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2012, Mathematical surveys and monographs, ISBN 9780821889817, Volume 183, vii, 317
Book
Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, ISSN 0294-1449, 01/1994, Volume 11, Issue 1, pp. 91 - 133
Given a function u:Ω⊆_ℝ →ℝ, we introduce a notion of total variation of u depending on a possibly discontinuous Finsler metric. We prove some integral... 
BV functions | semicontinuity | relaxation theory | MATHEMATICS, APPLIED | BV FUNCTIONS | INTEGRAL-REPRESENTATION | PERTURBATIONS | RELAXATION THEORY | SEMICONTINUITY
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 10/2016, Volume 284, Issue 1-2, pp. 575 - 593
We introduce a division formula on a possibly singular projective subvariety X of complex projective space , which, e.g., provides explicit representations of... 
MATHEMATICS | MEMBERSHIP | INTEGRAL-REPRESENTATION | Matematik | Mathematics
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 2019, Volume 472, Issue 1, pp. 1189 - 1219
In this article, a characterization of the class of Herglotz–Nevanlinna functions in several variables is given in terms of an integral representation. The... 
Integral representations | Several complex variables | Herglotz–Nevanlinna functions | MATHEMATICS | MATHEMATICS, APPLIED | Herglotz-Nevanlinna functions
Journal Article
Optics express, ISSN 1094-4087, 2006, Volume 14, Issue 23, pp. 11277 - 11291
We present a fast calculation of the electromagnetic field near the focus of an objective with a high numerical aperture ( NA). Instead of direct integration,... 
IMAGE FIELD | WAVES | OPTICAL SYSTEMS | ELECTROMAGNETIC DIFFRACTION | INTEGRAL-REPRESENTATION | OPTICS | FRESNEL-NUMBER
Journal Article
Journal of computational and applied mathematics, ISSN 0377-0427, 2018, Volume 336, pp. 54 - 62
In the paper, by induction and recursively, the author proves that the generating function of multivariate logarithmic polynomials and its reciprocal are a... 
Multivariate logarithmic polynomial | Completely monotonic function | Bernstein function | Generating function | Integral representation | Lévy-Khintchine representation | MATHEMATICS, APPLIED | Levy-Khintchine representation
Journal Article
Russian Mathematics, ISSN 1066-369X, 05/2018, Volume 62, Issue 5, pp. 34 - 43
To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.3103/S1066369X18050067 We obtain... 
Entire function | Integral representation | Plana formula
Journal Article
Journal of Siberian Federal University - Mathematics and Physics, ISSN 1997-1397, 2018, Volume 11, Issue 3, pp. 364 - 369
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 01/2020, Volume 268, Issue 2, pp. 738 - 783
We consider a class of parabolic equations with critical electromagnetic potentials, for which we obtain a classification of local asymptotics, unique... 
Parabolic equations | Singular electromagnetic potentials | Unique continuation | Integral representation | DIFFERENTIAL EQUATIONS | MATHEMATICS | CARLEMAN INEQUALITIES | DECAY | THEOREM | BEHAVIOR | SCHRODINGER
Journal Article
Journal of elasticity, ISSN 1573-2681, 2018, Volume 133, Issue 1, pp. 1 - 35
In this paper we apply both the procedure of dimension reduction and the incorporation of structured deformations to a three-dimensional continuum in the form... 
Dimension reduction | Relaxation | 49J45 | 74Kxx | 74A60 | Structured deformations | Integral representation of functionals | 74G65 | Classical Mechanics | Automotive Engineering | Physics | Explicit formulas | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | MATERIALS SCIENCE, MULTIDISCIPLINARY | VECTOR | Interfacial energy | Reduction | Deformation
Journal Article
Applied Mathematics and Information Sciences, ISSN 1935-0090, 09/2011, Volume 5, Issue 3, pp. 390 - 444
In the vast literature in Analytic Number Theory, one can find systematic and extensive investigations not only of the classical Bernoulli, Euler and Genocchi... 
Bernoulli polynomials and numbers | Basic (or q-) extensions | Euler polynomials and numbers | Taylor-Maclaurin series expansion | FOURIER EXPANSIONS | ZETA-FUNCTIONS | NUMBERS | IDENTITIES | PHYSICS, MATHEMATICAL | EXPLICIT FORMULA | ORDER | FAMILIES | APOSTOL-BERNOULLI | INTEGRAL-REPRESENTATIONS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2019, Volume 266, Issue 2-3, pp. 1176 - 1220
We obtain a blow-up result for solutions to a semi-linear wave equation with scale-invariant dissipation and mass and power non-linearity, in the case in which... 
Time-dependent speed of propagation | Power non-linearity | Semi-linear wave equation | Integral representation formula | Critical case | Blow-up | MATHEMATICS | GLOBAL EXISTENCE | TIME-DEPENDENT DISSIPATION
Journal Article
Neural computation, ISSN 1530-888X, 2016, Volume 28, Issue 5, pp. 970 - 998
Two linear recurrent neural networks for generating outer inverses with prescribed range and null space are defined. Each of the proposed recurrent neural... 
APPROXIMATION | OPERATOR | GENERALIZED INVERSE | A(T,S)() | INTEGRAL-REPRESENTATION | NEUROSCIENCES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Recurrent neural networks | Computer simulation | Computation | Neural networks | Mathematical analysis | Inversions | Differential equations | Inverse
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2016, Volume 440, Issue 2, pp. 421 - 436
We study the Weierstrass division theorem for function germs in strongly non-quasianalytic Denjoy–Carleman classes CM. For suitable divisors... 
Denjoy–Carleman classes | Subanalytic geometry | Integral representations | Weierstrass division theorem | Denjoy-Carleman classes
Journal Article
European Journal of Operational Research, ISSN 0377-2217, 2010, Volume 201, Issue 1, pp. 222 - 230
Installment options are path-dependent contingent claims in which the premium is paid discretely or continuously in installments, instead of paying a lump sum... 
Continuous-installment options | Free boundary problem | Laplace transforms | Integral representation | Finance | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VALUATION | Finance Continuous-installment options Free boundary problem Integral representation Laplace transforms
Journal Article
Advances in Mathematics, ISSN 0001-8708, 12/2018, Volume 339, pp. 599 - 641
Hans J. Zassenhaus conjectured that for any unit u of finite order in the integral group ring of a finite group G there exists a unit a in the rational group... 
Zassenhaus conjecture | Group ring | Integral representations | Unit group | MATHEMATICS | METACYCLIC GROUPS | FROBENIUS GROUPS | METABELIAN-GROUPS | INTEGRAL GROUP-RINGS | FINITE-GROUPS | S-5 | TORSION UNITS
Journal Article
Optik, ISSN 0030-4026, 11/2016, Volume 127, Issue 22, pp. 10554 - 10560
We build an integral representation of solutions of the wave equation as a superposition of other solutions. Investigations are based on continuous shearlet... 
Wave equation | Shearlet system | Integral representation | OPTICS | QUANTUM-THEORY
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2015, Volume 426, Issue 2, pp. 1164 - 1173
It is known that an analytical expression of solutions to nonlinear wave equations in higher dimensions may be helpful to recognizing new nonlinear physical... 
Integral representations of solutions of PDEs | Nonlinear wave equations | Nonlinear phenomena | Robin boundary conditions | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
1979, Lecture notes in mathematics, ISBN 0387095462, Volume 744., 275
Book
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