混合方次的Waring——Goldbach问题

研究混合方次的Waring--Goldbach     

凹角区域双曲外问题的精确人工边界条件

研究一类凹角区域双曲型外问题的数值方法.先用Newmark方法对时间进行离散化,在每个时间步求解一个椭圆外问题.然后引入人工边界,并获得精确的人工边界条件.给出半离散化问题的变分问题,证明了变分问题的适定性,并给出了误差估计.最后给出数值例子,以示该方法的可行性与有效性.     

Constructing orthogonal pandiagonal Latin squares and panmagic squares from modular n‐queens solutions

In this article, we show how to construct pairs of orthogonal pandiagonal Latin squares and panmagic squares from certain types of modular n‐queens solutions. We prove that when these modular n‐queens solutions are symmetric, the panmagic squares thus constructed will be associative, where for an n × n associative magic square A = (a_ij), for all i and j it holds that a_ij + an?i?1,n?j?1 = c for a fixed c. We further show how to construct orthogonal Latin squares whose modular difference diagonals are Latin from any modular n‐queens solution. As well, we analyze constructing orthogonal pandiagonal Latin squares from particular classes of non‐linear modular n‐queens solutions. These pandiagonal Latin squares are not row cyclic, giving a partial solution to a problem of Hedayat. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 221–234, 2007     

On solving energy-dependent partitioned eigenvalue problem by genetic algorithm: The case of real symmetric Hamiltonian matrices

An energy-dependent partitioning scheme is explored for extracting a small number of eigenvalues of a real symmetric matrix with the help of genetic algorithm. The proposed method is tested with matrices of different sizes (30 × 30 to 1000 × 1000). Comparison is made with Löwdin’s strategy for solving the problem. The relative advantages and disadvantages of the GA-based method are analyzed     

A competitive algorithm in searching for many edges in a hypergraph

We give a competitive algorithm to identify all d defective edges in a hypergraph with d unknown. Damaschke did the d=1 case for 2-graphs, Triesch extended the d=1 case to r-graphs, and Johann did the general d case for 2-graphs. So ours is the first attempt to solve the searching for defective edges problem in its full generality. Further, all the above three papers assumed d known. We give a competitive algorithm where d is unknown.     

Regularization of some linear ill-posed problems with discretized random noisy data

For linear statistical ill-posed problems in Hilbert spaces we introduce an adaptive procedure to recover the unknown solution from indirect discrete and noisy data. This procedure is shown to be order optimal for a large class of problems. Smoothness of the solution is measured in terms of general source conditions. The concept of operator monotone functions turns out to be an important tool for the analysis.

     

Blow Up of Solutions to Semilinear Wave Equations with Critical Exponent in High Dimensions

In this paper, the author considers the Cauchy problem for semilinear wave equations with critical exponent in n≥4 space dimensions. Under some positivity conditions on the initial data, it is proved that there can be no global solutions no matter how small the initial data are.     

Deformations of functionals and bifurcations of extremals

We study homology characteristics of critical values and extremals of Lipschitz functionals defined on bounded closed convex subsets of a reflexive space that are invariant under deformations. Sufficient conditions for the existence of a bifurcation point of a multivalued potential operator (the switch principle for the typical number of an extremal) are established.     

The Cauchy Problem of the Nonlinear Schr■dinger Equations in R~(1 1)

In this paper,we consider the local and global solution for the nonlinear Schrdinger equationwith data in the homogeneous and nonhomogeneous Besov space and the scattering result for small data.Thetechniques to be used are adapted from the Strichartz type estimate,Kato's smoothing effect and the maximalfunction(in time)estimate for the free Schrdinger operator.     

Inverse Piston Problem for the System of One-Dimensional Isentropic Flow

In this paper, the authors consider the inverse piston problem for the system of one-dimensional isentropic flow and obtain that, under suitable conditions, the piston velocity can be uniquely determined by the initial state of the gas on the right side of the piston and the position of the forward shock.