The compactified Jacobian of any projective curve X is defined as the Simpson moduli space of torsion free rank one degree d sheaves that are semistable with respect to a fixed polarization H on X. In this paper we give explicitly the structure of this compactified Simpson Jacobian in the case where X is a generalized tree-like curve, i.e., a projective, reduced and connected curve such that th...

Filon-Simpson quadrature rules are derived for integrals of the type ∫ b a dx f(x) sin(xy)/(xy) and ∫ b a dx f(x) 4 sin(xy/2)/(xy) which are needed in applications of the worldline variational approach to Quantum Field Theory. These new integration rules reduce to the standard Simpson rule for y = 0 and are exact for y → ∞ when a = 0 and f(0) 6= 0. The subleading term in the asymptotic expansio...

This paper presents a symbolic model checking algorithm for continuous-time Markov chains for an extension of the continuous stochastic logic CSL of Aziz et al 1]. The considered logic contains a time-bounded until-operator and a novel operator to express steady-state probabilities. We show that the model checking problem for this logic reduces to a system of linear equations (for unbounded unt...

In this paper, we studied the numerical solution of nonlinear weakly singular Volterra-Fredholm integral equations by using the product integration method. Also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear Volterra-Fredholm integral equations. The reliability and efficiency of the proposed scheme are...

In this paper, a numerical method for solving the constrained optimal control of time-varying singular systems with quadratic performance index is presented. Presented method is based on Bernste in polynomials. Operational matrices of integration, differentiation and product are introduced and utilized to reduce the optimal control of time-varying singular problems to the solution of algebraic ...

new product development (npd) is described in the literature as the transformation of a market opportunity into a product available for sale. in the automotive industry, within the context of iso/ts16949:2002 (the automotive quality management system international standard),  these related to the product realization process (prp) which consists of three main phases such as planning, implementat...

In this study, the Bernoulli polynomials are used to obtain an approximate solution of a class of nonlinear two-dimensional integral equations. To this aim, the operational matrices of integration and the product for Bernoulli polynomials are derived and utilized to reduce the considered problem to a system of nonlinear algebraic equations. Some examples are presented to illustrate the efficien...

Background: The banking industry can create sustainable development and be a competitive advantage of the enterprise by promoting a sustainable environment and investment focused on social responsibility. Therefore, the present study was formed with the aim of identifying the components of innovative green banking based on bioethics. Method: The research method in the present study was qualita...