01/2019, ISBN 9783039216215

This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics....

eBook

Physical Review Letters, ISSN 0031-9007, 01/2016, Volume 116, Issue 1, p. 010402

It is a recent realization that many of the concepts and tools of causal discovery in machine learning are highly relevant to problems in quantum information,...

NONLOCALITY | PHYSICS, MULTIDISCIPLINARY | QUANTUM | GEOMETRY | Bells | Mathematical analysis | Inequalities | Causation | Derivation | Mathematical models | Polynomials | Representations | Physics - Quantum Physics

NONLOCALITY | PHYSICS, MULTIDISCIPLINARY | QUANTUM | GEOMETRY | Bells | Mathematical analysis | Inequalities | Causation | Derivation | Mathematical models | Polynomials | Representations | Physics - Quantum Physics

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 10/2014, Volume 244, pp. 149 - 157

The main objective in this paper is first to establish new identities for the λ-Stirling type numbers of the second kind, the λ-array type polynomials, the...

Bernoulli polynomials and Bernoulli numbers | Apostol–Bernoulli polynomials and Apostol–Bernoulli numbers | [formula omitted]-Stirling numbers of the second kind | [formula omitted]-Array polynomials | [formula omitted]-Bell numbers and [formula omitted]-Bell polynomials | λ-Bell numbers and λ-Bell polynomials | λ-Array polynomials | λ-Stirling numbers of the second kind | Apostol-Bernoulli polynomials and Apostol-Bernoulli numbers | MATHEMATICS, APPLIED | lambda-Array polynomials | lambda-Stirling numbers of the second kind | lambda-Bell numbers and lambda-Bell polynomials | APOSTOL-BERNOULLI | GENERATING-FUNCTIONS | EULER

Bernoulli polynomials and Bernoulli numbers | Apostol–Bernoulli polynomials and Apostol–Bernoulli numbers | [formula omitted]-Stirling numbers of the second kind | [formula omitted]-Array polynomials | [formula omitted]-Bell numbers and [formula omitted]-Bell polynomials | λ-Bell numbers and λ-Bell polynomials | λ-Array polynomials | λ-Stirling numbers of the second kind | Apostol-Bernoulli polynomials and Apostol-Bernoulli numbers | MATHEMATICS, APPLIED | lambda-Array polynomials | lambda-Stirling numbers of the second kind | lambda-Bell numbers and lambda-Bell polynomials | APOSTOL-BERNOULLI | GENERATING-FUNCTIONS | EULER

Journal Article

Frontiers of Mathematics in China, ISSN 1673-3452, 10/2013, Volume 8, Issue 5, pp. 1139 - 1156

A class of trilinear differential operators is introduced through a technique of assigning signs to derivatives and used to create trilinear differential...

Trilinear differential equation | Bell polynomial | Mathematics, general | Mathematics | 37K40 | 35Q51 | superposition principle | MATHEMATICS | BACKLUND-TRANSFORMATIONS | FORM | BKP EQUATIONS | CONSTRUCTION | WATER-WAVE EQUATION | DE-VRIES EQUATION | Studies | Theorems | Algebra | Differential equations | Mathematical models | Polynomials | Linear equations | Operators | Dependent variables | Mathematical analysis | China | Derivatives | Combinatorial analysis

Trilinear differential equation | Bell polynomial | Mathematics, general | Mathematics | 37K40 | 35Q51 | superposition principle | MATHEMATICS | BACKLUND-TRANSFORMATIONS | FORM | BKP EQUATIONS | CONSTRUCTION | WATER-WAVE EQUATION | DE-VRIES EQUATION | Studies | Theorems | Algebra | Differential equations | Mathematical models | Polynomials | Linear equations | Operators | Dependent variables | Mathematical analysis | China | Derivatives | Combinatorial analysis

Journal Article

Axioms, ISSN 2075-1680, 10/2019, Volume 8, Issue 4, p. 112

The aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with...

cauchy numbers | binomial coefficients | bernstein basis functions | bernoulli numbers | daehee numbers and polynomials | generating functions | euler numbers | stirling numbers | poisson-charlier polynomials | bell polynomials | functional equations | p-adic integral | special numbers and polynomials | probability distribution | partial differential equations | combinatorial sums

cauchy numbers | binomial coefficients | bernstein basis functions | bernoulli numbers | daehee numbers and polynomials | generating functions | euler numbers | stirling numbers | poisson-charlier polynomials | bell polynomials | functional equations | p-adic integral | special numbers and polynomials | probability distribution | partial differential equations | combinatorial sums

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 02/2019, Volume 347, pp. 330 - 342

In this paper, we investigate the integral of xnlogp(sin(x)) for natural numbers n and p. In doing so, we recover some well-known results and remark on some...

