scholarly journals Certain results associated with hybrid relatives of the q-Sheffer sequences

2022 ◽  
Vol 40 ◽  
pp. 1-15
Author(s):  
Subuhi Khan ◽  
Tabinda Nahid
Keyword(s):  
Numerical Simulations ◽  
Generating Function ◽  
Orthogonality Condition ◽  
Appell Polynomials ◽  
New Class ◽  
Sheffer Sequences ◽  
Sheffer Polynomials

The intended objective of this paper is to introduce a new class of the hybrid q-Sheffer polynomials by means of the generating function and series definition. The determinant definition and other striking properties of these polynomials are established. Certain results for the continuous q-Hermite-Appell polynomials are obtained. The graphical depictions are performed for certain members of the hybrid q-Sheffer family. The zeros of these members are also explored using numerical simulations. Finally, the orthogonality condition for the hybrid q-Sheffer polynomials is established.

scholarly journals A New Class of Higher-Order Hypergeometric Bernoulli Polynomials Associated with Lagrange–Hermite Polynomials

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 648
Author(s):  
Ghulam Muhiuddin ◽  
Waseem Ahmad Khan ◽  
Ugur Duran ◽  
Deena Al-Kadi
Keyword(s):  
Generating Function ◽  
Functional Equations ◽  
Laguerre Polynomials ◽  
Hermite Polynomials ◽  
Bernoulli Polynomials ◽  
Higher Order ◽  
New Class

The purpose of this paper is to construct a unified generating function involving the families of the higher-order hypergeometric Bernoulli polynomials and Lagrange–Hermite polynomials. Using the generating function and their functional equations, we investigate some properties of these polynomials. Moreover, we derive several connected formulas and relations including the Miller–Lee polynomials, the Laguerre polynomials, and the Lagrange Hermite–Miller–Lee polynomials.

AN ANALOGUE OF EULER’S IDENTITY AND SPLIT PERFECT PARTITIONS

2018 ◽  
Vol 99 (03) ◽  
pp. 353-361
Author(s):  
MEGHA GOYAL
Keyword(s):  
Generating Function ◽  
New Class ◽  
Appl Math ◽  
Euler’S Identity

We give the generating function of split$(n+t)$-colour partitions and obtain an analogue of Euler’s identity for split$n$-colour partitions. We derive a combinatorial relation between the number of restricted split$n$-colour partitions and the function$\unicode[STIX]{x1D70E}_{k}(\unicode[STIX]{x1D707})=\sum _{d|\unicode[STIX]{x1D707}}d^{k}$. We introduce a new class of split perfect partitions with$d(a)$copies of each part$a$and extend the work of Agarwal and Subbarao [‘Some properties of perfect partitions’,Indian J. Pure Appl. Math 22(9) (1991), 737–743].

scholarly journals Magnetically driven jets and winds from weakly magnetized accretion discs

2019 ◽  
Vol 490 (3) ◽  
pp. 3112-3133 ◽  
Author(s):  
J Jacquemin-Ide ◽  
J Ferreira ◽  
G Lesur
Keyword(s):  
Numerical Simulations ◽  
Energy Content ◽  
Initial Energy ◽  
Accretion Discs ◽  
Analytical Models ◽  
Magnetorotational Instability ◽  
New Class ◽  
Analytical Criterion ◽  
First Time

