient Mesopotamia, many mathematicians are still trying hard to see primes better. I shall relate here a part of my impressions that I have gathered in a corner of my mind through my own research and excursions outside my profession. This is in essence a translation of my Japanese article that was prepared for my public talk at the general assembly ...

  14. Carlitz q-Bernoulli numbers and q-Stirling numbers

    OpenAIRE

    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.

  15. The number system

    CERN Document Server

    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

  16. Topics in number theory

    CERN Document Server

    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

  17. Cohomology of number fields

    CERN Document Server

    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

  18. Nomogram for sunspot numbers.

    Science.gov (United States)

    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.

  19. 7 CFR 29.9205 - Identification number (farm serial number).

    Science.gov (United States)

    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...

  20. Qubits from Number States and Bell Inequalities for Number Measurements

    OpenAIRE

    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.

  1. Lepton family number violation

    Energy Technology Data Exchange (ETDEWEB)

    Herczeg, P.

    1999-03-01

    At present there is evidence from neutrino oscillation searches that the neutrinos are in fact massive particles and that they mix. If confirmed, this would imply that the conservation of LFN is not exact. Lepton family number violation (LFNV) has been searched for with impressive sensitivities in many processes involving charged leptons. The present experimental limits on some of them (those which the author shall consider here) are shown in Table 1. These stringent limits are not inconsistent with the neutrino oscillation results since, given the experimental bounds on the masses of the known neutrinos and the neutrino mass squared differences required by the oscillation results, the effects of LFNV from neutrino mixing would be too small to be seen elsewhere (see Section 2). The purpose of experiments searching for LFNV involving the charged leptons is to probe the existence of other sources of LFNV. Such sources are present in many extensions of the SM. In this lecture the author shall discuss some of the possibilities, focusing on processes that require muon beams. Other LFNV processes, such as the decays of the kaons and of the {tau}, provide complementary information. In the next Section he shall consider some sources of LFNV that do not require an extension of the gauge group of the SM (the added leptons or Higgs bosons may of course originate from models with extended gauge groups). In Section 3 he discusses LFNV in left-right symmetric models. In Section 4 he considers LFNV in supersymmetric models, first in R-parity conserving supersymmetric grand unified models, and then in the minimal supersymmetric standard model with R-parity violation. The last section is a brief summary of the author`s conclusions.

  2. Lower Bound of Newton Number

    OpenAIRE

    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.

  3. 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

  4. Series of Reciprocal Triangular Numbers

    Science.gov (United States)

    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.

  5. Automatic Number Plate Recognition System

    OpenAIRE

    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...

  6. Construction of the real numbers

    OpenAIRE

    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...

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

    CERN Document Server

    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?

  8. Perfect numbers - a lower bound for an odd perfect number

    OpenAIRE

    Berdellima, Arian

    2011-01-01

    In this work we construct a lower bound for an odd perfect number in terms of the number of its distinct prime factors. We further generalize the formula for any natural number for which the number of its distinct prime factors is known.

  9. Cordial Languages and Cordial Numbers

    OpenAIRE

    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.

  10. 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.

  11. Representing Numbers: Prime and Irrational

    Science.gov (United States)

    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…

  12. 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

  13. THE RELATIONSHIP BETWEEN NUMBER NAMES AND NUMBER CONCEPTS

    DEFF Research Database (Denmark)

    Ejersbo, Lisser Rye; Misfeldt, Morten

    regularity or irregularity of number naming affects children’s formation of number concepts and arithmetic performance. We investigate this issue by reviewing relevant literature and undertaking a design research project addressing the specific irregularities of the Danish number names. In this project, a...... second, regular set of number names is introduced in primary school. The study’s findings suggest that the regularity of number names influences the development of number concepts and creates a positive impact on the understanding of the base-10 system....

  14. Prime numbers: periodicity, chaos, noise

    OpenAIRE

    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.

  15. Computational Complexity on Signed Numbers

    OpenAIRE

    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...

  16. Countability of the Real Numbers

    OpenAIRE

    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.

  17. Chromatic number of graphs and edge Folkman numbers

    OpenAIRE

    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.

  18. A Relation between Prime Numbers and Twin Prime Numbers

    OpenAIRE

    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.

  19. Multiple Bracket Function, Stirling Number, and Lah Number Identities

    OpenAIRE

    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.

  20. How Spencer Made Number: First Uses of the Number Words

    Science.gov (United States)

    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.…

  1. 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.

  2. The concrete theory of numbers: initial numbers and wonderful properties of numbers repunit

    OpenAIRE

    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.

  3. The method for converting numbers represented in a positional number system into the residue number system

    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

  4. Poison control center - emergency number

    Science.gov (United States)

    ... 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 ...

  5. Butterflies and topological quantum numbers

    OpenAIRE

    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.

  6. 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.

  7. Ethnolinguistic Peculiarities of Sacred Numbers

    Directory of Open Access Journals (Sweden)

    Nurgul Abdrazakova

    2012-11-01

    Full Text Available The article deals with ethnolinguistic peculiarities of sacred numbers in Kazakh and English languages, reflecting the spiritual life, traditions and customs. The authors examine the sacred numbers in fixed expressions compared languages.

  8. The theory of algebraic numbers

    CERN Document Server

    Pollard, Harry

    1975-01-01

    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.

  9. Higher-order Nielsen numbers

    OpenAIRE

    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...

  10. The status of Cantorian numbers

    OpenAIRE

    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...

  11. Periods and elementary real numbers

    OpenAIRE

    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...

  12. Distribution theory of algebraic numbers

    CERN Document Server

    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.

  13. Elementary number theory with programming

    CERN Document Server

    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

  14. The world of pentagonal numbers

    OpenAIRE

    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...

  15. Linear or Exponential Number Lines

    Science.gov (United States)

    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,…

  16. Random Numbers and Quantum Computers

    Science.gov (United States)

    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…

  17. Picard numbers of quintic surfaces

    OpenAIRE

    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.

  18. Data Compression with Prime Numbers

    OpenAIRE

    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.

  19. Tree domatic number in graphs

    OpenAIRE

    Xue-gang Chen

    2007-01-01

    A dominating set \\(S\\) in a graph \\(G\\) is a tree dominating set of \\(G\\) if the subgraph induced by \\(S\\) is a tree. The tree domatic number of \\(G\\) is the maximum number of pairwise disjoint tree dominating sets in \\(V(G)\\). First, some exact values of and sharp bounds for the tree domatic number are given. Then, we establish a sharp lower bound for the number of edges in a connected graph of given order and given tree domatic number, and we characterize the extremal graphs. Finally, we sh...

  20. 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.

  1. Children's mappings between number words and the approximate number system.

    Science.gov (United States)

    Odic, Darko; Le Corre, Mathieu; Halberda, Justin

    2015-05-01

    Humans can represent number either exactly--using their knowledge of exact numbers as supported by language, or approximately--using their approximate number system (ANS). Adults can map between these two systems--they can both translate from an approximate sense of the number of items in a brief visual display to a discrete number word estimate (i.e., ANS-to-Word), and can generate an approximation, for example by rapidly tapping, when provided with an exact verbal number (i.e., Word-to-ANS). Here we ask how these mappings are initially formed and whether one mapping direction may become functional before the other during development. In two experiments, we gave 2-5 year old children both an ANS-to-Word task, where they had to give a verbal number response to an approximate presentation (i.e., after seeing rapidly flashed dots, or watching rapid hand taps), and a Word-to-ANS task, where they had to generate an approximate response to a verbal number request (i.e., rapidly tapping after hearing a number word). Replicating previous results, children did not successfully generate numerically appropriate verbal responses in the ANS-to-Word task until after 4 years of age--well after they had acquired the Cardinality Principle of verbal counting. In contrast, children successfully generated numerically appropriate tapping sequences in the Word-to-ANS task before 4 years of age--well before many understood the Cardinality Principle. We further found that the accuracy of the mapping between the ANS and number words, as captured by error rates, continues to develop after this initial formation of the interface. These results suggest that the mapping between the ANS and verbal number representations is not functionally bidirectional in early development, and that the mapping direction from number representations to the ANS is established before the reverse. PMID:25721021

  2. 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.

  3. Neutrosophic Quadruple Numbers, Refined Neutrosophic Quadruple Numbers, Absorbance Law, and the Multiplication of Neutrosophic Quadruple Numbers

    OpenAIRE

    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.

