Discrete Applied Mathematics, ISSN 0166-218X, 01/2020, Volume 272, pp. 90 - 99

In the paper we introduce and study partitions of vectors in Np, as a natural extension of the classical partitions of integers. We show that these vector...

Multi-dimensional Bell polynomials | Vector partitions | Multi-dimensional Faà di Bruno formulae | MATHEMATICS, APPLIED | Multi-dimensional Faa di Bruno formulae | Partitions | Polynomials | Algorithms | Mathematical analysis | Combinatorial analysis | Mathematics | Computer Science | Classical Analysis and ODEs | Discrete Mathematics

Multi-dimensional Bell polynomials | Vector partitions | Multi-dimensional Faà di Bruno formulae | MATHEMATICS, APPLIED | Multi-dimensional Faa di Bruno formulae | Partitions | Polynomials | Algorithms | Mathematical analysis | Combinatorial analysis | Mathematics | Computer Science | Classical Analysis and ODEs | Discrete Mathematics

Journal Article

MATHEMATICAL INEQUALITIES & APPLICATIONS, ISSN 1331-4343, 01/2020, Volume 23, Issue 1, pp. 123 - 135

In the paper, with the help of the Faa di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem for the Stirling...

LOG-CONCAVITY | Faa di Bruno formula | logarithmic concavity | generating function | determinantal inequality | product inequality | EQUATIONS | Toucbard polynomial | absolute monotonicity | Bell number | inversion theorem | Exponential polynomial | complete monotonicity | white noise distribution theory | logarithmic convexity | MATHEMATICS | explicit formula | higher order derivative | Bell polynomial of the second kind | Stirling number of the first kind | Stirling number of the second kind

LOG-CONCAVITY | Faa di Bruno formula | logarithmic concavity | generating function | determinantal inequality | product inequality | EQUATIONS | Toucbard polynomial | absolute monotonicity | Bell number | inversion theorem | Exponential polynomial | complete monotonicity | white noise distribution theory | logarithmic convexity | MATHEMATICS | explicit formula | higher order derivative | Bell polynomial of the second kind | Stirling number of the first kind | Stirling number of the second kind

Journal Article

Journal of King Saud University - Science, ISSN 1018-3647, 01/2020, Volume 32, Issue 1, pp. 858 - 861

In this work, a new algorithm is proposed for computing the differential transform of two-dimensional nonlinear functions. This algorithm overcomes the...

Nonlinear partial differential equations | Multivariable Faa di Bruno formula | Differential transform method | MULTIDISCIPLINARY SCIENCES

Nonlinear partial differential equations | Multivariable Faa di Bruno formula | Differential transform method | MULTIDISCIPLINARY SCIENCES

Journal Article

Journal of Taibah University for Science, ISSN 1658-3655, 12/2019, Volume 13, Issue 1, pp. 947 - 950

In the paper, by the Faà di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify...

Faà di Bruno formula | Secondary: 11B65 | nonlinear ordinary differential equation | coefficient | generating function | Catalan number | Bell polynomial of the second kind | Simplifying | Primary: 05A15 | inversion theorem | BELL POLYNOMIALS | Faa di Bruno formula | MULTIDISCIPLINARY SCIENCES | SPECIAL VALUES | FAMILY | FORMULAS | faà di bruno formula | catalan number | simplifying | bell polynomial of the second kind

Faà di Bruno formula | Secondary: 11B65 | nonlinear ordinary differential equation | coefficient | generating function | Catalan number | Bell polynomial of the second kind | Simplifying | Primary: 05A15 | inversion theorem | BELL POLYNOMIALS | Faa di Bruno formula | MULTIDISCIPLINARY SCIENCES | SPECIAL VALUES | FAMILY | FORMULAS | faà di bruno formula | catalan number | simplifying | bell polynomial of the second kind

Journal Article

5.
SHARPNESS AND GENERALIZATION OF JORDAN, BECKER-STARK AND PAPENFUSS INEQUALITIES WITH AN APPLICATION

JOURNAL OF MATHEMATICAL INEQUALITIES, ISSN 1846-579X, 12/2019, Volume 13, Issue 4, pp. 1209 - 1234

In this paper, we present an identity related to Jordan's inequality. More precisely, we provide a formula for determining the coefficients b(n )(math) b(n)...

