SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2013, Volume 45, Issue 6, pp. 3382 - 3403

.... We present a converse of this simple monotonicity relation and use it to solve the shape reconstruction (a.k.a...

Electrical impedance tomography | Inverse problems | Shape reconstruction | Monotonicity | MATHEMATICS, APPLIED | COMPLETE ELECTRODE MODEL | BOUNDARY-VALUE PROBLEM | INCLUSIONS | monotonicity | NUMERICAL IMPLEMENTATION | ELLIPTIC PROBLEMS | INVERSE CONDUCTIVITY PROBLEM | FACTORIZATION METHOD | PROBE METHOD | electrical impedance tomography | inverse problems | shape reconstruction

Electrical impedance tomography | Inverse problems | Shape reconstruction | Monotonicity | MATHEMATICS, APPLIED | COMPLETE ELECTRODE MODEL | BOUNDARY-VALUE PROBLEM | INCLUSIONS | monotonicity | NUMERICAL IMPLEMENTATION | ELLIPTIC PROBLEMS | INVERSE CONDUCTIVITY PROBLEM | FACTORIZATION METHOD | PROBE METHOD | electrical impedance tomography | inverse problems | shape reconstruction

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2018, Volume 2018, Issue 1, pp. 1 - 11

We generalize several monotonicity and convexity properties as well as sharp inequalities for the complete elliptic integrals to the complete p-elliptic...

Complete elliptic integral | 26D20 | Complete p -elliptic integral | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Convexity | 33E05 | Gaussian hypergeometric function | 33C05 | Monotonicity | Complete p-elliptic integral | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | Integrals | Elliptic functions | Research

Complete elliptic integral | 26D20 | Complete p -elliptic integral | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Convexity | 33E05 | Gaussian hypergeometric function | 33C05 | Monotonicity | Complete p-elliptic integral | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | Integrals | Elliptic functions | Research

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 15

In this paper, by using the monotonicity rule for the ratio of two Laplace transforms, we prove that the function x ↦ 1 24 x ( ln Γ ( x + 1 / 2 ) − x ln x + x...

33B15 | inequality | 26A51 | Analysis | gamma function | Mathematics, general | Mathematics | Applications of Mathematics | 26A48 | Laplace transform | 26D15 | complete monotonicity | MATHEMATICS | MATHEMATICS, APPLIED | SERIES | APPROXIMATION | FACTORIAL FUNCTION | BURNSIDES FORMULA | ASYMPTOTIC FORMULAS | Laplace transforms | Transformations (mathematics) | Gamma function | Inequalities

33B15 | inequality | 26A51 | Analysis | gamma function | Mathematics, general | Mathematics | Applications of Mathematics | 26A48 | Laplace transform | 26D15 | complete monotonicity | MATHEMATICS | MATHEMATICS, APPLIED | SERIES | APPROXIMATION | FACTORIAL FUNCTION | BURNSIDES FORMULA | ASYMPTOTIC FORMULAS | Laplace transforms | Transformations (mathematics) | Gamma function | Inequalities

Journal Article

4.
Full Text
On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics

Journal of Computational Physics, ISSN 0021-9991, 07/2015, Volume 293, pp. 70 - 80

The three parameters Mittag-Leffler function (often referred to as the Prabhakar function) has important applications, mainly in physics of dielectrics, in...

Prabhakar function | Mittag-Leffler functions | Laplace transform | Havriliak-Negami | Complete monotonicity | MITTAG-LEFFLER FUNCTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DISPERSION | PLANE | ABSORPTION | PHYSICS, MATHEMATICAL | Analysis | Dielectrics | Computer simulation | Computation | Mathematical analysis | Graphs | Feasibility | Mathematical models

Prabhakar function | Mittag-Leffler functions | Laplace transform | Havriliak-Negami | Complete monotonicity | MITTAG-LEFFLER FUNCTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DISPERSION | PLANE | ABSORPTION | PHYSICS, MATHEMATICAL | Analysis | Dielectrics | Computer simulation | Computation | Mathematical analysis | Graphs | Feasibility | Mathematical models

Journal Article

Periodica Mathematica Hungarica, ISSN 0031-5303, 12/2017, Volume 75, Issue 2, pp. 159 - 166

...) and investigate their Shannon, Rényi, and Tsallis entropies with respect to complete monotonicity.

