A complexified adjoint representations of the complexification Lie algebras associated with the special orthogonal group SO(3) and special linear group SL(2,₵)  have been obtained. A new representation of their tensor product is naturally arisen and computed in details.

Tow   results  are  proved.  The  first  gives necessary  and   ullicient

conditions for a permutation group to have the prope1ty that each of its rational - valued character can be written as (integral) linear combination of characters induced from the principal characters of certain subgroup. The mher presents that this property is extendable to direct product of groups.

Examples give.

Background: Several factors render chronic lymphocytic leukemia (CLL) an interesting subject for study by researchers. These include marked progress in understanding the molecular biology of normal and neoplastic lymphocytes and recent advances in molecular genetics techniques. Among molecular markers, p53 cancer suppressor gene and the antiapoptotic gene Bcl-2 have been widely studied. 
Patients and methods: A retrospective cross-sectional study done on 60 patients with chronic lymphocytic leukemia compared with 20 controls (anemic patients), all recruited at the Medical City Teaching Hospital laboratories from January 2004 to December 2007. The bone marrow biopsy of each was re-examined histologica

The experimental proton resonance data for the reaction P+48Ti have been used to calculate and evaluate the level density by employed the Gaussian Orthogonal Ensemble, GOE version of RMT, Constant Temperature, CT and Back Shifted Fermi Gas, BSFG models at certain spin-parity and at different proton energies. The results of GOE model are found in agreement with other, while the level density calculated using the BSFG Model showed less values with spin dependence more than parity, due the limitation in the parameters (level density parameter, a, Energy shift parameter, E1and spin cut off parameter, σc). Also, in the CT Model the level density results depend mainly on two parameters (T and ground state back shift energy, E0), which are app

The main objective of this thesis is to study new concepts (up to our knowledge) which are P-rational submodules, P-polyform and fully polyform modules. We studied a special type of rational submodule, called the P-rational submodule. A submodule N of an R-module M is called P-rational (Simply, N≤_prM), if N is pure and Hom_R (M/N,E(M))=0 where E(M) is the injective hull of M. Many properties of the P-rational submodules were investigated, and various characteristics were given and discussed that are analogous to the results which are known in the concept of the rational submodule. We used a P-rational submodule to define a P-polyform module which is contained properly in the polyform module. An R-module M is called P-polyform if every es

   The purpose of this paper is to study   new  types of open sets in bitopological spaces.    We shall introduce the concepts of  L- pre-open and L-semi-p-open sets

In this paper, we define a new type of pairwise separation axioms called pairwise semi-p- separation axioms in bitopological spaces, also we study some properties of these spaces and relationships of each one with the ordinary separation axioms in the bitopological spaces.

The significance of the work is to introduce the new class of open sets, which is said Ǥ- -open set with some of properties. Then clarify how to calculate the boundary area for these sets using the upper and lower approximation and obtain the best accuracy.

N-type Tin dioxide thin films with thickness (350 nm) prepared by thermal evaporation method. The thin film SnO2 was doped with Ag by the rate (0.01, 0.02 and 0.03). Atomic Force Microscopic (AFM) was adopted to determine the grain size and roughness of the film surface. The electrical properties were determined by mean of Hall Measurement system and mobility was calculated. SnO2: Ag/P–Si photodetectors demonstration the highest described visible responsivity of (0.287 A/W) with the Ag ratio of (0.03). I–V characteristics with different power density were measured. The best sensitive value of the spectral response, specific detectivity and quantum efficiency at wavelength (422 nm).