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Probability theory --- Uniform distribution (Probability theory) --- 511 --- Series --- Distribution, Rectangular (Probability theory) --- Distribution, Uniform (Probability theory) --- Rectangular distribution (Probability theory) --- Probabilities --- Algebra --- Mathematics --- Processes, Infinite --- Sequences (Mathematics) --- Number theory --- 511 Number theory
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Mathematical analysis --- Numerical analysis --- Probability theory --- Number theory --- Sequences (Mathematics) --- Uniform distribution (Probability theory) --- 511 --- 511.3 --- Distribution, Uniform (Probability theory) --- #WWIS:ALTO --- Distribution, Rectangular (Probability theory) --- Rectangular distribution (Probability theory) --- Probabilities --- Mathematical sequences --- Numerical sequences --- Algebra --- Mathematics --- Analytical, additive and other number-theory problems. Diophantine approximations --- Sequences (Mathematics). --- Uniform distribution (Probability theory). --- 511.3 Analytical, additive and other number-theory problems. Diophantine approximations --- 511 Number theory --- Suites (mathématiques) --- Distribution (théorie des probabilités) --- Distribution (Probability theory) --- Suites (mathématiques) --- Distribution (théorie des probabilités)
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Probability theory --- Geometric measure theory. --- Mesure géométrique, Théorie de la. --- Uniform distribution (Probability theory) --- Distribution uniforme (théorie des probabilités) --- Gaussian processes. --- Processus gaussiens. --- Gaussian processes --- Geometric measure theory --- Sobolov spaces --- Distribution, Rectangular (Probability theory) --- Distribution, Uniform (Probability theory) --- Rectangular distribution (Probability theory) --- Probabilities --- Measure theory --- Distribution (Probability theory) --- Stochastic processes
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What is the minimum dimension of a niche space necessary to represent the overlaps among observed niches? This book presents a new technique for obtaining a partial answer to this elementary question about niche space. The author bases his technique on a relation between the combinatorial structure of food webs and the mathematical theory of interval graphs. Professor Cohen collects more than thirty food webs from the ecological literature and analyzes their statistical and combinatorial properties in detail. As a result, he is able to generalize: within habitats of a certain limited physical and temporal heterogeneity, the overlaps among niches, along their trophic (feeding) dimensions, can be represented in a one-dimensional niche space far more often than would be expected by chance alone and perhaps always. This compatibility has not previously been noticed. It indicates that real food webs fall in a small subset of the mathematically possible food webs. Professor Cohen discusses other apparently new features of real food webs, including the constant ratio of the number of kinds of prey to the number of kinds of predators in food webs that describe a community. In conclusion he discusses possible extensions and limitations of his results and suggests directions for future research.
Niche (Ecology) --- Food chains (Ecology) --- Accipiter. --- Conus. --- Desmognathus. --- Hawaii. --- Lake Nyasa. --- Monte Carlo simulation. --- algorithm. --- aspen forest. --- column average. --- column variance. --- composite community. --- creek. --- eating relation. --- feeding relation. --- gastropods. --- independence of niche dimensions. --- inequalities. --- intersection graph. --- marine bench. --- niche overlap graph. --- overlap. --- predator. --- pseudo-random food web. --- qualitative stability. --- resource partitioning. --- salamanders. --- sampling. --- sink food web. --- temperature. --- uniform distribution. --- variance test. --- Food chains (Ecology). --- Niche (Ecology).
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The main purpose of this book is to give an overview of the developments during the last 20 years in the theory of uniformly distributed sequences. The authors focus on various aspects such as special sequences, metric theory, geometric concepts of discrepancy, irregularities of distribution, continuous uniform distribution and uniform distribution in discrete spaces. Specific applications are presented in detail: numerical integration, spherical designs, random number generation and mathematical finance. Furthermore over 1000 references are collected and discussed. While written in the style of a research monograph, the book is readable with basic knowledge in analysis, number theory and measure theory.
Mathematical analysis --- Distribution [Rectangular ] (Probability theory) --- Distribution [Uniform ] (Probability theory) --- Distribution uniforme (Théorie des probabilités) --- Mathematical sequences --- Numerical sequences --- Numerieke reeksen --- Rectangular distribution (Probability theory) --- Reeksen (Wiskunde) --- Sequences (Mathematics) --- Suites (Mathématiques) --- Suites numériques --- Uniform distribution (Probability theory) --- Uniforme verdeling (Theorie van de probabiliteiten) --- Verdeling [Uniforme ] (Theorie van de probabiliteiten) --- Wiskundige reeksen --- Applied Mathematics --- Mathematical Theory --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Number theory. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra --- Distribution, Rectangular (Probability theory) --- Distribution, Uniform (Probability theory) --- Probabilities --- Theorie des nombres --- Theorie probabiliste
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This book provides the first comprehensive treatment of Benford's law, the surprising logarithmic distribution of significant digits discovered in the late nineteenth century. Establishing the mathematical and statistical principles that underpin this intriguing phenomenon, the text combines up-to-date theoretical results with overviews of the law's colorful history, rapidly growing body of empirical evidence, and wide range of applications.An Introduction to Benford's Law begins with basic facts about significant digits, Benford functions, sequences, and random variables, including tools from the theory of uniform distribution. After introducing the scale-, base-, and sum-invariance characterizations of the law, the book develops the significant-digit properties of both deterministic and stochastic processes, such as iterations of functions, powers of matrices, differential equations, and products, powers, and mixtures of random variables. Two concluding chapters survey the finitely additive theory and the flourishing applications of Benford's law.Carefully selected diagrams, tables, and close to 150 examples illuminate the main concepts throughout. The text includes many open problems, in addition to dozens of new basic theorems and all the main references. A distinguishing feature is the emphasis on the surprising ubiquity and robustness of the significant-digit law. This text can serve as both a primary reference and a basis for seminars and courses.