Entropies | 60E15 | 26A51 | Inequalities | 94A17 | Mathematics, general | Mathematics | Concavity | Complete monotonicity | MATHEMATICS | MATHEMATICS, APPLIED | OPERATORS | CONJECTURE | Distribution (Probability theory)

Entropies | 60E15 | 26A51 | Inequalities | 94A17 | Mathematics, general | Mathematics | Concavity | Complete monotonicity | MATHEMATICS | MATHEMATICS, APPLIED | OPERATORS | CONJECTURE | Distribution (Probability theory)

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 2017, Volume 2017, Issue 1, pp. 1 - 13

In the article, we provide a monotonicity rule for the function [P(x) + A(x)]/[P(x) + B(x)], where P(x) is a positive differentiable and decreasing function defined...

relative error | monotonicity rule | absolute error | complete elliptic integral | MATHEMATICS | COMPLETE ELLIPTIC INTEGRALS | MATHEMATICS, APPLIED | INEQUALITIES | BOUNDS | APPROXIMATIONS | TERMS | Power series | Research | 26A48 | 33E05

relative error | monotonicity rule | absolute error | complete elliptic integral | MATHEMATICS | COMPLETE ELLIPTIC INTEGRALS | MATHEMATICS, APPLIED | INEQUALITIES | BOUNDS | APPROXIMATIONS | TERMS | Power series | Research | 26A48 | 33E05

Journal Article

Numerische Mathematik, ISSN 0029-599X, 4/2017, Volume 135, Issue 4, pp. 1221 - 1251

... of electric current and voltage. Recently it was shown that a simple monotonicity property of the related Neumann-to-Dirichlet map can be used to characterize shapes of inhomogeneities in a known background conductivity...

35R30 | Theoretical, Mathematical and Computational Physics | Mathematics | Complete electrode model | 35Q60 | Electrical impedance tomography | Mathematical Methods in Physics | Inverse problems | Direct reconstruction methods | Numerical Analysis | Monotonicity method | Appl.Mathematics/Computational Methods of Engineering | Mathematics, general | Numerical and Computational Physics, Simulation | 65N21 | Regularization | 35R05 | MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM | INCLUSIONS | GLOBAL UNIQUENESS | INVERSION | FACTORIZATION METHOD | DOMAINS | Tomography | Algorithms | Analysis | Electric properties | Mathematics - Analysis of PDEs

35R30 | Theoretical, Mathematical and Computational Physics | Mathematics | Complete electrode model | 35Q60 | Electrical impedance tomography | Mathematical Methods in Physics | Inverse problems | Direct reconstruction methods | Numerical Analysis | Monotonicity method | Appl.Mathematics/Computational Methods of Engineering | Mathematics, general | Numerical and Computational Physics, Simulation | 65N21 | Regularization | 35R05 | MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM | INCLUSIONS | GLOBAL UNIQUENESS | INVERSION | FACTORIZATION METHOD | DOMAINS | Tomography | Algorithms | Analysis | Electric properties | Mathematics - Analysis of PDEs

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2014, Volume 410, Issue 1, pp. 307 - 315

We present some monotonicity results for Dirichlet L-functions associated to real primitive characters...

Dirichlet L-function | Logarithmically complete monotonicity | Complete monotonicity | MATHEMATICS | MATHEMATICS, APPLIED | HARMONIC MEASURE | POLYGAMMA FUNCTIONS | GAMMA-FUNCTIONS | QUOTIENTS | ZEROS

Dirichlet L-function | Logarithmically complete monotonicity | Complete monotonicity | MATHEMATICS | MATHEMATICS, APPLIED | HARMONIC MEASURE | POLYGAMMA FUNCTIONS | GAMMA-FUNCTIONS | QUOTIENTS | ZEROS

Journal Article

Applied mathematics and computation, ISSN 0096-3003, 2015, Volume 258, pp. 130 - 137

We prove complete monotonicity of sums of squares of generalized Baskakov basis functions by deriving the corresponding results for hypergeometric functions...

Baskakov operator | Distribution of zeros | Convexity | Complete monotonicity | Chebyshev-Grüss-type inequality | Complete elliptic integral of the first kind | HYPERGEOMETRIC POLYNOMIALS | MATHEMATICS, APPLIED | INEQUALITIES | Chebyshev-Gruss-type inequality

Baskakov operator | Distribution of zeros | Convexity | Complete monotonicity | Chebyshev-Grüss-type inequality | Complete elliptic integral of the first kind | HYPERGEOMETRIC POLYNOMIALS | MATHEMATICS, APPLIED | INEQUALITIES | Chebyshev-Gruss-type inequality

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 01/2016, Volume 131, pp. 32 - 47

In this paper, we extend the Hamilton’s gradient estimates (Hamilton 1993) and a monotonicity formula of entropy (Ni 2004...