Riemann zeta function | Bell polynomial | Binomial coefficients | Combinatorics | Harmonic numbers | Log-sine integral | MATHEMATICS, APPLIED | Mathematics - Number Theory

Riemann zeta function | Bell polynomial | Binomial coefficients | Combinatorics | Harmonic numbers | Log-sine integral | MATHEMATICS, APPLIED | Mathematics - Number Theory

Journal Article

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Full Text
Some identities for a sequence of unnamed polynomials connected with the Bell polynomials

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, ISSN 1578-7303, 04/2019, Volume 113, Issue 2, pp. 557 - 567

In the paper, by virtue of (1) the Stirling inversion theorem and the binomial inversion theorem, (2) the Faa di Bruno formula and two identities for the Bell...

MATHEMATICS | Bell polynomial | Explicit formula | Inversion theorem | Unnamed polynomial | Binomial coefficient | Identity | Stirling number

MATHEMATICS | Bell polynomial | Explicit formula | Inversion theorem | Unnamed polynomial | Binomial coefficient | Identity | Stirling number

Journal Article

Modern Physics Letters B, ISSN 0217-9849, 05/2015, Volume 29, Issue 12, p. 1550051

In this paper, a (3+1)-dimensional generalized variable-coefficients Kadomtsev–Petviashvili (gvcKP) equation is proposed, which describes many nonlinear...

Bell polynomial | Infinite conservation law | Hirota bilinear form | Lax pair | Solitary wave solution | Bäcklund transformation | PHYSICS, CONDENSED MATTER | DARBOUX TRANSFORMATION | PHYSICS, APPLIED | PHYSICS, MATHEMATICAL | PERIODIC-WAVE SOLUTIONS | infinite conservation law | solitary wave solution | BOUSSINESQ | EXPANSION | Backlund transformation | NONLINEAR EVOLUTION-EQUATIONS | TODA LATTICE | SOLITON

Bell polynomial | Infinite conservation law | Hirota bilinear form | Lax pair | Solitary wave solution | Bäcklund transformation | PHYSICS, CONDENSED MATTER | DARBOUX TRANSFORMATION | PHYSICS, APPLIED | PHYSICS, MATHEMATICAL | PERIODIC-WAVE SOLUTIONS | infinite conservation law | solitary wave solution | BOUSSINESQ | EXPANSION | Backlund transformation | NONLINEAR EVOLUTION-EQUATIONS | TODA LATTICE | SOLITON

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 4/2017, Volume 111, Issue 2, pp. 435 - 446

Recently, several authors have studied the degenerate Bernoulli and Euler polynomials and given some intersting identities of those polynomials. In this paper,...

11B83 | Degenerate Bell numbers and polynomials | Theoretical, Mathematical and Computational Physics | 11B73 | Mathematics, general | 05A19 | Mathematics | Degenerate Stirling numbers of the second kind | Applications of Mathematics | 11B37 | MATHEMATICS | BERNOULLI NUMBERS

11B83 | Degenerate Bell numbers and polynomials | Theoretical, Mathematical and Computational Physics | 11B73 | Mathematics, general | 05A19 | Mathematics | Degenerate Stirling numbers of the second kind | Applications of Mathematics | 11B37 | MATHEMATICS | BERNOULLI NUMBERS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2017, Volume 446, Issue 1, pp. 87 - 100

This paper deals with a unified matrix representation for the Sheffer polynomials. The core of the proposed approach is the so-called creation matrix, a...

Binomial type polynomials | Generalized Pascal matrix | Sheffer polynomials | Appell polynomials | Creation matrix | MATHEMATICS | DETERMINANTAL APPROACH | MATHEMATICS, APPLIED | BELL POLYNOMIALS | SEQUENCES | IDENTITIES

Binomial type polynomials | Generalized Pascal matrix | Sheffer polynomials | Appell polynomials | Creation matrix | MATHEMATICS | DETERMINANTAL APPROACH | MATHEMATICS, APPLIED | BELL POLYNOMIALS | SEQUENCES | IDENTITIES

Journal Article

中国科学：数学英文版, ISSN 1674-7283, 2015, Volume 58, Issue 10, pp. 2095 - 2104

We investigate Bell polynomials, also called Touchard polynomials or exponential polynomials, by using and without using umbral calculus. We use three...

