Symmetric Division Deg index is one of the 148 discrete Adriatic indices that showed good predictive properties on the testing sets provided by International Academy of Mathematical Chemistry. Symmetric Division Deg index is defined by $$ SDD(G) = sumE left( frac{min{d_u,d_v}}{max{d_u,d_v}} + frac{max{d_u,d_v}}{min{d_u,d_v}} right), $$ where $d_i$ is the degree of vertex $i$ in graph $G$. In th...

the aim of this paper is to introduce the concepts of fuzzy upper and fuzzy lower almost continuous, weakly continuous and almost weakly continuous multifunctions. several characterizations and properties of these multifunctions along with their mutual relationships are established in $l$-fuzzy topological spaces

We use upper and lower solutions to study the existence and properties of solutions to differential Riccati equations arising from stochastic linear quadratic regulator (LQR) problems. The main results include an interpretation of upper and lower solutions, comparison theorems, an upper-lower solution theorem, necessary and sufficient conditions for existence of solutions, an estimation of maxi...

In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the ...

This paper investigates the solvability of discrete Dirichlet boundary value problems by the lower and upper solution method. Here, the second order difference equation with a nonlinear right hand side f is studied and f(t, u, v) can have a superlinear growth both in u and in v. Moreover, the growth conditions on f are one-sided. We compute a priori bounds on solutions to the discrete problem a...