Mathematics and Computational Sciences
Volume:2 Issue: 4, Autumn 2021

In this paper, we employ a collocation method based on Legendre polynomials (LPs) to solve the time-fractional stochastic Allen-Cahn equation. This method is applied to convert the solution of this stochastic equation to the solution of a nonlinear system of algebraic equations. The numerical approach is completely described. Finally, a test example is implemented to validate the robustness of the proposed scheme.

The Rath's mannequin approximation is generalized in this work to generate finite strength level(s) quantum structures in Hermitian and non-Hermitian quantum systems. On one hand, in Hermitian systems, an extensive variety of bounded single properly,triple nicely, and pentic proper systems is utilized. On the other hand, isospectral Hermitian structures are considered. Further mannequin is extended to PT-symmetric structures involving an isospectral condition.

The novel coronavirus 2019 known as (COVID-19) pandemic caused by SARS-CoV-2 occurred in Wuhan town of China in 2019. The virus has rapidly spread all over the world and has continued to affect the public well-being. This paper focuses on a mathematical model with vaccination acceptability of COVID-19 with which to examine to what extent the vaccine would be accepted in Nigeria. Specifically, the paper introduces a compartmental model to measure the potential impact of the COVID-19 vaccine. The vaccination acceptability model results show that up to 80% of the Nigerian populace accepted the vaccination campaign, despite the gabs on the COVID-19 vaccine by some health workers and the communities in Nigeria. It also shows that 90% vaccinated susceptible plus 50% effectiveness of face-mask use has brought about a decrease of the pandemic while mortality rate has decreased drastically which shows that the vaccine is effective. The result also reveals that the recovered individuals from COVID-19 have increased in alignment and, the vaccine has a significant impact on the populace. Finally, possible extensions of the model as well as open challenges associated with the formulation and analysis of COVID-19 dynamics will be addressed.

In this paper, the Galerkin Method (GM) is employed for finding the solution of Volterra integro-differential equations with the aid of Chebyshev polynomial basis function. Some examples are presented to demonstrate the effectiveness of the method and its reliability. The approximate solutions are in agreement with the exact solutions and are compared favorably with an existing method available in the literature.

A bounded linear operator $T$ on a Hilbert space $mathfrak{H}$ isconvex, if $$|mathfrak{T}^{2}v|^2-2|mathfrak{T}v|^2+|v|^2 geq 0.$$ In this paper, sufficient conditions to hypercyclicity of adjoint of unilateral (bilateral) forward (backward) weighted shift operator is given. Also, we present some example of convex operators such that it's adjoint is hypercyclic. Finally, the spectrum of convex multiplication operators is obtained and an example of convex, multiplication operators is given such that it's adjoint is hypercyclic.

In this paper, we consider the seven major sources of the importance of meaning andpurpose in life proposed on the world, namely; cross-culturally, including achievement, acceptance, relationship, intimacy, religion, self-trancedence, and fairness. Here, the effect of seven major resources on each other is measured using the opinion of experts for adolescent girls in brilliant talent high schools in Qom. In this research measures of influence effect and effect on life is expected. By applying the DEMATEL method its concluded that factors of meaning and purpose in life are ordered. Finally, strategies for brilliant talent high schools are presented.