Advances in Difference Equations, ISSN 1687-1839, 12/2015, Volume 2015, Issue 1, pp. 1 - 10

The degenerate Bernoulli polynomials were introduced by Carlitz and rediscovered later by Ustiniv under the name of Korobov polynomials of the second kind (see...

05A30 | Mathematics | 11B68 | q -analogs of degenerate Bernoulli polynomials of the second kind | q -analogs of λ -Daehee polynomials | Ordinary Differential Equations | Functional Analysis | 11B83 | Analysis | Difference and Functional Equations | Mathematics, general | 05A19 | q -analogs of degenerate Bernoulli polynomials | Partial Differential Equations | q-analogs of degenerate Bernoulli polynomials of the second kind | q-analogs of λ-Daehee polynomials | q-analogs of degenerate Bernoulli polynomials | MATHEMATICS | MATHEMATICS, APPLIED | IDENTITIES | q-analogs of lambda-Daehee polynomials | Usage | Polynomials | Formulae | Names | Difference equations | Arches | Formulas (mathematics)

05A30 | Mathematics | 11B68 | q -analogs of degenerate Bernoulli polynomials of the second kind | q -analogs of λ -Daehee polynomials | Ordinary Differential Equations | Functional Analysis | 11B83 | Analysis | Difference and Functional Equations | Mathematics, general | 05A19 | q -analogs of degenerate Bernoulli polynomials | Partial Differential Equations | q-analogs of degenerate Bernoulli polynomials of the second kind | q-analogs of λ-Daehee polynomials | q-analogs of degenerate Bernoulli polynomials | MATHEMATICS | MATHEMATICS, APPLIED | IDENTITIES | q-analogs of lambda-Daehee polynomials | Usage | Polynomials | Formulae | Names | Difference equations | Arches | Formulas (mathematics)

Journal Article

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, ISSN 1073-7928, 06/2018, Volume 2018, Issue 12, pp. 3621 - 3670

Let G be a simply connected simple algebraic group over C, B and B- its two opposite Borel subgroups, and W the associated Weyl group. It is shown that the...

Q-ANALOG | MATHEMATICS | BASES

Q-ANALOG | MATHEMATICS | BASES

Journal Article

Symmetry, ISSN 2073-8994, 09/2018, Volume 10, Issue 9, p. 395

The goal of this paper is to define the (p, q)-analogue of tangent numbers and polynomials by generalizing the tangent numbers and polynomials and Carlitz-type...

Carlitz-type q-tangent numbers | (p, q)-analogue of tangent numbers and polynomials | Symmetric identities | (p, q)-analogue of tangent zeta function | Zeros | Carlitz-type q-tangent polynomials | Tangent numbers | Tangent polynomials | tangent numbers | NUMBERS | MULTIDISCIPLINARY SCIENCES | Q-EXTENSIONS | (p-q)-analogue of tangent numbers and polynomials | zeros | POLYNOMIALS | tangent polynomials | (p-q)-analogue of tangent zeta function | symmetric identities | Q-BERNOULLI | EULER | Numbers | Applied mathematics | Analogue | Numerical methods | Conflicts of interest | Polynomials | Symmetry | (p,q)-analogue of tangent numbers and polynomials | (p,q)-analogue of tangent zeta function

Carlitz-type q-tangent numbers | (p, q)-analogue of tangent numbers and polynomials | Symmetric identities | (p, q)-analogue of tangent zeta function | Zeros | Carlitz-type q-tangent polynomials | Tangent numbers | Tangent polynomials | tangent numbers | NUMBERS | MULTIDISCIPLINARY SCIENCES | Q-EXTENSIONS | (p-q)-analogue of tangent numbers and polynomials | zeros | POLYNOMIALS | tangent polynomials | (p-q)-analogue of tangent zeta function | symmetric identities | Q-BERNOULLI | EULER | Numbers | Applied mathematics | Analogue | Numerical methods | Conflicts of interest | Polynomials | Symmetry | (p,q)-analogue of tangent numbers and polynomials | (p,q)-analogue of tangent zeta function

Journal Article

QUARTERLY JOURNAL OF MATHEMATICS, ISSN 0033-5606, 09/2019, Volume 70, Issue 3, pp. 895 - 925

The quantum co-ordinate algebra A(q) (g) associated to a Kac-Moody Lie algebra g forms a Hopf algebra whose comodules are direct sums of finite-dimensional...

Q-ANALOG | MATHEMATICS | BASES

Q-ANALOG | MATHEMATICS | BASES

Journal Article

Representation Theory of the American Mathematical Society, ISSN 1088-4165, 09/2017, Volume 21, Issue 11, pp. 247 - 276

We reformulate the Kazhdan-Lusztig theory for the BGG category \mathcal {O} of Lie algebras of type D via the theory of canonical bases arising from quantum...

