In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

The 4-(?-bromo acetyl)-4?-toluene sulfonanilide (2) was used as key intermediate to synthesize new heterocyclic compounds. This bromo compound was synthesized via sulfonation of amino group of p-amino acetophenone using Hinsburg method with 4-toluene sulfonyl chloride to form 4-acetyl-4?-toluene sulfonanilide (1) which is used as a starting material in this work. This compound was brominated to yield compound (2) which is used as a precursor to synthesize new five and seven membered heterocyclic compounds such as substituted 1,3-oxazoles (3,4), 1,3-thiazole derivatives (5-7), thiourea compounds (8a,b), 1,3-Thiazoline-2-thione compounds (9a-f) and 1,2,5-triazepine compounds (11a-d). The synthesized compounds were identified depending u

The primary purpose of this paper is to introduce the, 2- coprobabilistic normed space, coprobabilistic dual space of 2- coprobabilistic normed space and give some facts that are related of them

In this thesis, we introduced some kinds of fibrewise topological spaces by using totally continuous function is called fibrewise totally topological spaces. We generalize some fundamental results from fibrewise topology into fibrewise totally topological spaces. We also introduce the concepts of fibrewise totally separation axioms, fibrewise totally compact and locally totally compact topological spaces. As well as fibrewise totally perfect topological spaces. We explain and discuss new notion of fibrewise topological spaces, namely fibrewise totally topological spaces. We, also introduce the concepts of fibrewise totally closed topological spaces, fibrewise totally open topological spaces, fibrewise locally sliceable and locally s

In this paper, we define some generalizations of topological group namely -topological group, -topological group and -topological group with illustrative examples. Also, we define grill topological group with respect to a grill. Later, we deliberate the quotient on generalizations of topological group in particular -topological group. Moreover, we model a robotic system which relays on the quotient of -topological group.

In this thesis, we introduced some types of fibrewise topological spaces by using a near soft set, various related results also some fibrewise near separation axiom concepts and a fibrewise soft ideal topological spaces. We introduced preliminary concepts of topological spaces, fibrewise topology, soft set theory and soft ideal theory. We explain and discuss new notion of fibrewise topological spaces, namely fibrewise soft near topological spaces, Also, we show the notions of fibrewise soft near closed topological spaces, fibrewise soft near open topological spaces, fibrewise soft near compact spaces and fibrewise locally soft near compact spaces. On the other hand, we studied fibrewise soft near forms of the more essent

The aim of this paper is to introduce and study the notion type of fibrewise topological spaces, namely fibrewise fuzzy j-topological spaces, Also, we introduce the concepts of fibrewise j-closed fuzzy topological spaces, fibrewise j-open fuzzy topological spaces, fibrewise locally sliceable fuzzy j-topological spaces and fibrewise locally sectionable fuzzy j-topological spaces. Furthermore, we state and prove several Theorems concerning these concepts, where j = {δ, θ, α, p, s, b, β}.

Three complexes of copper(II) and iron(II) with mixed ligands acetylacetonebis(thio-semicarbazone)- ABTSH2 and benzaldazine- BA have been prepared and characterized using different physico-chemical techniques including the determination of metal contents, mole-cular weight, measurement of molar conductivity, magnetic moment, molar refraction, infrared and electronic spectra. Accordingly, octahedral complexes having general formulaes [Cu2(ABTSH2)2(BA)2Cl2]Cl2 and [M2(ABTSH2)2(BA)2(SO4)2] {M= Cu(II) or (Fe(II)} have been proposed. The resulted complexes screened for antifungal activity in vitro against the citrus pathogen Aspergillus niger and Fusarium sp. which caused root rot of sugar and the beans pathogen Alternaria sp. All the complex