Let  be a commutative ring with 1 and  be left unitary  . In this paper we introduced and studied concept of semi-small compressible module (a     is said to be semi-small compressible module if  can be embedded in every nonzero semi-small submodule of . Equivalently,  is  semi-small compressible module if there exists a monomorphism  , ,     is said to be semi-small retractable module if  , for every non-zero  semi-small sub module in . Equivalently,  is semi-small retractable if there exists a homomorphism  whenever  .     In this paper we introduce and study the concept of semi-small compressible and semi-small retractable s as a generalization of compressible  and retractable  respectively and give some of their adv

Background: Potentially malignant oral disorders (PMODs) are common precursors of oral squamous cell carcinoma (OSCC). Neoangiogenesis and signalling are important intermediate biomarkers that may govern the progression of dysplastic mucosa into carcinoma. Aims: Evaluate the importance of CD34 and Wnt3 expression in PMODs and OSCCs in relation to their clinicopathological parameters. Settings and Design: Prospective cross-sectional study. Materials and Methods: Immunohistochemical staining for CD34 and Wnt3 was performed for 41 samples. These included 27 PMODs, six OSCCs and eight normal gingival and alveolar mucosa. Analysis of variance (ANOVA) and post-hoc tests were applied. P<0.05 was considered statistically significant. Results: CD34

The research article deals with the process of building or rebuilding the state in Iraq after 2003 in its various dimensions, in light of the vision and foundational procedures that were developed and supervised by the United States in cooperation with the new leaders of Iraq based on the mechanism of sectarianethnic representation, and diagnosing the imbalances that arose out of that vision and the accompanying procedures, which led to the emergence of new variables in the political process, especially in the post-ISIS* phase, which produced important challenges to the political system and the Iraqi state. The political dynamics and balances emerging after ISIS* represented at the same time opportunities and risks in the process of

Capillary pressure is a significant parameter in characterizing and modeling petroleum reservoirs. However, costly laboratory measurements may not be sufficiently available in some cases. The problem amplifies for carbonate reservoirs because relatively enormous capillary pressure curves are required for reservoir study due to heterogeneity. In this work, the laboratory measurements of capillary pressure and formation resistivity index were correlated as both parameters are functions of saturation. Forty-one core samples from an Iraqi carbonate reservoir were used to develop the correlation according to the hydraulic flow units concept. Flow zone indicator (FZI) and Pore Geometry and Structure (PGS) approaches were used to identify

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This research aims to distinguish the reef environment from the non-reef environment. The Oligocene-Miocene-succussion in western Iraq was selected as a case study, represented by the reefal limestone facies of the Anah Formation (Late Oligocene) deposited in reef-back reef environments, dolomitic limestone of the Euphrates Formation (Early Miocene) deposited in open sea environments, and gypsiferous marly limestone of the Fatha Formation (Middle Miocene) deposited in a lagoonal environment. The content of the rare earth elements (REEs) (La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Er, Ho, Tm, Yb, Lu, and Y) in reef facies appear to be much lower than of those in the non-reef facies. The open sea facies have a low content of REEs due to bein

Broyden update is one of the one-rank updates which solves the unconstrained optimization problem but this update does not guarantee the positive definite and the symmetric property of Hessian matrix.

In this paper the guarantee of positive definite and symmetric property for the Hessian matrix will be established by updating the vector  which represents the difference between the next gradient and the current gradient of the objective function assumed to be twice continuous and differentiable .Numerical results are reported to compare the proposed method with the Broyden method under standard problems.

The majority of statisticians, if not most of them, are primarily concerned with the theoretical aspects of their field of work rather than their application to the practical aspects. Its importance as well as its direct impact on the development of various sciences. Although the theoretical aspect is the first and decisive basis in determining the degree of accuracy of any research work, we always emphasize the importance of the applied aspects that are clear to everyone, as well as its direct impact on the development of different sciences. The measurements of public opinion is one of the most important aspects of the application of statistics, which has taken today, a global resonance and has become a global language that everyone can

Some have considered the dialectic in form and meaning from different points of view, and dismantled them from each other, and this view is correct if we adopt according to the logic of Aristotle when it comes to dialectic, the dialectic of form and meaning has different aspects and does not share a single line in terms of conceptual meaning, the form is the appearance What the recipient sees with the help of cognitive tools, the content or content is the mental meaning, which in turn depends on his own tools, and to this extent this view is correct, and the intellectual content or meaning of the artwork or the human message that the artist wants to convey to the viewer.
The research included four chapters. The first chapter included