It is shown that if a subset of a topological space (χ, τ) is δ-semi.closed, then it is semi.closed. By use this fact, we introduce the concept regularity of a topological space (χ, τ) via δ-semi.open sets. Many properties and results were investigated and studied. In addition we study some maps that preserve the δ-semi.regularity of spaces.

The security of message information has drawn more attention nowadays, so; cryptography has been used extensively. This research aims to generate secured cipher keys from retina information to increase the level of security. The proposed technique utilizes cryptography based on retina information. The main contribution is the original procedure used to generate three types of keys in one system from the retina vessel's end position and improve the technique of three systems, each with one key. The distances between the center of the diagonals of the retina image and the retina vessel's end (diagonal center-end (DCE)) represent the first key. The distances between the center of the radius of the retina and the retina vessel's end (ra

     Let  be an R-module, and let  be a submodule of . A submodule  is called -Small submodule () if for every submodule  of  such that  implies that . In our work we give the definition of -coclosed submodule and -hollow-lifiting modules with many properties.

Let be a commutative ring with unity and let be a non-zero unitary module. In
this work we present a -small projective module concept as a generalization of small
projective. Also we generalize some properties of small epimorphism to δ-small
epimorphism. We also introduce the notation of δ-small hereditary modules and δ-small
projective covers.

Weosay thatotheosubmodules A, B ofoan R-module Moare µ-equivalent , AµB ifoand onlyoif <<_µand <<_µ. Weoshow thatoµ relationois anoequivalent relationoand hasegood behaviorywith respectyto additionmof submodules, homorphismsr, andydirectusums, weaapplyothese resultsotoointroduced theoclassoof H-µ-supplementedomodules. Weosay thatoa module Mmis H-µ-supplementedomodule ifofor everyosubmodule A of M, thereois a directosummand D ofoM suchothat AµD. Variousoproperties ofothese modulesoarepgiven.

    Gangyong Lee, S. Tariq Rizvi, and Cosmin S. Roman studied Dual Rickart modules. The main purpose of this paper is to define strong dual Rickart module. Let M and N be R- modules , M is called N- strong dual Rickart module (or relatively sd-Rickart to N)which is  denoted by M it is N-sd- Rickart if for every submodule A of M and every homomorphism fHom (M , N) , f (A) is a direct summand of N. We prove that for an R- module M , if R is M-sd- Rickart , then every cyclic submodule of M is a direct summand . In particular, if M<

A total of 200 clinical samples included Burns and Wounds infections were collected from Baghdad Governorate. Results showed that rate all isolates of P. mirabilis was 31(15.5%) and rate of Burns infections was 14 (45%) and rate of wounds infection 17 (55%). Where was diagnostic based on conventional biochemical tests and confirmed by the Vitek-2 Compact system and the specific primer of the16SrRNA gene, the ability of bacterial isolates to biofilm formation to be studied. It's considered an important virulence factor in Incidence of diseases and play important role in increasing resistance to antibiotic of encased bacteria, by two methods Congo Red Agar method and Microtiter Plate method. The Congo Red Agar method showed that most isolates

Objective: This experiment was conducted to study the effects of ionized water on certain egg quality traits and the levels of proteins and enzymes in the blood of the Japanese quail Coturnix japonica . Materials and Methods: One hundred 42-day-old quail were randomly distributed among five treatment groups with four replicates for each group. The following treatments were used: T1 (control): The birds were provided normal water, T2: The birds were provided alkaline water (pH = 8), T3: The birds were provided alkaline water (pH = 9), T4: The birds were provided acidic water (pH = 6) and T5: The birds were provided acidic water (pH = 5). A Complete Randomized Design (CRD) was used to investigate the effects of the studied treatments on diffe