Let G be a graph, each edge e of which is given a weight w(e). The shortest path problem is a path of minimum weight connecting two specified vertices a and b, and from it we have a pre-topology. Furthermore, we study the restriction and separators in pre-topology generated by the shortest path problems. Finally, we study the rate of liaison in pre-topology between two subgraphs. It is formally shown that the new distance measure is a metric

In this work, we apply the notion of a filter of a KU-Algebra and investigate several properties. The paper defined some filters such as strong filter, n-fold filter and P-filter and discussed a few theorems and examples.

Infertility can be detected when the couples have not completed pregnancy after a year or more of normal coitus. So, in order to treat infertility, there are many supported reproductive techniques are in practice. The success rate of these techniques depends upon the way by which preparation of the paternal semen sample. Over the past 30 years, the manual has been standard as providing global standards and has been used extensively by research and clinical laboratories throughout the world. The spermatozoa of all placental (eutherian) mammals, including humans, are in a protective, no labile formal at ejaculation and are incapable of fertilization even if they are placed in direct contact with an oocyte. Accordingly, they must undergo a sub

This work aims to introduce the concepts of left and right derivations in an AT-algebra and discuss some interesting theorems of these concepts. Also, a fuzzy derivation of an AT-subalgebra, a fuzzy right (left) derivation ideal, a fuzzy derivation of AT-subalgebra, and a fuzzy right (left) derivation ideal are studied. Finally, a level derivation of AT-algebras is defined and some propositions are achieved.

In this paper the queuing system (M/Er/1/N) has been considered in equilibrium. The method of stages introduced by Erlang has been used. The system of equations which governs the equilibrium probabilities of various stages has been given. For general N the probability of j stages of service are left in the system, has been introduced. And the probability for the empty system has been calculated in the explicit form.

Linear and nonlinear optical properties of epoxy/ Al2O3 nanocomposites system were studied for epoxy neat and (0.5, 1.5, 3, and 5) % Al2O3 nanocomposites.The band gap of epoxy and its nanocomposites was obtained at these weight ratios. Nonlinear optical properties experiments were performed using Q-switched Nd:YAG laser z-scan system.These experiments were carried out for different parameters: wavelengths (1064 nm and 532 nm), laser intensities (0.530, 0.679, and 0.772) GW/cm2 and weight ratio of Al2O3 nanocomposites. The results showed that the band gaps were decreased with increasing the weight ratio of nanoalumina except at 5wt% and the nonlinear refractive index coefficient is directly proportional to the incident intensities while o

The study includes the relationship between the ecologia and Abbaside's community in the middle ages, and the role of Baghdad capital city to increasing the sensibility of the people to the outwardly peripheral.

The study explains the efforts between the people and Abbaside's government to cure the knowledge of ecologia, to prevent the separation of diseases and  pollutions of the community. 

 Keywords: Ecologia, Abbasid's, diseases, pollutions.

The research aims at shedding light on the impact of information technology in reducing tax evasion in the General Authority for Taxation. In order to achieve this, the research relied on the analysis of its variables as a main tool for collecting data and information. The results showed that there is a positive and positive effect of information technology on tax evasion. The impact of information technology on increasing tax revenues and reducing the phenomenon of tax evasion In the performance of the research sample, the research sought to highlight the importance of tax information technology through its data and information to the tax administration for the purpose of completing the process Taxpayers for persons subject to income ta

This paper is an attempt to demonstrate the syntactic behavior of -ly adverbs and -ly adjectives. It mainly deals with -ly as an inflectional suffix that forms adverbs and adjectives It is hypothesized that there are differences between adjective-forming –ly and adverb-forming –ly.The researcher first made general and specific observations about the morphological processes of -ly adverbs and -ly adjectives. Since the study focuses on a linguistic phenomenon, its data is a set of -ly adverbs and -ly adjectives used as examples to support the hypothesis. The importance of studying the syntactic behavior of -ly stems from the fact that thousands of English adjectives and adverbs are created by adding the suffix "-ly" to their roots