In this work, a class of stochastically perturbed differential systems with standard Brownian motion of ordinary unperturbed differential system is considered and studied. The necessary conditions for the existence of a unique solution of the stochastic perturbed semi-linear system of differential equations are suggested and supported by concluding remarks. Some theoretical results concerning the mean square exponential stability of the nominal unperturbed deterministic differential system and its equivalent stochastically perturbed system with the deterministic and stochastic process as a random noise have been stated and proved. The proofs of the obtained results are based on using the stochastic quadratic Lyapunov function meth

   In this work, a novel technique to obtain an accurate solutions to nonlinear form by multi-step combination with Laplace-variational approach (MSLVIM) is introduced. Compared with the  traditional approach for variational it overcome all difficulties and enable to provide us more an accurate solutions with extended of the convergence region as well as covering to larger intervals which providing us a continuous representation of approximate analytic solution and it give more better information of the solution over the whole time interval. This technique is more easier for obtaining the general Lagrange multiplier with reduces the time and calculations. It converges rapidly to exact formula with simply computable terms wit

In this case report we discuss essential issue to be considered with regard to the clinical genetic testing in the epilepsies. The identification of genes that influence risk for the epilepsies has extremely important implications for both research and clinical practice. In a research context, information obtained may lead to the development of new treatments targeted to specific mechanisms, or even to ways of preventing epileptogenesis. In clinical practice, the use of genetic information can either clarify the diagnosis in people already known or suspected to have epilepsy (diagnostic testing), or to predict onset of epilepsy in people at risk of developing epilepsy because of a family history (predictive testing). This 8-year old girl

In this paper, the continuous classical boundary optimal control problem (CCBOCP) for triple linear partial differential equations of parabolic type (TLPDEPAR) with initial and boundary conditions (ICs & BCs) is studied. The Galerkin method (GM) is used to prove the existence and uniqueness theorem of the state vector solution (SVS) for given continuous classical boundary control vector (CCBCV). The proof of the existence theorem of a continuous classical boundary optimal control vector (CCBOCV) associated with the TLPDEPAR is proved. The derivation of the Fréchet derivative (FrD) for the cost function (CoF) is obtained. At the end, the theorem of the necessary conditions for optimality (NCsThOP) of this problem is stated and prov

This paper aims to find new analytical closed-forms to the  solutions of the nonhomogeneous functional differential equations of the n^th order with finite and constants delays and various initial delay conditions in terms of elementary functions using Laplace transform method. As well as, the definition of dynamical systems for ordinary differential equations is used to introduce the definition of dynamical systems for delay differential equations which contain multiple delays with a discussion of their dynamical properties: The exponential stability and strong stability

    Our aim in this work is to study the classical continuous boundary control vector  problem for triple nonlinear partial differential equations of elliptic type involving a Neumann boundary control. At first, we prove that the triple nonlinear partial differential equations of elliptic type with a given classical continuous boundary control vector have a unique "state" solution vector,  by using the Minty-Browder Theorem. In addition, we prove the existence of a classical continuous boundary optimal control vector ruled by the triple nonlinear partial differential equations of elliptic type with equality and inequality constraints. We study the existence of the unique solution for the triple adjoint equations

In this research, the removal of cadmium (Cd) from simulated wastewater was investigated by using a fixed bed bio-electrochemical reactor. The effects of the main controlling factors on the performance of the removal process such as applied cell voltage, initial Cd concentration, pH of the catholyte, and the mesh number of the cathode were investigated. The results showed that the applied cell voltage had the main impact on the removal efficiency of cadmium where increasing the applied voltage led to higher removal efficiency. Meanwhile increasing the applied voltage was found to be given lower current efficiency and higher energy consumption.  No significant effect of initial Cd concentration on the removal efficie

In this research, the removal of cadmium (Cd) from simulated wastewater was investigated by using a fixed bed bio-electrochemical reactor. The effects of the main controlling factors on the performance of the removal process such as applied cell voltage, initial Cd concentration, pH of the catholyte, and the mesh number of the cathode were investigated. The results showed that the applied cell voltage had the main impact on the removal efficiency of cadmium where increasing the applied voltage led to higher removal efficiency. Meanwhile increasing the applied voltage was found to be given lower current efficiency and higher energy consumption.  No significant effect of initial Cd concentration on the removal efficiency of cadmium b

      In this paper, several types of space-time fractional partial differential equations has been solved by using most of special double linear integral transform ”double  Sumudu ”. Also, we are going to argue the truth of these solutions by another analytically method “invariant subspace method”. All results are illustrative numerically and graphically.