Abstract Semi-analytical models of disc outflows have successfully described magnetically driven, self-confined super-Alfvénic jets from near-Keplerian accretion discs. These jet-emitting discs (JEDs) are possible for high levels of disc magnetization μ defined as μ = 2/β, where beta is the usual plasma parameter. In near-equipartition JEDs, accretion is supersonic and jets carry away most of the disc angular momentum. However, these solutions prove difficult to compare with cutting-edge numerical simulations, for the reason that numerical simulations show wind-like outflows but in the domain of small magnetization. In this work, we present for the first time self-similar isothermal solutions for accretion–ejection structures at small magnetization levels. We elucidate the role of magnetorotational instability-like (MRI) structures in the acceleration processes that drive this new class of solutions. The disc magnetization μ is the main control parameter: Massive outflows driven by the pressure of the toroidal magnetic field are obtained up to μ ∼ 10−2, while more tenuous centrifugally driven outflows are obtained at larger μ values. The generalized parameter space and the astrophysical consequences are discussed. We believe that these new solutions could be a stepping stone in understanding the way astrophysical discs drive either winds or jets. Defining jets as self-confined outflows and winds as uncollimated outflows, we propose a simple analytical criterion based on the initial energy content of the outflow, to discriminate jets from winds. We show that jet solution is achieved at all magnetization levels, while winds could be obtained only in weakly magnetized discs that feature heating.

scholarly journals Multifarious Results for q-Hermite Based Frobenius Type Eulerian Polynomials

2019 ◽  
Author(s):  
Waseem Khan ◽  
Idrees Ahmad Khan ◽  
Mehmet Acikgoz ◽  
Ugur Duran
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Recurrence Relations ◽  
Series Representation ◽  
Bernoulli Polynomials ◽  
Stirling Numbers ◽  
Eulerian Polynomials ◽  
New Class ◽  
Genocchi Polynomials

In this paper, a new class of q-Hermite based Frobenius type Eulerian polynomials is introduced by means of generating function and series representation. Several fundamental formulas and recurrence relations for these polynomials are derived via different generating methods. Furthermore, diverse correlations including the q-Apostol-Bernoulli polynomials, the q-Apostol-Euler poynoomials, the q-Apostol-Genocchi polynomials and the q-Stirling numbers of the second kind are also established by means of the their generating functions.

scholarly journals Boundary conditions for semi-Lagrangian methods for the BGK model

2016 ◽  
Vol 7 (3) ◽  
pp. 138-164 ◽  
Author(s):  
Maria Groppi ◽  
Giovanni Russo ◽  
Giuseppe Stracquadanio
Keyword(s):  
Boltzmann Equation ◽  
Numerical Methods ◽  
Boundary Conditions ◽  
Numerical Simulations ◽  
Lagrangian Formulation ◽  
High Order Accuracy ◽  
Bgk Model ◽  
Order Accuracy ◽  
New Class ◽  
Iterative Procedures

Abstract A new class of high-order accuracy numerical methods based on a semi-Lagrangian formulation for the BGK model of the Boltzmann equation has been recently proposed in [1]. In this paper semi-Lagrangian schemes for the BGK equation have been extended to treat boundary conditions, in particular the diffusive ones. Two different techniques are proposed, using or avoiding iterative procedures. Numerical simulations illustrate the accuracy properties of these approaches and the agreement with the results available in literature.

scholarly journals Notes on $q$-Hermite Based Unified Apostol Type Polynomials

2019 ◽  
Author(s):  
Waseem Khan
Keyword(s):  
Generating Function ◽  
Recurrence Relations ◽  
Series Representation ◽  
Stirling Numbers ◽  
New Class

In this article, a new class of $q$-Hermite based unified Apostol type polynomials is introduced by means of generating function and series representation. Several important formulas and recurrence relations for these polynomials are derived via different generating methods. We also introduce $q$-analog of Stirling numbers of second kind of order $\nu$ by which we construct a relation including aforementioned polynomials.

scholarly journals Explicit formula of a new class of q-Hermite-based Apostol-type polynomials and generalization

2020 ◽  
Vol 26 (4) ◽  
pp. 93-102
Author(s):  
Mouloud Goubi ◽  
Keyword(s):  
Explicit Formula ◽  
Present Article ◽  
Generating Function ◽  
New Class

The present article deals with a recent study of a new class of q-Hermite-based Apostol-type polynomials introduced by Waseem A. Khan and Divesh Srivastava. We give their explicit formula and study a generalized class depending in any q-analog generating function.

