Acta Mathematicae Applicatae Sinica, English Series最新文献

For an integer r ≥ 2 and bipartite graphs H_i, where 1≤ i ≤ r the bipartite Ramsey number br(H₁, H₂, …, H_r) is the minimum integer N such that any r-edge coloring of the complete bipartite graph K_N,N contains a monochromatic subgraph isomorphic to H_i in color i for some 1 ≤ i ≤ r. We show that if (r ge 3,{alpha _1},{alpha _2} > 0,{alpha _{j + 2}} ge [(j + 2)! - 1]sumlimits_{i = 1}^{j + 1} {{alpha _i}} ) for j = 1, 2, …, r −2, then (br({C_{2leftlfloor {{alpha _1},n} rightrfloor }},{C_{2leftlfloor {{alpha _2},n} rightrfloor }}, cdots ,{C_{2leftlfloor {{alpha _r},n} rightrfloor }}) = (sumlimits_{j = 1}^r {{alpha _j} + o(1))n} ).

Given two graphs G and H, the Ramsey number R(G,H) is the minimum integer N such that any two-coloring of the edges of K_N in red or blue yields a red G or a blue H. Let v(G) be the number of vertices of G and χ(G) be the chromatic number of G. Let s(G) denote the chromatic surplus of G, the number of vertices in a minimum color class among all proper χ(G)-colorings of G. Burr showed that (R(G,H) ge (v(G) - 1)(chi (H) - 1) + s(H)) if G is connected and (v(G) ge s(H)). A connected graph G is H-good if (R(G,H) = (v(G) - 1)(chi (H) - 1) + s(H)). Let tH denote the disjoint union of t copies of graph H, and let (G vee H) denote the join of G and H. Denote a complete graph on n vertices by K_n, and a tree on n vertices by T_n. Denote a book with n pages by B_n, i.e., the join ({K_2} vee overline {{K_n}} ). Erdős, Faudree, Rousseau and Schelp proved that T_n is B_m-good if (n ge 3m - 3). In this paper, we obtain the exact Ramsey number of T_n versus 2B₂- Our result implies that T_n is 2B₂-good if n ≥ 5.

In this paper, we present a minimum residual based gradient iterative method for solving a class of matrix equations including Sylvester matrix equations and general coupled matrix equations. The iterative method uses a negative gradient as steepest direction and seeks for an optimal step size to minimize the residual norm of next iterate. It is shown that the iterative sequence converges unconditionally to the exact solution for any initial guess and that the norm of the residual matrix and error matrix decrease monotonically. Numerical tests are presented to show the efficiency of the proposed method and confirm the theoretical results.

In this paper we mainly deal with the global well-posedness and large-time behavior of the 2D tropical climate model with small initial data. We first establish the global well-posedness of solution in the Besov space, then we obtain the optimal decay rates of solutions by virtue of the frequency decomposition method. Specifically, for the low frequency part, we use the Fourier splitting method of Schonbek and the spectrum analysis method, and for the high frequency part, we use the global energy estimate and the behavior of exponentially decay operator.

The spatial and spatiotemporal autoregressive conditional heteroscedasticity (STARCH) models receive increasing attention. In this paper, we introduce a spatiotemporal autoregressive (STAR) model with STARCH errors, which can capture the spatiotemporal dependence in mean and variance simultaneously. The Bayesian estimation and model selection are considered for our model. By Monte Carlo simulations, it is shown that the Bayesian estimator performs better than the corresponding maximum-likelihood estimator, and the Bayesian model selection can select out the true model in most times. Finally, two empirical examples are given to illustrate the superiority of our models in fitting those data.

This paper mainly studies the contact extension of conservative or dissipative systems, including some old and new results for wholeness. Then extension of contact system is corresponding to the symplectification of contact Hamiltonian system. This is a reciprocal process and the relation between symplectic system and contact system has been discussed. We have an interesting discovery that by adding a pure variable p, the slope of the tangent of the orbit, every differential system can be regarded as an independent subsystem of contact Hamiltonian system defined on the projection space of contact phase space.

A coloring of graph G is an injective coloring if its restriction to the neighborhood of any vertex is injective, which means that any two vertices get different colors if they have a common neighbor. The injective chromatic number χ_i(G) of G is the least integer k such that G has an injective k-coloring. In this paper, we prove that (1) if G is a planar graph with girth g ≥ 6 and maximum degree Δ ≥ 7, then χ_i(G) ≤ Δ + 2; (2) if G is a planar graph with Δ ≥ 24 and without 3,4,7-cycles, then χ_i(G) ≤ Δ + 2.

In this paper the authors discuss a numerical simulation problem of three-dimensional compressible contamination treatment from nuclear waste. The mathematical model, a nonlinear convection-diffusion system of four PDEs, determines four major physical unknowns: the pressure, the concentrations of brine and radionuclide, and the temperature. The pressure is solved by a conservative mixed finite volume element method, and the computational accuracy is improved for Darcy velocity. Other unknowns are computed by a composite scheme of upwind approximation and mixed finite volume element. Numerical dispersion and nonphysical oscillation are eliminated, and the convection-dominated diffusion problems are solved well with high order computational accuracy. The mixed finite volume element is conservative locally, and get the objective functions and their adjoint vector functions simultaneously. The conservation nature is an important character in numerical simulation of underground fluid. Fractional step difference is introduced to solve the concentrations of radionuclide factors, and the computational work is shortened significantly by decomposing a three-dimensional problem into three successive one-dimensional problems. By the theory and technique of a priori estimates of differential equations, we derive an optimal order estimates in L² norm. Finally, numerical examples show the effectiveness and practicability for some actual problems.

In order to measure the uncertainty of financial asset returns in the stock market, this paper presents a new model, called SV-dtC model, a stochastic volatility (SV) model assuming that the stock return has a doubly truncated Cauchy distribution, which takes into account the high peak and fat tail of the empirical distribution simultaneously. Under the Bayesian framework, a prior and posterior analysis for the parameters is made and Markov Chain Monte Carlo (MCMC) is used for computing the posterior estimates of the model parameters and forecasting in the empirical application of Shanghai Stock Exchange Composite Index (SSECI) with respect to the proposed SV-dtC model and two classic SV-N (SV model with Normal distribution) and SV-T (SV model with Student-t distribution) models. The empirical analysis shows that the proposed SV-dtC model has better performance by model checking, including independence test (Projection correlation test), Kolmogorov-Smirnov test(K-S test) and Q-Q plot. Additionally, deviance information criterion (DIC) also shows that the proposed model has a significant improvement in model fit over the others.

We consider a Neumann problem driven by a (p(z), q(z))-Laplacian (anisotropic problem) plus a parametric potential term with λ > 0 being the parameter. The reaction is superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter λ moves on

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