  4. Reprint Series: Prime Numbers and Perfect Numbers. RS-2.

    Science.gov (United States)

    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)

  5. Quantum Random Number Generator using Photon-Number Path Entanglement

    OpenAIRE

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

    2008-01-01

    We report a novel quantum random number generator based on the photon-number$-$path entangled state which is prepared via two-photon quantum interference at a beam splitter. The randomness in our scheme is of truly quantum mechanical origin as it comes from the projection measurement of the entangled two-photon state. The generated bit sequences satisfy the standard randomness test.

  6. Dynamic Virtual Credit Card Numbers

    Science.gov (United States)

    Molloy, Ian; Li, Jiangtao; Li, Ninghui

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

  7. The neuronal code for number.

    Science.gov (United States)

    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. PMID:27150407

  8. q-Bernoulli Numbers Associated with q-Stirling Numbers

    OpenAIRE

    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 βn,q=∑m=0n∑k=mn1/(1-q)n+m-k∑d0+⋯+dk=n-kq∑i=0kidis1,q(k,m)(-1)n-m((m+1)/[m+1]q), where βn,q are called Carlitz q-Bernoulli numbers.

  9. Number Comparison and Number Line Estimation Rely on Different Mechanisms

    Directory of Open Access Journals (Sweden)

    Delphine Sasanguie

    2013-12-01

    Full Text Available The performance in comparison and number line estimation is assumed to rely on the same underlying representation, similar to a compressed mental number line that becomes more linear with age. We tested this assumption explicitly by examining the relation between the linear/logarithmic fit in a non-symbolic number line estimation task and the size effect (SE in a non-symbolic comparison task in first-, second-, and third graders. In two experiments, a correlation between the estimation pattern in number line estimation and the SE in comparison was absent. An ANOVA showed no difference between the groups of children with a linear or a logarithmic representation considering their SE in comparison. This suggests that different mechanisms underlie both basic number processing tasks.

  10. An introduction to number theory.

    OpenAIRE

    Everest, G.; Ward, T.

    2005-01-01

    An Introduction to Number Theory provides an introduction to the main streams of number theory. Starting with the unique factorization property of the integers, the theme of factorization is revisited several times throughout the book to illustrate how the ideas handed down from Euclid continue to reverberate through the subject. In particular, the book shows how the Fundamental Theorem of Arithmetic, handed down from antiquity, informs much of the teaching of modern number theory. The re...

  11. Expected gaps between prime numbers

    OpenAIRE

    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\\...

  12. The Set of Prime Numbers

    OpenAIRE

    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.

  13. Correlations between large prime numbers

    OpenAIRE

    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...

  14. An Introduction to Zoli Numbers

    OpenAIRE

    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.

  15. Number development and developmental dyscalculia.

    Science.gov (United States)

    von Aster, Michael G; Shalev, Ruth S

    2007-11-01

    There is a growing consensus that the neuropsychological underpinnings of developmental dyscalculia (DD) are a genetically determined disorder of 'number sense', a term denoting the ability to represent and manipulate numerical magnitude nonverbally on an internal number line. However, this spatially-oriented number line develops during elementary school and requires additional cognitive components including working memory and number symbolization (language). Thus, there may be children with familial-genetic DD with deficits limited to number sense and others with DD and comorbidities such as language delay, dyslexia, or attention-deficit-hyperactivity disorder. This duality is supported by epidemiological data indicating that two-thirds of children with DD have comorbid conditions while one-third have pure DD. Clinically, they differ according to their profile of arithmetic difficulties. fMRI studies indicate that parietal areas (important for number functions), and frontal regions (dominant for executive working memory and attention functions), are under-activated in children with DD. A four-step developmental model that allows prediction of different pathways for DD is presented. The core-system representation of numerical magnitude (cardinality; step 1) provides the meaning of 'number', a precondition to acquiring linguistic (step 2), and Arabic (step 3) number symbols, while a growing working memory enables neuroplastic development of an expanding mental number line during school years (step 4). Therapeutic and educational interventions can be drawn from this model. PMID:17979867

  16. A generalization of Stirling numbers

    OpenAIRE

    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...

  17. Unsolved problems in number theory

    CERN Document Server

    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.

  18. Euler Sums of Hyperharmonic Numbers

    OpenAIRE

    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...

  19. Jacobi and Kummer's Ideal Numbers

    OpenAIRE

    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.

  20. Number theory and its history

    CERN Document Server

    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.

  1. Know Your Blood Sugar Numbers

    Science.gov (United States)

    Know Your Blood Sugar Numbers If you have diabetes, keeping your blood sugar (glucose) numbers in your target range can help you feel ... Prevention There are two ways to measure blood sugar. 1 The A1C is a lab test that ...

  2. On the Three Primordial Numbers

    NARCIS (Netherlands)

    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

  3. Generalized Ramsey numbers for graphs

    NARCIS (Netherlands)

    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

  4. Investigating the Randomness of Numbers

    Science.gov (United States)

    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…

  5. 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....... The tool is called Number Blocks and it combines physical interaction, learning, and immediate feedback. Number Blocks supports the children's understanding of place value in the sense that it allows them to experiment with creating large numbers. We found the blocks contributed to the learning...... process in several ways. The blocks combined mathematics and play, and they included and supported children at different academic levels. The auditory representation, especially the enhanced rhythmic effects due to using speech synthesis, and the rhythm helped the children to pronounce large numbers. This...

  6. 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.

  7. Fundamental number theory with applications

    CERN Document Server

    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

  8. Elliptic rook and file numbers

    OpenAIRE

    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...

  9. Efficient computation of root numbers and class numbers of parametrized families of real abelian number fields

    Science.gov (United States)

    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^+ .

  10. Poison control center - emergency number

    Science.gov (United States)

    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 ...

  11. Picard numbers of Delsarte surfaces

    OpenAIRE

    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.

  12. Universal Algebras of Hurwitz Numbers

    OpenAIRE

    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.

  13. Young Students Investigate Number Cubes.

    Science.gov (United States)

    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)

  14. Know Your Blood Sugar Numbers

    Science.gov (United States)

    ... 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 ...

  15. Fibonacci Numbers and the Spreadsheet.

    Science.gov (United States)

    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)

  16. 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.

  17. Some Remarkable Identities Involving Numbers

    OpenAIRE

    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.

  18. Classical theory of algebraic numbers

    CERN Document Server

    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...

  19. Exponential Decay of Lebesgue Numbers

    OpenAIRE

    Sun, Peng

    2010-01-01

    We study the exponential rate of decay of Lebesgue numbers of open covers in topological dynamical systems. We show that topological entropy is bounded by this rate multiplied by dimension. Some corollaries and examples are discussed.

  20. Women In Numbers - Europe workshop

    CERN Document Server

    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.

  1. Social Security Number (SSN) Verification

    Data.gov (United States)

    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...

  2. Occupation numbers from functional integral

    OpenAIRE

    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 ...

  3. 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.

  4. Conversion of Number Systems using Xilinx.

    OpenAIRE

    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.

  5. 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.

  6. Are Number Gestures Easier than Number Words for Preschoolers?

    Science.gov (United States)

    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'…

  7. Number Meaning and Number Grammar in English and Spanish

    Science.gov (United States)

    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…

  8. Periodical plane puzzles with numbers

    CERN Document Server

    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...

  9. Super congruences and Euler numbers

    OpenAIRE

    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 ...

  10. Big Numbers in String Theory

    CERN Document Server

    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.

  11. Quasiperpendicular high Mach number Shocks

    CERN Document Server

    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...

  12. Square Partitions and Catalan Numbers

    OpenAIRE

    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...

  13. Geometric Number Systems and Spinors

    CERN Document Server

    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.

  14. Cognitive Radio with Random Number of Secondary Number of Users

    OpenAIRE

    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...

  15. Residual number processing in dyscalculia

    Directory of Open Access Journals (Sweden)

    Marinella Cappelletti

    2014-01-01

    Full Text Available Developmental dyscalculia – a congenital learning disability in understanding numerical concepts – is typically associated with parietal lobe abnormality. However, people with dyscalculia often retain some residual numerical abilities, reported in studies that otherwise focused on abnormalities in the dyscalculic brain. Here we took a different perspective by focusing on brain regions that support residual number processing in dyscalculia. All participants accurately performed semantic and categorical colour-decision tasks with numerical and non-numerical stimuli, with adults with dyscalculia performing slower than controls in the number semantic tasks only. Structural imaging showed less grey-matter volume in the right parietal cortex in people with dyscalculia relative to controls. Functional MRI showed that accurate number semantic judgements were maintained by parietal and inferior frontal activations that were common to adults with dyscalculia and controls, with higher activation for participants with dyscalculia than controls in the right superior frontal cortex and the left inferior frontal sulcus. Enhanced activation in these frontal areas was driven by people with dyscalculia who made faster rather than slower numerical decisions; however, activation could not be accounted for by response times per se, because it was greater for fast relative to slow dyscalculics but not greater for fast controls relative to slow dyscalculics. In conclusion, our results reveal two frontal brain regions that support efficient number processing in dyscalculia.

