Probabilistic G-Metric space and some fixed point results

In this note we introduce the notions of generalized probabilistic metric spaces and generalized Menger probabilistic metric spaces. After making our elementary observations and proving some basic properties of these spaces, we are going to prove some fixed point result in these spaces

Solutions and the Generalized Hyers-Ulam-Rassias Stability of a Generalized Quadratic-Additive Functional Equation

We study general solutions and generalized Hyers-Ulam-Rassias stability of the following -dimensional functional equation ∑(=1∑)+(−2)=1(∑)==1∑=1,>(+), ≥3, on non-Archimedean normed spaces

On Regularized Quasi-Semigroups and Evolution Equations

We introduce the notion of regularized quasi-semigroup of bounded linear operators on Banach spaces and its infinitesimal generator, as a generalization of regularized semigroups of operators. After some examples of such quasi-semigroups, the properties of this family of operators will be studied. Also some applications of regularized quasi-semigroups in the abstract evolution equations will be considered. Next some elementary perturbation results on regularized quasi-semigroups will be discussed

Solving the optimal control problem of the parabolic PDEs in exploitation of oil

AbstractIn this paper, the optimal control problem is governed by weak coupled parabolic PDEs and involves pointwise state and control constraints. We use measure theory method for solving this problem. In order to use the weak solution of problem, first problem has been transformed into measure form. This problem is reduced to a linear programming problem. Then we obtain an optimal measure which is approximated by a finite combination of atomic measures. We find piecewise-constant optimal control functions which are an approximate control for the original optimal control problem

The hit problem for symmetric polynomials over the Steenrod algebra

We cite [18] for references to work on the hit problem for the polynomial algebra P(n) = [open face F]2[x1, ;…, xn] = [oplus B: plus sign in circle]d[gt-or-equal, slanted]0 Pd(n), viewed as a graded left module over the Steenrod algebra [script A] at the prime 2. The grading is by the homogeneous polynomials Pd(n) of degree d in the n variables x1, …, xn of grading 1. The present article investigates the hit problem for the [script A]-submodule of symmetric polynomials B(n) = P(n)[sum L: summation operator]n , where [sum L: summation operator]n denotes the symmetric group on n letters acting on the right of P(n). Among the main results is the symmetric version of the well-known Peterson conjecture. For a positive integer d, let [mu](d) denote the smallest value of k for which d = [sum L: summation operator]ki=1(2[lambda]i[minus sign]1), where [lambda]i [gt-or-equal, slanted] 0

Reconceptualizing Assessment in Initial Teacher Education from a Relational Lens

This chapter examines the challenges and possibilities of assessment practices in Initial Teacher Education (ITE) programs. Informed by Bakhtin (1986), speech genres, dialogic approaches and a democratic lens to assessment, the chapter questions the nature and purpose of assessment considering the COVID-19 pandemic. New understanding of the concept of ‘relationality’ through pandemic experience provides opportunities for ‘democratic’ assessment is perceived as a point of departure in the learning process for both students and teachers, and not a destination. This perspective incorporates students’ diverse voices and agency and encourages assessment practices to promote not only instrumental aspects of learning, but also the epistemological and ontological layers of learning and being. Though this conceptual interrogation can be applied to any educational context across programs locally and globally, the focus is on ITE in the Australian context, due to the important role of pre-service teachers in creating and designing assessment practices. The chapter provides case study a example that enabled pre-service teachers to play an active and influential role in the development of assessment artefacts and practices. It concludes by projecting opportunities and challenges to teaching and research practices, locally and globally