In this article, we apply the operational matrix to find the numerical solution of two- dimensional nonlinear Volterra integro-differential equation (2DNVIDE). Form this prospect, two-dimensional shifted Legendre functions (2DSLFs) has been presented for integration, product as well as differentiation. This method converts 2DNVIDE to an algebraic system of equations, so the numerical solution o...

This paper provides a bridge in the gap between the model-theoretic and the algebraic side of modal correspondence theory. We give a new, algebraic proof of the classical Sahlqvist correspondence theorem, as well as a new, algebraic proof of the analogous result for the atomic inductive formulas, which form a proper extension of the Sahlqvist class.

This paper presents a computational technique that called Tau-collocation method for the developed solution of non-linear integro-differential equations which involves a population model. To do this, the nonlinear integro-differential equations are transformed into a system of linear algebraic equations in matrix form without interpolation of non-poly-nomial terms of equations. Then, using coll...

The Taylor expansion of λ-terms, as introduced by Ehrhard and Regnier, expresses a λ-term as a series of multi-linear terms, called simple terms, which capture bounded computations. Normal forms of Taylor expansions give a notion of infinitary normal forms, refining the notion of Böhm trees in a quantitative setting. We give the algebraic conditions over a set of normal simple terms which chara...

We consider the relationship between -automata and a specific logical formulation based on a normal form for temporal logic formulae. While this normal form was developed for use with execution and clausal resolution in temporal logics, we here show how it can represent, syntactically, -automata in a high-level way. Technical proofs of the correctness of this representation are given.

free vibration analysis of higher-order shear deformation beam resting on one- and two-parameter elasticfoundation is studied using differential transform method (dtm) as a part of a calculation procedure. first,the governing differential equations of beam are derived in a general form considering the shear-freeboundary conditions (zero shear stress conditions at the top and bottom of a beam). ...

The developable surface is an important surface in computer aided design, geometric modeling and industrial manufactory. It is often given in the standard parametric form, but it can also be in the implicit form which is commonly used in algebraic geometry. Not all algebraic developable surfaces have rational parametrizations. In this paper, we focus on the rational developable surfaces. For a ...

Using the algebraic state space representation, this paper studies the robust consensus of networked evolutionary games (NEGs) with attackers and forbidden profiles. Firstly, an algebraic form is established for NEGs with attackers and forbidden profiles. Secondly, based on the algebraic form, a necessary and sufficient condition is presented for the robust constrained reachability of NEGs. Thi...

7 This paper deals with a particular question—When do powersets in lattice-valued mathematics form algebraic theories (ormonads) in clone form?Our approach in this and related papers is to consider “powersets over objects” in the ground categories Set and Set×C 9 from the standpoint of algebraic theories in clone form (C is a particular subcategory of the dual of the category of semi-quantales)...