恒等式 | 指数多项式 | 阶乘 | Bell多项式 | 贝尔 | 伯努利多项式 | 哑演算 | 柯西 | 11B83 | 05A40 | umbral calculus | Cauchy polynomial | 11B73 | higher-order Bernoulli polynomial | 05A19 | Mathematics | Applications of Mathematics | Bell-polynomial | poly-Bernoulli polynomial | MATHEMATICS | MATHEMATICS, APPLIED

恒等式 | 指数多项式 | 阶乘 | Bell多项式 | 贝尔 | 伯努利多项式 | 哑演算 | 柯西 | 11B83 | 05A40 | umbral calculus | Cauchy polynomial | 11B73 | higher-order Bernoulli polynomial | 05A19 | Mathematics | Applications of Mathematics | Bell-polynomial | poly-Bernoulli polynomial | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 08/2016, Volume 37, pp. 362 - 373

•The conditionally Painleve integrable Jimbo–Miwa equation is investigated for multi-soliton solutions.•Bell-polynomials are used to obtain Backlund...

Lax system | Jimbo–Miwa equation | Bäcklund transformations | Bell polynomials | Infinite conservation laws | Extended three wave method | Jimbo-Miwa equation | MATHEMATICS, APPLIED | INTEGRABILITY | PHYSICS, FLUIDS & PLASMAS | DE-VRIES EQUATION | PHYSICS, MATHEMATICAL | Backlund transformations | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SOLITON-SOLUTIONS | COMBINATORICS | Environmental law

Lax system | Jimbo–Miwa equation | Bäcklund transformations | Bell polynomials | Infinite conservation laws | Extended three wave method | Jimbo-Miwa equation | MATHEMATICS, APPLIED | INTEGRABILITY | PHYSICS, FLUIDS & PLASMAS | DE-VRIES EQUATION | PHYSICS, MATHEMATICAL | Backlund transformations | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SOLITON-SOLUTIONS | COMBINATORICS | Environmental law

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 1/2019, Volume 113, Issue 1, pp. 1 - 9

In the paper, the authors discuss the Bell polynomials and a sequence of polynomials applied to the theory of differential equations. Concretely speaking, the...

Faà di Bruno formula | 11C08 | Generating function | Secondary 11B73 | Differential equation | Theoretical, Mathematical and Computational Physics | 33B10 | Mathematics | Bell polynomial | Explicit formula | Primary 11B83 | Derivative | Mathematics, general | 26A06 | Applications of Mathematics | Identity | 26A09 | Stirling number | INEQUALITIES | Faa di Bruno formula | TERMS | DIAGONAL RECURRENCE RELATIONS | STIRLING NUMBERS | MATHEMATICS | 2ND KIND | Functions (mathematics) | Polynomials | Mathematical analysis | Combinatorial analysis | Differential equations | Identities

Faà di Bruno formula | 11C08 | Generating function | Secondary 11B73 | Differential equation | Theoretical, Mathematical and Computational Physics | 33B10 | Mathematics | Bell polynomial | Explicit formula | Primary 11B83 | Derivative | Mathematics, general | 26A06 | Applications of Mathematics | Identity | 26A09 | Stirling number | INEQUALITIES | Faa di Bruno formula | TERMS | DIAGONAL RECURRENCE RELATIONS | STIRLING NUMBERS | MATHEMATICS | 2ND KIND | Functions (mathematics) | Polynomials | Mathematical analysis | Combinatorial analysis | Differential equations | Identities

Journal Article

Reports on Mathematical Physics, ISSN 0034-4877, 08/2013, Volume 72, Issue 1, pp. 41 - 56

A class of bilinear differential operators is introduced by assigning specific signs to derivatives. The corresponding bilinear differential equations,...

resonant solution | Bell polynomials | bilinear equation | Resonant solution | Bilinear equation | BOUSSINESQ EQUATION | BACKLUND-TRANSFORMATIONS | FORM | BKP EQUATIONS | CONSTRUCTION | DE-VRIES EQUATION | PHYSICS, MATHEMATICAL | Algorithms | Dependent variables | Mathematical analysis | Differential equations | Mathematical models | Polynomials | Derivatives | Recognition | Combinatorial analysis

resonant solution | Bell polynomials | bilinear equation | Resonant solution | Bilinear equation | BOUSSINESQ EQUATION | BACKLUND-TRANSFORMATIONS | FORM | BKP EQUATIONS | CONSTRUCTION | DE-VRIES EQUATION | PHYSICS, MATHEMATICAL | Algorithms | Dependent variables | Mathematical analysis | Differential equations | Mathematical models | Polynomials | Derivatives | Recognition | Combinatorial analysis

Journal Article

Afrika Matematika, ISSN 1012-9405, 12/2017, Volume 28, Issue 7, pp. 1167 - 1183

In this paper, we show that the r-Stirling numbers of both kinds, the r-Whitney numbers of both kinds, the r-Lah numbers and the r-Whitney-Lah numbers form...

