Suppose that  is a finite group and  is a non-empty subset of  such that  and . Suppose that  is the Cayley graph whose vertices are all elements of  and two vertices  and  are adjacent if and only if . In this paper, we introduce the generalized Cayley graph denoted by  that  is a graph with vertex set consists of all column matrices  which all components are in  and two vertices  and  are adjacent if and only if , where  is a column matrix that each entry is the inverse of similar entry of  and  is  matrix with all entries in  ,  is the transpose of  and . In this paper, we clarify some basic properties of the new graph and assign the structure of  when  is complete graph , complete bipartite graph  and complete

The activity of Alanine aminopeptidase( AAP ) was measured in the urine of healthy and urinary tract cancer patients , the results showed higher activity of (AAP) in patients compared to healthy . AAP was Purified from the urine of healthy and patients with urinary tract cancer by dialysis and gel filtration (Sephadex G – 50) and two isoenzymes of (AAP) were separated from urine by using ion-exchang resin (DEAE – Sephadex A – 50 ) in previous study. The kinetics studies showed that both isoenzymes I and II obeyed Michaelis – Menton equation . with optimal concentration of alanine-4-nitroanilide as substrate for isoenzymes I and II which was (2 x 10-3 mol/L ). The two isoenzymes obeyed Arrhenius equation up two 37° C and t

     In this work proton exchange membranes were prepared by a modified microwave casting solution technique, using the polymers blend (polyethersulfone (PES), polystyrene (PS), polyvinylidenefluride (PVDF)). Modified casting method was used to overcome the poor compatibility between hydrophilic, (PES, PS) and hydrophobic PVDF, by cooling the substrate during the film casting process to (4.5-5.5^oC). Membranes were chemically modified by three reaction types to study the differences between their effects on the required properties for microbial fuel cell application. These methods use blend organic sulfonic acid precasting process and sulfonation by sulfuric acid post-casting process (APS), blending organic

Coupling reaction of 2-amino benzoic acid with 8-hydroxy quinoline gave bidentate azo ligand. The prepared ligand has been identified by Microelemental Analysis,1HNMR,FT-IR and UV-Vis spectroscopic techniques. Treatment of the prepared ligand with the following metal ions (ZnII,CdII and HgII) in aqueous ethanol with a 1:2 M:L ratio and at optimum pH, yielded a series of neutral complexes of the general formula [M(L)2]. The prepared complexes have been characterized by using flame atomic absorption, (C.H.N) Analysis, FT-IR and UV-Vis spectroscopic methods as well as conductivity measurements. The nature of the complexes formed were studied following the mole ratio and continuous variation methods, Beer's law obeyed over a concentration ra

A new compound  2-(4-methoxyphcnyl)-5-(4-aminophenyl)-1,3,4-

oxadiazole (VI) was prepared by intramol ecular condensation reaction followed  by elimination  of some simple  moieties such  as IhO  and HCI by using  POCI3 with acid hydrazide. A series of new Shiffs­

bases 2-(4-methoxyphenyl)-5-[4(4:alkoxybenzoyloxy) benzylidene amino phenyl] I,3,4-oxadia:t.ole (VII].was synthesized from treatment

of oxadiazole derivative [VI] with an appropriate  aromatic aldehyde

(IU). Struct\lfe of the resulting products have been ascertaim:d by their melting pointS, elemental analysis ( some of them) and spectral data.

The compound 2,2'-(((1H-benzo(d)imidazol-2-yl)methyl)azanediyl)bis(ethan-1-ol) was reacted with benzyl bromide to afford compound (1) which used as row material to prepare a series of compounds through condensation reaction, the starting compound were reacted with tosyl chloride to protect the OH group  to afford compound 2, then reacted benzyl bromide to produce compound (2), then the compound (2) treated with three compounds ( 2-mercaptobenzthiazole, 2-mercaptobenimidazol and 2-chloromethyl benzimidazole) to form compounds 3a,b, 4a,b and 5a,b respectively. In the another step the click reaction of compound 2,2'-(((1H-benzo(d)imidazol-2-yl)methyl)azanediyl)bis(ethan-1-ol) with Propargyl bromide produce compound  6  which reacted

In this work, we will combine the Laplace transform method with the Adomian decomposition method and modified Adomian decomposition method for semi-analytic treatments of the nonlinear integro-fractional differential equations of the Volterra-Hammerstein type with difference kernel and such a problem which the kernel has a first order simple degenerate kind which the higher-multi fractional derivative is described in the Caputo sense. In these methods, the solution of a functional equation is considered as the sum of infinite series of components after applying the inverse of Laplace transformation usually converging to the solution, where a closed form solution is not obtainable, a truncated number of terms is usually used for numerical

Some metal ions (Mn
+2
, Fe
+2
,Co
+2
,Ni
+2
,Cu
+2
, Cd
+2
and Hg
+2
) complexes of N-acetyl
Tryptophan( AcetrpH) and (2, 2′-bipyridine) (2, 2′-Bipy)have been synthesized and then
characterized on the basis of their FT-IR, UV-Vis spectroscopy, magneticsuscptibity
conductivity measurements and atomic absorption;from the results obtained and the propsed
molecular structure for these complexes as octahedral geometry,the following general formula
has been given for the prepared complexes.
[M
+n
(Acetrp)2(2, 2′-Bipy)].
Where M= Mn
+2
, Fe
+2
,Co
+2
,Ni
+2
,Cu
+2
, Cd
+2
,Hg
+2
(Acetrp)
-=Ligand ion(N-acetyl