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Polynomial and its applications are well known for their proven properties and excellent applicability in interdisciplinary fields of science. Until now, research on polynomial and its applications has been done in mathematics, applied mathematics, and sciences. This book is based on recent results in all areas related to polynomial and its applications. This book provides an overview of the current research in the field of polynomials and its applications. The following papers have been published in this volume: ‘A Parametric Kind of the Degenerate Fubini Numbers and Polynomials’; ‘On 2-Variables Konhauser Matrix Polynomials and Their Fractional Integrals’; ‘Fractional Supersymmetric Hermite Polynomials’; ‘Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation’; ‘Iterating the Sum of Möbius Divisor Function and Euler Totient Function’; ‘Differential Equations Arising from the Generating Function of the (r, β)-Bell Polynomials and Distribution of Zeros of Equations’; ‘Truncated Fubini Polynomials’; ‘On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights’; ‘Ground State Solutions for Fractional Choquard Equations with Potential Vanishing at Infinity’; ‘Some Identities on Degenerate Bernstein and Degenerate Euler Polynomials’; ‘Some Identities Involving Hermite Kampé de Fériet Polynomials Arising from Differential Equations and Location of Their Zeros.’

Research & information: general --- Mathematics & science --- differential equations, heat equation --- Hermite Kampé de Fériet polynomials --- Hermite polynomials --- generating functions --- degenerate Bernstein polynomials --- degenerate Bernstein operators --- degenerate Euler polynomials --- variational methods --- fractional Choquard equation --- ground state solution --- vanishing potential --- positively quadratically hyponormal --- quadratically hyponormal --- unilateral weighted shift --- recursively generated --- Fubini polynomials --- Euler polynomials --- Bernoulli polynomials --- truncated exponential polynomials --- Stirling numbers of the second kind --- differential equations --- Bell polynomials --- r-Bell polynomials --- (r, β)-Bell polynomials --- zeros --- Möbius function --- divisor functions --- Euler totient function --- hydraulic resistance --- pipe flow friction --- Colebrook equation --- Colebrook–White experiment --- floating-point computations --- approximations --- Padé polynomials --- symbolic regression --- orthogonal polynomials --- difference-differential operator --- supersymmetry --- Konhauser matrix polynomial --- generating matrix function --- integral representation --- fractional integral --- degenerate Fubini polynomials --- Stirling numbers

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The special issue contains research papers with various topics in many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theory, methods, and their application based on current and recent developing symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and contains the most recent advances made in the area of symmetric functions and polynomials.

