Weosay thatotheosubmodules A, B ofoan R-module Moare µ-equivalent , AµB ifoand onlyoif <<_µand <<_µ. Weoshow thatoµ relationois anoequivalent relationoand hasegood behaviorywith respectyto additionmof submodules, homorphismsr, andydirectusums, weaapplyothese resultsotoointroduced theoclassoof H-µ-supplementedomodules. Weosay thatoa module Mmis H-µ-supplementedomodule ifofor everyosubmodule A of M, thereois a directosummand D ofoM suchothat AµD. Variousoproperties ofothese modulesoarepgiven.

       The Sr doped La1Ba1-xSrx Ca2Cu4O8.5+δ samples with 0 ≤ x ≤ 0.3 had been prepared using the solid state reaction. The samples were claimed at 800°C for 3hr, palletized and sintered at 860°C for 20hr in air . Dielectric constant and loss by means of capacitance have been investigated with frequencies in the range of 1kHZ to 1MHZ for our samples at room temperature. Also, Shore hardness has been measured. The dielectric constant and loss decrease slightly with the increase of frequency for all compounds. Additionally, the partial substitution of Sr+2 into Ba+2 sites never have effect on the dielectric properties. X-ray diffraction (XRD) analysis showed a tetragonal structure and the

Some metal ions (Mn+2, Fe+2, Co+2,Ni+2,Cu+2 and Cd+2) complexes of  N-acetyl Tryptophan (AcetrpH) and  α-Picoline (α-Pic) have been synthesized and characterized on the basis of their FTIR,UV-Vis spectroscopy , conductivety measurements , magnetic susceptibility.  From the results obtained, the following general formula has suggested for the prepared complexes.            [M+2(Acetrp)2(α-Pic)2]. XH2O Where  M = Mn+2, Fe+2, Co+2,Ni+2,Cu+2 and Cd+2                         X =  0  ,    0   ,  &nb

       In this study, light elements 19F ,22Na for  (α,n) and (n,α) reactions as well as α-particle energy  from a threshold energy  to 10 MeV are used according to the available data of reaction cross sections.  The more recent cross sections data of (α,n) and (n,α) reactions are reproduced in fine steps 86.4 KeV for 22Na (n,α) 19F  in the specified energy range, as well as cross section (α,n)  values were derived from the published data of (n,α) as a function of αenergy in the same fine energy steps by using the principle inverse reactions. This calculation involves only the ground state of  19F ,22Na in the reactions 19F (α,n) 22Na ,  2

The objective of this study was to investigate the release profile of different fat and water soluble bases using diazepam as a model drug , and then to develop  a satisfactory formula with a rapid release of diazepam from suppository bases .The study was conducted using theobroma oil ,glycerol-gelatin and glycerol-PEG1540 bases using conventional mold method for preparation .while the later base was utilized to incorporate diazepam ( buffered solution ) in a hollow type suppositories. The results indicated that all types of bases can be utilized to formulate diazepam as  rectal suppositories with acceptable disintegration time ( 12, 10, 6, and 6min.), respectively . While 100% of the  released drug had been shown differen

Biaxial hollow slab is a reinforced concrete slab system with a grid of internal spherical voids included to reduce the self-weight. This paper presents an experimental study of behavior of one-way prestressed concrete bubbled slabs. Twelve full-scale one-way concrete slabs of (3000mm) length with rectangular cross-sectional area of (460mm) width and (150mm) depth. Different parameters like type of specimen (solid or bubbled slabs), type of reinforcement (normal or prestress), range of PPR and diameter of plastic spheres (100 or 120mm) are considered. Due to the using of prestressing force in bubbled slabs (with ratio of plastic sphere diameter D to slab thickness H, D/H=0.67), the specimens showed an increase in ultimat

Let R be a commutative ring with identity 1 ¹ 0, and let M be a unitary left module over R. A submodule N of an R-module M is called essential, if whenever N ⋂ L = (0), then L = (0) for every submodule L of M. In this case, we write N ≤e M. An R-module M is called extending, if every submodule of M is an essential in a direct summand of M. A submodule N of an R-module M is called semi-essential (denoted by N ≤sem M), if N ∩ P ≠ (0) for each nonzero prime submodule P of M. The main purpose of this work is to determine and study two new concepts (up to our knowledge) which are St-closed submodules and semi-extending modules. St-closed submodules is contained properly in the class of closed submodules, where a submodule N of