2010, De Gruyter studies in mathematics, ISBN 3110215306, Volume 37, xi, 313

Book

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2010, Volume 2010, Issue 1, pp. 1 - 84

By looking back at the long history of bounding the ratio Gamma (x+a)/ Gamma (x+b) for x>-min[Function{a,b} and a,b[isin]R, various origins of this topic...

Mathematics, general | Mathematics | Applications of Mathematics | Analysis | MATHEMATICS | MATHEMATICS, APPLIED | DIGAMMA | REFINEMENTS | INCOMPLETE GAMMA | INEQUALITIES | EXTENSIONS | CONVEXITY | PROPERTY | PRODUCT | MONOTONIC FUNCTIONS | UNIT BALL | Studies | Computer science | Laplace transforms | Convex analysis | Gamma function | Origins | Inequalities

Mathematics, general | Mathematics | Applications of Mathematics | Analysis | MATHEMATICS | MATHEMATICS, APPLIED | DIGAMMA | REFINEMENTS | INCOMPLETE GAMMA | INEQUALITIES | EXTENSIONS | CONVEXITY | PROPERTY | PRODUCT | MONOTONIC FUNCTIONS | UNIT BALL | Studies | Computer science | Laplace transforms | Convex analysis | Gamma function | Origins | Inequalities

Journal Article

Annals of Statistics, ISSN 0090-5364, 10/2009, Volume 37, Issue 5 B, pp. 3059 - 3097

Journal Article

Annals of Physics, ISSN 0003-4916, 08/2018, Volume 395, pp. 238 - 274

.... In this paper we consider a log-regularized version of this family and use it as a family of potential functions to generate covariant (0,2...

Quantum divergence | Quantum information theory | Quantum relative entropy | Quantum metric tensor | TRACE | PHYSICS, MULTIDISCIPLINARY | INFORMATION | MONOTONE RIEMANNIAN METRICS | Atoms | Freedom of speech

Quantum divergence | Quantum information theory | Quantum relative entropy | Quantum metric tensor | TRACE | PHYSICS, MULTIDISCIPLINARY | INFORMATION | MONOTONE RIEMANNIAN METRICS | Atoms | Freedom of speech

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 2018, Volume 553, pp. 238 - 251

This paper concerns three classes of real-valued functions on intervals, operator monotone functions, operator convex functions, and strongly operator convex functions...

Operator convex functions | Strongly operator convex functions | Operator monotone functions | Completely monotone functions | Loewner theorem | Pick functions | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | MAJORIZATION | Operators (mathematics) | Monotone functions | Mathematical analysis | Inequalities | Mathematical functions | Convexity | Convex analysis | Continuity (mathematics)

Operator convex functions | Strongly operator convex functions | Operator monotone functions | Completely monotone functions | Loewner theorem | Pick functions | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | MAJORIZATION | Operators (mathematics) | Monotone functions | Mathematical analysis | Inequalities | Mathematical functions | Convexity | Convex analysis | Continuity (mathematics)

Journal Article

Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, ISSN 1350-7265, 2013, Volume 19, Issue 4, pp. 1327 - 1349

Isotropic positive definite functions on spheres play important roles in spatial statistics, where they occur as the correlation functions of homogeneous random fields and star-shaped random particles...

Integers | Mathematical theorems | Great circles | Correlations | Mathematical independent variables | Mathematical functions | Euclidean space | Coefficients | Fourier coefficients | Completely monotone | Radial basis function | Covariance localization | Isotropic | Schoenberg coefficients | Interpolation of scattered data | Locally supported | Multiquadric | Fractal index | Pólya criterion | multiquadric | completely monotone | METRIC-SPACES | isotropic | Polya criterion | fractal index | STATISTICS & PROBABILITY | covariance localization | KERNELS | CIRCLE | FAMILY | INTERPOLATION | radial basis function | MODELS | locally supported | interpolation of scattered data

Integers | Mathematical theorems | Great circles | Correlations | Mathematical independent variables | Mathematical functions | Euclidean space | Coefficients | Fourier coefficients | Completely monotone | Radial basis function | Covariance localization | Isotropic | Schoenberg coefficients | Interpolation of scattered data | Locally supported | Multiquadric | Fractal index | Pólya criterion | multiquadric | completely monotone | METRIC-SPACES | isotropic | Polya criterion | fractal index | STATISTICS & PROBABILITY | covariance localization | KERNELS | CIRCLE | FAMILY | INTERPOLATION | radial basis function | MODELS | locally supported | interpolation of scattered data

