Relation on a set is a simple mathematical model to which many real-life data can be connected. A binary relation  on a set  can always be represented by a digraph. Topology on a set  can be generated by binary relations on the set . In this direction, the study will consider different classical categories of topological spaces whose topology is defined by the binary relations adjacency and reachability on the vertex set of a directed graph. This paper analyses some properties of these topologies and studies the properties of closure and interior of the vertex set of subgraphs of a digraph. Further, some applications of topology generated by digraphs in the study of biological systems are cited.

    In this work, we study a new class of meromorphicmultivalent functions, defined by fractional differ-integral operator.We obtain some geometricproperties, such ascoefficient inequality, growth and distortion bounds, convolution properties, integral representation, radii of starlikeness, convexity, extreme pointsproperties, weighted mean and arithmetic meanproperties.

Ab – initio density function theory (DFT) calculations coupled with Large Unit Cell (LUC) method were carried out to evaluate the electronic structure properties of III-V zinc blend (GaAs). The nano – scale that have dimension (1.56-2.04)nm. The Gaussian 03 computational packages has been employed through out this study to compute the electronic properties include lattice constant, energy gap, valence and conduction band width, total energy, cohesive energy and density of state etc. Results show that the total energy and energy gap are decreasing with increase the size of nano crystal . Results revealed that electronic properties converge to some limit as the size of LUC increase .

The concepts of generalized higher derivations, Jordan generalized higher derivations, and Jordan generalized triple higher derivations on Γ-ring M into ΓM-modules X are presented. We prove that every Jordan generalized higher derivation of Γ-ring M into 2-torsion free ΓM-module X, such that aαbβc=aβbαc, for all a, b, c M and α,βΓ, is Jordan generalized triple higher derivation of M into X.

Let R be a commutative ring with non-zero identity element. For two fixed positive integers m and n. A right R-module M is called fully (m,n) -stable relative to ideal A of , if for each n-generated submodule of Mm and R-homomorphism . In this paper we give some characterization theorems and properties of fully (m,n) -stable modules relative to an ideal A of . which generalize the results of fully stable modules relative to an ideal A of R.

The three parameters distribution called modified weibull distribution (MWD) was introduced first by Sarhan and Zaindin (2009)[1]. In theis paper, we deal with interval estimation to estimate the parameters of modified weibull distribution based on singly type one censored data, using Maximum likelihood method and fisher information to obtain the estimates of the parameters for modified weibull distribution, after that applying this technique to asset of real data which taken for Leukemia disease in the hospital of central child teaching .

     In this paper, the structure of  and  have  been introduced and studied. We also obtain that a is  of a  if and only if there exists an  on such that . In addition, we obtain  that  of if and only if there is an   on  such that  , where  are subspaces of  with eigenvalues 1 and  −1, respectively. We also find  t that the existence of  on  implies that there exists a compatible  under appropriate condition.

The effect of thickness variation on some physical properties of hematite α-Fe2O3 thin films was investigated. An Fe2O3 bulk in the form of pellet was prepared by cold pressing of Fe2O3 powder with subsequent sintering at 800 . Thin films with various thicknesses were obtained on glass substrates by pulsed laser deposition technique. The films properties were characterized by XRD, and FT-IR. The deposited iron oxide thin films showed a single hematite phase with polycrystalline rhombohedral crystal structure .The thickness of films were estimated by using spectrometer to be (185-232) nm. Using Debye Scherrerś formula, the average grain size for the samples was found to be (18-32) nm. Atomic force microscopy indicated that the films had

   The purpose of this paper is to study   new  types of open sets in bitopological spaces.    We shall introduce the concepts of  L- pre-open and L-semi-p-open sets

Gangyong Lee, S.Tariq Rizvi, and Cosmin S.Roman studied Rickart modules.

The main purpose of this paper is to develop the properties of Rickart modules .

We prove that each injective and prime module is a Rickart module. And we give characterizations of some kind of rings in term of Rickart modules.