Distribution (Probability theory) --- Probability measures. --- Measures, Normalized --- Measures, Probability --- Normalized measures --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Bayesian models. --- Benford distribution. --- Benford distributions. --- Benford functions. --- Benford sequences. --- Benford's law. --- First-digit law. --- Significant-digit law. --- base-invariance property. --- computations. --- computer science. --- diagnostics. --- differential equations. --- exponential growth. --- finitely additive probability. --- fraud detection. --- functions. --- geometric Brownian motion. --- linear processes. --- logarithmic distribution. --- mathematical hypotheses. --- mathematical theory. --- multi-dimensional models. --- natural phenomena. --- one-dimensional deterministic systems. --- one-dimensional difference. --- pedagogical tool. --- polynomial growth. --- random matrices. --- random processes. --- random variables. --- scale-invariance property. --- sequences. --- significand functions. --- significands. --- significant digits. --- statistical distribution. --- stochastic process. --- sum-invariance property. --- superexponential growth. --- surveys. --- uniform distribution.
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Metal-based composites represent a unique way of tailoring the properties of metals, through the selection of type, size, and amount of reinforcement. In this way, the properties of metallic matrices can be adjusted depending on end applications. In view of the dynamic capabilities they can exhibit, this Special Issue will cover all aspects of metal matrix composites: synthesis (including solid, liquid, two-phase and 3D printing); secondary processing; properties (tensile, compressive, fatigue, impact, creep, tribological, etc.); corrosion behavior; and joining techniques. The main objective is to share the latest results on metal matrix composites with the research community worldwide.
History of engineering & technology --- Mg-3Al-0.4Ce alloy --- nano ZnO particles --- uniform distribution --- strength --- titanium matrix composite --- constitutive model --- interfacial debonding --- high temperature --- elastoplastic properties --- nano-sized SiCp --- aluminum matrix composites --- mechanical properties --- microstructures --- Mg-Al-RE alloy --- magnesium alloy --- damping --- Al11La3 phase --- nanosize reinforcement --- spark plasma sintering --- Cu-TiC --- in-situ composites --- mechanical milling --- iron aluminum alloys --- cold/hot PM --- compressibility factor --- wear resistance --- Al-Zn-Cr alloys --- powder metallurgy --- strengthening --- extrusion --- dry sliding wear --- synthesis of core-shell metal nanoparticles --- Cu@Ag composite nanoparticle --- metal mesh --- screen printing --- touch screen panel --- tungsten composites --- tungsten-fibre-net reinforcement --- tensile strength --- metal matrix composites --- nickel --- aluminum --- carbon nanotubes --- ultrasonication --- microstructural characterization --- Magnesium --- Sm2O3 nanoparticles --- compression properties --- microstructure --- ignition --- carbon nanotube --- nanocomposite --- dispersion --- interfacial adhesion --- phase transformation --- physicomechanical properties --- nanoparticles --- metal matrix nanocomposite (MMNC) --- AlN --- magnesium alloy AM60 --- strengthening mechanisms --- in situ titanium composites --- microstructure analysis --- TiB precipitates --- 7075 Al alloy --- reduced graphene oxide --- strengthening mechanism --- metal matrix nanocomposite --- copper --- graphene --- thermal expansion coefficient --- thermal conductivity --- electrical resistance --- thixoforging --- magnesium-based composite --- fracture --- magnesium-alloy-based composite --- Halpin-Tsai-Kardos model --- deformation behavior --- composite strengthening --- fracture behavior --- magnesium --- high entropy alloy --- composite --- hardness --- compressive properties --- tricalcium phosphate --- compression --- corrosion --- Mg-3Al-0.4Ce alloy --- nano ZnO particles --- uniform distribution --- strength --- titanium matrix composite --- constitutive model --- interfacial debonding --- high temperature --- elastoplastic properties --- nano-sized SiCp --- aluminum matrix composites --- mechanical properties --- microstructures --- Mg-Al-RE alloy --- magnesium alloy --- damping --- Al11La3 phase --- nanosize reinforcement --- spark plasma sintering --- Cu-TiC --- in-situ composites --- mechanical milling --- iron aluminum alloys --- cold/hot PM --- compressibility factor --- wear resistance --- Al-Zn-Cr alloys --- powder metallurgy --- strengthening --- extrusion --- dry sliding wear --- synthesis of core-shell metal nanoparticles --- Cu@Ag composite nanoparticle --- metal mesh --- screen printing --- touch screen panel --- tungsten composites --- tungsten-fibre-net reinforcement --- tensile strength --- metal matrix composites --- nickel --- aluminum --- carbon nanotubes --- ultrasonication --- microstructural characterization --- Magnesium --- Sm2O3 nanoparticles --- compression properties --- microstructure --- ignition --- carbon nanotube --- nanocomposite --- dispersion --- interfacial adhesion --- phase transformation --- physicomechanical properties --- nanoparticles --- metal matrix nanocomposite (MMNC) --- AlN --- magnesium alloy AM60 --- strengthening mechanisms --- in situ titanium composites --- microstructure analysis --- TiB precipitates --- 7075 Al alloy --- reduced graphene oxide --- strengthening mechanism --- metal matrix nanocomposite --- copper --- graphene --- thermal expansion coefficient --- thermal conductivity --- electrical resistance --- thixoforging --- magnesium-based composite --- fracture --- magnesium-alloy-based composite --- Halpin-Tsai-Kardos model --- deformation behavior --- composite strengthening --- fracture behavior --- magnesium --- high entropy alloy --- composite --- hardness --- compressive properties --- tricalcium phosphate --- compression --- corrosion
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