Metric measure space | Curvature-dimension condition | Hamilton’s gradient estimates | Hamilton's gradient estimates | MATHEMATICS, APPLIED | LIPSCHITZ FUNCTIONS | RICCI CURVATURE | BAKRY-EMERY CURVATURE | EQUIVALENCE | MATHEMATICS | KERNEL | COMPLETE MANIFOLDS | BOUNDS | EQUATION | GEOMETRY | Manifolds | Nonlinearity | Heat transmission | Nickel | Estimates | Heat transfer

Metric measure space | Curvature-dimension condition | Hamilton’s gradient estimates | Hamilton's gradient estimates | MATHEMATICS, APPLIED | LIPSCHITZ FUNCTIONS | RICCI CURVATURE | BAKRY-EMERY CURVATURE | EQUIVALENCE | MATHEMATICS | KERNEL | COMPLETE MANIFOLDS | BOUNDS | EQUATION | GEOMETRY | Manifolds | Nonlinearity | Heat transmission | Nickel | Estimates | Heat transfer

Journal Article

Advances in Difference Equations, ISSN 1687-1847, 12/2019, Volume 2019, Issue 1, pp. 1 - 10

In this paper, we prove complete monotonicity of some functions involving k-polygamma functions...

33B15 | k -digamma function | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | Mathematics | 26A48 | Partial Differential Equations | Complete monotonicity | k -polygamma functions | GAMMA | MATHEMATICS | CONVEXITY PROPERTIES | SHARP INEQUALITIES | ZETA | MATHEMATICS, APPLIED | DIGAMMA | PSI | k-digamma function | k-polygamma functions | Lower bounds

33B15 | k -digamma function | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | Mathematics | 26A48 | Partial Differential Equations | Complete monotonicity | k -polygamma functions | GAMMA | MATHEMATICS | CONVEXITY PROPERTIES | SHARP INEQUALITIES | ZETA | MATHEMATICS, APPLIED | DIGAMMA | PSI | k-digamma function | k-polygamma functions | Lower bounds

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2008, Volume 340, Issue 2, pp. 1362 - 1370

In this paper we study the monotonicity properties of some functions involving the Mills' ratio of the standard normal law...

Schwarz's inequality | Normal distribution | Turán-type inequality | Monotone form of l'Hospital's rule | Mills' ratio | Functional inequality | Complete monotonicity | MATHEMATICS | MATHEMATICS, APPLIED | monotone form of 1'Hospital's rule | normal distribution | Turan-type inequality | RULES | functional inequality | complete monotonicity

Schwarz's inequality | Normal distribution | Turán-type inequality | Monotone form of l'Hospital's rule | Mills' ratio | Functional inequality | Complete monotonicity | MATHEMATICS | MATHEMATICS, APPLIED | monotone form of 1'Hospital's rule | normal distribution | Turan-type inequality | RULES | functional inequality | complete monotonicity

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2018, Volume 466, Issue 2, pp. 1609 - 1617

Let d∈N and let γi∈[0,∞), xi∈(0,1) be such that ∑i=1d+1γi=M∈(0,∞) and ∑i=1d+1xi=1. We prove thata↦Γ(aM+1)∏i=1d+1Γ(aγi+1)∏i=1d+1xiaγi is completely monotonic on...

Simplex | Gamma function | Combinatorial inequalities | Bernstein polynomials | Complete monotonicity | Multinomial probability | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | DENSITY-ESTIMATION | BEHAVIOR | SMOOTH ESTIMATION | Mathematics - Probability

Simplex | Gamma function | Combinatorial inequalities | Bernstein polynomials | Complete monotonicity | Multinomial probability | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | DENSITY-ESTIMATION | BEHAVIOR | SMOOTH ESTIMATION | Mathematics - Probability

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2018, Volume 2018, Issue 1, pp. 1 - 9

.... Hence, we give complete monotonicity property of a determinant function involving all kinds of derivatives of the generalized digamma function.

