On the spectral radius of ‡-shape trees

Let A(G) be the adjacency matrix of G. The characteristic polynomial of the adjacency matrix A is called the characteristic polynomial of the graph G and is denoted by φ(G, λ) or simply φ(G). The spectrum of G consists of the roots (together with their multiplicities) λ ₁(G) ? λ ₂(G) ? … ? λ _n (G) of the equation φ(G, λ) = 0. The largest root λ ₁(G) is referred to as the spectral radius of G. A ?-shape is a tree with exactly two of its vertices having maximal degree 4. We will denote by G(l ₁, l ₂, … l ₇) (l ₁ ? 0, l _i ? 1, i = 2, 3, …, 7) a ?-shape tree such that $G\left( {l_1 ,l_2 , \ldots l_7 } \right) - u - v = P_{l_1 } \cup P_{l_2 } \cup \ldots P_{l_7 }$ , where u and v are the vertices of degree 4. In this paper we prove that ${{3\sqrt 2 } \mathord{\left/ {\vphantom {{3\sqrt 2 } 2}} \right. \kern-0em} 2} < \lambda _1 \left( {G\left( {l_1 ,l_2 , \ldots l_7 } \right)} \right) < {5 \mathord{\left/ {\vphantom {5 2}} \right. \kern-0em} 2}$ .     

Local convergence analysis of several inexact Newton-type algorithms for general nonlinear eigenvalue problems

We study the local convergence of several inexact numerical algorithms closely related to Newton’s method for the solution of a simple eigenpair of the general nonlinear eigenvalue problem $T(\lambda )v=0$ . We investigate inverse iteration, Rayleigh quotient iteration, residual inverse iteration, and the single-vector Jacobi–Davidson method, analyzing the impact of the tolerances chosen for the approximate solution of the linear systems arising in these algorithms on the order of the local convergence rates. We show that the inexact algorithms can achieve the same order of convergence as the exact methods if appropriate sequences of tolerances are applied to the inner solves. We discuss the connections and emphasize the differences between the standard inexact Newton’s method and these inexact algorithms. When the local symmetry of $T(\lambda )$ is present, the use of a nonlinear Rayleigh functional is shown to be fundamental in achieving higher order of convergence rates. The convergence results are illustrated by numerical experiments.     

A general vectorial Ekeland’s variational principle with a P-distance

In this paper, by using p-distances on uniform spaces, we establish a general vectorial Ekeland variational principle （in short EVP）, where the objective function is defined on a uniform space and taking values in a pre-ordered real linear space and the perturbation involves a p-distance and a monotone function of the objective function. Since p-distances are very extensive, such a form of the perturbation in deed contains many different forms of perturbations appeared in the previous versions of EVP. Besides, we only require the objective function has a very weak property, as a substitute for lower semi-continuity, and only require the domain space （which is a uniform space） has a very weak type of completeness, i.e., completeness with respect to a certain p-distance. Such very weak type of completeness even includes local completeness when the uniform space is a locally convex topological vector space. From the general vectorial EVP, we deduce a general vectorial Caristi＇s fixed point theorem and a general vectorial Takahashi＇s nonconvex minimization theorem. Moreover, we show that the above three theorems are equivalent to each other. We see that the above general vectorial EVP includes many particular versions of EVP, which extend and complement the related known results.     

Clustering of Patients’ Trajectories with an Auto-Stopped Bisecting K-Medoids Algorithm

Nowadays, long wait, cancellations and resource overload frequently occur in healthcare, especially in those sectors related to the patients passing through the operating theatre in both United States and the European Union. Since more and more hospitals seek to develop the overall patient pathways instead of the effectiveness of “isolated” departments, the most important work has been defining suitable patient groups for employing process management and simulation tools developed in the recent decades. In this study, we proposed a data mining method, an auto-stopped Bisecting K-Medoids clustering algorithm, to classify patients into groups with homogenous trajectories. This method classifies the patient trajectories with two stages. At the first stage, patients are classified by the complexity of outpatient visits; afterwards, the groups obtained at the first stage are further classified by the original information of the trajectories where all medical appointments including outpatient ones are taken into account. By using a real data set collected from a medium-size Belgian hospital, we demonstrate how the proposed approach works and examine which kinds of trajectories are grouped into the same clusters. According to the experimental results, the proposed method can be used to classify patients into manageable groups with homogenous trajectories, which can be used as a base for the process modelling techniques and simulation tools.     

