Acta Mathematicae Applicatae Sinica, English Series最新文献

In this paper, we study mulit-dimensional oblique reflected backward stochastic differential equations (RBSDEs) in a more general framework over finite or infinite time horizon, corresponding to the pricing problem for a type of real option. We prove that the equation can be solved uniquely in L^p(1 < p ≤ 2)-space, when the generators are uniformly continuous but each component taking values independently. Furthermore, if the generator of this equation fulfills the infinite time version of Lipschitzian continuity, we can also conclude that the solution to the oblique RBSDE exists and is unique, despite the fact that the values of some generator components may affect one another.

Let G be a graph. We use χ(G) and ω(G) to denote the chromatic number and clique number of G respectively. A P₅ is a path on 5 vertices, and an HVN is a K₄ together with one more vertex which is adjacent to exactly two vertices of K₄. Combining with some known result, in this paper we show that if G is (P₅, HVN)-free, then χ(G) ≤ max{min{16, ω(G) + 3}, ω(G) + 1}. This upper bound is almost sharp.

Follow-up experimental designs are widely applied to explore the relationship between factors and responses step by step in various fields such as science and engineering. When some additional resources or information become available after the initial design of experiment is carried out, some additional runs and/or factors may be added in the follow-up stage. In this paper, the issue of the uniform row augmented designs and column augmented designs with mixed two-, three- and four-level is investigated. The uniformity of augmented designs is discussed under the wrap-around L₂-discrepancy. Some lower bounds of wrap-around L₂-discrepancy for the augmented designs are obtained, which can be used to assess uniformity of augmented design. Numerical results show that augmented designs have high efficiency, which have low discrepancy and close to the proposed lower bounds.

An incidence of a graph G is a vertex-edge pair (v, e) such that v is incidence with e. A conflict-free incidence coloring of a graph is a coloring of the incidences in such a way that two incidences (u, e) and (v, f) get distinct colors if and only if they conflict each other, i.e., (i) u = v, (ii) uv is e or f, or (iii) there is a vertex w such that uw = e and vw = f. The minimum number of colors used among all conflict-free incidence colorings of a graph is the conflict-free incidence chromatic number. A graph is outer-1-planar if it can be drawn in the plane so that vertices are on the outer-boundary and each edge is crossed at most once. In this paper, we show that the conflict-free incidence chromatic number of an outer-1-planar graph with maximum degree Δ is either 2Δ or 2Δ + 1 unless the graph is a cycle on three vertices, and moreover, all outer-1-planar graphs with conflict-free incidence chromatic number 2Δ or 2Δ + 1 are completely characterized. An efficient algorithm for constructing an optimal conflict-free incidence coloring of a connected outer-1-planar graph is given.

The Ananthakrishna model, seeking to explain the Portevin-Le Chatelier effect, is studied with or without non-synchronous perturbations. For the unperturbed model, Bogdanov-Takens bifurcation and zero-Hopf bifurcation are detected. For the perturbed model, rich dynamical behaviors are given by researching the Poincaré map, including solutions of different periods, quasi-periodic solutions, chaotic solutions, and bistability. Moreover, an augmented temperature-dependent perturbation amplitude induces a transition from non-serrated to serrated flow on the stress-time curve. Notably, on the stress-strain curve, the phenomenon of repeated yielding diminishes with an increase in the value of a temperature-dependent parameter, while it persists with an increase in the value of a temperature-independent parameter. Sensitivity analysis sheds light on the factors exerting the most significant influence on dislocation density.

In this paper, we obtain the thickness for some complete k–partite graphs for k = 2, 3. We first compute the thickness of K_n,n+8 by giving a planar decomposition of K_4k−1,4k+7 for k ≥ 3. Then, two planar decompositions for K_1,g,g(g−1) when g is even and for (K_{1,g,{1over{2}}(g-1)^{2}}) when g is odd are obtained. Using a recursive construction, we also obtain the thickness for some complete tripartite graphs. The results here support the long-standing conjecture that the thickness of K_m,n is (lceil {mnover{2(m+n-2)}}rceil) for any positive integers m, n.

In this paper, we prove an existence and uniqueness theorem for backward doubly stochastic differential equations under a new kind of stochastic non-Lipschitz condition which involves stochastic and time-dependent condition. As an application, we use the result to obtain the existence of stochastic viscosity solution for some nonlinear stochastic partial differential equations under stochastic non-Lipschitz conditions.

This paper is devoted to solving a reflected backward stochastic differential equation (BSDE in short) with one continuous barrier and a quasi-linear growth generator g, which has a linear growth in (y, z), except the upper direction in case of y < 0, and is more general than the usual linear growth generator. By showing the convergence of a penalization scheme we prove existence and comparison theorem of the minimal L^p (p > 1) solutions for the reflected BSDEs. We also prove that the minimal L^p solution can be approximated by a sequence of L^p solutions of certain reflected BSDEs with Lipschitz generators.

The purpose of this work is to investigate the existence and uniqueness of weak solutions to the initial-boundary value problem for a coupled system of an incompressible non-Newtonian fluid and the Vlasov equation. The coupling arises from the acceleration in the Vlasov equation and the drag force in the incompressible viscous non-Newtonian fluid with the stress tensor of a power-law structure for (pgeqslant {11over 5}). The main idea of the existence analysis is to reformulate the coupled system by means of a so-called truncation function. The advantage of the new formulation is to control the external force term (G=-int_mathbb{{R}^{d}}(mathbf{u}-mathbf{v})fdmathbf{v} (d=2,3)). The global existence of weak solutions to the reformulated system is shown by using the Faedo-Galerkin method and weak compactness techniques. We further prove the uniqueness of weak solutions to the considered system.

The paper deals with a Cauchy problem for the chemotaxis system with the effect of fluid

where d ≥ 2. It is known that for each ϵ > 0 and all sufficiently small initial data (u₀, n₀, c₀) belongs to certain Fourier space, the problem possesses a unique global solution (u^ϵ, n^ϵ, c^ϵ) in Fourier space. The present work asserts that these solutions stabilize to (u^∞, n^∞, c^∞) as ϵ⁻¹ → 0. Moreover, we show that c^ϵ(t) has the initial layer as ϵ⁻¹ → 0. As one expects its limit behavior maybe give a new viewlook to understand the system.