This paper contains an equivalent statements of a pre-  space, where  are considered subsets of with the product topology. An equivalence relation between the preclosed set  and a pre-  space, and a relation between a pre-  space and the preclosed set  with some conditions on a function  are found. In addition, we have proved that the graph  of  is preclosed in if  is a pre-  space, where the equivalence relation  on  is open.

     On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that

The current research aims to recognize the exploratory and confirmatory factorial structure of the test-wiseness scale on a sample of Hama University students, using the descriptive method. Thus, the sample consists of (472) male and female students from the faculties of the University of Hama. Besides, Abu Hashem’s 50 item test-wiseness scale (2008) has been used. The validity and reliability of the items of the scale have also been verified, and six items have been deleted accordingly. The results of the exploratory factor analysis of the first degree have shown the presence of the following five acceptable factors: (exam preparation, test time management, question paper handling, answer sheet handling, and revision).  Moreover,

The purpose of this study was to examine the histological structure of the kidney in snake Eryx gaculus gaculus. In present study, the snakes were collected from the city of Baghdad and transferred to the laboratory where their kidneys were dissected out. The samples were then processed to be prepared for histological examination microscopial observations showed that there is no border between the cortex and medulla regions of kidney. The kidney consists of nephrons which are composed of glomerulus surrounded by Bowman’s capsule; the other segments are proximal tubule, distal tubule and connecting tubule. The epithelial tissue lining of these segments simple cuboidal tissue.

This article deals with the approximate algorithm for two dimensional multi-space fractional bioheat equations (M-SFBHE). The application of the collection method will be expanding for presenting a numerical technique for solving M-SFBHE based on “shifted Jacobi-Gauss-Labatto polynomials” (SJ-GL-Ps) in the matrix form. The Caputo formula has been utilized to approximate the fractional derivative and to demonstrate its usefulness and accuracy, the proposed methodology was applied in two examples. The numerical results revealed that the used approach is very effective and gives high accuracy and good convergence.

In this paper, we introduce an exponential of an operator defined on a Hilbert space H, and we study its properties and find some of properties of T inherited to exponential operator, so we study the spectrum of exponential operator e^T according to the operator T.

Hamiltonians, momentum operators, and other quantum-mechanical perceptible take the form of self-adjoint operators when understood in quantized physical schemes. Unbounded and self-adjoint recognition are required in the situation of positive measurements. The selection of the proper Hilbert space(s) and the selection of the self-adjoint extension must be made in order for this to operate. In this effort, we define a new extension positive measure depending on the measurable field of nonzero positive self-adjoint operator in unbounded Hilbert space of analytic functions of complex variables. Consequently, we define an extension norm in the same space. We show several new properties of the suggested operator and its adjoin operator. These pr

The present paper focuses on the nature of the different interactions between cometary nucleus and tail with solar wind. The dynamics of the comet will impose many features that provide unique behavior of the comet when entering the solar system. These features are reviewed in this paper and few investigations are made. The calculations made in this work represent the analysis and interpretation of the different features of the comet, such as perihelion and eccentricity dependence on the gas production rate, and the dependence of the latter on the composition of the comet nucleus. The dependences of the heliocentric, bow shock, contact surface, and stand-off distances with gas production rate for many types of comets that cover linear and n

Intrinsic viscosities have been studied for polyethylene oxide in water which has wide industrial applications. The polyethylene oxide samples had two different structures, the first one was linear and covers a wide range of molecular weight of 1, 3, 10, 20, 35, 99, 370, 1100, 4600, and 8000 kg/mol and the second one was branched and had molecular weights of 0.55 and 40 kg/mol.
Intrinsic viscosities and Huggins constants have been determined for all types and molecular weights mentioned above at 25ºC using a capillary viscometer. The values of Mark-Houwink parameters (K and a) were equal to 0.0068 ml/g and 0.67 respectively, and have not been published for this range of molecular weight in as yet.

The current study deals with host-guest complex formation between cucurbit [7] urils as host and lansoprazole as guesti using PM3 (semi empirical molecules orbital calculations) also DFT calculations. In this complex, the formation of hydrogen bonding may be occurred through portal oxygen atoms(O2) of cucurbit [7] urils and amine groups (NH 2 )of the drug. The energies of HOMO and LUMO orbital’s have been computed for the host guest complex and its components. The result of the stabilization energy explained a complex formation.