Acta Mathematicae Applicatae Sinica, English Series最新文献

Interior-point methods (IPMs) for linear programming (LP) are generally based on the logarithmic barrier function. Peng et al. (J. Comput. Technol. 6: 61–80, 2001) were the first to propose non-logarithmic kernel functions (KFs) for solving IPMs. These KFs are strongly convex and smoothly coercive on their domains. Later, Bai et al. (SIAM J. Optim. 15(1): 101–128, 2004) introduced the first KF with a trigonometric barrier term. Since then, no new type of KFs were proposed until 2020, when Touil and Chikouche (Filomat. 34(12): 3957–3969, 2020; Acta Math. Sin. (Engl. Ser.), 38(1): 44–67, 2022) introduced the first hyperbolic KFs for semidefinite programming (SDP). They established that the iteration complexities of algorithms based on their proposed KFs are ({cal O}(n^{2 over 3} log {n over epsilon})) and ({cal O}(n^{3 over 4} log {n over epsilon})) for large-update methods, respectively. The aim of this work is to improve the complexity result for large-update method. In fact, we present a new parametric KF with a hyperbolic barrier term. By simple tools, we show that the worst-case iteration complexity of our algorithm for the large-update method is ({cal O}({sqrt n} log n log{n over epsilon})) iterations. This coincides with the currently best-known iteration bounds for IPMs based on all existing kind of KFs.

The algorithm based on the proposed KF has been tested. Extensive numerical simulations on test problems with different sizes have shown that this KF has promising results.

In this paper, a stochastic SEITR model is formulated to describe the transmission dynamics of tuberculosis with incompletely treatment. Sufficient conditions for the existence of a stationary distribution and extinction are obtained. In addition, numerical simulations are given to illustrate these analytical results. Theoretical and numerical results show that large environmental perturbations can inhibit the spread of tuberculosis.

Let X = {X(t), t ∈ ℝ₊} be a centered space anisotropic Gaussian process values in ℝ^d with non-stationary increments, whose components are independent but may not be identically distributed. Under certain conditions, then almost surely c₁ ≤ ϕ − m(X([0, 1])) ≤ c₂, where ϕ denotes the exact Hausdorff measure associated with function (phi left( s right) = {s^{{1 over {{alpha _k}}} + sumlimits_{i = 1}^k {left( {1 - {{{alpha _i}} over {{alpha _k}}}} right)} }}log ,log,{1 over s}) for some 1 ≤ k ≤ d, (α₁,⋯, α_d) ∈ (0, 1]^d. We also obtain the exact Hausdorff measure of the graph of X on [0, 1].

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.

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.

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.

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.

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 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.