  16. Residual number processing in dyscalculia.

    Science.gov (United States)

    Cappelletti, Marinella; Price, Cathy J

    2014-01-01

    Developmental dyscalculia - a congenital learning disability in understanding numerical concepts - is typically associated with parietal lobe abnormality. However, people with dyscalculia often retain some residual numerical abilities, reported in studies that otherwise focused on abnormalities in the dyscalculic brain. Here we took a different perspective by focusing on brain regions that support residual number processing in dyscalculia. All participants accurately performed semantic and categorical colour-decision tasks with numerical and non-numerical stimuli, with adults with dyscalculia performing slower than controls in the number semantic tasks only. Structural imaging showed less grey-matter volume in the right parietal cortex in people with dyscalculia relative to controls. Functional MRI showed that accurate number semantic judgements were maintained by parietal and inferior frontal activations that were common to adults with dyscalculia and controls, with higher activation for participants with dyscalculia than controls in the right superior frontal cortex and the left inferior frontal sulcus. Enhanced activation in these frontal areas was driven by people with dyscalculia who made faster rather than slower numerical decisions; however, activation could not be accounted for by response times per se, because it was greater for fast relative to slow dyscalculics but not greater for fast controls relative to slow dyscalculics. In conclusion, our results reveal two frontal brain regions that support efficient number processing in dyscalculia. PMID:24266008

  17. 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.

  18. 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)

  19. An introduction to Catalan numbers

    CERN Document Server

    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...

  20. 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).

  1. Finite temperature induced fermion number

    OpenAIRE

    Dunne, Gerald V.

    2001-01-01

    The induced fractional fermion number at zero temperature is topological (in the sense that it is only sensitive to global asymptotic properties of the background field), and is a sharp observable (in the sense that it has vanishing rms fluctuations). In contrast, at finite temperature, it is shown to be generically nontopological, and not a sharp observable.

  2. Upper bounds on Nusselt number at finite Prandtl number

    CERN Document Server

    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...

  3. Higher-order Nielsen numbers

    Directory of Open Access Journals (Sweden)

    Peter Saveliev

    2005-04-01

    Full Text Available Suppose X, Y are manifolds, f,g:X→Y are maps. The well-known coincidence problem studies the coincidence set C={x:f(x=g(x}. The number m=dim X−dim Y is called the codimension of the problem. More general is the preimage problem. For a map f:X→Z and a submanifold Y of Z, it studies the preimage set C={x:f(x∈Y}, and the codimension is m=dim X+dim Y−dim Z. In case of codimension 0, the classical Nielsen number N(f,Y is a lower estimate of the number of points in C changing under homotopies of f, and for an arbitrary codimension, of the number of components of C. We extend this theory to take into account other topological characteristics of C. The goal is to find a “lower estimate” of the bordism group Ωp(C of C. The answer is the Nielsen group Sp(f,Y defined as follows. In the classical definition, the Nielsen equivalence of points of C based on paths is replaced with an equivalence of singular submanifolds of C based on bordisms. We let Sp'(f,Y=Ωp(C/∼N, then the Nielsen group of order p is the part of Sp'(f,Y preserved under homotopies of f. The Nielsen number Np(F,Y of order p is the rank of this group (then N(f,Y=N0(f,Y. These numbers are new obstructions to removability of coincidences and preimages. Some examples and computations are provided.

  4. Lozenge Tilings and Hurwitz Numbers

    Science.gov (United States)

    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.

  5. How to Differentiate a Number

    Science.gov (United States)

    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.

  6. On Buffon Machines and Numbers

    OpenAIRE

    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...

  7. On quantum state of numbers

    OpenAIRE

    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 ...

  8. More Sets, Graphs and Numbers

    CERN Document Server

    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.

  9. 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

  10. Topics in prime number theory

    OpenAIRE

    Ghosh, Amit

    1981-01-01

    The thesis is divided into five sections: (a) Trigonometric sums involving prime numbers and applications, (b) Mean-values and Sign-changes of S(t)-- related to Riemann's Zeta function, (c) Mean-values of strongly additive arithmetical functions, (d) Combinatorial identities and sieves, (e) A Goldbach-type problem. Parts (b) and (c) are related by means of the techniques used but otherwise the sections are disjoint. (a) We consider the question of finding upper bounds for...

  11. Magic Numbers in Protein Structures

    DEFF Research Database (Denmark)

    Lindgård, Per-Anker; Bohr, Henrik

    1996-01-01

    domains. We have performed a statistical analysis of available protein structures and found agreement with the predicted preferred abundances. Furthermore, a connection between sequence information and fold classes is established in terms of hinge forces between the structural elements.......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...

  12. When a number is not only a number

    DEFF Research Database (Denmark)

    Christensen, Ken Ramshøj; Roepstorff, Andreas; Saddy, Douglas

    +3). 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...... ongoing fMRI study which involves numerical processing as well as WM and error detection. Three types of stimuli: (a) repeated chunks (x, y, z, x, y, z…), (b) smaller structured chunks requiring minimal calculation (x, x+1, y, y+1, z, z+1…), and (c) strings with an increased calculation requirement (x = x...... three conditions conform to the same general pattern with massive activation in the posterior parietal cortex, dorsal frontal and premotor cortex (BA 6, 8), and DLPFC, though with distinct differences in extent which reflects different demands for WM and calculation. Applying an event related analysis...

  13. Bridge Number and Conway Products

    OpenAIRE

    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...

  14. 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

  15. Counting Square-Free Numbers

    OpenAIRE

    Pawlewicz, Jakub

    2011-01-01

    The main topic of this contribution is the problem of counting square-free numbers not exceeding $n$. Before this work we were able to do it in time (Comparing to the Big-O notation, Soft-O ($\\softO$) ignores logarithmic factors) $\\softO(\\sqrt{n})$. Here, the algorithm with time complexity $\\softO(n^{2/5})$ and with memory complexity $\\softO(n^{1/5})$ is presented. Additionally, a parallel version is shown, which achieves full scalability. As of now the highest computed value was for $n=10^{1...

  16. Number & operations task & drill sheets

    CERN Document Server

    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

  17. Topological number of edge states

    Science.gov (United States)

    Hashimoto, Koji; Kimura, Taro

    2016-05-01

    We show that the edge states of the four-dimensional class A system can have topological charges, which are characterized by Abelian/non-Abelian monopoles. The edge topological charges are a new feature of relations among theories with different dimensions. From this novel viewpoint, we provide a non-Abelian analog of the TKNN number as an edge topological charge, which is defined by an SU(2) 't Hooft-Polyakov BPS monopole through an equivalence to Nahm construction. Furthermore, putting a constant magnetic field yields an edge monopole in a noncommutative momentum space, where D-brane methods in string theory facilitate study of edge fermions.

  18. Topological Number of Edge States

    CERN Document Server

    Hashimoto, Koji

    2016-01-01

    We show that the edge states of the four-dimensional class A system can have topological charges, which are characterized by Abelian/non-Abelian monopoles. The edge topological charges are a new feature of relations among theories with different dimensions. From this novel viewpoint, we provide a non-Abelian analogue of the TKNN number as an edge topological charge, which is defined by an SU(2) 't Hooft-Polyakov BPS monopole through an equivalence to Nahm construction. Furthermore, putting a constant magnetic field yields an edge monopole in a non-commutative momentum space, where D-brane methods in string theory facilitate study of edge fermions.

  19. Functional units for natural numbers

    CERN Document Server

    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.

  20. Arithmetic geometry and number theory

    CERN Document Server

    Weng, Lin

    2006-01-01

    Mathematics is very much a part of our culture; and this invaluable collection serves the purpose of developing the branches involved, popularizing the existing theories and guiding our future explorations.More precisely, the goal is to bring the reader to the frontier of current developments in arithmetic geometry and number theory through the works of Deninger-Werner in vector bundles on curves over p-adic fields; of Jiang on local gamma factors in automorphic representations; of Weng on Deligne pairings and Takhtajan-Zograf metrics; of Yoshida on CM-periods; of Yu on transcendence of specia

  1. Number Theory, Analysis and Geometry

    CERN Document Server

    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

  2. Number theory III Diophantine geometry

    CERN Document Server

    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 ...

  3. Topics in Number Theory Conference

    CERN Document Server

    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. ...

