Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices

We present a lower and an upper bound for the second smallest eigenvalue of Laplacian matrices in terms of the averaged minimal cut of weighted graphs. This is used to obtain an upper bound for the real parts of the non-maximal eigenvalues of irreducible nonnegative matrices. The result can be applied to Markov chains.     

对流方程的两个高精度差分格式

This paper gives two patterns of high exact difference in solving convection equation. The er-ror of cut section is to O( △t^2 △x^4 ).     

Sequent systems for compact bilinear logic

Compact Bilinear Logic (CBL), introduced by Lambek [14], arises from the multiplicative fragment of Noncommutative Linear Logic of Abrusci [1] (also called Bilinear Logic in [13]) by identifying times with par and 0 with 1. In this paper, we present two sequent systems for CBL and prove the cut‐elimination theorem for them. We also discuss a connection between cut‐elimination for CBL and the Switching Lemma from [14].     

Fragile graphs with small independent cuts

A graph is called fragile if it has a vertex cut which is also an independent set. Chen and Yu proved that every graph with n vertices and at most 2n?4 edges is fragile, which was conjectured to be true by Caro. However, their proof does not give any information on the number of vertices in the independent cuts. The purpose of this paper is to investigate when a graph has a small independent cut. We show that if G is a graph on n vertices and at most (12n/7)?3 edges, then G contains an independent cut S with ∣S∣≤3. Upper bounds on the number of edges of a graph having an independent cut of size 1 or 2 are also obtained. We also show that for any positive integer k, there is a positive number ε such that there are infinitely many graphs G with n vertices and at most (2?ε)n edges, but G has no independent cut with less than k vertices. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 327–341, 2002     

一种改进的基于分水岭的图像分割算法

针对分水岭算法过分割现象,提出一种综合分水岭算法、中值过滤算法和归一化割算法的改进算法。该算法首先应用改进型的中值过滤算法对图像进行适当的除噪;然后通过分水岭变换对图像进行了初步分割,最后使用归一化割算法进行图像精度分割。算法集合了分水岭算法、中值过滤算法及归一化割算法的优点,既较好地解决了分水岭算法中过度分割的问题,又降低了归一化割算法的时间复杂度。实验结果表明该算法是一种切实可行的图像分割方法。     

Empirical investigation of precipitation of hexadecanoic acid from toluene/brine system: Implication to naphthenic acid precipitation from crude oils

Naphthenic acids, due to their tendency to precipitate out of solution when in contact with formation water, present a formidable challenge for the petroleum industry. In this study, precipitation of hexadecanoic acid from an idealized oil-water (toluene/brine) system was investigated. The FTIR results revealed that the acid was mainly precipitated as calcium hexadecanoate. Experiments designed to study the effect of water cut, acid concentration, brine concentration, and pH of the brine on the amount of the precipitate formed revealed that the amount of precipitate formed increased with increase in brine pH, concentration of the acid and calcium ions. Similar effect was observed with respect to water cut but with maximum amount of the precipitate formed at water cut of about 40%, below and above which relatively lower amount of the acid was precipitated irrespective of the levels of the other factors. In general, the observed effects of the factors suggest that precipitation of the naphthenic acid can be minimized with acidic formation water that contains relatively low concentration of calcium ions particularly when the concentration of the acid in the oil is as low as possible.     

On a Problem of Judicious k‐Partitions of Graphs

For positive integers and m , let be the smallest integer such that for each graph G with m edges there exists a k‐partition in which each contains at most edges. Bollobás and Scott showed that . Ma and Yu posed the following problem: is it true that the limsup of tends to infinity as m tends to infinity? They showed it holds when k is even, establishing a conjecture of Bollobás and Scott. In this article, we solve the problem completely. We also present a result by showing that every graph with a large k‐cut has a k‐partition in which each vertex class contains relatively few edges, which partly improves a result given by Bollobás and Scott.     

宫颈环形电切术联合纳米银凝胶应用于慢性宫颈炎的临床探讨

目的分析宫颈环形电切术联合纳米银凝胶应用于慢性宫颈炎的临床疗效。方法选择2014年10月至2015年10月在上栗县长平卫生院接受治疗的122例慢性宫颈炎患者作为研究对象。将122例患者随机分为常规组和实验组。常规组使用宫颈环形电切术进行治疗;实验组使用宫颈环形电切术联合纳米银凝胶进行治疗。对比两组患者的治疗效果以及阴道感染率及出血率。结果两组患者经过不同的治疗之后实验组患者的治疗总有效率(100.0%)显著高于常规组治疗总有效率(80.3%),数据差异显著,具备统计学意义(P0.05);实验组患者的阴道感染率(1.64%)及出血率(3.28%)分别明显低于常规组的阴道感染率(13.11%)与出血率(18.03%),两组数据差异显著,具备统计学意义(P0.05)。结论宫颈环形电切术联合纳米银凝胶应用于慢性宫颈炎的临床疗效显著,纳米银凝胶能够极大程度地帮助患者减少阴道出血、阴道感染的情况发生,能够很好地弥补宫颈环形电切术的不足,能够极大程度提升患者治疗效果,是慢性宫颈炎的理想治疗方式,值得临床推广。