Acta Mathematicae Applicatae Sinica, English Series最新文献

Aiming at the problem that the asset’s fluctuation influences the borrower’s repayment ability, a loan with a new and flexible repayment method is designed, which depends on the asset value of the borrower. The repayment method can reduce the loan default probability, but it causes the uncertainty of the pay off time. Because the repayment term is related to the regular repayment amount in this method, a boundary for the regular repayment amount is set up in order to avoid too long repayment term. This will balance the benefit of borrowers and lenders and improve the applicability of this method. By establishing a mathematical model of the residual value of the loan, this model can be transformed into an initial-boundary problem of a partial differential equation. The analytic solution and the expected time to pay off the loan are obtained. Finally, numerical analysis are shown.

The strong chromatic index of a graph is the minimum number of colors needed in a proper edge coloring so that no edge is adjacent to two edges of the same color. An outerplane graph with independent crossings is a graph embedded in the plane in such a way that all vertices are on the outer face and two pairs of crossing edges share no common end vertex. It is proved that every outerplane graph with independent crossings and maximum degree Δ has strong chromatic index at most 4Δ − 6 if Δ ≥ 4, and at most 8 if Δ ≤ 3. Both bounds are sharp.

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.