Lie algebra representations and 2-index 4-variable 1-parameter Hermite polynomials

This paper is an attempt to stress the usefulness of multi-variable special functions by expressing them in terms of the corresponding Lie algebra or Lie group. The problem of framing the 2-index 4-variable 1-parameter Hermite polynomials (2I4V1PHP) into the context of the irreducible representations $\uparrow _{\omega,\mu}$ of $\mathcal{G}(0,1)$ and $\uparrow^{'} _{\omega,\mu}$ of $\mathcal{K}_{5}$ is considered. Certain relations involving 2I4V1PHP $H_{m,n}(x,y,z,u;\rho)$ are obtained using the approach adopted by Miller. Certain examples involving other forms of Hermite polynomials are derived as special cases. Further, some properties of the 2I4V1PHP $H_{m,n}(x,y,z,u;\rho)$ are obtained by using a quadratic combination of four operators defined on a Lie algebra of endomorphisms of a vector space

Construction of a new family of Fubini-type polynomials and its applications

This paper gives an overview of systematic and analytic approach of operational technique involves to study multi-variable special functions significant in both mathematical and applied framework and to introduce new families of special polynomials. Motivation of this paper is to construct a new class of generalized Fubini-type polynomials of the parametric kind via operational view point. The generating functions, differential equations, and other properties for these polynomials are established within the context of the monomiality principle. Using the generating functions, various interesting identities and relations related to the generalized Fubini-type polynomials are derived. Further, we obtain certain partial derivative formulas including the generalized Fubini-type polynomials. In addition, certain members belonging to the aforementioned general class of polynomials are considered. The numerical results to calculate the zeros and approximate solutions of these polynomials are given and their graphical representation are shown. © 2021, The Author(s)

Gender Differences and Structural Relationships among Social Impacts, Performance Beliefs, Motivation and Academic Achievement of the Students at Intermediate Level

This research intended to scrutinize gender distinctions and the fundamental associations of task values, performance beliefs, teacher-student relationship, peers’ academic value, students’ intrinsic and extrinsic motivation and educational engagement and students’ achievement. The sample of this research was 400 second year science students (Pre- Medical), in Lahore City, Pakistan. The data were analyzed using Independent sample t-test and Structural Equation Modeling. The results revealed no gender differences across all variables except students’ extrinsic motivation. The results highlighted significant relationships between variables of the study. Results also demonstrated that those students who achieve higher grades were having good teacher- student relationships, and peer relationships, moreover such students were having higher performance beliefs, intrinsic motivation and extrinsic motivation. Most of the independent variables indirectly affected the dependent variables through different mediators. Besides, there was mediation effect of teacher student relationship, performance beliefs, academic value of peers, academic engagement, intrinsic motivation and extrinsic motivation on students’ academic achievement

Efficacy of Topical 0.05% Isotretinoin Gel Versus 0.1% Adapalene Gel in The Treatment of Mild to Moderate Acne Vulgaris

Objective: To compare the efficacy of topical 0.05% Isotretinoin gel versus 0.1% Adapalene gel in treating mild to moderate acne vulgaris. Study Design: Quasi-Experimental study. Place and Duration of Study: Department of Dermatology, Pak Emirates Military Hospital (PEMH), Rawalpindi Pakistan, From Feb to Jul 2018. Methodology: A total of ninety-two patients aged 12 to 25 years with mild to moderate facial acne vulgaris were enrolled and divided into two treatment Groups, Group-A (0.05% Isotretinoin Gel) and Group-B (0.1% Adapalene Gel). Efficacy was measured at 12 weeks post-treatment. Results: Treatment was found efficacious in 84.8% (n=39/46) of patients in Group-A and 50.0% (n=23/46) of patients in Group-B (p= 0.001). There were similar results when treatment efficacy in both Groups was disease severity. In all cases,efficacy was better in Group-A (p<0.05). Conclusions: The efficacy of topical 0.05% Isotretinoin gel was better than topical 0.1% Adapalene gel for treating mild to moderate acne vulgaris

FINDING MIXED FAMILIES OF SPECIAL POLYNOMIALS ASSOCIATED WITH GOULD-HOPPER MATRIX POLYNOMIALS

In this article, the general polynomials are taken as base with the Gould-Hopper matrix polynomials to introduce a family of 3-variable general-Gould-Hopper matrix polynomials (3VgGHMaP). These polynomials are framed within the context of monomiality principle and their properties are established. Examples of some members belonging to this family are considered. Certain bilateral and bilinear generating matrix functions for 3VgGHMaP are also derived

Lie-theoretic generating relations of two variable Laguerre polynomials

Generating relations involving two variable Laguerre polynomials $L_{n}(x,y)$ are derived. The process involves the construction of a three dimensional Lie algebra isomorphic to special linear algebra $sl(2)$ with the help of Weisner's method by giving suitable interpretations to the index $n$ of the polynomials $L_{n} (x,y)$

On generating relations involving Laguerre 2D functions

In this paper, we derive some generating relations involving Laguerre 2D-functions $l_{m,n}(z,z^*)$, introduced by Wunsche, from the Lie-theoretic treatment. Certain special cases are also discussed