Applications of interval arithmetic in solving polynomial equations by Wu''''s elimination method

Wu's elimination method is an important method for solving multivariate poly- nomial equations.In this paper,we apply interval arithmetic to Wu's method and convert the problem of solving polynomial equations into that of solving interval polynomial equa- tions.Parallel results such as zero-decomposition theorem are obtained for interval poly- nomial equations.The advantages of the new approach are two-folds:First,the problem of the numerical instability arisen from floating-point arithmetic is largely overcome.Second, the low efficiency of the algorithm caused by large intermediate coefficients introduced by exact compaction is dramatically improved.Some examples are provided to illustrate the effectiveness of the proposed algorithm.     

Chromatic Uniqueness of the Complement of T_m(l, 4, m - 6)

In the paper, we prove that the complement of Tm(1,4,m - 6)(m > 10) is chromatically unique if and only if m ≠5k(k ≥ 2).     

一类非线性抛物方程弱解的L~2 衰减(英文)

本文研究了非线性抛物方程弱解的L2 衰减 ,证明了若u是非线性抛物方程的一个弱解 ,则u满足‖u‖L2 ≤C( 1 t) -n/ 4,其中C是常数且仅依赖于初始值u0 的范数 .     

通过J/Ψ→N(N-)M衰变研究N*时的核子极点效应

研究了J／Ψ→pp^-π衰变过程中核子极点图的贡献，特别是由离壳效应带来的贡献．发现衰变宽度对形状因子是敏感的．在通过用J／Ψ→pp^-π衰变研究N^*时，核子极点图作为背景道的贡献是非常重要的；在通过J／Ψ→pp^-η和pp^-η研究N^*时，核子极点图的贡献可忽略不计；在通过J／Ψ→pp^-ω研究N^*时，核子极点图有明显的贡献．     

False Vacuum Decay with Gravity in a Critical Case

The vacuum decay in a de Sitter universe is studied for the class of effective inflaton potentials that curvature at the top is less than as well as greater than a critical value determined previously. By comparing the actions of the Hawking - Moss instanton and the Coleman - de Luccia instanton(s) the mode of vacuum decay is determined in this critical situation.     

Polynomial Stability to Three-Dimensional Magnetoelastic Waves

In this work we show that the energy associated to the linear three-dimensional magneto-elastic system decays polynomially to zero as time goes to infinity, provided the initial data is smooth enough.     

Specht modules and chromatic polynomials

An explicit formula for the chromatic polynomials of certain families of graphs, called bracelets', is obtained. The terms correspond to irreducible representations of symmetric groups. The theory is developed using the standard bases for the Specht modules of representation theory, and leads to an effective means of calculation.     

The interlace polynomial of a graph

Motivated by circle graphs, and the enumeration of Euler circuits, we define a one-variable “interlace polynomial” for any graph. The polynomial satisfies a beautiful and unexpected reduction relation, quite different from the cut and fuse reduction characterizing the Tutte polynomial.It emerges that the interlace graph polynomial may be viewed as a special case of the Martin polynomial of an isotropic system, which underlies its connections with the circuit partition polynomial and the Kauffman brackets of a link diagram. The graph polynomial, in addition to being perhaps more broadly accessible than the Martin polynomial for isotropic systems, also has a two-variable generalization that is unknown for the Martin polynomial. We consider extremal properties of the interlace polynomial, its values for various special graphs, and evaluations which relate to basic graph properties such as the component and independence numbers.     

Critical exponent for semilinear damped wave equations in the N-dimensional half space

We generalize a previous result of Ikehata (Math. Methods Appl. Sci., in press), which studies the critical exponent problem of a semilinear damped wave equation in the one-dimensional half space, to the general N-dimensional half space case. That is to say, one can show the small data global existence of solutions of a mixed problem for the equation u_tt−Δu+u_t=|u|^p with the power p satisfying p∗(N)=1+2/(N+1)<p?N/[N−2]+ if we deal with the problem in the N-dimensional half space.