Research & information: general --- Mathematics & science --- OWA operator --- RIM quantifier --- maximum entropy --- minimax ratio --- generating function --- minimal variability --- minimax disparity --- solution equivalence --- fuzzy sets --- extended minimax disparity --- OWA model --- RIM quantifier problem --- extended degenerate r-central factorial numbers of the second kind --- extended degenerate r-central bell polynomials --- type 2 Bernoulli polynomials --- type 2 Euler polynomials --- identities of symmetry --- Laplace distribution --- Fibonacci polynomials --- Lucas polynomials --- sums of powers --- divisible properties --- R. S. Melham's conjectures --- degenerate Bernoulli polynomials --- degenerate Bernstein operators --- extended r-central complete bell polynomials --- extended r-central incomplete bell polynomials --- complete r-Bell polynomials --- incomplete r-bell polynomials --- Fibonacci numbers --- Lucas numbers --- Chebyshev polynomials --- Legendre polynomials --- Jacobi polynomials --- Gegenbauer polynomials --- convolution formula --- Bernoulli polynomials --- random variables --- p-adic invariant integral on Zp --- integer power sums polynomials --- Stirling polynomials of the second kind --- degenerate Stirling polynomials of the second kind --- type 2 degenerate q-Bernoulli polynomials --- p-adic q-integral --- balancing numbers --- balancing polynomials --- combinatorial methods --- symmetry sums --- Chebyshev polynomials of the first kind --- power series --- polynomial identities --- polynomial inequalities --- Waring-Goldbach problem --- circle method --- exceptional set --- symmetric form --- type 2 degenerate Bernoulli polynomials of the second kind --- degenerate central factorial numbers of the second kind --- degenerate poly-Bernoulli polynomials --- degenerate poly-Genocchi polynomials --- stirling numbers --- Erdős-Ko-Rado theorem --- intersecting families --- polynomial method --- polylogarithm functions --- poly-Genocchi polynomials --- unipoly functions --- unipoly Genocchi polynomials --- OWA operator --- RIM quantifier --- maximum entropy --- minimax ratio --- generating function --- minimal variability --- minimax disparity --- solution equivalence --- fuzzy sets --- extended minimax disparity --- OWA model --- RIM quantifier problem --- extended degenerate r-central factorial numbers of the second kind --- extended degenerate r-central bell polynomials --- type 2 Bernoulli polynomials --- type 2 Euler polynomials --- identities of symmetry --- Laplace distribution --- Fibonacci polynomials --- Lucas polynomials --- sums of powers --- divisible properties --- R. S. Melham's conjectures --- degenerate Bernoulli polynomials --- degenerate Bernstein operators --- extended r-central complete bell polynomials --- extended r-central incomplete bell polynomials --- complete r-Bell polynomials --- incomplete r-bell polynomials --- Fibonacci numbers --- Lucas numbers --- Chebyshev polynomials --- Legendre polynomials --- Jacobi polynomials --- Gegenbauer polynomials --- convolution formula --- Bernoulli polynomials --- random variables --- p-adic invariant integral on Zp --- integer power sums polynomials --- Stirling polynomials of the second kind --- degenerate Stirling polynomials of the second kind --- type 2 degenerate q-Bernoulli polynomials --- p-adic q-integral --- balancing numbers --- balancing polynomials --- combinatorial methods --- symmetry sums --- Chebyshev polynomials of the first kind --- power series --- polynomial identities --- polynomial inequalities --- Waring-Goldbach problem --- circle method --- exceptional set --- symmetric form --- type 2 degenerate Bernoulli polynomials of the second kind --- degenerate central factorial numbers of the second kind --- degenerate poly-Bernoulli polynomials --- degenerate poly-Genocchi polynomials --- stirling numbers --- Erdős-Ko-Rado theorem --- intersecting families --- polynomial method --- polylogarithm functions --- poly-Genocchi polynomials --- unipoly functions --- unipoly Genocchi polynomials

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The special issue contains research papers with various topics in many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theory, methods, and their application based on current and recent developing symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and contains the most recent advances made in the area of symmetric functions and polynomials.

OWA operator --- RIM quantifier --- maximum entropy --- minimax ratio --- generating function --- minimal variability --- minimax disparity --- solution equivalence --- fuzzy sets --- extended minimax disparity --- OWA model --- RIM quantifier problem --- extended degenerate r-central factorial numbers of the second kind --- extended degenerate r-central bell polynomials --- type 2 Bernoulli polynomials --- type 2 Euler polynomials --- identities of symmetry --- Laplace distribution --- Fibonacci polynomials --- Lucas polynomials --- sums of powers --- divisible properties --- R. S. Melham’s conjectures --- degenerate Bernoulli polynomials --- degenerate Bernstein operators --- extended r-central complete bell polynomials --- extended r-central incomplete bell polynomials --- complete r-Bell polynomials --- incomplete r-bell polynomials --- Fibonacci numbers --- Lucas numbers --- Chebyshev polynomials --- Legendre polynomials --- Jacobi polynomials --- Gegenbauer polynomials --- convolution formula --- Bernoulli polynomials --- random variables --- p-adic invariant integral on Zp --- integer power sums polynomials --- Stirling polynomials of the second kind --- degenerate Stirling polynomials of the second kind --- type 2 degenerate q-Bernoulli polynomials --- p-adic q-integral --- balancing numbers --- balancing polynomials --- combinatorial methods --- symmetry sums --- Chebyshev polynomials of the first kind --- power series --- polynomial identities --- polynomial inequalities --- Waring–Goldbach problem --- circle method --- exceptional set --- symmetric form --- type 2 degenerate Bernoulli polynomials of the second kind --- degenerate central factorial numbers of the second kind --- degenerate poly-Bernoulli polynomials --- degenerate poly-Genocchi polynomials --- stirling numbers --- Erdős-Ko-Rado theorem --- intersecting families --- polynomial method --- n/a --- polylogarithm functions --- poly-Genocchi polynomials --- unipoly functions --- unipoly Genocchi polynomials --- R. S. Melham's conjectures --- Waring-Goldbach problem --- Erdős-Ko-Rado theorem