This paper aims to introduce a concept of an equilibrium point of a dynamical system which will call it almost global asymptotically stable. We also propose and analyze a prey-predator model with a suggested  function growth in prey species. Firstly the existence and local stability of all its equilibria are studied. After that the model is extended to an optimal control problem to obtain an optimal harvesting strategy. The discrete time version of Pontryagin's maximum principle is applied to solve the optimality problem. The characterization of the optimal harvesting variable and the adjoint variables are derived. Finally these theoretical results are demonstrated with numerical simulations.

New series of 2-mecapto benzoxazole derivatives (1-20) incorporated into fused to different nitrogen and suphur containing heterocyclic were prepared from 2-meracpto benzoxazole, when treated with hydrazine hydrate to afford 2-hydrazino benzoxazol (1). Compound (1) converted to a variety of pyridazinone andphthalazinone derivatives (2-4) by reaction with different carboxylic anhydride. Also, reaction of (1) with phenyl isothiocyanate and ethyl chloro acetate afforded 3-phenyl-1,3-thiazolidin-2,4-dione-2-(benzoxazole-2-yl-hydrazone) (6). Azomethines (7-10) were prepared through reaction of (1) with aromatic aldehyde, then (7, 8) converted to thaizolidinone derivatives (11, 12). Treatment of (1) with active methylene compounds afforded deriva

In this research, new series of Furo-2-quinolone [FQ] compounds have been synthesized. These novel [FQ] compounds were prepared from coumarin derivatives (Furocoumarins: psoralen and isopsoralen).Identifications of these FQ compounds were performed by using infrared spectrum (I.R), Ultraviolet spectrum (U.V) and Nuclear Magnetic Resonance spectrum (H¹-NMR) besides some physical data. The cytotoxic screening involves ;using HEP-2 cell line which gave differential responses against tested compounds : 4,6 Dimethyl furo[2, 3-g] coumarin (C₁), 1-(2`, 4`, Dimethoxy benzylideneimino)-2,6-dimethyl Furo [2, 3-g] quinoline-2-one (C₃) and the angular psoralen of the same derivative

In this work 2-hydrazino pyrimidine (1) was prepared from 2-mercapto pyrimidine with hydrazine hydrate. Treatment of (1) with active methylene compounds gave 2-(3,5-dimethyl -1 H – Pyrazole-1-yl) pyrimidine , whereas the reaction of (1) with carboxylic anhydride namely maleic anhydride or 1,2,3,6-tetra hydro phthalic anhydride yielded 1-Pyrimidine-2-yl-1,2-dihydro pyridazine-3,6-dione (3) and 2 – Pyrimidin -2-yl -2,3,4 a ,5,8 a – hexahydro phthalazine 1,4 – dione (4) . Reaction of (1) with phenyl isothiocyanate and ethyl chloro acetate afforded 3-Phenyl-1,3-thiazolidine-2,4-dione-2( pyrimidine -2- yl hydrazone (6) Azomethine (7-10) were prepared through condensation of (1) with aromatic aldehydes or ketones, then comp

In the present work, several new cyclic imides (succinimides) linked to benzothiazole or thiazole moieties through phenyl azo group were synthesized. Synthesis of the new imides was performed via multistep synthesis. The first step involved reaction of equimolar amounts of succinic anhydride and p-toluidine producing N-(4-tolyl) succinamic acid (1) which was dehydrated in the second step via treatment with acetic anhydride and anhydrous sodium acetate affording N-(4-tolyl)succinimide (2).
In the third step, substituted-2-aminobenzothiazoles were introduced in diazotization reaction with nitrous acid producing the corresponding diazonium salts and these inturn were introduced directly in coupling reaction with compound (2) affording th

In this paper we present the first ever measured experimental electron momentum density of Cu2Sb at an intermediate resolution (0.6 a.u.) using 59.54 keV 241Am Compton spectrometer. The measurements are compared with the theoretical Compton profiles using density function theory (DFT) within a linear combination of an atomic orbitals (LCAO) method. In DFT calculation, Perdew-Burke-Ernzerhof (PBE) scheme is employed to treat correlation whereas exchange is included by following the Becke scheme. It is seen that various approximations within LCAO-DFT show relatively better agreement with the experimental Compton data. Ionic model calculations for a number of configurations (Cu+x/2)2(Sb-x) (0.0≤x≤2.0) are also performed utilizing free a

Leucine aminopepotidase (LAP)[EC:3.4.11.1] activity has been assayed in (50) serum samples of patients with diabeties naphrophathy D.N (non-insulin dependent diabetic (NIDD) , and (50)serum sample of healthy individuals without any clinically detectable diseases have been as control group. The aim of this study is to measure leucine aminopeptidase activity and partially purifying the enzyme from sera of patients with diabetes nephropathy The results of this study revealed that Leucine aminopeptidase (LAP) activity of nephropathy patient’s serum shows a high signifiacant increase (p < 0.001) compared to that of the healthy subjects.LAP was purified from the serum of patients with diabetes nephropathy by dialysis and gel filtration (Se

New Schiff-base ligands bearing tetrazole moiety and their polymeric metal complexes with Co(II), Ni(II) and Cd(II) ions are reported. Ligands were prepared in a multiple-step reaction. The reaction of sodium 2,6- diformylphenolate and cyclohexane-1,3-dione with 5-amino-2-fluorobenzonitrile resulted in the isolation of two precursors sodium 2,6-bis((E)-(3-cyano-4-fluorophenylimino)methyl)-4-methylphenolate 1 and 5,5'- (1E,1'E)-cyclohexane-1,3-diylidenebis- (azan-1-yl-1-ylidene)bis(2-fluorobenzonitrile) 2, respectively. The reaction of precursors with azide gave the required ligands; sodium 2,6-bis((E)-(4-fluoro-3-(1H-tetrazol-5- yl)phenylimino)methyl)-4-methylphenolate (NaL) and (N,N'E,N,N'E)-N,N'-(cyclohexane-1,3-diylidene)bis(4- fluoro-3-

New Schiff-base ligands bearing tetrazole moiety and their polymeric metal complexes with Co(II), Ni(II) and Cd(II) ions are reported. Ligands were prepared in a multiple-step reaction. The reaction of sodium 2,6- diformylphenolate and cyclohexane-1,3-dione with 5-amino-2-fluorobenzonitrile resulted in the isolation of two precursors sodium 2,6-bis((E)-(3-cyano-4-fluorophenylimino)methyl)-4-methylphenolate 1 and 5,5'- (1E,1'E)-cyclohexane-1,3-diylidenebis- (azan-1-yl-1-ylidene)bis(2-fluorobenzonitrile) 2, respectively. The reaction of precursors with azide gave the required ligands; sodium 2,6-bis((E)-(4-fluoro-3-(1H-tetrazol-5- yl)phenylimino)methyl)-4-methylphenolate (NaL) and (N, N'E, N, N'E)-N, N'-(cyclohexane-1,3-diylidene)bis(4- fluor