Probabilistic interpretation | Whitney numbers | 11B73 | Mathematics, general | Mathematics Education | Mathematics | History of Mathematical Sciences | Applications of Mathematics | The partial Bell and r -Bell polynomials | Stirling numbers | Recurrence relations | 05A18 | The partial Bell and r-Bell polynomials

Probabilistic interpretation | Whitney numbers | 11B73 | Mathematics, general | Mathematics Education | Mathematics | History of Mathematical Sciences | Applications of Mathematics | The partial Bell and r -Bell polynomials | Stirling numbers | Recurrence relations | 05A18 | The partial Bell and r-Bell polynomials

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 7/2019, Volume 113, Issue 3, pp. 2507 - 2513

Here we study the degenerate central Bell numbers and polynomials as a degenerate version of the recently introduced central Bell numbers and polynomials,...

Central factorial numbers | 05A68 | Bell numbers | 11B83 | Theoretical, Mathematical and Computational Physics | 11B73 | Mathematics, general | Degenerate central Bell polynomials | Mathematics | Applications of Mathematics | 11B68 | MATHEMATICS | Numbers | Fibonacci numbers | Polynomials

Central factorial numbers | 05A68 | Bell numbers | 11B83 | Theoretical, Mathematical and Computational Physics | 11B73 | Mathematics, general | Degenerate central Bell polynomials | Mathematics | Applications of Mathematics | 11B68 | MATHEMATICS | Numbers | Fibonacci numbers | Polynomials

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2013, Volume 400, Issue 2, pp. 624 - 634

This paper investigates the integrability of a generalized (2+1)-dimensional Korteweg–de Vries equation. With the aid of binary Bell polynomials, its bilinear...

Darboux covariant Lax pair | Binary Bell polynomial | [formula omitted]-soliton solution | Infinite conservation law | Lax pair | Bäcklund transformation | N-soliton solution | MATHEMATICS, APPLIED | KP HIERARCHY | MATHEMATICS | WAVES | KDV EQUATION | Backlund transformation | CONSERVATION-LAWS | N-SOLITON SOLUTIONS | COMBINATORICS | TRANSFORMATIONS

Darboux covariant Lax pair | Binary Bell polynomial | [formula omitted]-soliton solution | Infinite conservation law | Lax pair | Bäcklund transformation | N-soliton solution | MATHEMATICS, APPLIED | KP HIERARCHY | MATHEMATICS | WAVES | KDV EQUATION | Backlund transformation | CONSERVATION-LAWS | N-SOLITON SOLUTIONS | COMBINATORICS | TRANSFORMATIONS

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 10/2015, Volume 82, Issue 1-2, pp. 311 - 318

In this paper, the binary Bell polynomials are employed to find the bilinear form, bilinear Backlund transformation and Lax pair for the (3+1)-dimensional BKP...

Multi-soliton solutions | Binary Bell polynomial | Bilinear Bäcklund transformation | Lax pair | TRAVELING-WAVE SOLUTIONS | MECHANICS | SOLITON-SOLUTIONS | Bilinear Backlund transformation | CONSERVATION-LAWS | ENGINEERING, MECHANICAL | Transformations | Polynomials | Solitary waves | Combinatorial analysis

Multi-soliton solutions | Binary Bell polynomial | Bilinear Bäcklund transformation | Lax pair | TRAVELING-WAVE SOLUTIONS | MECHANICS | SOLITON-SOLUTIONS | Bilinear Backlund transformation | CONSERVATION-LAWS | ENGINEERING, MECHANICAL | Transformations | Polynomials | Solitary waves | Combinatorial analysis

Journal Article

Journal of Computational Analysis and Applications, ISSN 1521-1398, 05/2020, Volume 28, Issue 3, pp. 457 - 462

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 06/2013, Volume 219, Issue 19, pp. 9978 - 9991

We discuss the generalized Touchard polynomials introduced recently by Dattoli et al. as well as their extension to negative order introduced by the authors...

Bell number | Generating function | Stirling number | Touchard polynomial | MATHEMATICS, APPLIED

Bell number | Generating function | Stirling number | Touchard polynomial | MATHEMATICS, APPLIED

Journal Article

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