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Current Trends in Symmetric Polynomials with their Applications

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ISBN: 9783039216208 9783039216215 Year: Pages: 238 DOI: 10.3390/books978-3-03921-621-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 16:10:12
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Abstract

This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials.

Keywords

Fubini polynomials --- w-torsion Fubini polynomials --- fermionic p-adic integrals --- symmetric identities --- Chebyshev polynomials --- sums of finite products --- hypergeometric function --- Fubini polynomials --- Euler numbers --- symmetric identities --- elementary method --- computational formula --- two variable q-Berstein polynomial --- two variable q-Berstein operator --- q-Euler number --- q-Euler polynomial --- Fubini polynomials --- Euler numbers --- congruence --- elementary method --- q-Bernoulli numbers --- q-Bernoulli polynomials --- two variable q-Bernstein polynomials --- two variable q-Bernstein operators --- p-adic integral on ?p --- the degenerate gamma function --- the modified degenerate gamma function --- the degenerate Laplace transform --- the modified degenerate Laplace transform --- Fibonacci --- Lucas --- linear form in logarithms --- continued fraction --- reduction method --- sums of finite products of Chebyshev polynomials of the third and fourth kinds --- Hermite --- generalized Laguerre --- Legendre --- Gegenbauer --- Jacobi --- third-order character --- classical Gauss sums --- rational polynomials --- analytic method --- recursive formula --- fermionic p-adic q-integral on ?p --- q-Euler polynomials --- q-Changhee polynomials --- symmetry group --- Apostol-type Frobenius–Euler polynomials --- three-variable Hermite polynomials --- symmetric identities --- explicit relations --- operational connection --- q-Volkenborn integral on ?p --- Bernoulli numbers and polynomials --- generalized Bernoulli polynomials and numbers of arbitrary complex order --- generalized Bernoulli polynomials and numbers attached to a Dirichlet character ? --- Changhee polynomials --- Changhee polynomials of type two --- fermionic p-adic integral on ?p --- Chebyshev polynomials of the first, second, third, and fourth kinds --- sums of finite products --- representation --- catalan numbers --- elementary and combinatorial methods --- recursive sequence --- convolution sums --- well-posedness --- stability --- acoustic wave equation --- perfectly matched layer --- Fibonacci polynomials --- Lucas polynomials --- trivariate Fibonacci polynomials --- trivariate Lucas polynomials --- generating functions --- central incomplete Bell polynomials --- central complete Bell polynomials --- central complete Bell numbers --- Legendre polynomials --- Laguerre polynomials --- generalized Laguerre polynomials --- Gegenbauer polynomials --- hypergeometric functions 1F1 and 2F1 --- Euler polynomials --- Bernoulli polynomials --- elementary method --- identity --- congruence --- new sequence --- Catalan numbers --- elementary and combinatorial methods --- congruence --- conjecture --- fluctuation theorem --- thermodynamics of information --- stochastic thermodynamics --- mutual information --- non-equilibrium free energy --- entropy production

Mathematical Analysis and Applications II

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ISBN: 9783039283842 9783039283859 Year: Pages: 226 DOI: 10.3390/books978-3-03928-385-9 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2020-04-07 23:07:09
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Abstract

This issue is a continuation of the previous successful Special Issue “Mathematical Analysis and Applications” . Investigations involving the theory and applications of mathematical analytical tools and techniques are remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. In this Special Issue, we invite and welcome review, expository and original research articles dealing with the recent advances in mathematical analysis and its multidisciplinary applications.

Keywords

common fixed point --- metric-like space --- ?-Geraghty contraction --- triangular ?-admissible mapping --- fixed circle --- common fixed circle --- fixed-circle theorem --- extended partial Sb-metric spaces --- Sb-metric spaces --- fixed point --- generalized hypergeometric functions --- Gauss and confluent hypergeometric functions --- summation theorems of hypergeometric functions --- partial symmetric --- fixed point --- contraction and weak contraction --- Nadler’s theorem --- linear elastostatics --- simple layer potentials --- displacement problem --- existence and uniqueness theorems --- Fredholm alternative --- singular data --- differential equations --- Sheffer polynomial sets --- generating functions --- monomiality principle --- quasi metric space --- Suzuki contractions --- fixed point theorems --- modified ?-distance --- almost perfect functions --- generating function --- series transformation --- gamma function --- Hankel contour --- Fermi–Dirac function --- Bose–Einstein function --- Weyl transform --- series representation --- Hermite–Hadamard inequalities --- (p, q)-derivative --- (p, q)-integral --- convex functions --- fixed point --- Reich contraction --- Hardy–Rogers contraction --- almost b-metric space --- additive (Cauchy) equation --- additive mapping --- Hyers–Ulam stability --- generalized Hyers–Ulam stability --- hyperstability --- bounded index --- bounded L-index in direction --- slice function --- entire function --- bounded l-index --- generalized hypergeometric functions --- classical summation theorems --- generalization --- laplace transforms --- gamma and beta functions --- Szász-Mirakjan operators --- Szász-Mirakjan Beta type operators --- extended Gamma and Beta functions --- confluent hypergeometric function --- Modulus of smoothness --- modulus of continuity --- Lipschitz class --- local approximation --- Voronovskaja type approximation theorem --- operators theory 44A99, 47B99, 47A62 --- special functions 33C52, 33C65, 33C99, 33B10, 33B15 --- Stirling numbers and Touchard polynomials 11B73 --- n/a

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