Let G be a graph, each edge e of which is given a weight w(e). The shortest path problem is a path of minimum weight connecting two specified vertices a and b, and from it we have a pre-topology. Furthermore, we study the restriction and separators in pre-topology generated by the shortest path problems. Finally, we study the rate of liaison in pre-topology between two subgraphs. It is formally shown that the new distance measure is a metric

THE Schiff base reaction played an important role of the condensation reaction between 2-aminophenol and Glyoxylic acid in the presence of calculated amounts of KOH as a catalyst. The reaction has been carried out in ethanol under reflux and stirring condition for 3.5 hrs. All syntheses were carried out under hydrogen gas forming a new potassium (E)-1-hydroxy-2-(2-hydroxyphenylimino)ethanolate ligand type [NO2]. The ligand of the general formula K2[Mn(L2)] type and its Mnп complex K2[Mn(N2O4)] type, has been characterized by spectroscopic methods (F.T-I.R. and U.V-Vis.), elemental analysis (C.H.N) metal content, magnetic susceptibility measurement, Thin-layer chromatography (T.L.C), X-RD powder diffraction, 1H-NMR, 13C-NMR molar conductanc

     2-amino-5-mercapto-1,3,4-thiadiazole [I] were prepared by the cyclization of thiosemecarbazide with carbon disulphide and anhydrous  sodium carbonate in ethanol as a solvent. The reaction of compound [I] with alkyl halides yielded 2- amino-5-thioalkyl-1,3,4- thiadiazole [II] and [III] . Compound [II] and [III] were reacted with different aromatic aldehydes to yieled 2-[(substituted benzyliden ) amino] -5- thioalkyl-1,3,4- thiadiazole [IV]a-c , [V]a-d and [VI]a-d .  Schiff ,s bases [IV]a-c , [V]a-d and [VI]a-d  were found to react with  2mercapto benzoic acid in the triethyl amine to give 3-[ 5-( alkylthio) -1,3,4- thiadiazol-2-yl] 2,3- dihydro- 2- (aryl) benzo [e] [1,3] thiazine -4-one [VII]a-

This research is a study of the difficulties of learning the Arabic language that faces Arabic language learners in the Kurdistan Region, by revealing its types and forms, which can be classified into two categories:

The first type has difficulties related to the educational system, the source of which is the Arabic language itself, the Arabic teacher or the learner studying the Arabic language or the educational curriculum, i.e. educational materials, or the educational process, i.e. the method used in teaching.

The second type: general difficulties related to the political aspect, the source of which is the policy of the Kurdistan Regional Government in marginalizing the Arabic language and replacing the forefront of th

This research includes synthesis of new heterocyclic derivatives of N-benzyl-5-bromoisatin. New 1, 2, 4-triazole, oxazoline and thiazoline derivatives of [N-benzyl-5-bromo-3-(Ethyliminoacetate)-indole-2-one] (2) have been synthesized. The preparation process started by the reaction of 5-bromoisatin with sodium hydride in dimethylformamide (DMF) at 0°C, gave suspension of sodium salt of 5-bromoisatin and subsequent reaction with benzylchloride to give N-benzyl-5-bromoisatin (1). Compound (1) reacted with ethylglycinate (Schiff base) obtained the intermediate compound (2) which reacted with different reagents in two ways. The first way, compound (2) reacted with (hydrazine hydrate, semicarbazide, phenylsemicarbazide and thiosemicarbazide)

The interacting boson models,  and  were used to perform a complete study  of even –even ^160-168Yb isotopes .The low –lying positive parity states, dynamic symmetries, reduced electric quadrupole transition probability , quadruple  momentum , and potential energy surface  for ^160-168Yb  were investigated. Energy level sequences and energy ratios showed the gradual transition of the properties of these nuclei from the γ-unstable features  to the rotational features . Adding the pairing parameter  to   Hamiltonian had a very slight effect on this feature, but it raised the β band, since it represents symmetry breaking such as in γ-unstable features . This applie

Mycotoxins are secondary by-products of mold metabolism and are accountable for human and animal mycotoxicosis. The most serious trichothecenic mycotoxin is the fungal T-2 mycotoxin. T-2 mycotoxin impaired nutrient absorption, metabolism, and then, eliciting severe oxidoreductive stress. Diet plays a key role beyond the supply of nutrients in order to promote animal and human health. Organic acids have been commonly used to exert antioxidative stress capacity in the liver and gut ecosystem. This study is planned to explore, the competence of using (X-MoldCid®) during chronic T-2 mycotoxicosis course in rat. Rats were allocated into 4 main groups, (CN-Gr), negative control and was allowed for the free access to the normal rats chow and the

The distribution of chilled water flow rate in terminal unit is an important factor used to evaluate the performance of central air conditioning unit. A prototype of A/C unit has been made, which contains three terminal units with a complete set of accessories (3-way valve, 2-way valve, and sensors) to study the effect of the main parameters, such as total water flow rate and chilled water supply temperature with variable valve opening. In this work, 40 tests were carried out. These tests were in two groups, 20 test for 3-way valve case and 20 test for 2-way valve case. These tests were performed at three levels of valve opening, total water flow rate and water supply temperature according to the design matrices establis

A new furfural Schiff base derivative ligand (L-FSB) named N-(4- Bromo-2-methylphenyl)-1-(furan-2-yl)methanimine, was synthesized from the condensation reaction of furfural (fur) with 4-Bromo-2- methylaniline (bma) in 1:1molar ratio. A new series of VO(II), Cr(III), Mn(II), Co(II), Ni(II), Cu(II), Zn(II), and Cd(II) metal complexes are synthesized according to the metal content analysis in an 2:1 ligand:metal ratio. The stereochemistry of the ligand complexes have been deduced by Fourier Transform-Infra Red (FT-IR), Atomic Adsorption (A.A), Ultra violate-Visible Spectra (UV-Vis Spectra), (Mass Spectra, Proton,13Carbon-Nuclear Magnetic Resonance) (1H-NMR,13CNMR) for ligand), magnetic susceptibility at 25oC and conductivity measurements. Fr

Objective: Schiff’s and Mannich bases of isatins are an important group of heterocyclic compounds which are of great importance in medicinal chemistry as antimicrobial agents. In the vision of these facts, new bis-Schiff bases and Mannich bases of isatins were synthesized. Methods: Three different bis-Schiff bases (3a-c) have been synthesized by reacting isatin, 5-fluoroisatin and 5-methoxy isatin with thiophene-2- carboxaldehyde using hydrazine hydrate to link between the carbonyl compounds, and then these bis- Schiff bases were condensed with two different secondary amines (piperidine and morpholine) separately, and formaldehyde to form the Mannich bases (4a-c and 5a-f), respectively. Results: The structures of the newly synthesized com