REFINEMENT | MATHEMATICS | MATHEMATICS, APPLIED | Yang Le inequality | Bell polynomials of the second kind | Papenfuss inequality | Faa di Bruno formula | Jordan's inequality | IMPROVEMENT | VERSION | Becker-Stark inequality

REFINEMENT | MATHEMATICS | MATHEMATICS, APPLIED | Yang Le inequality | Bell polynomials of the second kind | Papenfuss inequality | Faa di Bruno formula | Jordan's inequality | IMPROVEMENT | VERSION | Becker-Stark inequality

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 10/2019, Volume 223, Issue 10, pp. 4191 - 4225

Differential categories were introduced by Blute, Cockett, and Seely as categorical models of differential linear logic and have since led to abstract...

Faà di Bruno formula | Hurwitz series rings | Differential categories | Differential algebras | FORMS | MATHEMATICS | MATHEMATICS, APPLIED | MODELS | Faa di Bruno formula | Analysis | Algebra | Mathematics - Category Theory

Faà di Bruno formula | Hurwitz series rings | Differential categories | Differential algebras | FORMS | MATHEMATICS | MATHEMATICS, APPLIED | MODELS | Faa di Bruno formula | Analysis | Algebra | Mathematics - Category Theory

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

AIMS MATHEMATICS, ISSN 2473-6988, 2019, Volume 4, Issue 2, pp. 170 - 175

In the paper, by virtue of the Faa di Bruno formula, some properties of the Bell polynomials of the second kind, and an inversion formula for the Stirling...

MATHEMATICS, APPLIED | IDENTITIES | ordinary differential equation | Faa di Bruno formula | TERMS | STIRLING NUMBERS | simplification | inversion formula | FAMILY | POLYNOMIALS | MATHEMATICS | higher order Bernoulli number of the second kind | GENERATING FUNCTION | coefficient | Bell polynomial of the second kind | EXPLICIT FORMULAS | Stirling number of the first kind | Stirling number of the second kind | EULER | Faà di Bruno formula

MATHEMATICS, APPLIED | IDENTITIES | ordinary differential equation | Faa di Bruno formula | TERMS | STIRLING NUMBERS | simplification | inversion formula | FAMILY | POLYNOMIALS | MATHEMATICS | higher order Bernoulli number of the second kind | GENERATING FUNCTION | coefficient | Bell polynomial of the second kind | EXPLICIT FORMULAS | Stirling number of the first kind | Stirling number of the second kind | EULER | Faà di Bruno formula

Journal Article

UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, ISSN 1223-7027, 2019, Volume 81, Issue 1, pp. 123 - 136

In the paper, the authors give a motivation from central Delannoy numbers to a tridiagonal determinant, find a generating function for the tridiagonal...

Faà di Bruno formula | Generating function | Chebyshev polynomial | Fibonacci polynomial | Bell polynomial of the second kind | Cauchy product | Central Delannoy number | Tridiagonal determinant | Inverse of tridiagonal matrix | Fibonacci number | MATHEMATICS, APPLIED | tridiagonal determinant | PHYSICS, MULTIDISCIPLINARY | central Delannoy number | Faa di Bruno formula | generating function | inverse of tridiagonal matrix

Faà di Bruno formula | Generating function | Chebyshev polynomial | Fibonacci polynomial | Bell polynomial of the second kind | Cauchy product | Central Delannoy number | Tridiagonal determinant | Inverse of tridiagonal matrix | Fibonacci number | MATHEMATICS, APPLIED | tridiagonal determinant | PHYSICS, MULTIDISCIPLINARY | central Delannoy number | Faa di Bruno formula | generating function | inverse of tridiagonal matrix

Journal Article

ELECTRONIC JOURNAL OF PROBABILITY, ISSN 1083-6489, 2019, Volume 24

Take a continuous-time Galton-Watson tree and pick k distinct particles uniformly from those alive at a time T. What does their genealogical tree look like?...

coalescence | Faa di Bruno's formula | COALESCENCE TIMES | spines | Galton-Watson trees | STATISTICS & PROBABILITY | branching processes | Mathematics - Probability

coalescence | Faa di Bruno's formula | COALESCENCE TIMES | spines | Galton-Watson trees | STATISTICS & PROBABILITY | branching processes | Mathematics - Probability

Journal Article

MISKOLC MATHEMATICAL NOTES, ISSN 1787-2405, 2019, Volume 20, Issue 2, pp. 1129 - 1137

In the paper, starting from the Rodrigues formulas for the Chebyshev polynomials of the first and second kinds, by virtue of the Faa di Bruno formula, with the...

