Caspian Journal of Mathematical Sciences
Volume:8 Issue: 2, Summer Autumn 2019

In this article, we introduce the concept of co-covering which is the dual of covering concept. Then, we prove several theorems being similar to the theorems that have been de-veloped for the covering concept. For example, we provide the lifting criterion for co-coverings of a topological space X, which helps us to classify them by subgroups of the group of all homeomorphisms of X.

In this work, we prove the existence of a spectral function for singular q-Sturm-Liouville operator. Further, we establish a Parseval equality and expansion formula in eigenfunctions by terms of the spectral function.

Elzaki transform and Adomian polynomial is used to obtain the exact solutions of nonlinear fifth order Korteweg-de Vries (KdV) equations. In order to investigate the effectiveness of the method, three fifth order KdV equations were considered. Adomian polynomial is introduced as an essential tool to linearize all the nonlinear terms in any given equation because Elzaki transform cannot handle nonlinear functions on its own. In all the three problems considered, the series solutions obtained converges to the exact solutions. Three dimensional graphs were also plotted to give the shape of the solutions of some KdV equations considered. Hence, Elzaki transform and Adomian polynomial together gives a very powerful and ffective method for solving nonlinear partial differential equations.

In this paper we introduce controlled *-g-frame and *-g-multipliers in Hilbert C*-modules and investigate the properties. We demonstrate that any controlled *-g-frame is equivalent to a *-g-frame and define multipliers for (C,C')- controlled*-g-frames .

Recently‎, some researchers have established some results on existence of endpoints for multivalued mappings. In particular, Mohammadi and Rezapour's [Endpoints of Suzuki type quasi-contractive multifunctions, U.P.B. Sci. Bull., Series A, 2015] used the technique of $alpha-psi$-contractive mappings, due to Samet et al. (2012), to give some results about endpoints of Suzuki type quasi-contractive multifunctions satisfing property (BS). In this paper, we prove existence and uniqueness of endpoint for multivalued mappings satisfing the weaker conditions generalized $phi$-contractivity of integral type and property (HS). This result generalize and improve Mohammadi and Rezapour's result. Also, we give an example to illustrate the usability of the result.

In this study, we investigate the inverse problem for Sturm-Liouville differential operators on a finite interval having a discontinuous weight function. We give properties of the spectral characteristics and prove the uniqueness theorem for the inverse problem of recovering operators.

Deleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categorical context. In this note, it is shown that given an algebra, its exterior algebra is isomorphic to the Adams completion of the algebra with respect to a chosen set of morphisms in a suitable category.

We introduce the fundamental relation, $alpha^{*}$, on an $(m,n)$-hyperring $R$ and indicate that this relation is the smallest strongly regular equivalence relation on $R$ such that $R/alpha^{*}$ is an commutative $(m, n)$-ring. We use $alpha^{*}$-relation to construct the fundamental functor from category of $(m, n)$-hyperrings to the category of commutative $(m,n)$-rings. Finally, some necessary and sufficient conditions for transitivity of $alpha$ are given.

We defined new special curves in Euclidean 3-space which refer to clad helices and found the geometric invariants of clad helices [17]. These notions are generalizations of the notion of cylindrical helices and slant helices. Using the geometric invariants of clad helices in this article, we proposed approaches to construct examples of clad helices in E3 and on S2. Moreover, we obtained the classication of special developable surfaces under the condition of the existence of clad helices as a geodesic and existence of slant helices as a line of curvature.

In this study, position vectors of admissible curve in the natural representation and spherical indicatrices for tangent, normal and binormal vectors of a general helix in the pseudo-Galilean space are researched. Moreover some examples are given.