Let R be a ring and let M be a left R-module. In this paper introduce a small pointwise M-projective module as generalization of small M- projective module, also introduce the notation of small pointwise projective cover and study their basic properties.
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              In this paper, the packing problem for complete (  4)-arcs in  is partially solved. The minimum and the maximum sizes of complete (  4)-arcs in  are obtained. The idea that has been used to do this classification is based on using the algorithm introduced in Section 3 in this paper. Also, this paper establishes the connection between the projective geometry in terms of a complete ( , 4)-arc in  and the algebraic characteristics of a plane quartic curve over the field  represented by the number of its rational points and inflexion points. In addition, some sizes of complete (  6)-arcs in the projective plane of order thirteen are established, namely for  = 53, 54, 55, 56.

In this paper, we introduce the concept of e-small Projective modules as a generlization of Projective modules.

Introduction:

Renal artery aneurysm (RAA) occurs to focal dilatation of artery secondary to weakness of the arterial intima and media. RAA is a rare clinical entity with an incidence of 0.01 – 1%.1

Rupture RAA during pregnancy is extremely rare event. The obstetric and urologic literatures are deficient in this regard. Diagnosis of ru

         Let  be any group with identity element (e) . A subgroup intersection graph of  a subset  is the Graph with V ( ) =  - e and two separate peaks c and d contiguous for c and d if and only if      , Where  is a Periodic subset of resulting from  . We find some topological indicators in this paper and Multi-border (Hosoya and Schultz) of   , where    ,  is aprime number.

The use of real-time machine learning to optimize passport control procedures at airports can greatly improve both the efficiency and security of the processes. To automate and optimize these procedures, AI algorithms such as character recognition, facial recognition, predictive algorithms and automatic data processing can be implemented. The proposed method is to use the R-CNN object detection model to detect passport objects in real-time images collected by passport control cameras. This paper describes the step-by-step process of the proposed approach, which includes pre-processing, training and testing the R-CNN model, integrating it into the passport control system, and evaluating its accuracy and speed for efficient passenger flow

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.

In this paper, we introduce the concept of e-small M-Projective modules as a generalization of M-Projective modules.

Background: Iraq is an endemic area for visceral leishmaniasis (VK=L) (kala-azar) which is caused by the intracellular parasite leishmania donovani.

In the present paper we introduce and study new classes of soft separation axioms in soft bitopological spaces, namely, soft (1,2)*-omega separation axioms and weak soft (1,2)*-omega separation axioms by using the concept of soft (1,2)*-omega open sets. The equivalent definitions and basic properties of these types of soft separation axioms also have been studied.