BELL POLYNOMIALS | Faa di Bruno formula | DIFFERENTIAL-EQUATIONS | Chebyshev polynomial of the first kind | inversion formula | Chebyshev polynomial of the second kind | FAMILY | MATHEMATICS | EXPRESSIONS | GENERATING FUNCTION | explicit formula | Bell polynomial of the second kind | COEFFICIENTS | Rodrigues formula | INTEGRAL-REPRESENTATIONS

BELL POLYNOMIALS | Faa di Bruno formula | DIFFERENTIAL-EQUATIONS | Chebyshev polynomial of the first kind | inversion formula | Chebyshev polynomial of the second kind | FAMILY | MATHEMATICS | EXPRESSIONS | GENERATING FUNCTION | explicit formula | Bell polynomial of the second kind | COEFFICIENTS | Rodrigues formula | INTEGRAL-REPRESENTATIONS

Journal Article

Tatra Mountains Mathematical Publications, ISSN 1210-3195, 12/2018, Volume 72, Issue 1, pp. 67 - 76

In the paper, the authors apply Faà di Bruno formula, some properties of the Bell polynomials of the second kind, the inversion formulas of binomial numbers...

Faà di Bruno formula | higher order Frobenius–Euler number | Primary: 34A05 | Secondary: 05A16, 11A25, 11B37, 11B68, 11B73, 11B83, 33B10, 34A34 | ordinary differential equation | coefficient | Bell polynomial of the second kind | simplification | inversion formula | higher order Frobenius-Euler number

Faà di Bruno formula | higher order Frobenius–Euler number | Primary: 34A05 | Secondary: 05A16, 11A25, 11B37, 11B68, 11B73, 11B83, 33B10, 34A34 | ordinary differential equation | coefficient | Bell polynomial of the second kind | simplification | inversion formula | higher order Frobenius-Euler number

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 7/2018, Volume 28, Issue 3, pp. 2602 - 2608

We prove that a certain positivity condition, considerably more general than pseudoconvexity, enables one to conclude that the regular and singular orders of...

Faa di Bruno formula | Positivity property | 32F18 | Mathematics | Real hypersurface germ | Abstract Harmonic Analysis | Fourier Analysis | Finite type conditions | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Plurisubharmonic function | Differential Geometry | Dynamical Systems and Ergodic Theory | 32T27 | 32U05 | 32T25 | 32V35 | MATHEMATICS | PSEUDOCONVEX DOMAINS | NEUMANN PROBLEM | CONVEX DOMAINS

Faa di Bruno formula | Positivity property | 32F18 | Mathematics | Real hypersurface germ | Abstract Harmonic Analysis | Fourier Analysis | Finite type conditions | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Plurisubharmonic function | Differential Geometry | Dynamical Systems and Ergodic Theory | 32T27 | 32U05 | 32T25 | 32V35 | MATHEMATICS | PSEUDOCONVEX DOMAINS | NEUMANN PROBLEM | CONVEX DOMAINS

Journal Article

Computers and Fluids, ISSN 0045-7930, 06/2018, Volume 169, pp. 87 - 97

•A new method for the numerical solution of ODEs is presented.•Approach is based on an approximate formulation of Taylor methods.•Functions, and not...

Taylor methods | Faà di Bruno’s formula | ODE integrators | Faà di Bruno's formula | Derivatives (Financial instruments) | Methods

Taylor methods | Faà di Bruno’s formula | ODE integrators | Faà di Bruno's formula | Derivatives (Financial instruments) | Methods

Journal Article

COMPUTERS & FLUIDS, ISSN 0045-7930, 06/2018, Volume 169, pp. 87 - 97

A new method for the numerical solution of ODES is presented. This approach is based on an approximate formulation of the Taylor methods that has a much easier...

COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Faa di Bruno's formula | Taylor methods | ODE integrators | SCHEMES

COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Faa di Bruno's formula | Taylor methods | ODE integrators | SCHEMES

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 6/2018, Volume 46, Issue 2, pp. 323 - 344

The commutative ring $$R(P(t))=\mathbb C[t^{\pm 1},u \,|\, u^2=P(t)]$$ R(P(t))=C[t±1,u|u2=P(t)] , where $$P(t)=\sum _{i=0}^na_it^i=\prod _{k=1}^n(t-\alpha...

