Interval methods for verified integration of initial value problems (IVPs) for ODEs have been used for more than 40 years. For many classes of IVPs, these methods have the ability to compute guaranteed error bounds for the flow of an ODE, where traditional methods provide only approximations to a solution. Overestimation, however, is a potential drawback of verified methods. For some problems, the computed error bounds become overly pessimistic, or integration even breaks down. The dependency problem and the wrapping effect are particular sources of overestimations in interval computations. Berz (see [1]) and his co-workers have developed Taylor model methods, which extend interval arithmetic with symbolic computations. The latter is an ef

In this work , an effective procedure of Box-Behnken based-ANN (Artificial Neural Network) and GA (Genetic Algorithm) has been utilized for finding the optimum conditions of wt.% of doping elements (Ce,Y, and Ge) doped-aluminizing-chromizing of Incoloy 800H . ANN and Box-Behnken design method have been implanted for minimizing hot corrosion rate k_p (10^-12g².cm^-4.s^-1) in Incoloy 800H at 900^oC . ANN was used for estimating the predicted values of hot corrosion rate k_p (10^-12g².cm^-4.s^-1) . The optimal wt.% of doping elements combination to obtain minimum hot corrosion rate was calculated using genetic alg

The problem of Bi-level programming is to reduce or maximize the function of the target by having another target function within the constraints. This problem has received a great deal of attention in the programming community due to the proliferation of applications and the use of evolutionary algorithms in addressing this kind of problem. Two non-linear bi-level programming methods are used in this paper. The goal is to achieve the optimal solution through the simulation method using the Monte Carlo method using different small and large sample sizes. The research reached the Branch Bound algorithm was preferred in solving the problem of non-linear two-level programming this is because the results were better.

In this study, an unknown force function dependent on the space in the wave equation is investigated. Numerically wave equation splitting in two parts, part one using the finite-difference method (FDM). Part two using separating variables method. This is the continuation and changing technique for solving inverse problem part in (1,2). Instead, the boundary element method (BEM) in (1,2), the finite-difference method (FDM) has applied. Boundary data are in the role of overdetermination data. The second part of the problem is inverse and ill-posed, since small errors in the extra boundary data cause errors in the force solution. Zeroth order of Tikhonov regularization, and several parameters of regularization are employed to decrease error

The rise of edge-cloud continuum computing is a result of the growing significance of edge computing, which has become a complementary or substitute option for traditional cloud services. The convergence of networking and computers presents a notable challenge due to their distinct historical development. Task scheduling is a major challenge in the context of edge-cloud continuum computing. The selection of the execution location of tasks, is crucial in meeting the quality-of-service (QoS) requirements of applications. An efficient scheduling strategy for distributing workloads among virtual machines in the edge-cloud continuum data center is mandatory to ensure the fulfilment of QoS requirements for both customer and service provider. E

In this paper, our purpose is to study the classical continuous optimal control (CCOC)  for quaternary nonlinear parabolic boundary value problems (QNLPBVPs). The existence and uniqueness theorem (EUTh) for the quaternary state vector solution (QSVS) of the weak form (WF) for the QNLPBVPs with a given quaternary classical continuous control vector (QCCCV) is stated and proved via the Galerkin Method (GM) and the first compactness theorem under suitable assumptions(ASSUMS). Furthermore, the continuity operator for the existence theorem of a QCCCV dominated by the QNLPBVPs is stated and proved under suitable conditions.

This research investigates the subject of the impact of wars (as a manifestation of crisis) on architecture, and the extent of continuing wars physical and moral results of wars, even after the end of the cause of the crisis. The impact of different rebuilding which exposed to the effects of the war seems different in crisis regions.

The problem of research is about the uncertainty of the impact of the way chooses for reconstructing the buildings after wars in the continuity of the crisis of war. The goals of this research are to clarify the influence of methods of reconstruction of buildings in a city chosen which is Beirut, on the continuation of the war crisis with the argument of demolishing and rebuilding newly or keeping tr

Background: The change in the concepts of cavity preparation and the development of reliable adhesive materials lead to the development of alternative methods of caries removal. Chemo-mechanical caries removal (CMCR) involves the chemical softening of carious dentin, followed by its removal with manual excavation. The present study was conducted to evaluate clinically the efficiency of caries removal using a new chemo-mechanical agent (Papacarie) compared to the conventional drilling method in reduction of total bacterial count. Material and methods: The study is a split mouth design. The sample composes from sixty mandibular deciduous molars teeth in thirty children, between six to nine years of age with bilateral class I deep occlusal car