  4. Cryptography and computational number theory

    CERN Document Server

    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...

  5. Generalized Compositions and Weighted Fibonacci Numbers

    OpenAIRE

    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.

  6. Counting Square-Free Numbers

    CERN Document Server

    Pawlewicz, Jakub

    2011-01-01

    The main topic of this contribution is the problem of counting square-free numbers not exceeding $n$. Before this work we were able to do it in time (Comparing to the Big-O notation, Soft-O ($\\softO$) ignores logarithmic factors) $\\softO(\\sqrt{n})$. Here, the algorithm with time complexity $\\softO(n^{2/5})$ and with memory complexity $\\softO(n^{1/5})$ is presented. Additionally, a parallel version is shown, which achieves full scalability. As of now the highest computed value was for $n=10^{17}$. Using our implementation we were able to calculate the value for $n=10^{36}$ on a cluster.

  7. Note on the Theory of Perfect Numbers

    OpenAIRE

    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.

  8. Ramsey numbers for trees II

    OpenAIRE

    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}...

  9. 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.

  10. On Bernoulli Numbers and Its Properties

    OpenAIRE

    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.

  11. 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.

  12. Crosscap Numbers of Two-component Links

    OpenAIRE

    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.

  13. Some properties of θ-congruent numbers

    OpenAIRE

    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.

  14. How to be Brilliant at Numbers

    CERN Document Server

    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

  15. Fibonacci Numbers, Golden Section and Applications

    OpenAIRE

    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.

  16. The generalized r-Whitney numbers

    OpenAIRE

    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 ...

  17. Effective quantum number for axially symmetric problems

    OpenAIRE

    Trunov, N. N.

    2014-01-01

    We generalize the universal effective quantum number introduced earlier for centrally symmetric problems. The proposed number determines the semiclassical quantization condition for axially symmetric potentials.

  18. 7 CFR 987.102 - Lot number.

    Science.gov (United States)

    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,...

  19. 49 CFR 230.47 - Boiler number.

    Science.gov (United States)

    2010-10-01

    ... 49 Transportation 4 2010-10-01 2010-10-01 false Boiler number. 230.47 Section 230.47... Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known, shall be stamped on the steam dome or manhole flange. If the builder's number cannot be obtained,...

  20. 9 CFR 351.6 - Official number.

    Science.gov (United States)

    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...

  1. 7 CFR 900.5 - Docket number.

    Science.gov (United States)

    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....

  2. 7 CFR 29.32 - Identification number.

    Science.gov (United States)

    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...

  3. 14 CFR 47.15 - Identification number.

    Science.gov (United States)

    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...

  4. 9 CFR 355.8 - Official number.

    Science.gov (United States)

    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...

  5. 7 CFR 75.48 - Identification number.

    Science.gov (United States)

    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...

  6. 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.

  7. Experimental Number Theory, Part I : Tower Arithmetic

    OpenAIRE

    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.

  8. On the Harmonic and Hyperharmonic Fibonacci Numbers

    OpenAIRE

    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.

  9. The Irrationality Exponents of Computable Numbers

    OpenAIRE

    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.

  10. Girotondo dei Numeri (A Ring of Numbers).

    Science.gov (United States)

    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)

  11. Some properties of fuzzy real numbers

    OpenAIRE

    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.

  12. Fast integration using quasi-random numbers

    Energy Technology Data Exchange (ETDEWEB)

    Bossert, J. [Phi-T Physics Information Technologies GmbH, 76139 Karlsruhe (Germany); Feindt, M. [Phi-T Physics Information Technologies GmbH, 76139 Karlsruhe (Germany); Institut fuer Experimentelle Kernphysik, University of Karlsruhe (Germany); Kerzel, U. [Institut fuer Experimentelle Kernphysik, University of Karlsruhe (Germany)]. E-mail: ulrich.kerzel@cern.ch

    2006-04-01

    Quasi-random numbers are specially constructed series of numbers optimised to evenly sample a given s-dimensional volume. Using quasi-random numbers in numerical integration converges faster with a higher accuracy compared to the case of pseudo-random numbers. The basic properties of quasi-random numbers are introduced, various generators are discussed and the achieved gain is illustrated by examples.

  13. Quantum Mechanics interpreted in Quantum Real Numbers

    OpenAIRE

    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.

  14. 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.

  15. Galois theory, motives and transcendental numbers

    OpenAIRE

    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 ...

  16. 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.

  17. Prime number generation and factor elimination

    OpenAIRE

    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...

  18. Integrated-Circuit Pseudorandom-Number Generator

    Science.gov (United States)

    Steelman, James E.; Beasley, Jeff; Aragon, Michael; Ramirez, Francisco; Summers, Kenneth L.; Knoebel, Arthur

    1992-01-01

    Integrated circuit produces 8-bit pseudorandom numbers from specified probability distribution, at rate of 10 MHz. Use of Boolean logic, circuit implements pseudorandom-number-generating algorithm. Circuit includes eight 12-bit pseudorandom-number generators, outputs are uniformly distributed. 8-bit pseudorandom numbers satisfying specified nonuniform probability distribution are generated by processing uniformly distributed outputs of eight 12-bit pseudorandom-number generators through "pipeline" of D flip-flops, comparators, and memories implementing conditional probabilities on zeros and ones.

  19. On Legendre numbers of the second kind

    OpenAIRE

    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...

  20. Computation Methods for combinatorial sums and Euler type numbers related to new families of numbers

    OpenAIRE

    Simsek, Yilmaz

    2016-01-01

    The aim of this article is to define some new families of the special numbers. These numbers provide some further motivation for computation of combinatorial sums involving binomial coefficients and the Euler kind numbers of negative order. We can show that these numbers are related to the well-known numbers and polynomials such as the Stirling numbers of the second kind and the central factorial numbers, the array polynomials, the rook numbers and polynomials, the Bernstein basis functions a...

  1. New families of special numbers for computing negative order Euler numbers

    OpenAIRE

    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...

  2. Fibonacci number of the tadpole graph

    OpenAIRE

    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...

  3. On q-deformed Stirling numbers

    OpenAIRE

    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...

  4. 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.

  5. Poison control center - Emergency number (image)

    Science.gov (United States)

    ... 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 ...

  6. 40 CFR 86.1204 - Section numbering.

    Science.gov (United States)

    2010-07-01

    ... Test Procedures for New Gasoline-Fueled, Natural Gas-Fueled, Liquefied Petroleum Gas-Fueled and Methanol-Fueled Heavy-Duty Vehicles § 86.1204 Section numbering. The section numbering system set forth...

  7. 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.

  8. Number Theory in the High School Classroom.

    Science.gov (United States)

    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)

  9. What Do Numbers Do in Transnational Governance?

    DEFF Research Database (Denmark)

    Krause Hansen, Hans; Porter, Tony

    2012-01-01

    This study examines how numbers in transnational governance constitute actors, objects, and relationships, including relationships of power. We review the existing literatures on numbers for insights relevant to their role in transnational governance, including the ontology of numbers, the history...... of numbers and their role in governance. On this basis, we set out the main distinctive ways that numbers are implicated in transnational governance. We conclude that studies of transnational governance would benefit from paying more attention to the much overlooked performative role of numbers in...... governance processes. Numbers have properties that differ from words, and shifts from one to the other in governance, for instance in the displacement of laws or norms with risk models or rankings based on numbers, have particular effects, including political effects on states, firms, individuals, and other...

  10. Path count asymptotics and Stirling numbers

    OpenAIRE

    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.

  11. Power sum identities with generalized Stirling numbers

    OpenAIRE

    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.

  12. On Anti-Elite Prime Numbers

    Science.gov (United States)

    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.

  13. Using Simulated Annealing to Factor Numbers

    OpenAIRE

    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.

  14. Relativistic theory of tidal Love numbers

    OpenAIRE

    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...

  15. The occurrence of prime numbers revisited

    OpenAIRE

    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.

  16. Monotone Hurwitz numbers in genus zero

    OpenAIRE

    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...

  17. 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.

  18. Continental anthropogenic primary particle number emissions

    OpenAIRE

    P. Paasonen; Kupiainen, K.; Z. Klimont; Visshedijk, A.; H. A. C. Denier van der Gon; M. Amann

    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 model. This implementation allows for global estimates of particle number ...

  19. 7 CFR 29.133 - Identification number.

    Science.gov (United States)

    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...

  20. 7 CFR 1.414 - Docket number.

    Science.gov (United States)

    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...

  1. 27 CFR 24.115 - Registry number.

    Science.gov (United States)

    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...

  2. 40 CFR 264.11 - Identification number.

