In this thesis we study relation liftings in the context of coalgebraic modal logic. In the first part of the thesis we look for conditions on relation liftings that can be used to define a notion of bisimilarity between states in coalgebras, such that two states are bisimilar if and only if they are behaviorally equivalent. We show that this is the case for relation liftings that are lax exten...

Fractional difference operators possess nonlocal structure which largely affects and complicates the qualitative analysis of fractional equations. In this article, we discuss effect memory property on asymptotic behaviour solutions nabla

this paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + v(x)u=g(x, v), -triangle v - b(x)nabla v + v(x)v=f(x, u), end{array} right. $$ for $x in {r}^{n}$, where $v $, $b$ and $w$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. in this paper, we give a new technique to show the boundedness of cerami sequences and establi...

This paper is a study into some properties and applications of Moss’ coalgebraic or ‘cover’ modality ∇. First we present two axiomatizations of this operator, and we prove these axiomatizations to be sound and complete with respect to basic modal and positive modal logic, respectively. More precisely, we introduce the notions of a modal ∇-algebra and of a positive modal ∇-algebra. We establish ...

In this paper, we establish a functional generalization of Minkowski’s type inequality on time scales based on diamond-α integral, which is introduced as a linear combination of the delta and nabla integrals. Some related results are also obtained.

In this paper we study curves parametrized by a time scale parameter, introduce line delta and nabla integrals along time scale curves, and obtain an analog of Green’s formula in the time scale setting. © 2006 Elsevier Inc. All rights reserved.

This paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + V(x)u=g(x, v), -triangle v - b(x)nabla v + V(x)v=f(x, u), end{array} right. $$ for $x in {R}^{N}$, where $V $, $b$ and $W$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. In this paper, we give a new technique to show the boundedness of Cerami sequences and estab...