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2019, Volume 2019, Issue 1, pp. 1 - 42

Let Γ(x) $\varGamma (x)$ denote the classical Euler gamma function. The logarithmic derivative ψ(x)=[lnΓ(x)]′=Γ′(x)Γ(x) $\psi (x)=[\ln \varGamma (x)]'=\frac{\varGamma '(x)}{ \varGamma (x)}$, ψ′(x) $\psi '(x)$, and ψ″(x) $\psi ''(x...

Completely monotonic degree | 26A51 | 26D10 | Digamma function | Necessary and sufficient condition | Mathematics | Generalization | Polygamma function | Complete monotonicity | 33D05 | 44A10 | Ratio of gamma functions | Mathematics, general | Open problem | Applications of Mathematics | 26A48 | 33B15 | Divided difference | Logarithmically completely monotonic function | Analysis | Trigamma function | q -analog | Application | 26D15 | Tetragamma function | Inequality | q-analog | LAH NUMBERS | MATHEMATICS, APPLIED | STIRLING NUMBERS | MATHEMATICS | BOUNDS | INTEGRAL-REPRESENTATIONS | SHARP INEQUALITIES | DIGAMMA | POLYGAMMA | TRIGAMMA | PSI | DIVIDED DIFFERENCES | Gamma function | Inequalities

Completely monotonic degree | 26A51 | 26D10 | Digamma function | Necessary and sufficient condition | Mathematics | Generalization | Polygamma function | Complete monotonicity | 33D05 | 44A10 | Ratio of gamma functions | Mathematics, general | Open problem | Applications of Mathematics | 26A48 | 33B15 | Divided difference | Logarithmically completely monotonic function | Analysis | Trigamma function | q -analog | Application | 26D15 | Tetragamma function | Inequality | q-analog | LAH NUMBERS | MATHEMATICS, APPLIED | STIRLING NUMBERS | MATHEMATICS | BOUNDS | INTEGRAL-REPRESENTATIONS | SHARP INEQUALITIES | DIGAMMA | POLYGAMMA | TRIGAMMA | PSI | DIVIDED DIFFERENCES | Gamma function | Inequalities

Journal Article

Journal of computational and applied mathematics, ISSN 0377-0427, 2010, Volume 233, Issue 9, pp. 2149 - 2160

In the present paper, we establish necessary and sufficient conditions for the functions x α | ψ ( i ) ( x + β ) | and α | ψ ( i ) ( x + β ) | − x | ψ ( i + 1 ) ( x + β...

Completely monotonic function | Bernoulli numbers | Infinite series | Monotonicity | Polygamma function | GAMMA | MATHEMATICS, APPLIED | INEQUALITIES | PROPERTY | Mathematics - Classical Analysis and ODEs

Completely monotonic function | Bernoulli numbers | Infinite series | Monotonicity | Polygamma function | GAMMA | MATHEMATICS, APPLIED | INEQUALITIES | PROPERTY | Mathematics - Classical Analysis and ODEs

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 04/2006, Volume 134, Issue 4, pp. 1153 - 1160

We give an infinite family of functions involving the gamma function whose logarithmic derivatives are completely monotonic...

Income inequality | Mathematical theorems | Mathematical integrals | Mathematical independent variables | Mathematical inequalities | Mathematical functions | Gamma function | Monotonic functions | Completely monotonic functions | Inequalities | q-gamma function | MATHEMATICS | MATHEMATICS, APPLIED | inequalities | completely monotonic functions | HARMONIC MEAN INEQUALITY

Income inequality | Mathematical theorems | Mathematical integrals | Mathematical independent variables | Mathematical inequalities | Mathematical functions | Gamma function | Monotonic functions | Completely monotonic functions | Inequalities | q-gamma function | MATHEMATICS | MATHEMATICS, APPLIED | inequalities | completely monotonic functions | HARMONIC MEAN INEQUALITY

Journal Article

SIAM journal on computing, ISSN 1095-7111, 2011, Volume 40, Issue 6, pp. 1740 - 1766

Let f : 2(X) -> R+ be a monotone submodular set function, and let (X, I) be a matroid. We consider the problem max...

