Acta Mathematicae Applicatae Sinica, English Series最新文献

This article analyzes the Pareto optimal allocations, agreeable trades and agreeable bets under the maxmin Choquet expected utility (MCEU) model. We provide several useful characterizations for Pareto optimal allocations for risk averse agents. We derive the formulation descriptions for non-existence agreeable trades or agreeable bets for risk neutral agents. We build some relationships between ex-ante stage and interim stage on agreeable trades or bets when new information arrives.

This paper concerns a global optimality principle for fully coupled mean-field control systems. Both the first-order and the second-order variational equations are fully coupled mean-field linear FBSDEs. A new linear relation is introduced, with which we successfully decouple the fully coupled first-order variational equations. We give a new second-order expansion of Y^ε that can work well in mean-field framework. Based on this result, the stochastic maximum principle is proved. The comparison with the stochastic maximum principle for controlled mean-field stochastic differential equations is supplied.

In this paper, the authors discuss a three-dimensional problem of the semiconductor device type involved its mathematical description, numerical simulation and theoretical analysis. Two important factors, heat and magnetic influences are involved. The mathematical model is formulated by four nonlinear partial differential equations (PDEs), determining four major physical variables. The influences of magnetic fields are supposed to be weak, and the strength is parallel to the z-axis. The elliptic equation is treated by a block-centered method, and the law of conservation is preserved. The computational accuracy is improved one order. Other equations are convection-dominated, thus are approximated by upwind block-centered differences. Upwind difference can eliminate numerical dispersion and nonphysical oscillation. The diffusion is approximated by the block-centered difference, while the convection term is treated by upwind approximation. Furthermore, the unknowns and adjoint functions are computed at the same time. These characters play important roles in numerical computations of conductor device problems. Using the theories of priori analysis such as energy estimates, the principle of duality and mathematical inductions, an optimal estimates result is obtained. Then a composite numerical method is shown for solving this problem.

Let G = {G_i: i ∈ [n]} be a collection of not necessarily distinct n-vertex graphs with the same vertex set V, where G can be seen as an edge-colored (multi)graph and each G_i is the set of edges with color i. A graph F on V is called rainbow if any two edges of F come from different G_is’. We say that G is rainbow pancyclic if there is a rainbow cycle C_ℓ of length ℓ in G for each integer ℓ ∈ [3, n]. In 2020, Joos and Kim proved a rainbow version of Dirac’s theorem: If (delta ({G_i}) ge {n over 2}) for each i ∈ [n], then there is a rainbow Hamiltonian cycle in G. In this paper, under the same condition, we show that G is rainbow pancyclic except that n is even and G consists of n copies of ({K_{{n over 2},{n over 2}}}). This result supports the famous meta-conjecture posed by Bondy.

We investigate some relations between two kinds of semigroup regularities, namely the e-property and the eventual continuity, both of which contribute to the ergodicity for Markov processes on Polish spaces. More precisely, we prove that for Markov-Feller semigroup in discrete time and stochastically continuous Markov-Feller semigroup in continuous time, if there exists an ergodic measure whose support has a nonempty interior, then the e-property is satis ed on the interior of the support. In particular, it implies that, restricted on the support of each ergodic measure, the e-property and the eventual continuity are equivalent for the discrete-time and the stochastically continuous continuous-time Markov-Feller semigroups.

Let Ω be a bounded smooth domain in ℝ^N (N ≥ 3). Assuming that 0 < s < 1, (1 < p,q le {{N + 2s} over {N - 2s}}) with ((p,q) ne ({{N + 2s} over {N - 2s}},{{N + 2s} over {N - 2s}})), and a, b > 0 are constants, we consider the existence results for positive solutions of a class of fractional elliptic system below,

Under some assumptions of h_i(x, u, v, ∇u, ∇v)(i = 1, 2), we get a priori bounds of the positive solutions to the problem (1.1) by the blow-up methods and rescaling argument. Based on these estimates and degree theory, we establish the existence of positive solutions to problem (1.1).

In this paper, we consider a susceptible-infective-susceptible (SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique, the uniform boundedness of solution is established. In addition, the spatial-temporal risk index ({{cal R}_0}(rho)) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of ({{cal R}_0}(rho)) with respect to the diffusion coefficients of the infected d_I, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.

In this paper, we are concerned with the problem of the pathwise uniqueness of one-dimensional reflected stochastic differential equations with jumps under the assumption of non-Lipschitz continuous coefficients whose proof are based on the technique of local time.

The traditional simple random sampling (SRS) design method is ine cient in many cases. Statisticians proposed some new designs to increase e ciency. In this paper, as a variation of moving extremes ranked set sampling (MERSS), double MERSS (DMERSS) is proposed and its properties for estimating the population mean are considered. It turns out that, when the underlying distribution is symmetric, DMERSS gives unbiased estimators of the population mean. Also, it is found that DMERSS is more e cient than the SRS and MERSS methods for usual symmetric distributions (normal and uniform). For asymmetric distributions considered in this study, the DMERSS has a small bias and it is more e cient than SRS for usual asymmetric distribution (exponential) for small sample sizes.

The classical Archimedean approximation of π uses the semiperimeter or area of regular polygons inscribed in or circumscribed about a unit circle in ℝ² and it is well-known that by using linear combinations of these basic estimates, modern extrapolation techniques can greatly speed up the approximation process. Similarly, when n vertices are randomly selected on the circle, the semiperimeter and area of the corresponding random inscribed and circumscribing polygons are known to converge to π almost surely as n → ∞, and by further applying extrapolation processes, faster convergence rates can also be achieved through similar linear combinations of the semiperimeter and area of these random polygons. In this paper, we further develop nonlinear extrapolation methods for approximating π through certain nonlinear functions of the semiperimeter and area of such polygons. We focus on two types of extrapolation estimates of the forms ({{cal X}_n} = {cal S}_n^alpha {cal A}_n^beta ) and ({{cal Y}_n}(p) = {(alpha {cal S}_n^p + beta {cal A}_n^p)^{1/p}}) where α + β = 1, p ≠ 0, and ({{cal S}_n}) and ({{cal A}_n}) respectively represents the semiperimeter and area of a random n-gon inscribed in the unit circle in ℝ², and ({{cal X}_n}) may be viewed as the limit of ({{cal Y}_n}(p)) when p → 0. By deriving probabilistic asymptotic expansions with carefully controlled error estimates for ({{cal X}_n}) and ({{cal Y}_n}(p)), we show that the choice α = 4/3, β= −1/3 minimizes the approximation error in both cases, and their distributions are also asymptotically normal.