scholarly journals The Zeta-G Class: Some Computational and Analytical Aspects

2020 ◽  
Vol 42 ◽  
pp. e111
Author(s):  
Ana Carla Percontini ◽  
Frank Gomes-Silva ◽  
Gauss Moutinho Crdeiro ◽  
Pedro Rafael Marinho
Keyword(s):  
Maximum Likelihood ◽  
Generating Function ◽  
Real Data ◽  
Data Set ◽  
R Language ◽  
New Class ◽  
Mathematical Properties ◽  
Special Cases ◽  
Computational Aspects

We define a new class of distributions with one extra shapeparameter including some special cases. We provide numerical and computational aspects of the new class. We proposefunctions using the \textsf{R} language to fit any distribution in this family to a data set. In addition, such functions are implemented efficientlyusing the library \textsf{Rcpp} that enables the incorporation of the codes \textsf{C++} in \textsf{R} automatically. Some examples are presentedfor using the implemented routines in practice. We derive some mathematical properties of this class including explicit expressionsfor the moments, generating function and mean deviations. We discuss the estimation of the model parametersby maximum likelihood and provide an application to a real data set.

scholarly journals Understanding the Value of Fulfillment Flexibility in an Online Retailing Environment

2021 ◽  
Author(s):  
Levi DeValve ◽  
Yehua Wei ◽  
Di Wu ◽  
Rong Yuan
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Problem Definition ◽  
Order Fulfillment ◽  
Distribution Centers ◽  
Online Retailing ◽  
New Class ◽  
Managerial Implications ◽  
The Cost ◽  
Improve Service Quality

Problem definition: Fulfillment flexibility, the ability of distribution centers (DCs) to fulfill demand originating from other DCs, can help e-retailers reduce lost sales and improve service quality. Because the cost of full flexibility is prohibitive, we seek to understand the value of partially flexible fulfillment networks under simple and effective fulfillment policies. Academic/practical relevance: We propose a general method for understanding the practical value of (partial) fulfillment flexibility using a data-driven model, theoretical analysis, and numerical simulations. Our method applies to settings with local fulfillment (i.e., order fulfillment from the originating DC) prioritization and possible customer abandonment, two features that are new to the fulfillment literature. We then apply this method for a large e-retailer. We also introduce a new class of spillover limit fulfillment policies with attractive theoretical and practical features. Methodology: Our analysis uses dynamic and stochastic optimization, applied probability, and numerical simulations. Results: We derive optimal fulfillment policies in stylized settings, as well as bounds on the performance under an optimal policy using theoretical analysis, to provide guidelines on which policies to test in numerical simulations. We then use simulations to estimate for our industrial partner that a proposed fulfillment network with additional flexibility equates to a profit improvement on the order of tens of millions of U.S. dollars. Managerial implications: We provide an approach for e-retailers to understand when fulfillment flexibility is most valuable. We find that fulfillment flexibility provides the most benefit for our collaborator when gross profits are high relative to fulfillment costs or centrally held inventory is low. Also, we identify the risks of myopic fulfillment with additional flexibility and demonstrate that an effective spillover limit policy mitigates these risks.

scholarly journals Legendre-Gould Hopper-Based Sheffer Polynomials and Operational Methods

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2051
Author(s):  
Nabiullah Khan ◽  
Mohd Aman ◽  
Talha Usman ◽  
Junesang Choi
Keyword(s):  
Generating Function ◽  
Legendre Polynomials ◽  
Sheffer Polynomials ◽  
Operational Methods

A remarkably large of number of polynomials have been presented and studied. Among several important polynomials, Legendre polynomials, Gould-Hopper polynomials, and Sheffer polynomials have been intensively investigated. In this paper, we aim to incorporate the above-referred three polynomials to introduce the Legendre-Gould Hopper-based Sheffer polynomials by modifying the classical generating function of the Sheffer polynomials. In addition, we investigate diverse properties and formulas for these newly introduced polynomials.

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