树的3-彩虹控制数的上界

对树的3-彩虹控制数进行研究,首先用构造法找到直径较小的树的3-彩虹控制数的上界.再通过分类讨论思想和数学归纳法得到一般的阶n大于等于5的树的3-彩虹控制数的上界.     

多参数双分数布朗运动相遇局部时的存在性和联合连续性

本文研究了两个相互独立的(N,d)双分数布朗运动BH1,K1和BH2,K2的相遇局部时的问题.利用Fourier分析,获得了相遇局部时的存在性和联合连续性的结果,推广了分数布朗运动相遇局部时的相关结果.     

A Fourier pseudospectral method for a generalized improved Boussinesq equation

In this article, we propose a Fourier pseudospectral method for solving the generalized improved Boussinesq equation. We prove the convergence of the semi‐discrete scheme in the energy space. For various power nonlinearities, we consider three test problems concerning the propagation of a single solitary wave, the interaction of two solitary waves and a solution that blows up in finite time. We compare our numerical results with those given in the literature in terms of numerical accuracy. The numerical comparisons show that the Fourier pseudospectral method provides highly accurate results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 995–1008, 2015     

Strong Circuit Double Cover of Some Cubic Graphs

Let C be a given circuit of a bridgeless cubic graph G. It was conjectured by Seymour that G has a circuit double cover (CDC) containing the given circuit C. This conjecture (strong CDC [SCDC] conjecture) has been verified by Fleischner and Häggkvist for various families of graphs and circuits. In this article, some of these earlier results have been improved: (1) if contains a Hamilton path or a Y‐tree of order less than 14, then G has a CDC containing C; (2) if is connected and , then G has a CDC containing C.     

A class of solvable reaction-diffusion processes on a Cayley tree

Considering the most general one-species reaction-diffusion processes on a Cayley tree, it has been shown that there exist two integrable models. In the first model, the reactions are the various creation processes, i.e. °°→•°, °°→•• and °•→••, and in the second model, only the diffusion process •°→°• exists. For the first model, the probabilities P_l(m;t), of finding m particles on the lth shell of the Cayley tree, have been found exactly, and for the second model, the functions P_l(1;t) have been calculated. It has been shown that these are the only integrable models if one restricts consideration to the L+1-shell probabilities P(m₀,m₁,…,m_L;t).     

Top–down glycolipidomics: fragmentation analysis of ganglioside oligosaccharide core and ceramide moiety by chip‐nanoelectrospray collision‐induced dissociation MS2–MS6

We developed a straightforward approach for high‐throughput top–down glycolipidomics based on fully automated chip‐nanoelectrospray (nanoESI) high‐capacity ion trap (HCT) multistage mass spectrometry (MSⁿ) by collision‐induced dissociation (CID) in the negative ion mode. The method was optimized and tested on a polysialylated ganglioside fraction (GT1b), which was profiled by MS¹ and sequenced in tandem MS up to MS⁶ in the same experiment. Screening of the fraction in the MS¹ mode indicated the occurrence of six [M ? 2H]^2? ions which, according to calculation, support 13 GT1 variants differing in their relative molecular mass due to dissimilar ceramide (Cer) constitutions. By stepwise CID MS²–MS⁵ on the doubly charged ion at m/z 1077.20 corresponding to a ubiquitous GT1b structure, the complete characterization of its oligosaccharide core including the identification of sialylation sites was achieved. Structure of the lipid moiety was further elucidated by CID MS⁶ analysis carried out using the Y₀ fragment ion, detected in MS⁵, as a precursor. MS⁶ fragmentation resulted in a pattern supporting a single ceramide form having the less common (d20 : 1/18 : 0) configuration. The entire top–down experiment was performed in a high‐throughput regime in less than 3 min of measurement, with an analysis sensitivity situated in the subpicomolar range. Copyright © 2009 John Wiley & Sons, Ltd.     

On spanning tree congestion of graphs

Let G be a connected graph and T be a spanning tree of G. For e∈E(T), the congestion of e is the number of edges in G connecting two components of T−e. The edge congestion ofGinT is the maximum congestion over all edges in T. The spanning tree congestion ofG is the minimum congestion of G in its spanning trees. In this paper, we show the spanning tree congestion for the complete k-partite graphs and the two-dimensional tori. We also address lower bounds of spanning tree congestion for the multi-dimensional grids and the hypercubes.     

Approximation algorithms for constrained generalized tree alignment problem

In generalized tree alignment problem, we are given a set S of k biologically related sequences and we are interested in a minimum cost evolutionary tree for S. In many instances of this problem partial phylogenetic tree for S is known. In such instances, we would like to make use of this knowledge to restrict the tree topologies that we consider and construct a biologically relevant minimum cost evolutionary tree. So, we propose the following natural generalization of the generalized tree alignment problem, a problem known to be MAX-SNP Hard, stated as follows:

Constrained Generalized Tree Alignment Problem [S. Divakaran, Algorithms and heuristics for constrained generalized alignment problem, DIMACS Technical Report 2007-21, 2007]: Given a set S of k related sequences and a phylogenetic forest comprising of node-disjoint phylogenetic trees that specify the topological constraints that an evolutionary tree of S needs to satisfy, construct a minimum cost evolutionary tree for S.

In this paper, we present constant approximation algorithms for the constrained generalized tree alignment problem. For the generalized tree alignment problem, a special case of this problem, our algorithms provide a guaranteed error bound of 2−2/k.     

Genus distribution of ladder type and cross type graphs

In this paper a method is given to calculate the explicit expressions of embedding genus distribution for ladder type graphs and cross type graphs. As an example, we refind the genus distribution of the graph J _n which is the first class of graphs studied for genus distribution where its genus depends on n. This work was supported National Natural Science Foundation of China (Grant Nos. 10571013, 60433050) and the State Key Development Program of Basic Research of China (Grant No. 2004CB318004)