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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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This book consists of nine papers covering a number of basic ideas, concepts, and methods of nonlinear analysis, as well as some current research problems. Thus, the reader is introduced to the fascinating theory around Brouwer's fixed point theorem, to Granas' theory of topological transversality, and to some advanced techniques of critical point theory and fixed point theory. Other topics include discontinuous differential equations, new results of metric fixed point theory, robust tracker design problems for various classes of nonlinear systems, and periodic solutions in computer virus propagation models.

Krasnosel’skiĭ’s fixed point theorem --- positive solutions --- discontinuous differential equations --- differential system --- p-Laplacian --- choquard equation --- nonhomogeneous --- nehari method --- minimax methods --- essential maps --- homotopy --- selections --- PID controller --- sliding mode control --- hybrid Taguchi real coded DNA algorithm --- perturbation estimator --- ℳ?-function --- ℳ?(λ)-function --- τ-function --- essential distance (e-distance) --- e0-metric --- Du-Hung’s fixed point theorem --- Mizoguchi-Takahashi’s fixed point theorem --- Nadler’s fixed point theorem --- Banach contraction principle --- minimax --- multiplicity --- global minima --- Brouwer fixed point theorem --- Hamadard theorem --- Poincaré–miranda theorem --- nonlinear elliptic problem --- Robin boundary condition --- gradient dependence --- sub-supersolution --- positive solution --- periodic solutions --- SEIR-KS model --- computer virus model --- n/a --- Krasnosel'skiĭ's fixed point theorem --- Du-Hung's fixed point theorem --- Mizoguchi-Takahashi's fixed point theorem --- Nadler's fixed point theorem --- Poincaré-miranda theorem

Choose an application

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

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