Q-ANALOG | MATHEMATICS | ALGEBRAS

Q-ANALOG | MATHEMATICS | ALGEBRAS

Journal Article

ELECTRONIC JOURNAL OF COMBINATORICS, ISSN 1077-8926, 11/2019, Volume 26, Issue 4

In this paper, we study a new cyclic sieving phenomenon on the set SSTn(lambda) of semistandard Young tableaux with the cyclic action c arising from its...

Q-ANALOG | MATHEMATICS | MATHEMATICS, APPLIED

Q-ANALOG | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 10/2019, Volume 15, Issue 9, pp. 1919 - 1968

We establish a supercongruence conjectured by Almkvist and Zudilin, by proving a corresponding q -supercongruence. Similar q -supercongruences are established...

q -analogue | Apéry numbers | supercongruence | Gauss congruence | cyclic sieving phenomenon | MATHEMATICS | q-analogue | SERIES | Q-ANALOGS | Apery numbers | FERMAT | FIBONACCI NUMBERS

q -analogue | Apéry numbers | supercongruence | Gauss congruence | cyclic sieving phenomenon | MATHEMATICS | q-analogue | SERIES | Q-ANALOGS | Apery numbers | FERMAT | FIBONACCI NUMBERS

Journal Article

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, ISSN 1073-7928, 10/2019, Volume 2019, Issue 20, pp. 6179 - 6215

We will construct the Lusztig form for the quantum loop algebra of gl(n) by proving the conjecture [4, 3.8.6] and establish partially the Schur-Weyl duality at...

Q-ANALOG | MATHEMATICS | CRYSTAL BASES | CANONICAL BASES

Q-ANALOG | MATHEMATICS | CRYSTAL BASES | CANONICAL BASES

Journal Article

Advances in Mathematics, ISSN 0001-8708, 04/2019, Volume 346, pp. 329 - 358

By examining asymptotic behavior of certain infinite basic (q-) hypergeometric sums at roots of unity (that is, at a ‘q-microscopic’ level) we prove polynomial...

q-analogue | Cyclotomic polynomial | Basic hypergeometric function | Radial asymptotics | (Super)congruence | WZ pair | Q-ANALOG | MATHEMATICS | CONJECTURES | FORMULAS

q-analogue | Cyclotomic polynomial | Basic hypergeometric function | Radial asymptotics | (Super)congruence | WZ pair | Q-ANALOG | MATHEMATICS | CONJECTURES | FORMULAS

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 15

The object of this paper to construct Dunkl type Szász operators via post-quantum calculus. We obtain some approximation results for these new operators and...

33C45 | 41A25 | 41A36 | Szász operator | ( p , q ) $(p,q)$ -integers | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | modulus of continuity | ( p , q ) $(p,q)$ -analogues of the exponential function | Dunkl analogue | (p, q) -analogues of the exponential function | (p, q) -integers | (p,q)-analogues of the exponential function | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | (p, q)-integers | Szasz operator | Operators (mathematics) | Bivariate analysis | Convergence | documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(p,q)$\end{document}(p,q)-integers | documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(p,q)$\end{document}(p,q)-analogues of the exponential function | Research

33C45 | 41A25 | 41A36 | Szász operator | ( p , q ) $(p,q)$ -integers | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | modulus of continuity | ( p , q ) $(p,q)$ -analogues of the exponential function | Dunkl analogue | (p, q) -analogues of the exponential function | (p, q) -integers | (p,q)-analogues of the exponential function | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | (p, q)-integers | Szasz operator | Operators (mathematics) | Bivariate analysis | Convergence | documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(p,q)$\end{document}(p,q)-integers | documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(p,q)$\end{document}(p,q)-analogues of the exponential function | Research

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 12/2016, Volume 308, pp. 318 - 329

This paper is concerned with a new generalization of rational Bernstein–Bézier curves involving q-integers as shape parameters. A one parameter family of...

Lupaş [formula omitted]-analogue of Bernstein operator | Conic sections | Shape parameter | Weighted Lupaş [formula omitted]-Bernstein basis | Normalized totally positive basis | Rational Bézier curve | Lupaş q-analogue of Bernstein operator | Weighted Lupaş q-Bernstein basis | Weighted Lupas q-Bernstein basis | Q-ANALOG | TOTAL POSITIVITY | MATHEMATICS, APPLIED | BASES | Q-BERNSTEIN POLYNOMIALS | SPACES | Lupas q-analogue of Bernstein operator | Rational Bezier curve

Lupaş [formula omitted]-analogue of Bernstein operator | Conic sections | Shape parameter | Weighted Lupaş [formula omitted]-Bernstein basis | Normalized totally positive basis | Rational Bézier curve | Lupaş q-analogue of Bernstein operator | Weighted Lupaş q-Bernstein basis | Weighted Lupas q-Bernstein basis | Q-ANALOG | TOTAL POSITIVITY | MATHEMATICS, APPLIED | BASES | Q-BERNSTEIN POLYNOMIALS | SPACES | Lupas q-analogue of Bernstein operator | Rational Bezier curve

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2017, Volume 448, Issue 2, pp. 1633 - 1650

In this work, following a new approach of Baliarsingh (2016) [6], we introduce the concepts of statistically weighted ΨΔp,q-summability, weighted...