    Science.gov (United States)

    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)....

  3. 7 CFR 1200.6 - Docket number.

    Science.gov (United States)

    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...

  4. 21 CFR 1210.21 - Permit number.

    Science.gov (United States)

    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...

  5. Identifying Fractions on a Number Line

    Science.gov (United States)

    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…

  6. 47 CFR 95.671 - Serial number.

    Science.gov (United States)

    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....

  7. 40 CFR 265.11 - Identification number.

    Science.gov (United States)

    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...

  8. 7 CFR 900.54 - Docket number.

    Science.gov (United States)

    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...

  9. 24 CFR 3280.6 - Serial number.

    Science.gov (United States)

    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...

  10. 46 CFR 10.207 - Identification number.

    Science.gov (United States)

    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...

  11. Children's Use of Number Line Estimation Strategies

    Science.gov (United States)

    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…

  12. 7 CFR 1.134 - Docket number.

    Science.gov (United States)

    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...

  13. A developmental model of number representation

    OpenAIRE

    Kucian, K; Kaufmann, L.

    2009-01-01

    We delineate a developmental model of number representations. Notably, developmental dyscalculia (DD) is rarely associated with an all-or-none deficit in numerosity processing as would be expected if assuming abstract number representations. Finally, we suggest that the “generalist genes” view might be a plausible – though thus far speculative – explanatory framework for our model of how number representations develop.

  14. 75 FR 18572 - Facility Control Numbers

    Science.gov (United States)

    2010-04-12

    ... Internal Revenue Service Facility Control Numbers AGENCY: Internal Revenue Service (IRS), Treasury. ACTION: Notice of planned use of Facility Control Numbers. SUMMARY: The IRS has developed and is publishing in this issue of the Federal Register, Facility Control Numbers to communicate to the motor fuel...

  15. The characteristic numbers of quartic plane curves

    OpenAIRE

    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.

  16. An Introduction to Conway's Games and Numbers

    OpenAIRE

    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.

  17. 47 CFR 32.20 - Numbering convention.

    Science.gov (United States)

    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...

  18. 32 CFR 1602.19 - Numbers.

    Science.gov (United States)

    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....

  19. Fascinating Fibonaccis: Mystery and Magic in Numbers.

    Science.gov (United States)

    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…

  20. Remarkable and Reversible Prime Number Patterns

    OpenAIRE

    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.

  1. Baxter Algebras, Stirling Numbers and Partitions

    OpenAIRE

    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.

  2. Linking numbers for handlebody-links

    OpenAIRE

    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.

  3. On a unified theory of numbers

    OpenAIRE

    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.

  4. A note on Quarks and numbers theory

    OpenAIRE

    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.

  5. Teach Kids about Numbers All around Us

    Science.gov (United States)

    Hudson, Hannah Trierweiler

    2011-01-01

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

  6. 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.

  7. An adventurer's guide to number theory

    CERN Document Server

    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

  8. Fibonacci and Catalan Numbers An Introduction

    CERN Document Server

    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

  9. Bit recycling for scaling random number generators

    OpenAIRE

    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...

  10. ARITHMETIC PROGRESSIONS FOR COUNTING PRIME NUMBERS

    Directory of Open Access Journals (Sweden)

    V.J.DEVASIA

    2014-11-01

    Full Text Available In this paper two arithmetic progressions are proposed for listing and counting the prime numbers less than or equal to a given integer. From these progressions, how one can filter out prime numbers is the topic of discussion in this paper. An easy to implement formula is presented to compute the number of primes by eliminating the number of composite numbers in an iterative and recursive manner. Numerical examples are presented to demonstrate how the procedure works in an efficient and simple way.

  11. Certain number-theoretic episodes in algebra

    CERN Document Server

    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.

  12. 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.

  13. 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

  14. Random Numbers in Scientific Computing: An Introduction

    CERN Document Server

    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.

  15. An Evaluation of App-Based and Paper-Based Number Lines for Teaching Number Comparison

    Science.gov (United States)

    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…

  16. 27 CFR 20.179 - Package identification number or serial number.

    Science.gov (United States)

    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...

  17. 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}.

  18. Beyond natural numbers: Representation of negative numbers in the parietal cortex

    Directory of Open Access Journals (Sweden)

    Miriam Rosenberg-Lee

    2012-02-01

    Full Text Available 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 fMRI design, we examined brain responses in 22 adults while they performed magnitude comparisons of negative and positive numbers that were quantitatively near (difference < 4 or far apart (difference > 6. Reaction times 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 reaction times. 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.

  19. 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.

  20. A short hand of Prime number distribution

    Directory of Open Access Journals (Sweden)

    Vinoo Cameron

    2012-11-01

    Full Text Available This is a short paper to demonstrate how complacent scientists and mathematicians have been and how complacent the mysteries of the sciences are (actually there are no mysteries, the almighty has made mathematics and the sciences in our image .This is simple mathematics, including the mathematics of the unified theorem that follows this paper, that mathematicians have botched for 500 years. This is also made possible by a unique prime number sieve that is continuum at 6 and 1:3, the denOtter- Hope research continuous sieve for prime numbers, the most accurate prime number sieve. Whilst the discovery of large prime number does nothing for the understanding of prime numbers, the short hand does. We have presented a short series and if so called mathematicians cannot extend the series mathematically, they should join a historical line of western mathematicians that convoluted the reality of mathematics on prime numbers for 500 years. 

  1. Tests of sunspot number sequences: 4. Discontinuities around 1946 in various sunspot number and sunspot group number reconstructions

    CERN Document Server

    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 ...

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

    Science.gov (United States)

    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.

  3. Percon8 Algorithm for Random Number Generation

    OpenAIRE

    Dr. Mrs. Saylee Gharge; Mr. Honey Brijwani

    2014-01-01

    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 o...

  4. Measuring human salivary amylase copy number variation

    OpenAIRE

    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...

  5. Generalized Ramsey numbers through adiabatic quantum optimization

    OpenAIRE

    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...

  6. Dimensions, nodes and phases in quantum numbers

    OpenAIRE

    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...

  7. Notes on the Theory of Algebraic Numbers

    OpenAIRE

    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.

  8. From Taub Numbers to the Bondi Mass

    OpenAIRE

    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...

  9. Conferences on Combinatorial and Additive Number Theory

    CERN Document Server

    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.

  10. Continental anthropogenic primary particle number emissions

    OpenAIRE

    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...

  11. 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.

  12. Unique Physician Identification Number (UPIN) Directory

    Data.gov (United States)

    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...

  13. On the Turan number of forests

    CERN Document Server

    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.

  14. Algebra and Number Theory An Integrated Approach

    CERN Document Server

    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

  15. Numbers and other math ideas come alive

    CERN Document Server

    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

  16. Pegging Numbers For Various Tree Graphs

    CERN Document Server

    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.

  17. The new problem of numbers in morality

    OpenAIRE

    Woollard, Fiona

    2014-01-01

    Discussion of the “problem of numbers” in morality has focused almost exclusively on the moral significance of numbers in whom-to-rescue cases: when you can save either of two groups of people, but not both, does the number of people in each group matter morally? I suggest that insufficient attention has been paid to the moral significance of numbers in other types of case. According to common-sense morality, numbers make a difference in cases, like the famous Trolley Case, where we must choo...

  18. Vector perturbations of galaxy number counts

    CERN Document Server

    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.

  19. Continental anthropogenic primary particle number emissions

    Science.gov (United States)

    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

  20. Application of Chaotic Number Generators in Econophysics

    CERN Document Server

    Pellicer-Lostao, Carmen

    2011-01-01

    Agent-based models have demonstrated their power and flexibility in Econophysics. However their major challenge is still to devise more realistic simulation scenarios. The complexity of Economy makes appealing the idea of introducing chaotic number generators as simulation engines in these models. Chaos based number generators are easy to use and highly configurable. This makes them just perfect for this application.

  1. Analytic number theory an introductory course

    CERN Document Server

    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.

  2. Cellular Automata Rules and Linear Numbers

    OpenAIRE

    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.

  3. Finite groups in Axiomatic Index Number Theory

    OpenAIRE

    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.

  4. Carmichael Numbers on a Quantum Computer

    OpenAIRE

    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.

  5. Topological quantum numbers in the Hall effect

    OpenAIRE

    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.

  6. Quantum chromatic numbers via operator systems

    OpenAIRE

    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.

  7. On the abundance of the irrational numbers

    OpenAIRE

    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.

  8. s-Numbers sequences for homogeneous polynomials

    OpenAIRE

    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.

