For any group G, we define G/H (read” G mod H”) to be the set of left cosets of H in G and this set forms a group under the operation (a)(bH) = abH. The character table of rational representations study to gain the K( SL(2,81)) and K( SL(2, 729)) in this work.

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

Iraqi kaolin was used for the preparation and characterization of NaY zeolite for biodiesel production via esterification reaction. Oleic acid was used usually as a typical simulated feedstock of high acid number for the esterification reaction.

   The chemical composition for the prepared Nay zeolite is as following:  (Ca₂.6Na₁.K_0.1)(Al₆.3Si₁₇.₇)O₄₈.16H₂O, the silica to alumina ratio in the prepared catalyst was found equal to 2.6 and Na₂O content was 12.26 wt. %, with relative crystallinity equal to 147.4 % obtained by the X-ray diffraction. The surface area result shows that the prepared catalyst has 330 m²

Theatrical production mechanisms were determined according to the extents of the theatrical performance, the directing plan, and the ideas that the theatrical performance seeks to convey to the audience. Accordingly, theatrical production mechanisms differ between one theatrical performance and another according to the requirements of each of them and the surrounding circumstances that accompany the production of theatrical performance, and in order to search for production mechanisms and their repercussions on the show. Theatrical The current research was divided into four chapters, namely (Chapter One - Methodology), which identified the research problem in the following question: What are the production mechanisms and their implicatio

Alloys of GaxSb1-x system with different Ga concentration (x=0.4, 0.5, 0.6) have been prepared in evacuated quartz tubes. The structure of the alloys were examined by X-ray diffraction analysis (XRD) and found to be polycrystalline of zincblend structure with strong crystalline orientation (220). Thin films of GaxSb1-x system of about 1.0 μm thickness have been deposited by flash evaporation method on glass substrate at 473K substrate temperature (Ts) and under pressure 10-6 mbar. This study concentrated on the effect of Ga concentration (x) on some physical properties of GaxSb1-x thin films such as structural and optical properties. The structure of prepared films for various values of x was polycrystalline. The X-ray diffraction analy

In light of accelerating environmental degradation, the transition to a green economy is an imperative for achieving sustainable development. This study provides a critical analysis of the international legal and institutional framework governing this transition, revealing a significant gap between normative developments and the institutional framework on one hand, and their practical implementation on the other. The transition faces legal obstacles, including reliance on non-binding voluntary commitments and conflicts between environmental obligations and global trade and investment rules. It also reveals a significant financing gap, as financial flows to developing countries continue to lag behind commitments, in add

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.