Current Issue : October-December Volume : 2022 Issue Number : 4 Articles : 5 Articles
In this paper, we study the problem of solving Seal’s type partial integro-differential equations (PIDEs) for the classical compound Poisson risk model. A data-driven deep neural network (DNN) method is proposed to calculate finite-time survival probability, and an alternative scheme is also investigated when claim payments are exponentially distributed. The DNN method is then extended to the numerical solution of generalized PIDEs. Numerical approximation results under different claim distributions are given, which show that the proposed scheme can obtain accurate results under different claim distributions....
We envision utilizing the versatility of a Computer Algebra System, specifically Mathematica to explore designing physics problems. As a focused project, we consider for instance a thermo-mechanical-physics problem showing its development from the ground up. Following the objectives of this investigation first by applying the fundamentals of physics principles we solve the problem symbolically. Applying the solution we investigate the sensitivities of the quantities of interest for various scenarios generating feasible numeric parameters. Although a physics problem is investigated, the proposed methodology may as well be applied to other scientific fields. The codes needed for this particular project are included enabling the interested reader to duplicate the results, extend and modify them as needed to explore various extended scenarios....
The geometrical effect is one of the most important factors in the kinetic modeling of crowd evacuation, besides the interaction between agents. More precisely, in the process of crowd evacuation, agents have the desire to reach the exit, and the ability to avoid the walls or obstacles. In this study, we propose the evacuation vector field which incorporates the geometrical effects in crowd evacuation. This is useful for modeling the crowd evacuation from complex venue....
In this paper, we establish discrete flexural lattice chain models of Bragg and locally resonant phononic crystals by setting mass defect atoms and local resonant elements on the flexural lattice chain. The bandgap characteristics of flexural wave in phononic crystals are studied by establishing the governing equations of the model. The results from models show that with the change of the mass ratio of defective atoms to normal atoms, the bandgap of the flexural wave produced by Bragg scattering shows a certain rule. When the local resonant bandgap and Bragg scattering bandgap are close to each other, the two bandgaps will be coupled to form a wider flexural wave bandgap. The effect of axial strain on bending wave propagation is only the shift of bandgap position. The effect of material damping on the propagation of a bending wave is only energy dissipation at high frequency. In addition, we use finite element simulation to calculate the bandgap of flexural wave in phononic crystals with mass defects, and the results are consistent with lattice chain model. This shows that lattice chain model can effectively guide the bandgap design of phononic crystals. This comprehensive study may help to elucidate the rule of bandgap generation of flexural wave in one-dimensional phononic crystals....
In this paper, we obtain some new weighted Hermite–Hadamard-type inequalities for (n + 2)−convex functions by utilizing generalizations of Steffensen’s inequality via Taylor’s formula....
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