Journal of Mathematical Extension
Volume:16 Issue: 3, Mar 2022

The present paper aims to introduce the concepts of adding a strong arc, cobondage set, cobondage number, t-cobondage set, and t-cobondage number in the vague graphs, as well as expressing some of the new segmentation of the additions of arc and reduce the effect of adding a strong arc on domination parameters in vague graphs. Finally, some of their applications are pinpointed.

 We consider stochastic differential equation driven by αstable processes. Three methods of drifting split-step Euler, diffused split-step Euler and three-stage Milstein for approximation of solution are used. The strong convergence of these three methods is proven and the upper bounds of their stabilities are obtained and depicted.

It is known that even duals of a Banach algebra A with one of Arens products are Banach algebras, these products are natural multiplications extending the one on A. But the essence of A ∗ is completely different. By defining new products, we investigate some algebraic and spectral properties of odd duals of A. We will show relations between these products and Arens products, weak or weak-star continuity, commutativity and unit elements of these algebras. We also determine the spectrum and multiplier algebra for A ∗ , and we calculate the quasi-inverses, spectrum and spectral radius for elements of these kinds of algebras.

We provide criteria for identifying exact pairs of zero-divisors from zero-divisor graphs of commutative rings, and extend these criteria to compressed zero-divisor graphs. Finally, our results are translated as constructions for exact zero-divisor subgraphs.

In this paper, we study the existence of nontrivial solutions for a fractional boundary value problem in H¨older spaces by a technical approach based on Leray-Schauder nonlinear alternative. Moreover, using the concept of orthogonal set on Banach fixed point theorem we obtain another existence result with weaker conditions. Also, recent results are extended and improved. In addition, we give some examples to illustrate the feasibility and effectiveness of our results.

In this paper, firstly, we define the Mannheim partner curve of Mannheim curve with respect to the vertical, complete and horizontal lifts on space R 3 to its tangent space T R3 = R 6 . Secondly, we examine the Frenet-Serret aparatus {T ∗ (s), N∗ (s), B∗ (s), κ∗ (s), τ ∗ (s)} of the Mannheim partner curve α ∗ according to the vertical, complete and horizontal lifts on T R3 by depend on the lifting of Frenet-Serret aparatus {T(s), N(s), B(s), κ(s), τ (s)} of the first curve α on space R 3 . In addition, we include all special cases the curvature κ ∗ (s) and torsion τ ∗ (s) of the Frenet-Serret aparatus of the Mannheim partner curve α ∗ with respect to the vertical, complete and horizontal lifts on space R 3 to its tangent space T R3 . As a result of this transformation on space R 3 to its tangent space T R3 , we can speak about the features of Mannheim partner curve of any curve on space T R3 by looking at the characteristics of the first curve α.