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.
Surface parameterizations are widely applied in computer graphics,medical imaging,and transformation *** this paper,we rigorously derive the gradient vector and Hessian matrix of the discrete conformal energy for sphe...
Surface parameterizations are widely applied in computer graphics,medical imaging,and transformation *** this paper,we rigorously derive the gradient vector and Hessian matrix of the discrete conformal energy for spherical conformal parameterizations of simply connected closed surfaces of *** addition,we give the sparsity structure of the Hessian matrix,which leads to a robust Hessian-based trust region algorithm for the computation of spherical conformal *** experiments demonstrate the local quadratic convergence of the proposed algorithm with low conformal *** subsequently propose an application of our method to surface registrations that still maintain local quadratic convergence.
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.
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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The numerical integration of phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties of the solution such as energy dissipation and maximum *** the theory of energy d...
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The numerical integration of phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties of the solution such as energy dissipation and maximum *** the theory of energy dissipation for classical phase field models is well established,the corresponding theory for time-fractional phase-field models is still *** this article,we study certain nonlocal-in-time energies using the first-order stabilized semi-implicit L1 *** particular,we will establish a discrete fractional energy law and a discrete weighted energy *** extension for a(2-α)-order L1 scalar auxiliary variable scheme will be ***,we demonstrate that the energy bound is preserved for the L1 schemes with nonuniform time *** numerical experiments are carried to verify our theoretical analysis.
We devise fast and provably accurate algorithms to transform between an N × N × N Cartesian voxel representation of a three-dimensional function and its expansion into the ball harmonics, that is, the eigenb...
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Let R be a unitary operator whose spectrum is the circle. We show that the set of unitaries U which essentially commute with R (i.e., [U, R] ≡ UR − RU is compact) is path-connected. Moreover, we also calculate the se...
Physics-informed deep learning approaches have been developed to solve forward and inverse stochastic differential equation (SDE) problems with high-dimensional stochastic space. However, the existing deep learning mo...
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In this manuscript, we introduce a novel Decision Flow (DF) framework for sampling decisions from a target distribution while incorporating additional guidance from a prior sampler. DF can be viewed as an AI-driven al...
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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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