Examples of non-conjugated holomorphic vector fields and foliations

We consider germs of holomorphic vector fields near the origin of with a saddle-node singularity, and the induced singular foliations. In a previous article we described the invariants addressing the analytical classification of these vector fields. They split into three parts: a formal, an orbital and a tangential component. For a fixed formal class, the orbital invariant (associated to the foliation) was obtained by Martinet and Ramis; we give it an integral representation. We then derive examples of non-orbitally conjugated foliations by the use of a “first-step” normal form, whose first-significative jet is an invariant. The tangential invariant also admits an integral representation, hence we derive explicit examples of vector fields, inducing the same foliation, that are not mutually conjugated. In addition, we provide a family of normal forms for vector fields orbitally equivalent to the model of Poincaré-Dulac.     

Some class 1 graphs on <Emphasis Type="Italic">g</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript>-colorings

An edge-coloring of a graph G is an assignment of colors to all the edges of G. A g _c -coloring of a graph G is an edge-coloring of G such that each color appears at each vertex at least g(v) times. The maximum integer k such that G has a g _c -coloring with k colors is called the g _c -chromatic index of G and denoted by \(\chi\prime_{g_{c}}\)(G). In this paper, we extend a result on edge-covering coloring of Zhang and Liu in 2011, and give a new sufficient condition for a simple graph G to satisfy \(\chi\prime_{g_{c}}\)(G) = δ _g (G), where \(\delta_{g}\left(G\right) = min_{v\epsilon V (G)}\left\{\lfloor\frac{d\left(v\right)}{g\left(v\right)}\rfloor\right\}\).     

Stochastic modelling of reservoir operations

The nature of hydrologic parameters in reservoir management models is uncertain. In mathematical programming models the uncertainties are dealt with either indirectly (sensitivity analysis of a deterministic model) or directly by applying a chance-constrained type of formulation or some of the stochastic programming techniques (LP and DP based models). Various approaches are reviewed in the paper. Moran's theory of storage is an alternative stochastic modelling approach to mathematical programming techniques. The basis of the approach and its application is presented. Reliability programming is a stochastic technique based on the chance-constrained approach, where the reliabilities of the chance constraints are considered as extra decision variables in the model. The problem of random event treatment in the reservoir management model formulation using reliability programming is addressed in this paper.     

The left-definite Legendre type boundary problem

The left-definite Legendre type boundary problem concerns the study of a fourth-order singular differential expressionM _k [–] in a weighted Sobolev spaceH generated by a Dirichlet inner product. The fourth-order differential equation

The GHS inequality and the Riemann hypothesis

LetV(t) be the even function on (–, ) which is related to the Riemann xi-function by (x/2)=4 _– exp(ixt–V(t))dt. In a proof of certain moment inequalities which are necessary for the validity of the Riemann Hypothesis, it was previously shown thatV'(t)/t is increasing on (0, ). We prove a stronger property which is related to the GHS inequality of statistical mechanics, namely thatV' is convex on [0, ). The possible relevance of the convexity ofV' to the Riemann Hypothesis is discussed.Communicated by Richard Varga.     

一维空洞卷积神经网络的矿物光谱分类

矿物光谱综合反映了岩矿的物理化学特性、组分和内部结构特征,已被应用于岩矿识别研究.传统的矿物光谱分类方法需要先对矿物光谱进行预处理,再采用不同方法分析光谱特征,从而实现分类目的.但同时也会造成部分光谱信息丢失,导致最终分类精度不高且操作过程繁琐、效率低下,难以应对日益增长的大数据处理需求.因此,建立一个准确、高效的矿物...     

基于DCGAN的拉曼光谱样本扩充及应用研究

拉曼光谱检测方法依赖于化学计量学算法,深度学习是当下最炙手可热的方向,可应用于拉曼光谱进行建模.但是深度学习需要大样本进行训练,而拉曼光谱采集受制于器材和人力成本,获取大批量的样本需要更大成本,且易受荧光等因素干扰,这些问题都制约了将深度学习应用于拉曼光谱.针对以上问题,通过引入深度卷积生成对抗网络(DCGAN)提取拉...     

Tail order and intermediate tail dependence of multivariate copulas

In order to study copula families that have tail patterns and tail asymmetry different from multivariate Gaussian and t copulas, we introduce the concepts of tail order and tail order functions. These provide an integrated way to study both tail dependence and intermediate tail dependence. Some fundamental properties of tail order and tail order functions are obtained. For the multivariate Archimedean copula, we relate the tail heaviness of a positive random variable to the tail behavior of the Archimedean copula constructed from the Laplace transform of the random variable, and extend the results of Charpentier and Segers [7] [A. Charpentier, J. Segers, Tails of multivariate Archimedean copulas, Journal of Multivariate Analysis 100 (7) (2009) 1521–1537] for upper tails of Archimedean copulas. In addition, a new one-parameter Archimedean copula family based on the Laplace transform of the inverse Gamma distribution is proposed; it possesses patterns of upper and lower tails not seen in commonly used copula families. Finally, tail orders are studied for copulas constructed from mixtures of max-infinitely divisible copulas.     

Gaining insight into student satisfaction using comprehensible data mining techniques

As a consequence of the heightened competition on the education market, the management of educational institutions often attempts to collect information on what drives student satisfaction by e.g. organizing large scale surveys amongst the student population. Until now, this source of potentially very valuable information remains largely untapped. In this study, we address this issue by investigating the applicability of different data mining techniques to identify the main drivers of student satisfaction in two business education institutions. In the end, the resulting models are to be used by the management to support the strategic decision making process. Hence, the aspect of model comprehensibility is considered to be at least equally important as model performance. It is found that data mining techniques are able to select a surprisingly small number of constructs that require attention in order to manage student satisfaction.     

神经元的形态分类和识别——2010年全国研究生数学建模竞赛C题论文

根据神经元的空间几何特征参数,研究神经元的空间形态分类方法,将神经元根据几何形态分类识别.首次提出利用模糊C均值算法(FCM)建立了模糊聚类分析模型,对所给的神经元样本进行了分类,这一模型用来对神经元进行分类比较合理,且计算结果准确.同时,还利用相关分析原理分析了不同动物神经系统中同一类神经元的形态特征有着很高的相似度.