  9. Generalized Fibonacci Numbers and Blackwell's Renewal Theorem

    OpenAIRE

    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.

  10. Estimating Nielsen Numbers on Wedge Product Spaces

    Directory of Open Access Journals (Sweden)

    Kim Seung Won

    2007-01-01

    Full Text Available Let be a self-map of a finite polyhedron that is an aspherical wedge product space . In this paper, we estimate the Nielsen number of . In particular, we study some algebraic properties of the free products and then estimate Nielsen numbers on torus wedge surface with boundary, Klein bottle wedge surface with boundary, and torus wedge torus.

  11. 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.

  12. Hodge Numbers for All CICY Quotients

    CERN Document Server

    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.

  13. New string theories and their generation number

    International Nuclear Information System (INIS)

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

  14. A Thermodynamic Classification of Real Numbers

    OpenAIRE

    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.

  15. 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

  16. Particle creation and Dirac's large numbers hypothesis

    International Nuclear Information System (INIS)

    Reference is made to cosmologies based on Dirac's large numbers hypothesis (Nature 139:323 (1937) and Proc. Roy. Soc. A333:403 (1973)). Dirac suggested that continuous creation of matter is required. Two modes of particle creation have been proposed and cosmological models corresponding to each mode have been studied. It is here shown that, within the context of the large numbers hypothesis, the number of particles in the Universe varies as expected (N proportional to t2) so that particle creation is unnecessary. Some undesirable features of cosmologies based on the large numbers hypothesis are also discussed. In order to appreciate fully the results presented for cosmologies based on the large numbers hypothesis a review is made of the corresponding relationship in conventional cosmologies in which the gravitational constant G does not vary with time. It is found, amongst other things that there is no nucleosynthesis in cosmologies based on the large numbers hypothesis, making the large and uniform abundance of He inexplicable. Another undesirable finding with the large numbers hypothesis is the extremely steep decline in the number of particles in the Universe with increasing temperature. Yet another undesirable finding concerns the scattering of photons by electrons in the early Universe; there is no way to establish thermodynamic equilibrium between the photons and electrons, and the black body spectrum of the background radiation is without explanation. (U.K.)

  17. A Generalization of the Prime Number Theorem

    Science.gov (United States)

    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…

  18. Toward a dynamical model for prime numbers

    OpenAIRE

    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.

  19. Keypad Geometry and Divisibility of Numbers

    Science.gov (United States)

    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…

  20. Queneau numbers - recent results and a bibliography

    NARCIS (Netherlands)

    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

  1. Number & operations drill sheets : grades PK-2

    CERN Document Server

    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.

  2. On perfect and near-perfect numbers

    OpenAIRE

    Shevelev, Vladimir

    2010-01-01

    We call positive integer n a near-perfect number, if it is sum of all its proper divisors, except of one of them ("redundant divisor"). We prove an Euclid-like theorem for near-perfect numbers and obtain some other results for them.

  3. Tunnel number one, genus one fibered knots

    OpenAIRE

    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.

  4. Ground state number fluctuations of trapped particles

    Science.gov (United States)

    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

  5. Complex numbers from A to Z

    CERN Document Server

    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 ...

  6. A small world network of prime numbers

    Science.gov (United States)

    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.

  7. Topics from the theory of numbers

    CERN Document Server

    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...

  8. True random numbers from amplified quantum vacuum

    CERN Document Server

    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...

  9. 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)

  10. Planar complex numbers in even n dimensions

    OpenAIRE

    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...

  11. Topological Numbers and the Weyl Semimetal

    CERN Document Server

    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.

  12. Bit recycling for scaling random number generators

    CERN Document Server

    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.

  13. Random numbers spring from alpha decay

    Energy Technology Data Exchange (ETDEWEB)

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

    1980-05-01

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

  14. Random numbers spring from alpha decay

    International Nuclear Information System (INIS)

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

  15. Zooming in and out from the Mental Number Line: Evidence for a Number Range Effect

    Science.gov (United States)

    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…

  16. Lower bounds for algebraic connectivity of graphs in terms of matching number or edge covering number

    OpenAIRE

    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.

  17. Number Worlds: Visual and Experimental Access to Elementary Number Theory Concepts

    Science.gov (United States)

    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…

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

    CERN Document Server

    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.

  19. Carmichael number variable relations: three-prime Carmichael numbers up to 10^24

    OpenAIRE

    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...

  20. DISTRIBUTION OF PRIME NUMBERS. ALGORITHM OF TWINS NUMBERS AND THEIR INFINITE

    OpenAIRE

    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...

  1. Predicting landfalling hurricane numbers from basin hurricane numbers: statistical analysis and predictions

    OpenAIRE

    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...

  2. Limits on hypothesizing new quantum numbers

    International Nuclear Information System (INIS)

    According to a recent theorem, for a general quantum-mechanical system undergoing a process, one can tell from measurements on this system whether or not it is characterized by a quantum number, the existence of which is unknown to the observer, even though the detecting equipment used by the observer is unable to distinguish among the various possible values of the ''secret'' quantum number and hence always averages over them. The present paper deals with situations in which this averaging is avoided and hence the ''secret'' quantum number remains ''secret.'' This occurs when a new quantum number is hypothesized in such a way that all the past measurements pertain to the system with one and the same value of the ''secret'' quantum number, or when the new quantum number is related to the old ones by a specific dynamical model providing a one-to-one correspondence. In the first of these cases, however, the one and the same state of the ''secret'' quantum number needs to be a nondegenerate one. If it is degenerate, the theorem can again be applied. This last feature provides a tool for experimentally testing symmetry breaking and the reestablishment of symmetries in asymptotic regions. The situation is illustrated on historical examples like isospin and strangeness, as well as on some contemporary schemes involving spaces of higher dimensionality

  3. 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)

  4. Variations in measured computed tomography number values

    International Nuclear Information System (INIS)

    Computed Tomography (CT) scans of a water phantom have been performed on a number of different CT scanners, and variations in the measured mean pixel value for a central region have been observed. In addition, a positional variation of mean CT number was noted. In particular, the head rest on an EMI CT1010 scanner had a significant effect on the pixel values. To simulate head scanning, a phantom with a Teflon annulus surrounding a water bath was used. This annulus affected both the mean and standard deviation of the pixels in a central area of the scan. Both an mAS and beam width dependence on CT numbers was noted. The effect of calibration on the measured CT numbers for each reconstruction filter was examined on one machine. The variation of CT number with reconstruction matrix and compensation filter was also investigated. These measurements suggest caution must be exercised when interpreting actual CT number values. This will be particularly relevant when the numbers are used to differentiate between tissue types for diagnostic or therapeutic purposes. (author)

  5. 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.

  6. Numbers at work a cultural perspective

    CERN Document Server

    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

  7. Hyperimmunity and A-computable universal numberings

    Science.gov (United States)

    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.

  8. Critical points and number of master integrals

    CERN Document Server

    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.

  9. Ramsey numbers and adiabatic quantum computing

    OpenAIRE

    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...

  10. Topological quantum numbers in nonrelativistic physics

    CERN Document Server

    Thouless, David James

    1998-01-01

    Topological quantum numbers are distinguished from quantum numbers based on symmetry because they are insensitive to the imperfections of the systems in which they are observed. They have become very important in precision measurements in recent years, and provide the best measurements of voltage and electrical resistance. This book describes the theory of such quantum numbers, starting with Dirac's argument for the quantization of electric charge, and continuing with discussions on the helium superfluids, flux quantization and the Josephson effect in superconductors, the quantum Hall effect,

  11. Number projected multi-quasiparticle states

    International Nuclear Information System (INIS)

    The particle-number fluctuation effect on high-K isomers is investigated in the 177Ta nucleus. For this purpose an exact particle-number projection including blocking is performed by means of the Fixed Sharp-BCS method. The deduced multi-quasiparticle energies are compared on one hand to those obtained by means of the blocked-BCS method and on the other hand, to the observed excitation energies of the band heads. The obtained results show that an exact particle-number projection would be necessary for the description of the multi-quasiparticle states, the simple blocked-BCS method being insufficient

  12. Chapter 7. Morphology: Numbers and Numerals

    OpenAIRE

    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...

  13. New bounds for the distance Ramsey number

    OpenAIRE

    Kupavskii, Andrey; Raigorodskii, Andrei; Titova, Maria

    2013-01-01

    In this paper we study the distance Ramsey number $R_{{\\it D}}(s,t,d)$. The \\textit{distance Ramsey number} $R_{{\\it D}}(s,t,d) $ is the minimum number $n$ such that for any graph $ G $ on $ n $ vertices, either $G$ contains an induced $ s $-vertex subgraph isomorphic to a distance graph in $ \\Real^d $ or $ \\bar {G} $ contains an induced $ t $-vertex subgraph isomorphic to the distance graph in $ \\Real^d $. We obtain the upper and lower bounds on $R_{{\\it D}}(s,s,d),$ which are similar to the...