The difference operator [formula omitted] | Korovkin type approximations for functions of two variables | [formula omitted]-analogue of Bernstein–Schurer operator | Weighted statistical convergence and statistical summability | The rate of convergence | (p,q)-analogue of Bernstein–Schurer operator | The difference operator Δ | FRACTIONAL ORDER | MATHEMATICS | MATHEMATICS, APPLIED | SEQUENCE-SPACES | KOROVKIN | (p, q)-analogue of Bernstein-Schurer operator | The difference operator Delta(alpha,beta,gamma)(h,p,q)

The difference operator [formula omitted] | Korovkin type approximations for functions of two variables | [formula omitted]-analogue of Bernstein–Schurer operator | Weighted statistical convergence and statistical summability | The rate of convergence | (p,q)-analogue of Bernstein–Schurer operator | The difference operator Δ | FRACTIONAL ORDER | MATHEMATICS | MATHEMATICS, APPLIED | SEQUENCE-SPACES | KOROVKIN | (p, q)-analogue of Bernstein-Schurer operator | The difference operator Delta(alpha,beta,gamma)(h,p,q)

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2016, Volume 443, Issue 2, pp. 752 - 764

In this work, we first define a difference operator Δp,q[m] of natural order m with respect to (p,q)-integers. We then introduce the concepts of...

The difference operator [formula omitted] | Korovkin and Voronovskaja type approximations for functions of two variables | Statistical convergence and statistical summability | [formula omitted]-analogue of Bernstein operator | (p, q)-analogue of Bernstein operator | The difference operator δ | FRACTIONAL ORDER | MATHEMATICS | Q)-ANALOG | MATHEMATICS, APPLIED | The difference operator Delta([m])(p,q) | DIFFERENCE SEQUENCE-SPACES

The difference operator [formula omitted] | Korovkin and Voronovskaja type approximations for functions of two variables | Statistical convergence and statistical summability | [formula omitted]-analogue of Bernstein operator | (p, q)-analogue of Bernstein operator | The difference operator δ | FRACTIONAL ORDER | MATHEMATICS | Q)-ANALOG | MATHEMATICS, APPLIED | The difference operator Delta([m])(p,q) | DIFFERENCE SEQUENCE-SPACES

Journal Article

Journal of Combinatorial Designs, ISSN 1063-8539, 11/2015, Volume 23, Issue 11, pp. 463 - 480

Intersection numbers for subspace designs are introduced and q‐analogs of the Mendelsohn and Köhler equations are given. As an application, we are able to...

block design | subspace design | q‐analog | Fano plane | intersection number | q-analog | MATHEMATICS | Q-ANALOGS | 2-DESIGNS | T-DESIGNS | Mathematics - Combinatorics

block design | subspace design | q‐analog | Fano plane | intersection number | q-analog | MATHEMATICS | Q-ANALOGS | 2-DESIGNS | T-DESIGNS | Mathematics - Combinatorics

Journal Article

Proceedings of the Royal Society of Edinburgh Section A: Mathematics, ISSN 0308-2105, 2019, pp. 1 - 12

AbstractWe prove some congruences on sums involving fourth powers of centralq-binomial coefficients. As a conclusion, we confirm the following supercongruence...

cyclotomic polynomials | q-analogue of Wolstenholme's binomial congruence | q-binomial coefficients | q-analogue of Morley's congruence | q-WZ method

cyclotomic polynomials | q-analogue of Wolstenholme's binomial congruence | q-binomial coefficients | q-analogue of Morley's congruence | q-WZ method

Journal Article

International Mathematics Research Notices, ISSN 1073-7928, 11/2014, Volume 2014, Issue 5, pp. 1312 - 1366

We give an explicit construction of irreducible modules over Khovanov-Lauda-Rouquier algebras R and their cyclotomic quotients R-lambda for finite classical...

