The interplay of species in a polluted environment is one of the most critical aspects of the ecosystem. This paper explores the dynamics of the two-species Lokta–Volterra competition model. According to the type I functional response, one species is affected by environmental pollution. Whilst the other degrades the toxin according to the type II functional response. All equilibrium points of the system are located, with their local and global stability being assessed. A numerical simulation examination is carried out to confirm the theoretical results. These results illustrate that competition and pollution can significantly change the coexistence and extinction of each species.

To obtain the approximate solution to Riccati matrix differential equations, a new variational iteration approach was ‎proposed, which is suggested to improve the accuracy and increase the convergence rate of the approximate solutons to the ‎exact solution. This technique was found to give very accurate results in a few number of iterations. In this paper, the ‎modified approaches were derived to give modified solutions of proposed and used and the convergence analysis to the exact ‎solution of the derived sequence of approximate solutions is also stated and proved. Two examples were also solved, which ‎shows the reliability and applicability of the proposed approach. ‎

Some new complexes of 4-(5-(1,5-dimethyl-3-oxo-2-phenyl pyrazolidin-4- ylimino)-3,3-dimethyl cyclohexylideneamino) -1,5- dimethyl-2- phenyl -1H- pyrazol -3(2H) –one (L) with Mn(II), Fe(III), Co(II), Ni(II), Cu(II), Pd(II), Re(V) and Pt(IV) were prepared. The ligand and its metal complexes were characterized by phisco- chemical spectroscopic techniques. The spectral data were suggested that the (L) as a neutral tetradentate ligand is coordinated with the metal ions through two nitrogen and two oxygen atoms. These studies revealed Octahedral geometries for all metal complexes, except square planar for Pd(II) complex. Moreover, the thermodynamic activation parameters, such as ?E*, ?H, ?S, ?G and K are calculated from the TGA curves using Coa

A watermark is a pattern or image defined in a paper that seems as different shades of light/darkness when viewed by the transmitted light which used for improving the robustness and security. There are many ways to work Watermark, including the addition of an image or text to the original image, but in this paper was proposed another type of watermark is add curves, line or forms have been drawn by interpolation, which produces watermark difficult to falsify and manipulate it. Our work suggests new techniques of watermark images which is embedding Cubic-spline interpolation inside the image using Bit Plane Slicing. The Peak to Signal Noise Ratio (PSNR) and Mean Square Error (MSE) value is calculated so that the quality of the original i

This work include synthesized and characterization the compound [I] by reaction 1,4-phenylenediamine with chloro acetic acid then this compound reaction with methanol in present sulfuric acid to synthesized ester compound [II] after that reaction with hydrazine hydrate to synthesized acide hydrazide [III] and the later compound reaction with substituted acetophenone[IV]n to synthesized substituted acetophenone hydrazones[V-XI]. In addition synthesized4-formylpyrazole derivatives [XIIXVIII] via cyclisation substituted acetophenone hydrazones [V-XI] with Vilsmeier-Haack reagent DMF/POCl3. The compounds characterized by melting points, FTIR, 1HNMR and mass spectroscopy. The mesomorphic behavior studied by using polarized optical microscopy and

In this paper some chalcones (C1-C8) are prepared based on the reaction of one mole of substituted acetophenone with one mole of substituted benzaldehydes in the presence of (40%) sodium hydroxide as a base. Pyrazolines (P1–P8) are prepared from the reaction of chalcones (C1-C8) with hydrazine hydrate. Isoxazoline (I1-I8) is prepared from the reaction of chalcones (C1-C8) with hydroxyl amine hydrochloride in the presence of (10%) sodium hydroxide as a base. These compounds are characterized by using various physical and spectral methods. The compounds are screened for their in vitro antibacterial activity using gram-positive bacteria and gram-negative bacteria. Several derivatives of pyrazolines and isoxazolines are produced well to moder

Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

In this work, a series of new maleimides linked to substituted benzothiazole moiety were synthesized. Synthesis of these new cyclic imides were performed via three steps, the first one involved preparation of a series of 2-aminobenzothiazole substituted with different substituents via reaction of different primary aromatic amines with ammonium thiocyanate and bromine in glacial acetic acid. The prepared 2- amino benzothiozoles were introduced in the second step in reaction with maleic anhydride producing a series of N-(substituted benzothiazole-2-yl) maleamic acids.The resulted maleamic acids were dehydrated in the third step via treatment with acetic anhydride and anhydrous sodium acetate to afford a series of the desirable N-(substitu

The ligand Schiff base [(E)-3-(2-hydroxy-5-methylbenzylideneamino)- 1- phenyl-1H-pyrazol-5(4H) –one] with some metals ion as Mn(II); Co(II); Ni(II); Cu(II); Cd(II) and Hg(II) complexes have been preparation and characterized on the basic of mass spectrum for L, elemental analyses, FTIR, electronic spectral, magnetic susceptibility, molar conductivity measurement and functions thermodynamic data study (∆H°, ∆S° and ∆G°). Results of conductivity indicated that all complexes were non electrolytes. Spectroscopy and other analytical studies reveal distorted octahedral geometry for all complexes. The antibacterial activity of the ligand and preparers metal complexes was also studied against gram and negative bacteria.