In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].

The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.

We study the physics of flow due to the interaction between a viscous dipole and boundaries that permit slip. This includes partial and free slip, and interactions near corners. The problem is investigated by using a two relaxation time lattice Boltzmann equation with moment-based boundary conditions. Navier-slip conditions, which involve gradients of the velocity, are formulated and applied locally. The implementation of free-slip conditions with the moment-based approach is discussed. Collision angles of 0°, 30°, and 45° are investigated. Stable simulations are shown for Reynolds numbers between 625 and 10 000 and various slip lengths. Vorticity generation on the wall is shown to be affected by slip length, angle of incidence,

A novel technique Sumudu transform Adomian decomposition method (STADM), is employed to handle some kinds of nonlinear time-fractional equations. We demonstrate that this method finds the solution without discretization or restrictive assumptions. This method is efficient, simple to implement, and produces good results. The fractional derivative is described in the Caputo sense. The solutions are obtained using STADM, and the results show that the suggested technique is valid and applicable and provides a more refined convergent series solution. The MATLAB software carried out all the computations and graphics. Moreover, a graphical representation was made for the solution of some examples. For integer and fractional order problems, solutio

This paper deals with the Magnetohydrodynyamic (Mill)) flow for a viscoclastic fluid of the generalized Oldroyd-B model. The fractional calculus approach is used to establish the constitutive relationship of the non-Newtonian fluid model. Exact analytic solutions for the velocity and shear stress fields in terms of the Fox H-function are obtained by using discrete Laplace transform. The effect of different parameter that controlled the motion and shear stress equations are studied through plotting using the MATHEMATICA-8 software.

A new class of higher derivatives  for harmonic univalent functions defined by a generalized fractional integral operator inside an open unit disk E is the aim of this paper.

Determination of the level of adipokines (obestatin, vaspin, tumor necrosis factor-? and interleukin-6)in hypo-and hyperthyroid patients from Educational Baghdad Hospital in Baghdad City was investigated. Fifty patients with hypothyroidism and Fifty patients with hyperthyroidism were selected. A control group of thirty euthyroid persons was included. Blood was collected by vein puncture and serum was separated and stored at –20C. Adipokines (obestatin, vaspin, tumor necrosis factor-? and interleukin-6) were estimated using ELISA method. The findings show a significant (p<0.05) increase in obestatin level in hypothyroid patients, while there is no significant difference in hyperthyroid patientsas compared with the euthyroid subjects.

   This study aimed to evaluate the reservoir petrophysical properties (porosity, water saturation, and permeability) for optimal flow unit assessment within the Sadi Formation. Utilizing open hole logging data from five wells, the Sadi formation was divided into two rock units. The upper unit (A) is 45-50 meters thick, mainly consisting of limestone, mainly consisting of shaly limestone at the lower part. The lower unit (B) has a thickness of approximately 75-80 meters and is primarily composed of limestone, further subdivided into three subunits (B1, B2, B3). The average water resistivity is 0.04 ohm-m, and the average mud filtrate resistivity is 0.06 ohm-m. The Pickett plot was utilized to determine Archie parameters (tortuosit