Social welfare | Monotone submodular set function | Generalized assignment problem | Approximation algorithm | Matroid | LOCATION | MATHEMATICS, APPLIED | social welfare | APPROXIMATIONS | ALGORITHM | approximation algorithm | monotone submodular set function | COMPUTER SCIENCE, THEORY & METHODS | COMBINATORIAL AUCTIONS | matroid | generalized assignment problem

Social welfare | Monotone submodular set function | Generalized assignment problem | Approximation algorithm | Matroid | LOCATION | MATHEMATICS, APPLIED | social welfare | APPROXIMATIONS | ALGORITHM | approximation algorithm | monotone submodular set function | COMPUTER SCIENCE, THEORY & METHODS | COMBINATORIAL AUCTIONS | matroid | generalized assignment problem

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2010, Volume 368, Issue 1, pp. 293 - 310

Associated to a lower semicontinuous function, one can define its proximal mapping and farthest mapping...

Limiting subdifferential | Moreau envelope | Farthest mapping | Hypoconvex function | Proximal mapping | Essentially strictly convex function | Monotone operator | Strongly convex function | Klee function | Chebyshev function | Prox-regular function | Klee envelope | Prox-bounded lower semicontinuous function | MATHEMATICS, APPLIED | PROX-REGULAR FUNCTIONS | MATHEMATICS | BANACH-SPACES | SETS

Limiting subdifferential | Moreau envelope | Farthest mapping | Hypoconvex function | Proximal mapping | Essentially strictly convex function | Monotone operator | Strongly convex function | Klee function | Chebyshev function | Prox-regular function | Klee envelope | Prox-bounded lower semicontinuous function | MATHEMATICS, APPLIED | PROX-REGULAR FUNCTIONS | MATHEMATICS | BANACH-SPACES | SETS

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 1/2014, Volume 160, Issue 1, pp. 67 - 89

... (convexity, log-convexity, reciprocal concavity) of a certain function of several arguments that had manifested in a number of contexts concerned with optimization problems...

Bernstein function | Harmonically convex function | Borwein–Affleck–Girgensohn function | Completely monotone function | Mathematics | Theory of Computation | Optimization | Quasi-arithmetic mean | Kolmogorov–Nagumo mean | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | Laplace transform | Borwein-Affleck-Girgensohn function | Kolmogorov-Nagumo mean | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COUPON-COLLECTORS PROBLEM | TIME | Studies | Mathematical functions | Laplace transforms | Mathematical analysis | Concavity | Convexity

Bernstein function | Harmonically convex function | Borwein–Affleck–Girgensohn function | Completely monotone function | Mathematics | Theory of Computation | Optimization | Quasi-arithmetic mean | Kolmogorov–Nagumo mean | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | Laplace transform | Borwein-Affleck-Girgensohn function | Kolmogorov-Nagumo mean | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COUPON-COLLECTORS PROBLEM | TIME | Studies | Mathematical functions | Laplace transforms | Mathematical analysis | Concavity | Convexity

Journal Article

Statistics & probability letters, ISSN 0167-7152, 2020, Volume 157, p. 108620

...d of positive definite radial functions. In particular, we study the positive definiteness of the operator...

Positive definite | Completely monotonic | Fourier transforms | Radial functions | STATISTICS & PROBABILITY | DIMENSION

Positive definite | Completely monotonic | Fourier transforms | Radial functions | STATISTICS & PROBABILITY | DIMENSION

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 03/2019, Volume 180, Issue 3, pp. 751 - 774

The signed distance function (or oriented distance function) of a set in a metric space determines the distance of a given point from the boundary of the set, with the sign determined by whether the point is in the set or in its...