33B15 | Ordinary Differential Equations | Functional Analysis | Analysis | Generalized digamma function | Difference and Functional Equations | Mathematics, general | Mathematics | Partial Differential Equations | Complete monotonicity | Concavity | Inequality | GAMMA | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | Inequalities

33B15 | Ordinary Differential Equations | Functional Analysis | Analysis | Generalized digamma function | Difference and Functional Equations | Mathematics, general | Mathematics | Partial Differential Equations | Complete monotonicity | Concavity | Inequality | GAMMA | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | Inequalities

Journal Article

INVERSE PROBLEMS AND IMAGING, ISSN 1930-8337, 02/2019, Volume 13, Issue 1, pp. 93 - 116

...; one such method is the monotonicity method of Harrach, Seo, and Ullrich [17, 15]. We formulate the method for irregular indefinite inclusions, meaning that we make...

TOMOGRAPHY | Electrical impedance tomography | MATHEMATICS, APPLIED | FACTORIZATION METHOD | inverse problems | SHAPE-RECONSTRUCTION | direct reconstruction methods | monotonicity method | indefinite inclusions | complete electrode model | PHYSICS, MATHEMATICAL

TOMOGRAPHY | Electrical impedance tomography | MATHEMATICS, APPLIED | FACTORIZATION METHOD | inverse problems | SHAPE-RECONSTRUCTION | direct reconstruction methods | monotonicity method | indefinite inclusions | complete electrode model | PHYSICS, MATHEMATICAL

Journal Article

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

...) complete monotonicity, necessary and sufficient conditions, equivalences to inequalities for sums, applications, and the like...

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, 2004, Volume 172, Issue 2, pp. 289 - 312

We prove monotonicity properties of certain combinations of complete elliptic integrals of the first and second kind, K and E...

Arc length of an ellipse | Complete elliptic integrals | Mean values | Monotonicity | Inequalities | DISTORTION | MATHEMATICS, APPLIED | inequalities | FUNCTIONAL INEQUALITIES | APPROXIMATIONS | monotonicity | complete elliptic integrals | mean values

Arc length of an ellipse | Complete elliptic integrals | Mean values | Monotonicity | Inequalities | DISTORTION | MATHEMATICS, APPLIED | inequalities | FUNCTIONAL INEQUALITIES | APPROXIMATIONS | monotonicity | complete elliptic integrals | mean values

Journal Article

Integral transforms and special functions, ISSN 1476-8291, 2014, Volume 26, Issue 1, pp. 36 - 50

We consider two operations on the Mittag-Leffler function which cancel the exponential term in the expansion at infinity, and generate a completely monotonic...

incomplete Gamma function | Abelian transform | Mittag-Leffler function | complete monotonicity | Mellin transform | Stieltjes transform | 33E12 | MATHEMATICS | MATHEMATICS, APPLIED | 60G52 | 26A33 | 26A48 | Operators | Subtraction | Infinity | Gamma function | Integrals | Transforms

incomplete Gamma function | Abelian transform | Mittag-Leffler function | complete monotonicity | Mellin transform | Stieltjes transform | 33E12 | MATHEMATICS | MATHEMATICS, APPLIED | 60G52 | 26A33 | 26A48 | Operators | Subtraction | Infinity | Gamma function | Integrals | Transforms

Journal Article

19.
MONOTONICITY PATTERNS AND FUNCTIONAL INEQUALITIES FOR CLASSICAL AND GENERALIZED WRIGHT FUNCTIONS

MATHEMATICAL INEQUALITIES & APPLICATIONS, ISSN 1331-4343, 07/2019, Volume 22, Issue 3, pp. 901 - 916

Our aim in this paper is to present the completely monotonicity and convexity properties for the Wright function...

MATHEMATICS | Turan type inequalities | SERIES | Wright function | four-parametric Mittag-Leffler function | VOLTERRA | generalized Wright function | complete monotonicity

MATHEMATICS | Turan type inequalities | SERIES | Wright function | four-parametric Mittag-Leffler function | VOLTERRA | generalized Wright function | complete monotonicity

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2007, Volume 336, Issue 2, pp. 812 - 822

We present some complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions...

Gamma function | Logarithmically complete monotonicity | Psi function | Complete monotonicity | MATHEMATICS | MATHEMATICS, APPLIED | psi function | logarithmically complete monotonicity | gamma function | complete monotonicity

Gamma function | Logarithmically complete monotonicity | Psi function | Complete monotonicity | MATHEMATICS | MATHEMATICS, APPLIED | psi function | logarithmically complete monotonicity | gamma function | complete monotonicity

Journal Article