单圈图和双圈图的连续边着色

设G是简单图,用颜色1,2,3,…对G的边正常着色,如果在每一顶点表现的颜色构成一个连续的整数集合,那么就称这个着色是连续的.图G的亏度def(G)是粘在G上使得它可连续着色的悬挂边的最小数目.在本文中,我们完全确定了单圈图和双圈图的亏度.     

The extreme set condition of a graph

Let G be a simple graph. The size of any largest matching in G is called the matching number of G and is denoted by ν(G). Define the deficiency of G, def(G), by the equation def(G)=|V(G)|−2ν(G). A set of points X in G is called an extreme set if def(G−X)=def(G)+|X|. Let c₀(G) denote the number of the odd components of G. A set of points X in G is called a barrier if c₀(G−X)=def(G)+|X|. In this paper, we obtain the following:

(1) Let G be a simple graph containing an independent set of size i, where i2. If X is extreme in G for every independent set X of size i in G, then there exists a perfect matching in G.

(2) Let G be a connected simple graph containing an independent set of size i, where i2. Then X is extreme in G for every independent set X of size i in G if and only if G=(U,W) is a bipartite graph with |U|=|W|i, and |Γ(Y)||U|−i+m+1 for any Y U, |Y|=m (1mi−1).

(3) Let G be a connected simple graph containing an independent set of size i, where i2. Then X is a barrier in G for every independent set X of size i in G if and only if G=(U,W) is a bipartite graph with |U|=|W|=i, and |Γ(Y)|m+1 for any Y U, |Y|=m (1mi−1).     

On the Existence of 3-Generator, 3-Relation Finite 2-Groups with a Given (Co)Class

In this article, we show that for any positive integer k there is a 3-generator, 3-relation finite 2-group of class (respectively, coclass) k provided that k ≥ 4 (respectively, k ≥ 5).     

Some 3-Generator, 3-Relation Finite 2-Groups

Using computational methods, we first show that there are exactly eighteen 3-generator 2-groups of order 2¹⁰ with trivial Schur multiplier all having deficiency zero. We next generalize one of the groups obtained to exhibit two infinite classes of 3-generator, 3-relation finite 2-groups of high nilpotency class providing an affirmative answer to a problem posed by Havas et al.     

The deficiency of a regular graph

A proper edge coloring c:E(G)→Z of a finite simple graph G is an interval coloring if the colors used at each vertex form a consecutive interval of integers. Many graphs do not have interval colorings, and the deficiency of a graph is an invariant that measures how close a graph comes to having an interval coloring. In this paper we search for tight upper bounds on the deficiencies of k-regular graphs in terms of the number of vertices. We find exact values for 1?k?4 and bounds for larger k.     

Metabonomic study on 'Kidney-Yang Deficiency syndrome' and intervention effects of Rhizoma Drynariae extracts in rats using ultra performance liquid chromatography coupled with mass spectrometry

This paper was designed to study metabonomic characters of the ‘Kidney-Yang Deficiency syndrome’ induced by high dose of hydrocortisone and the therapeutic effects of Rhizoma Drynariae, classic traditional Chinese medicine (TCM) in treating the syndrome. A urinary metabonomics method based on ultra-performance liquid chromatography coupled with mass spectrometry (UPLC/MS) was developed. The significant difference in metabolic profiling was observed from model group (hydrocortisone-induced group) compared with the pre-dose group (rats before hydrocortisone inducing) by using the principal components analysis (PCA). The time-dependent regression tendency in Rhizoma Drynariae treatment group (hydrocortisone-induced rats followed by being administered with Rhizoma Drynariae ethanol extracts) from day 3 to 15 was obtained, indicating the time-dependent recovery effect of Rhizoma Drynariae on ‘Kidney-Yang Deficiency syndrome’ rats. Some significantly changed metabolites like phenylalanine, phenylacetylglycine, N₂-succinyl-l-ornithine, l-proline, creatinine, hippurate and citrate have been identified. These biochemical changes are related to the disturbance in energy metabolism, amino acid metabolism and gut microflora, which are helpful to further understand the ‘Kidney-Yang Deficiency syndrome’ and the therapeutic mechanism of Rhizoma Drynariae. The work shows that the metabonomics method is a valuable tool for studying the essence of Chinese medicine's syndrome theory and therapeutic effect mechanism of TCM.     

Relative deficiency of quantile estimators for left truncated and right censored data

The quantity deficiency which was proposed by Hodges and Lehmann (1970) is used to compare different statistical procedures. In this article, the deficiency of the sample quantile estimator with respect to the kernel quantile estimator for left truncated and right censored (LTRC) data in the sense of Hodges and Lehmann is considered. We also give the optimal bandwidth for the kernel quantile estimator. Monte Carlo studies are conducted to illustrate our results.     

奇异线性哈密顿算子自伴扩张的新描述

研究了具有一个奇异端点的线性哈密顿算子的白伴扩张的解析描述.设最小哈密顿算子h的亏指数为(d,d),将Im(h~*y,y)表示为秩为2d的二次型,该文利用二次型的表示矩阵得到了最小哈密顿算子h的自伴扩张域的一种新的完全描述.     

A FURTHER CLASS OF 3-GENERATOR, 3-RELATION FINITE GROUPS

We exhibit a further class of 3-generator, 3-relation finite metabelian groups.     

Essential spectra of singular matrix differential operators of mixed order

The present paper deals with the essential spectrum of the singular matrix differential operator of mixed order