Q-ANALOG | MATHEMATICS | CRYSTAL BASES

Q-ANALOG | MATHEMATICS | CRYSTAL BASES

Journal Article

Designs, Codes and Cryptography, ISSN 0925-1022, 8/2014, Volume 72, Issue 2, pp. 405 - 421

Lower and upper bounds on the size of a covering of subspaces in the Grassmann graph $$\mathcal{G }_q(n,r)$$ by subspaces from the Grassmann graph $$\mathcal{G...

Information and Communication, Circuits | Subspace transversal design | 05B40 | Data Encryption | q$$ -analog | Mathematics | 51E10 | Lifted MRD codes | Covering designs | 94B25 | Data Structures, Cryptology and Information Theory | Discrete Mathematics in Computer Science | Coding and Information Theory | Spreads | Combinatorics | Projective geometry | q -analog | MATHEMATICS, APPLIED | FINITE-FIELDS | Q-ANALOGS | PROJECTIVE SPACES | GF(Q) | DESIGNS | q-analog | ERROR-CORRECTING CODES | 2-DESIGNS | CONSTRUCTION | COMPUTER SCIENCE, THEORY & METHODS | Computer science

Information and Communication, Circuits | Subspace transversal design | 05B40 | Data Encryption | q$$ -analog | Mathematics | 51E10 | Lifted MRD codes | Covering designs | 94B25 | Data Structures, Cryptology and Information Theory | Discrete Mathematics in Computer Science | Coding and Information Theory | Spreads | Combinatorics | Projective geometry | q -analog | MATHEMATICS, APPLIED | FINITE-FIELDS | Q-ANALOGS | PROJECTIVE SPACES | GF(Q) | DESIGNS | q-analog | ERROR-CORRECTING CODES | 2-DESIGNS | CONSTRUCTION | COMPUTER SCIENCE, THEORY & METHODS | Computer science

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2019, Volume 475, Issue 2, pp. 1636 - 1646

There are many instances known when the Fourier coefficients of modular forms are congruent to partial sums of hypergeometric series. In our previous work,...

Cyclotomic polynomial | Basic hypergeometric function | Ramanujan | (Super)congruence | q-Analogue | Q-ANALOG | 1/PI | MATHEMATICS | MATHEMATICS, APPLIED | RAMANUJAN-TYPE FORMULAS | SUPERCONGRUENCE | CONGRUENCES

Cyclotomic polynomial | Basic hypergeometric function | Ramanujan | (Super)congruence | q-Analogue | Q-ANALOG | 1/PI | MATHEMATICS | MATHEMATICS, APPLIED | RAMANUJAN-TYPE FORMULAS | SUPERCONGRUENCE | CONGRUENCES

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 05/2019, Volume 65, Issue 5, pp. 2648 - 2660

We study array codes which are based on subspaces of a linear space over a finite field, using spreads, q...

distributed storage | Distributed databases | Bandwidth | Maintenance engineering | Drives | Extraterrestrial measurements | Locally repairable codes | availability | Block codes | q -analog">q -analog | q-analog | FRACTIONAL REPETITION CODES | COMPUTER SCIENCE, INFORMATION SYSTEMS | GRAPHS | ENGINEERING, ELECTRICAL & ELECTRONIC | Availability | Spreads | Fields (mathematics) | Subspaces | Repair | Nodes

distributed storage | Distributed databases | Bandwidth | Maintenance engineering | Drives | Extraterrestrial measurements | Locally repairable codes | availability | Block codes | q -analog">

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 06/2017, Volume 317, pp. 458 - 477

This paper deals with the extension of rational Lupaş Bernstein functions, Lupaş Bèzier curves and surfaces involving (p,q)-integers as shape parameters for...

[formula omitted]-analogue of Lupaş Bernstein operators | [formula omitted]-integers | Lupaş [formula omitted]-Bèzier curves and surfaces | de Casteljau algorithm | Tensor product | Korovkin’s type approximation | Korovkin's type approximation | (p,q)-integers | Lupaş (p,q)-Bèzier curves and surfaces | (p,q)-analogue of Lupaş Bernstein operators | POLYNOMIALS | (p,q)-analogue of Lupas Bernstein operators | MATHEMATICS, APPLIED | Lupas (p,q)-Bezier curves and surfaces | OPERATORS | Analysis | Algorithms

[formula omitted]-analogue of Lupaş Bernstein operators | [formula omitted]-integers | Lupaş [formula omitted]-Bèzier curves and surfaces | de Casteljau algorithm | Tensor product | Korovkin’s type approximation | Korovkin's type approximation | (p,q)-integers | Lupaş (p,q)-Bèzier curves and surfaces | (p,q)-analogue of Lupaş Bernstein operators | POLYNOMIALS | (p,q)-analogue of Lupas Bernstein operators | MATHEMATICS, APPLIED | Lupas (p,q)-Bezier curves and surfaces | OPERATORS | Analysis | Algorithms

Journal Article

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