This paper included derivative method for the even r power sums of even integer numbers formula to approach high even (r+2) power sums of even integer numbers formula so on we can approach from derivative odd r power sums of even integer numbers formula to high odd (r+2) power sums of even integer numbers formula this derivative excellence have ability to used by computer programming language or any application like Microsoft Office Excel. Also this research discovered the relationship between r power sums of even integer numbers formula and both formulas for same power sums of odd integer numbers formula and for r power sums of all integer numbers formula in another way.

Activation of farnesoid X receptor (FXR) markedly attenuates development of atherosclerosis in animal models. However, the underlying mechanism is not well elucidated. Here, we show that the FXR agonist, obeticholic acid (OCA), increases fecal cholesterol excretion and macrophage reverse cholesterol transport (RCT) dependent on activation of hepatic FXR. OCA does not increase biliary cholesterol secretion, but inhibits intestinal cholesterol absorption. OCA markedly inhibits hepatic cholesterol 7α‐hydroxylase (Cyp7a1) and sterol 12α‐hydroxylase (Cyp8b1) partly through inducing small heterodimer partner, leading to reduced bile acid pool size and al

This research was conducted to study the feasibility of using fruit peels as biosorbent for removal of Pb⁺², Cu⁺² and Zn⁺² ions from simulated wastewater. A waste biomass of Pomegranate Peel or Punicagranatum L. (P. granatum L.) was chosen as neutral biosorbent in this study.Fourier transformation infrared (FTIR) was used to characterize the surface of PGP, the results confirm that amino, carboxylic, hydroxyl and carbonyl group on the surface of PGP. Different parameters such as initial concentration range between (25-200) mg/L, pH (3-7), contact time (1-2) hour, amount of sorbent (0.1- 4) gm, agitation speed range (200- 500) rpm and temperature (25- 50^oC), influencing the sorp

The present study aims to evaluate the biosorption of reactive orange dye by using garden grass. Experiments were carried out in a batch reactor to obtain equilibrium and thermodynamic data. Experimental parameters affecting the biosorption process such as pH, shaking time, initial dye concentrations, and temperature were thoroughly examined. The optimum pH for removal was found to be 4. Fourier transform infrared spectroscopy analysis indicated that the electronegative groups on the surface of garden grass were the major groups responsible for the biosorption process. Four sorption isotherm models were employed to analyze the experimental data of which Temkin and Pyzhey model was found to be most suitable one. The maxim

     Fractional calculus has paid much attention in recent years, because it plays an essential role in many fields of science and  engineering, where the study of stability theory of fractional differential equations emerges to be very important. In this paper, the stability of fractional order ordinary differential equations will be studied and introduced the backstepping method. The Lyapunov function  is easily found by this method. This method also gives a guarantee of stable solutions for the fractional order differential equations. Furthermore it gives asymptotically stable.

Abstract: Despite the distinct features of the continuous wave (CW) Terahertz (THz) emitter using photomixing technique, it suffers from the relatively low radiation output power. Therefore, one of effective ways to improve the photomixer emitter performance was using nanodimensions electrodes inside the optical active region of the device. Due to the nanodimension sizes and good electrical conductivity of silver nanowires (Ag-NWs), they have been exploited as THz emitter electrodes. The excited surface plasmon polariton waves (SPPs) on the surface of nanowire enhances the incident excitation signal. Therefore, the photomixer based Ag-NW compared to conventional one significantly exhibits higher THz output signal. In thi

This paper is illustrates the sufficient conditions of the uniformly asymptotically stable and the bounded of the zero solution of fifth order nonlinear differential equation with a variable delay τ(t)

The current research aims to identify 1) the differences of emotional stability development level according to the variable of age; and 2) the differences of emotional stability development level according to the variable of gender (male, female). This study employed a descriptive approach, whereby a total of 165 primary and secondary school student was randomly selected from the directorate of AL -rusafa side (1^st rusafa) of Baghdad province to constitute the sample of the study. The questionnaire was created based on the previous testes and studies that are relevant to emotional stability, and all its psychometrics features were examined. The researcher analyzed the data using SPSS statistic

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.