  14. Number of radiological examinations in Sweden 2005

    International Nuclear Information System (INIS)

    An investigation of diagnostic radiology examinations performed in Swedish hospitals for the year 2005 was performed. The investigation revealed the following: - the number of reported investigations was 5,4 million; - conventional x-ray examinations are the most common investigations (approx. 70 %); - the number of computer tomography investigations has increased with 100 % during the last 10 years and is contributing to 55-60 % of the total radiation dose from all examinations; - county hospitals perform most of the examinations, approximately one third; - regional differences can be observed concerning both the number of examinations and how these are distributed amongst the different modalities

  15. 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.

  16. 40 CFR 86.113-07 - Fuel specifications.

    Science.gov (United States)

    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...

  17. Medicare Managed Care: Numbers and Trends

    OpenAIRE

    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.

  18. Unpredictability and the transmission of numbers

    CERN Document Server

    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...

  19. Rhizobial gibberellin negatively regulates host nodule number.

    Science.gov (United States)

    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

  20. An Application of Number Theory to Cryptology.

    Science.gov (United States)

    Snow, Joanne R.

    1989-01-01

    Discussed is an application of number theory to cryptology that can be used with secondary school students. Background on the topics is given first, followed by an explanation for use of the topic. (MNS)

  1. 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.

  2. Positional codes of complex numbers and vectors

    OpenAIRE

    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.

  3. 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....

  4. Chaotic behaviour of high Mach number flows

    Science.gov (United States)

    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.

  5. Bone Mass Measurement: What the Numbers Mean

    Science.gov (United States)

    ... 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 ...

  6. Factorization numbers of finite abelian groups

    OpenAIRE

    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.

  7. 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.

  8. 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.

  9. Character Sums Over The Prime Numbers

    OpenAIRE

    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.

  10. 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)

  11. Generation of Random Numbers by Micromechanism

    Science.gov (United States)

    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.

  12. 10 conjectures in additive number theory

    OpenAIRE

    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 ...

  13. On the Number of 2-SAT Functions

    CERN Document Server

    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.

  14. 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.

  15. Bethe's quantum numbers and rigged configurations

    OpenAIRE

    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).

  16. An algorithm for multipication of Kaluza numbers

    OpenAIRE

    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...

  17. An algorithm for multiplication of Dirac numbers

    OpenAIRE

    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...

  18. Generalizations of Bernoulli numbers and polynomials

    OpenAIRE

    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.

  19. Diophantine approximation and special Liouville numbers

    OpenAIRE

    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...

  20. Two-dimensional Einstein numbers and associativity

    OpenAIRE

    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...

  1. 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.

  2. A monadic, functional implementation of real numbers

    OpenAIRE

    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...

  3. Factorization of the tenth Fermat number

    Science.gov (United States)

    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}.

  4. Determine Ramsey numbers on a quantum computer

    OpenAIRE

    Wang, Hefeng

    2015-01-01

    We present a quantum algorithm for computing the Ramsey numbers whose computational complexity grows super-exponentially with the number of vertices of a graph on a classical computer. The problem is mapped to a decision problem on a quantum computer, a probe qubit is coupled to a register that represents the problem and detects the energy levels of the problem Hamiltonian. The decision problem is solved by determining whether the probe qubit exhibits resonance dynamics. The algorithm shows a...

  5. Fibonacci and Lucas numbers with applications

    CERN Document Server

    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

  6. Factorization of numbers with physical systems

    OpenAIRE

    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...

  7. Virtual Betti numbers of real algebraic varieties

    OpenAIRE

    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).

  8. Hyperbolic complex numbers in two dimensions

    OpenAIRE

    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...

  9. Multiperfect Numbers in Certain Quadratic Rings

    OpenAIRE

    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.

  10. The number and probability of canalizing functions

    OpenAIRE

    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...

  11. The NumbersWithNames Program

    OpenAIRE

    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...

  12. A number-phase Wigner function

    Energy Technology Data Exchange (ETDEWEB)

    Moya-Cessa, Hector [INAOE, Coordinacion de Optica, Apartado Postal 51 y 216, 72000 Puebla, Puebla (Mexico)

    2003-06-01

    One of the most prominent quasiprobability functions in quantum mechanics is the Wigner function, which gives the correct marginal probability functions if integrated over position or momentum. Here we depart from the definition of the position-momentum Wigner function to, by analogy, construct a number-phase Wigner function that, if summed over photon numbers, gives the correct phase distribution and, if integrated over phase, gives the correct photon distribution.

  13. Realism’s understanding of negative numbers

    Directory of Open Access Journals (Sweden)

    Bojanić Petar

    2016-01-01

    Full Text Available Our topic is the understanding of the nature of negative numbers - the entities to which expressions such as ‘-1’ refer. Following Frege, we view positive whole numbers as providing the answer to the question „how many?“ In this light, how are we to view negative numbers? Both positive and negative numbers can be ordered through the relation of larger or smaller. It is then true of all negative numbers that they are entities which are (somehow smaller than zero. For many, this has been understood as an ontological paradox: how can something be „less than nothing?“ Some propose to avoid the paradox by treating negative numbers as mere façons de parler. In this paper, we propose a more realist account, taking as our starting point the thesis that there is at least one familiar type of object, the magnitude of which can be expressed with negative numbers, namely, debt. How can the sense of an expression be ontologically paradoxical, yet the expression itself still plausibly refer to a social object such as a debt? Or, put differently, how is it possible to be, at the same time, a realist in financial theory and a nominalist in mathematical theory? The paper first shows that the paradox arises when the two distinct ways in which negative numbers are connected to real objects are run together. The first of the two refers to debt only, whereas the second could refer to debt, as well as to physical objects. Finally, we claim that a debt is at once a specifically social object and part of reality as described by physics.

  14. Some Exact Ramsey-Tur\\'an Numbers

    OpenAIRE

    Balogh, József; Lenz, John

    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)

  15. Persistent consequences of atypical early number concepts

    Directory of Open Access Journals (Sweden)

    MichèleM. M.Mazzocco

    2013-09-01

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

  16. Patterns in rational base number systems

    CERN Document Server

    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 ...

  17. Mechanisms of Chromosome Number Evolution in Yeast

    Science.gov (United States)

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

    2011-01-01

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

  18. Chromosome number evolution in skippers (Lepidoptera, Hesperiidae).

    Science.gov (United States)

    Lukhtanov, Vladimir A

    2014-01-01

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

  19. Chromosome number evolution in skippers (Lepidoptera, Hesperiidae

    Directory of Open Access Journals (Sweden)

    Vladimir Lukhtanov

    2014-11-01

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

  20. Mining for Numbers. A Heuristic Approach to Some Prime Number Work

    Science.gov (United States)

    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)

  1. 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

  2. Summation Formulas Involving Binomial Coefficients, Harmonic Numbers, and Generalized Harmonic Numbers

    OpenAIRE

    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...

  3. 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.

  4. 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.

  5. Variable copy number DNA sequences in rice.

    Science.gov (United States)

    Kikuchi, S; Takaiwa, F; Oono, K

    1987-12-01

    We have cloned two types of variable copy number DNA sequences from the rice embryo genome. One of these sequences, which was cloned in pRB301, was amplified about 50-fold during callus formation and diminished in copy number to the embryonic level during regeneration. The other clone, named pRB401, showed the reciprocal pattern. The copy numbers of both sequences were changed even in the early developmental stage and eliminated from nuclear DNA along with growth of the plant. Sequencing analysis of the pRB301 insert revealed some open reading frames and direct repeat structures, but corresponding sequences were not identified in the EMBL and LASL DNA databases. Sequencing of the nuclear genomic fragment cloned in pRB401 revealed the presence of the 3'rps12-rps7 region of rice chloroplast DNA. Our observations suggest that during callus formation (dedifferentiation), regeneration and the growth process the copy numbers of some DNA sequences are variable and that nuclear integrated chloroplast DNA acts as a variable copy number sequence in the rice genome. Based on data showing a common sequence in mitochondria and chloroplast DNA of maize (Stern and Lonsdale 1982) and that the rps12 gene of tobacco chloroplast DNA is a divided gene (Torazawa et al. 1986), it is suggested that the sequence on the inverted repeat structure of chloroplast DNA may have the character of a movable genetic element. PMID:3481021

