In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

The research aims to know the impact of the innovative matrix strategy and the problem tree strategy in teaching mathematics to intermediate grade female students on mathematical proficiency. To achieve the research objectives, an experimental approach and a quasi-experimental design were used for two equivalent experimental groups. The first is studied according to the innovative matrix strategy, the second group is studied according to the problem tree strategy. The research sample consisted of (32) female students of the first intermediate grade, who were intentionally chosen after ensuring their equivalence, taking into several factors, most notably (chronological age, previous achievement, and intelligence test). The research tools con

The determination of critical micelle concentration of selected non-ionic surfactants (Tween 20,40 and 80) have been investigated using magnetic water(MW)as an aqueous medium.Conductometry technique is used to determine critical micelle concentration.The effect of alcohol addition and temperature variation at the range(293.15 -303.15K) are also pursued. It is concluded that the process of micellization is spontaneous and endothermic because of the observed free energy of micellization (ΔG^om) , enthalpy change of micellization  (ΔH^om), and entropy change of micellization (ΔS^om) for the system was also studied.The properties of the non-ionic surfactants were studied, both in absence and presence of

This paper is concerned with combining two different transforms to present a new joint transform FHET and its inverse transform IFHET. Also, the most important property of FHET was concluded and proved, which is called the finite Hankel – Elzaki transforms of the Bessel differential operator property, this property was discussed for two different boundary conditions, Dirichlet and Robin. Where the importance of this property is shown by solving axisymmetric partial differential equations and transitioning to an algebraic equation directly. Also, the joint Finite Hankel-Elzaki transform method was applied in solving a mathematical-physical problem, which is the Hotdog Problem. A steady state which does not depend on time was discussed f

Wireless Body Area Network (WBAN) is a tool that improves real-time patient health observation in hospitals, asylums, especially at home. WBAN has grown popularity in recent years due to its critical role and vast range of medical applications. Due to the sensitive nature of the patient information being transmitted through the WBAN network, security is of paramount importance. To guarantee the safe movement of data between sensor nodes and various WBAN networks, a high level of security is required in a WBAN network. This research introduces a novel technique named Integrated Grasshopper Optimization Algorithm with Artificial Neural Network (IGO-ANN) for distinguishing between trusted nodes in WBAN networks by means of a classifica

this paper presents a novel method for solving nonlinear optimal conrol problems of regular type via its equivalent two points boundary value problems using the non-classical

Today’s academics have a major hurdle in solving combinatorial problems in the actual world. It is nevertheless possible to use optimization techniques to find, design, and solve a genuine optimal solution to a particular problem, despite the limitations of the applied approach. A surge in interest in population-based optimization methodologies has spawned a plethora of new and improved approaches to a wide range of engineering problems. Optimizing test suites is a combinatorial testing challenge that has been demonstrated to be an extremely difficult combinatorial optimization limitation of the research. The authors have proposed an almost infallible method for selecting combinatorial test cases. It uses a hybrid whale–gray wol

Artificial fish swarm algorithm (AFSA) is one of the critical swarm intelligent algorithms. In this
paper, the authors decide to enhance AFSA via diversity operators (AFSA-DO). The diversity operators will
be producing more diverse solutions for AFSA to obtain reasonable resolutions. AFSA-DO has been used to
solve flexible job shop scheduling problems (FJSSP). However, the FJSSP is a significant problem in the
domain of optimization and operation research. Several research papers dealt with methods of solving this
issue, including forms of intelligence of the swarms. In this paper, a set of FJSSP target samples are tested
employing the improved algorithm to confirm its effectiveness and evaluate its ex

level of effectiveness of Glutathione - S - Transferees (GST), Glutathione peroxides (GPX),Malondialdehyde (MDA) the product of lipid peroxidation and some trace elements ( zinc,seleinum,iron ,copper ) had been measured in sera of (50) women with breast disease.which had been divided to : Control group (25),The first group (A) benign breast tumors (25),the second group (B) breast cancer (25). The results showed a clear moral high level of Glutathione - S - Transferees (GST), Glutathione peroxidase (GPX) , and Malondialdehyde (MDA) level in breast cancer group while a slight increase were observed in the levels of these enzymes and(MDA) in benign breast group. A significant reduction was evident in the levels of selenium and zinc