In this paper we use the symmetry reduction method to obtain invariant solutions of the ideal magnetohydrodynamic equations in (3+1) dimensions. These equations are invariant under a Galilean-similitude Lie algebra for which the classification by conjugacy classes of r-dimensional subalgebras (1 ≤ r ≤ 4) was already known. So we restrict our study to the three-dimensional Galilean-similitude su...

Computing an invariant of a graph such as treewidth and pathwidth is one of the fundamental problems in graph algorithms. In general, determining the pathwidth of a graph is NP-hard. In this paper, we propose several reduction methods for decreasing the instance size without changing the pathwidth, and implemented the methods together with an exact algorithm for computing pathwidth of graphs. O...

We give a generating function for the number of pairs n×n matrices (A,B) over finite field that are mutually annihilating, namely, AB=BA=0. This can be viewed as singular analogue series considered by Cohen and Lenstra. show this has factorization allows it to meromorphically extended entire complex plane. also use count annihilating nilpotent matrices. work is essentially study motivic aspects...

The statistical mechanics of a noninteracting polymer chain in the limit of a large number of monomers is considered when the total angular momentum L is fixed. The radius of gyration for a ring polymer in this situation is derived exactly in closed form by functional integration techniques. Even when L=0 the radius of gyration differs from that of a random walk by a prefactor of order unity. T...

We provide simple formulas that can be used to calculate ideal bootstrap or exact recombination estimates of group statistics from experimental data. When resampling is done over small numbers of groups, the ideal bootstrap is more accurate than the exact recombinant estimate, however the former is biased. For large sample sizes there is no discernable difference between the two approaches and ...

Given an undirected graph with weight for each vertex, the maximum weight clique problem is to find the clique of the maximum weight. Östergård proposed a fast exact algorithm for solving this problem. We show his algorithm is not efficient for very dense graphs. We propose an exact algorithm for the problem, which is faster than Östergård’s algorithm in case the graph is dense. We show the eff...