DJKM algebras | Functions of a Complex Variable | Universal central extensions | Superelliptic Lie algebras | Superelliptic curves | Field Theory and Polynomials | Mathematics | Fáa di Bruno’s formula | 14H55 | Automorphism groups | 42C10 | Fourier Analysis | Pell’s equation | Bell polynomials | 17B65 | Krichever–Novikov algebras | Associated Legendre polynomials | Number Theory | Combinatorics | 05E35 | CENTRAL EXTENSIONS | Faa di Bruno's formula | KRICHEVER-NOVIKOV-TYPE | MATHEMATICS | Pell's equation | Krichever-Novikov algebras | Algebra

DJKM algebras | Functions of a Complex Variable | Universal central extensions | Superelliptic Lie algebras | Superelliptic curves | Field Theory and Polynomials | Mathematics | Fáa di Bruno’s formula | 14H55 | Automorphism groups | 42C10 | Fourier Analysis | Pell’s equation | Bell polynomials | 17B65 | Krichever–Novikov algebras | Associated Legendre polynomials | Number Theory | Combinatorics | 05E35 | CENTRAL EXTENSIONS | Faa di Bruno's formula | KRICHEVER-NOVIKOV-TYPE | MATHEMATICS | Pell's equation | Krichever-Novikov algebras | Algebra

Journal Article

Topology and its Applications, ISSN 0166-8641, 02/2018, Volume 235, pp. 375 - 427

In this paper, we consider abelian functor calculus, the calculus of functors of abelian categories established by the second author and McCarthy. We carefully...

Abelian categories | Faà di Bruno formula | Chain rule | Functor calculus | Cartesian differential categories | MATHEMATICS | MATHEMATICS, APPLIED | Faadi Bruno formula

Abelian categories | Faà di Bruno formula | Chain rule | Functor calculus | Cartesian differential categories | MATHEMATICS | MATHEMATICS, APPLIED | Faadi Bruno formula

Journal Article

Tbilisi Mathematical Journal, ISSN 1875-158X, 12/2017, Volume 10, Issue 4, pp. 153 - 158

In the paper, by virtue of the Faá di Bruno formula and two identities for the Bell polynomial of the second kind, the authors find a closed form for the...

Bell polynomial | Bernoulli number | Faá di Bruno's formula | Stirling polynomial | Closed form | Stirling number

Bell polynomial | Bernoulli number | Faá di Bruno's formula | Stirling polynomial | Closed form | Stirling number

Journal Article

Computers and Fluids, ISSN 0045-7930, 12/2017, Volume 159, pp. 156 - 166

•A new method for the numerical solution of ODEs is presented.•Approach is based on an approximate formulation of Taylor methods.•Functions, and not...

Taylor methods | Faà di Bruno’s formula | ODE integrators | Faà di Bruno's formula | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Faa di Bruno's formula | SCHEMES | Derivatives (Financial instruments) | Methods

Taylor methods | Faà di Bruno’s formula | ODE integrators | Faà di Bruno's formula | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Faa di Bruno's formula | SCHEMES | Derivatives (Financial instruments) | Methods

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 8

In the paper, by the Faà di Bruno formula, the authors establish two explicit formulas for the Motzkin numbers, the generalized Motzkin numbers, and the...

Faà di Bruno formula | 05A20 | Motzkin number | generating function | Mathematics | restricted hexagonal number | 11B37 | explicit formula | 11B83 | Analysis | generalized Motzkin number | Catalan number | Bell polynomial of the second kind | Mathematics, general | 05A19 | Applications of Mathematics | 05A15 | MATHEMATICS | MATHEMATICS, APPLIED | Faa di Bruno formula | CATALAN NUMBERS | Inequalities | Research

Faà di Bruno formula | 05A20 | Motzkin number | generating function | Mathematics | restricted hexagonal number | 11B37 | explicit formula | 11B83 | Analysis | generalized Motzkin number | Catalan number | Bell polynomial of the second kind | Mathematics, general | 05A19 | Applications of Mathematics | 05A15 | MATHEMATICS | MATHEMATICS, APPLIED | Faa di Bruno formula | CATALAN NUMBERS | Inequalities | Research

Journal Article

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.