  6. True random numbers from amplified quantum vacuum.

    Science.gov (United States)

    Jofre, M; Curty, M; Steinlechner, F; Anzolin, G; Torres, J P; Mitchell, M W; Pruneri, V

    2011-10-10

    Random numbers are essential for applications ranging from secure communications to numerical simulation and quantitative finance. Algorithms can rapidly produce pseudo-random outcomes, series of numbers that mimic most properties of true random numbers while quantum random number generators (QRNGs) exploit intrinsic quantum randomness to produce true random numbers. Single-photon QRNGs are conceptually simple but produce few random bits per detection. In contrast, vacuum fluctuations are a vast resource for QRNGs: they are broad-band and thus can encode many random bits per second. Direct recording of vacuum fluctuations is possible, but requires shot-noise-limited detectors, at the cost of bandwidth. We demonstrate efficient conversion of vacuum fluctuations to true random bits using optical amplification of vacuum and interferometry. Using commercially-available optical components we demonstrate a QRNG at a bit rate of 1.11 Gbps. The proposed scheme has the potential to be extended to 10 Gbps and even up to 100 Gbps by taking advantage of high speed modulation sources and detectors for optical fiber telecommunication devices. PMID:21997077

  7. Unpredictability and the transmission of numbers

    Science.gov (United States)

    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.

  8. Approximate particle number projection in hot nuclei

    International Nuclear Information System (INIS)

    Heated finite systems like, e.g., hot atomic nuclei have to be described by the canonical partition function. But this is a quite difficult technical problem and, as a rule, the grand canonical partition function is used in the studies. As a result, some shortcomings of the theoretical description appear because of the thermal fluctuations of the number of particles. Moreover, in nuclei with pairing correlations the quantum number fluctuations are introduced by some approximate methods (e.g., by the standard BCS method). The exact particle number projection is very cumbersome and an approximate number projection method for T ≠ 0 basing on the formalism of thermo field dynamics is proposed. The idea of the Lipkin-Nogami method to perform any operator as a series in the number operator powers is used. The system of equations for the coefficients of this expansion is written and the solution of the system in the next approximation after the BCS one is obtained. The method which is of the 'projection after variation' type is applied to a degenerate single j-shell model. 14 refs., 1 tab

  9. Detection of Chern numbers and entanglement in topological multi-component systems through subsystem winding numbers

    NARCIS (Netherlands)

    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

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

    OpenAIRE

    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.

  11. Quantum random number generator based on the photon number decision of weak laser pulses

    OpenAIRE

    Wei, Wei; Zhang, J W; Liu, Tian; Guo, Hong

    2008-01-01

    We propose an approach to realize a quantum random number generator (QRNG) based on the photon number decision of weak laser pulses. This type of QRNG can generate true random numbers at a high speed and can be adjusted to zero bias conveniently, thus is suitable for the applications in quantum cryptography.

  12. Chamber Structure of Double Hurwitz numbers

    CERN Document Server

    Cavalieri, Renzo; Markwig, Hannah

    2010-01-01

    Double Hurwitz numbers count covers of the projective line by genus g curves with assigned ramification profiles over 0 and infinity, and simple ramification over a fixed branch divisor. Goulden, Jackson and Vakil have shown double Hurwitz numbers are piecewise polynomial in the orders of ramification, and Shadrin, Shapiro and Vainshtein have determined the chamber structure and wall crossing formulas for g=0. This paper gives a unified approach to these results and strengthens them in several ways -- the most important being the extension of the results of Shapiro, Shadrin and Vainshtein to arbitrary genus. The main tool is the authors' previous work expressing double Hurwitz number as a sum over certain labeled graphs. We identify the labels of the graphs with lattice points in the chambers of certain hyperplane arrangements, which are well known to give rise to piecewise polynomial functions. Our understanding of the wall crossing for these functions builds on the work of Varchenko, and could have broader ...

  13. Optimal Strouhal number for swimming animals

    Science.gov (United States)

    Eloy, Christophe

    2012-04-01

    To evaluate the swimming performances of aquatic animals, an important dimensionless quantity is the Strouhal number, St=fA/U, with f the tail-beat frequency, A the peak-to-peak tail amplitude, and U the swimming velocity. Experiments with flapping foils have exhibited maximum propulsive efficiency in the interval 0.25animals likely evolved to swim in the same narrow interval. Using Lighthill's elongated-body theory to address undulatory propulsion, it is demonstrated here that the optimal Strouhal number increases from 0.15 to 0.8 for animals spanning from the largest cetaceans to the smallest tadpoles. To assess the validity of this model, the swimming kinematics of 53 different species of aquatic animals have been compiled from the literature and it shows that their Strouhal numbers are consistently near the predicted optimum.

  14. Boundary induced nonlinearities at small Reynolds numbers

    Science.gov (United States)

    Sbragaglia, M.; Sugiyama, K.

    2007-04-01

    We investigate the importance of boundary slip at finite Reynolds numbers for mixed boundary conditions. Nonlinear effects are induced by the non-homogeneity of the boundary condition and change the symmetry properties of the flow with an overall mean flow reduction. To explain the observed drag modification, exact reciprocal relations in the presence of heterogeneous boundary conditions are derived. The small-Reynolds-number limit predicts a reduction of the mean flow rate from the creeping flow to be proportional to the second power of the Reynolds number. To further support our theoretical analysis, numerical simulations with the lattice Boltzmann method (LBM) and finite difference method (FDM) are performed and reveal a pronounced numerical efficiency of LBM with respect to FDM.

  15. 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.

  16. Number Counts and Dynamical Vacuum Cosmologies

    CERN Document Server

    Devi, N Chandrachani; Carneiro, S; Alcaniz, J S

    2014-01-01

    We study non-linear structure formation in an interacting model of the dark sector of the Universe in which the dark energy density decays linearly with the Hubble parameter, $\\rho_{\\Lambda} \\propto H$, leading to a constant-rate creation of cold dark matter. We derive all relevant expressions to calculate the mass function and the cluster number density using the Sheth-Torman formalism and show that the effect of the interaction process is to increase the number of bound structures of large masses ($M \\gtrsim 10^{14} M_{\\odot}h^{-1}$) when compared to the standard $\\Lambda$CDM model. Since these models are not reducible to each other, this number counts signature can in principle be tested in future surveys.

  17. Factorization of numbers using chirped pulses

    International Nuclear Information System (INIS)

    Full text: In this work we present a physical system that combines wavepacket dynamics and number theory. It has been shown that Gauss-sums, which involve quadratic phase factors, may be utilized to obtain the prime factor components of a given number N. As the physical system we choose a two-photon transition which is driven by a chirped laser pulse. In addition to a ground and an excited state the underlying level scheme contains a harmonic manifold of intermediate states. Quantum interference of multiple excitation paths is the key mechanism of this factorization scheme. We show how quadratic phase factors enter and present a recipe to encode the number N and reveal its prime components. Refs. 2 (author)

  18. Optimal Strouhal number for swimming animals

    CERN Document Server

    Eloy, Christophe

    2011-01-01

    To evaluate the swimming performances of aquatic animals, an important dimensionless quantity is the Strouhal number, St = fA/U, with f the tail-beat frequency, A the peak-to-peak tail amplitude, and U the swimming velocity. Experiments with flapping foils have exhibited maximum propulsive efficiency in the interval 0.25 < St < 0.35 and it has been argued that animals likely evolved to swim in the same narrow interval. Using Lighthill's elongated-body theory to address undulatory propulsion, it is demonstrated here that the optimal Strouhal number increases from 0.15 to 0.8 for animals spanning from the largest cetaceans to the smallest tadpoles. To assess the validity of this model, the swimming kinematics of 53 different species of aquatic animals have been compiled from the literature and it shows that their Strouhal numbers are consistently near the predicted optimum.

  19. 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.

  20. The energy key numbers 1983-1984

    International Nuclear Information System (INIS)

    ''The energy key numbers 1983-1984'' present synthetically, in tabular and diagram form, the essential data 1) of the different energy sources (petroleum, natural gas, coal) in France and in the world: the production, the reserves the consumption and the foreign trade evolution; 2) of the electricity consumption, of the hydraulic and nuclear origin electricty in France and in the world; 3) of the renewable energies in France; 4) of the rational use of energy: aims and results in the industrial, residential, tertiary and transport sectors. The numbers given in this book cover the years 1960-1990. The estimated numbers have been established from a hypothesis of the 3,1% growth of the gross domestic product a year from 1985 to 1990, taking into account the realizations or estimations fo economic growth from 1981 to 1984