The authors carry out numerical experiments with regard to the Monte Carlo integration method, using as input the pseudorandom vectors that are generated by the algorithm proposed in [Mok, C. P., Pseudorandom Vector G...
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The authors carry out numerical experiments with regard to the Monte Carlo integration method, using as input the pseudorandom vectors that are generated by the algorithm proposed in [Mok, C. P., Pseudorandom Vector Generation Using Elliptic Curves and Applications to Wiener Processes, Finite Fields and Their Applications, 85, 2023,102129], which is based on the arithmetic theory of elliptic curves over finite fields. They consider integration in the following two cases: The case of Lebesgue measure on the unit hypercube [0, 1]d, and as well as the case of Wiener measure. In the case of Wiener measure, the construction gives discrete time simulation of an independent sequence of standard Wiener processes, which is then used for the numerical evaluation of FeynmanKac formulas.
Dielectric properties of the hydrogen-bonded ferroelectric crystal KH_(2)PO_(4)(KDP)differ significantly from those of KD_(2)PO_(4)(DKDP).It is well established that deuteration affects the interplay of hydrogenbond s...
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Dielectric properties of the hydrogen-bonded ferroelectric crystal KH_(2)PO_(4)(KDP)differ significantly from those of KD_(2)PO_(4)(DKDP).It is well established that deuteration affects the interplay of hydrogenbond switches and heavy ion displacements that underlie the emergence of macroscopic polarization,but a detailed microscopic model is *** show that all-atompath integral molecular dynamics simulations can predict the isotope effects,revealing the microscopic mechanism that differentiates KDP and *** tunneling generates phosphate configurations that do not contribute to the *** low temperatures,these quantum dipolar defects are substantial in KDP but negligible in *** intrinsic defects explain why KDP has lower spontaneous polarization and transition entropy than *** prominent role of quantum fluctuations in KDP is related to the unusual strength of the hydrogen bonds and should be equally important in other crystals of the KDP family,which exhibit similar isotope effects.
The notion of Neutrosophic sets first introduced by Smarandache in 1998 as a generalization of intu-itionistic fuzzy sets. Furthermore, Al-Tahan in 2022 introduced the notion of NeutroHyperstructures. Inspired by this...
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Faced with the complexities of managing natural gas-dependent power system amid the surge of renewable integration and load unpredictability, this study explores strategies for navigating emergency transitions to cost...
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We obtain an asymptotic Hölder estimate for expectations of a quite general class of discrete stochastic processes. Such expectations can also be described as solutions to a dynamic programming principle or as so...
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In the present paper,we study uniqueness and nondegeneracy of positive solutions to the general Kirchhoff type equations-M(∫_(R^(N))|∇_(v)|^(2)dx)Δ^(v)=g(v)in R^(N);where M:[0;+∞)→R is a continuous function satisf...
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In the present paper,we study uniqueness and nondegeneracy of positive solutions to the general Kirchhoff type equations-M(∫_(R^(N))|∇_(v)|^(2)dx)Δ^(v)=g(v)in R^(N);where M:[0;+∞)→R is a continuous function satisfying some suitable conditions and v∈H^(1)(R^(N)).Applying our results to the case M(t)=at+b,a;b>0,we make it clear all the positive solutions for all dimensions N≥*** results can be viewed as a generalization of the corresponding results of Li et al.
In this paper,based on some prior estimates,we show that the essential spectrum λ=0 is a bifurcation point for a superlinear elliptic equation with only local conditions,which generalizes a series of earlier results ...
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In this paper,based on some prior estimates,we show that the essential spectrum λ=0 is a bifurcation point for a superlinear elliptic equation with only local conditions,which generalizes a series of earlier results on an open problem proposed by Stuart(1983).
Birds exhibit a variety of flight styles, primarily classified as flapping, which is characterized by rapid up-and-down wing movements, and soaring, which involves gliding with wings outstretched. Each species usually...
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Note that some classic fluid dynamical systems such as the Navier-Stokes equations, Magnetohydrodynamics (MHD for short), Boussinesq equations and etc., are observably different from each other but obey some energy in...
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Note that some classic fluid dynamical systems such as the Navier-Stokes equations, Magnetohydrodynamics (MHD for short), Boussinesq equations and etc., are observably different from each other but obey some energy inequalities of the similar *** this paper, the authors attempt to axiomatize the extending mechanism of solutions to these systems, merely starting from several basic axiomatized conditions such as the local existence, joint property of solutions and some energy inequalities. The results established have nothing to do with the concrete forms of the systems and, thus, give the extending mechanisms in a unified way to all systems obeying the axiomatized conditions. The key tools are several new multiplicative interpolation inequalities of Besov type, which have their own interests.
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