Maximally monotone operator | Skeleton of a convex set | Not convex subdifferential domain | Subdifferential | Paramonotone operator | Signed distance function | Nearly convex sets | Fenchel conjugate | Boundary projection | MATHEMATICS, APPLIED | CONVEXITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SETS | MONOTONE-OPERATORS | Knowledge | Analysis | Domains | Fuzzy sets | Applications of mathematics | Metric space | Mathematical analysis

Maximally monotone operator | Skeleton of a convex set | Not convex subdifferential domain | Subdifferential | Paramonotone operator | Signed distance function | Nearly convex sets | Fenchel conjugate | Boundary projection | MATHEMATICS, APPLIED | CONVEXITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SETS | MONOTONE-OPERATORS | Knowledge | Analysis | Domains | Fuzzy sets | Applications of mathematics | Metric space | Mathematical analysis

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2017, Volume 2017, Issue 1, pp. 1 - 17

... ∗ ) $x\in(0, x^{\ast})$ and Γ ( x + 1 ) < ( x 2 + 1 / γ ) / ( x + 1 / γ ) $\Gamma(x+1)<(x^{2}+1/\gamma)/(x+1/\gamma )$ for x ∈ ( x ∗ , 1 ) $x\in(x^{\ast}, 1)$ , where Γ ( x ) $\Gamma(x)$ is the classical gamma function...

33B15 | rational bound | psi function | Analysis | gamma function | Mathematics, general | Mathematics | 41A60 | Applications of Mathematics | 26D07 | completely monotonic function | MATHEMATICS | MATHEMATICS, APPLIED | FUNCTION INEQUALITY | completely monotonicn function | Gamma function | Research

33B15 | rational bound | psi function | Analysis | gamma function | Mathematics, general | Mathematics | 41A60 | Applications of Mathematics | 26D07 | completely monotonic function | MATHEMATICS | MATHEMATICS, APPLIED | FUNCTION INEQUALITY | completely monotonicn function | Gamma function | Research

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2016, Volume 19, Issue 5, pp. 1105 - 1160

...) and Excess wing model are among the most famous. Their description in the time domain involves some mathematical functions whose knowledge is of fundamental importance for a full understanding of the models...

fractional calculus | Mittag-Leffler functions | Primary 26A33 | 44A10 | Secondary 33E12 | differential operators | 26A48 | dielectric models | 91B74 | 34A08 | complete monotonicity | Differential operators | Complete monotonicity | Fractional calculus | Dielectric models | MATHEMATICS, APPLIED | ALPHA-RELAXATION | STRETCHED EXPONENTIAL FUNCTION | FRACTIONAL RELAXATION | DISPERSION | DIFFERENTIAL-EQUATIONS | WILLIAMS-WATTS | MATHEMATICS | ANOMALOUS DIFFUSION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | OPERATORS | DERIVATIVES | Usage | Models | Dielectrics | Properties | Monotonic functions | Dielectric relaxation

fractional calculus | Mittag-Leffler functions | Primary 26A33 | 44A10 | Secondary 33E12 | differential operators | 26A48 | dielectric models | 91B74 | 34A08 | complete monotonicity | Differential operators | Complete monotonicity | Fractional calculus | Dielectric models | MATHEMATICS, APPLIED | ALPHA-RELAXATION | STRETCHED EXPONENTIAL FUNCTION | FRACTIONAL RELAXATION | DISPERSION | DIFFERENTIAL-EQUATIONS | WILLIAMS-WATTS | MATHEMATICS | ANOMALOUS DIFFUSION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | OPERATORS | DERIVATIVES | Usage | Models | Dielectrics | Properties | Monotonic functions | Dielectric relaxation

Journal Article

数学物理学报：B辑英文版, ISSN 0252-9602, 2015, Volume 35, Issue 5, pp. 1214 - 1224

In this paper, the q-analogue of the Stirling formula for the q-gamma function （Moak formula） is exploited to prove the complete monotonicity properties...

k公式 | 完全单调性 | Gamma函数 | 不等式 | 单调函数 | 实数 | Moa | 调和数 | inequalities | completely monotonic functions | q-gamma function | q-polygamma function | 26A48 | 26D15 | 33D05 | Completely monotonic functions | Q-gamma function | Q-polygamma function | Inequalities | MATHEMATICS | Q-DIGAMMA FUNCTIONS

k公式 | 完全单调性 | Gamma函数 | 不等式 | 单调函数 | 实数 | Moa | 调和数 | inequalities | completely monotonic functions | q-gamma function | q-polygamma function | 26A48 | 26D15 | 33D05 | Completely monotonic functions | Q-gamma function | Q-polygamma function | Inequalities | MATHEMATICS | Q-DIGAMMA FUNCTIONS

Journal Article