Let  be a commutative ring with 1 and  be left unitary  . In this papers we introduced and studied concept P-small compressible  (An     is said to be P-small compressible if  can be embedded in every of it is nonzero P-small submodule of . Equivalently,  is P-small compressible if there exists a monomorphism  , ,     is said to be P-small retractable if  , for every non-zero P-small submodule of . Equivalently,  is P-small retractable if there exists a homomorphism  whenever  as a generalization of compressible  and retractable  respectively and give some of their advantages characterizations and examples.

All the prepared metal complexes of Pt (IV), Au(III), Rh (III), Co (II) and V(IV) with new ligand sodium [5-(p-nitro phenyl)-/4-phenyl-1,2,4-triazole-3-dithiocarbamato hydrazide] (TRZ.DTC) have been synthesized and characterized in solid state by using flame atomic absorption, elemental analysis C.H.N.S, FT-IR ,UV-Vis Spectroscopy, conductivity and magnetic susceptibility measurements. The nature of the complexes formed in ethanolic solution has been studied following the molar ratio method also was studied stability constant and found to be stable in molar ratio1:1 of VL (IV) and CoL(II) while Pt(IV), Au(III) and Rh(III) complexes stable in molar ratio 1:2 as well as the molar absorptivity for these complexes were calculated. From the prev

This study describes the preparation of tetradentate Schiff base derived from the condensation of 2-Hydroxy naphthaldehyde with 2-amine benzhydrazide and the synthesis of new complexes series with a good yield.The prepared ligand was characterized using a microanalysis technique, UV-visible, FT-IR, nuclear magnetic resonance ¹H-NMR, mass spectrometry, thermal gravimetric analysis TGA, and the addition of conductivity measurement and magnetic moment of complexes. The invitro antimicrobial activity of the prepared compounds was tested against  Gram-negative Klebsiella pneumonia, Gram-positive Staphylococcus aureu, and Candida albicans by the agar well diffusion method. The spectroscopy and measurement studies showed that the li

 Charge  transfer (CT) at  liquid/liquid  interfaces are described  theoretically depending on  the quantum theory .A model that derived used to calculate the rate constant  of transport at liquid/liquid  interfaces. The calculation of the rate constant of  charge  transfer depends on  the calculation of the reorganization energy, driving force ,and the coupling coefficient . Large reorganization energies  and large rate constant  for charge transfer ,indicate that the transitions involve more energy to happen . The system have large 𝐸0 (𝑒𝑉) refers that  type  of  liquid  is more reactive media than other liquid types with same d

The radial wave function R(r) and the radial distribution function P(r) as a function of (r), for the Hydrogen atom was calculated for several atomic state (1s,2s,2p,3s,3p,3d) The results were compared with Hydrogen like atom(He+,Li+2,Be+3).

Based on the diazotization-coupling reaction, a new, simple, and sensitive spectrophotometric method for determining of a trace amount of (BPF) is presented in this paper. Diazotized metoclopramide reagent react with bisphenol F produces an orange azo-compound with a maximum absorbance at 461 nm in alkaline solution. The experimental parameters were optimized such as type of alkaline medium, concentration of NaOH, diazotized metoclopramide amount, order additions, reaction time, temperature, and effect of organic solvents to achieve the optimal performance for the proposed method. The absorbance increased linearly with increasing bisphenol F concentration in the range of 0.5-10 μg mL^-1 under ideal conditions, with a correlati