This paper discusses the Sums of Squares of “m” consecutive Woodall Numbers. These discussions are made from the definition of Woodall numbers. Also learn the comparability of Woodall numbers and other special numbers. An attempt to communicate the formula for the sums of squares of ‘m’ Woodall numbers and its matrix form are discussed. Further, this study expresses some more correlations between Woodall numbers and other special numbers.

In this research the change in the distance of the two stars in two binary star systems (13.6+8)M₈and (13+10)M₈ was studied, through the calculations the value  (rate of mass transfer) of the two phases of dynamical stages of mass which are mass loss and mass transfer has been extracted in its own way ,by extracting the value of  the value of (the distance variation between the two stars) has been found only in the mass transfer stage by using mathematical model ,in mass loss stage  and   were calculated from the change and the difference between the values of each at different times of binary star system evolution ,it was found that  the maximum values of  and  are in ma

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

     Let R1be a commutative2ring with identity and M be a unitary R-module. In this6work we7present almost pure8ideal (submodule) concept as a9generalization of pure10ideal (submodule).  lso, we1generalize some9properties of8almost pure ideal (submodule). The 7study is almost regular6ring (R-module).

        A new generalizations of coretractable modules are introduced where a module  is called t-essentially (weakly t-essentially) coretractable if for all proper submodule  of , there exists f End( ), f( )=0 and Imf _tes  (Im f + _tes ). Some basic properties are studied and many relationships between these classes and other related one are presented.

The   study   of  torsion  {torsion   free)  fuzzy  modules   over   fuzzy

integtal  domain  as a generalization oftorsion (torsion free) modules.

The present study aims to detect CTX-M-type ESBL from Escherichia coli clinical isolates and to analyze their antibotic susceptibility patterns. One hundred of E. coli isolates were collected from different clinical samples from a tertiary hospital. ESBL positivity was determined by the disk diffusion method. PCR used for amplification of CTX-M-type ESBL produced by E. coli. Out of 100 E. coli isolates, twenty-four isolates (24%) were ESBL-producers. E. coli isolated from pus was the most frequent clinical specimen that produced ESBL (41.66%) followed by urine (34.21%), respiratory (22.23%), and blood (19.05%).  After PCR amplification of these 24 isolates, 10 (41.66%) isolates were found to possess CTX-M genes. The CTX-M type ESBL

   A potentiostatic study for the corrosion of pure zinc in 0.01 M HCl was achieved in absence and presence of (linear alkylbenzene solfonate LAS) detergents in a range of concentrations (0-50) mg/L. The electrochemical studies included anodic, cathodic polarization by using potentiostat over temperature rang (293- 323) K.     The mechanism of corrosion rate of pure zinc was suggested by evaluating of αa , αc , ba , bc , i0 , Rp and the kinetic parameters also calculated ( Ea , A) at the above temperature rang, The thermodynamic of corrosion, corrosion accelerating and corrosion  protecting were investigated by calculating  (∆G, ∆H and ∆s) values