Variable Exponent Sobolev Spaces for Semilinear Elliptic Systems

In this work, the semilinear elliptic systems with Dirichlet boundary value are considered. We extend the notion of subcritical growth from polynomial growth to variable exponent growth. Under the variable exponent growth, nontrivial solutions are obtained via variable exponent Sobolev spaces and variational methods. In article final, we make a remark to explain that our main result is a extention of a recent result of D. G. de Figueiredo, J. M. do Óand B. Ruf [D. G. de Figueiredo, J. M. do Ó, B. Ruf, An Orlicz-space approach to superlinear elliptic systems, J. Funct. Anal. 224 (2005) 471–496].     

Effects of time delay and coupling strength on synchronization transitions in excitable homogeneous random network

In this paper we numerically investigate the effects of time delay and coupling strength on synchronization transitions in excitable homogeneous random network. Different roles of time delay and coupling strength have been discovered by synchronization parameter and space–time plots. Specifically, we have found three distinct parameter regions, i.e., asynchronous region (domain I for small time delay), transition region (domain II for moderate time delay) and synchronous region (domain III for large time delay) as time delay is increased. The phenomenon of multi-stability is observed in the transition region. While coupling strength can enhance synchronization in the transition region and can reduce synchronization time in the synchronous region. All these results are independence on the system size.     

基于一种新的分解-集成模型的我国猪肉年度需求量预测研究

根据我国猪肉消费量的特点,建立了一个新的我国猪肉年度消费需求量预测的分解-集成模型.首先,为了预测我国猪肉消费需求量,根据全国猪肉农村和城市猪肉消费量的不同特点,将我国猪肉消费需求量分解农村和城市猪肉消费量.其次,根据GANN和WNN时间序列模型,建立了一个综合集成预测模型,分别对我国农村和城市的猪肉消费量进行了预测.最后,将农村和城市猪肉需求量的预测结果进行集成,得到全国猪肉需求量.为了验证所提出方法的有效性,将其与其他常用预测方法进行了对比,实证研究结果表明,提出的集成预测模型在我国全国猪肉消费需求量预测上取得了较好的效果.     

商品价格极端波动影响期现价格联动及套期保值吗?

试图将极端价格波动成因归结于系统惯性因素和极端随机冲击因素,借助Copulas-GARCH模型,将其引入期货和现货价格联动的计量模型之中,以持有便利收益高的沪铜作为研究样本,实证研究发现:1)引入极端价格波动因素后将显著提升价格联动计量模型的解释能力;2)当负向基差扩大,系统惯性因素引起商品价格剧烈变动,将导致市场联动性下降,而极端随机冲击却具有正向效应,即市场受到极端随机冲击时会增强期现价格联动关系;3)极端随机冲击效应中正向冲击和负向冲击的非对称性特征不显著;4)考虑极端价格波动效应可明显降低生产企业的套期保值成本.研究结论对于商品期货市场套期保值等期货交易具有重要管理启示.     

关于K_(2n)-E(C_m)的点可区别边色数

图G的一个k-正常边染色f被称为点可区别边染色是指任何两点的点及其关联边的色集合不同,所用最小的正整数k被称为G的点可区别边色数,记为X'_(vd)(G).用k_(2n)-E(C_m)表示2n阶完全图删去其中一条m阶路的边后得到的图,得到了K_(14)-E(C_4),K_(16)-E(C_4),K_(18)-E(C_5),K_(20)-E(C_5)的点可区别边色数分别为14,16,18,20.     

Study on the Joint Toxicity of BPZ,BPS, BPC and BPF to Zebrafish

Bisphenol Z (BPZ), bisphenol S (BPS), bisphenol C (BPC), and bisphenol F (BPF) had been widely used as alternatives to bisphenol A (BPA), but the toxicity data of these bisphenol analogues were very limited. In this study, the joint toxicity of BPZ, BPS, BPC, and BPF to zebrafish (Danio rerio) was investigated. The median half lethal concentrations (LC50) of BPZ, BPS, BPC, and BPF to zebrafish for 96 h were 6.9 × 10⁵ µM, 3.9 × 10⁷ µM, 7.1 × 10⁵ µM, and1.6 × 10⁶ µM, respectively. The joint toxicity effect of BPF–BPC (7.7 × 10⁵–3.4 × 10⁵µM) and BPZ–BPC (3.4 × 10⁵–3.5 × 10⁵µM) with the same toxic ratio showed a synergistic effect, which may be attributed to enzyme inhibition or induction theory. While the toxicity effect of the other two bisphenol analogue combined groups and multi-joint pairs showed an antagonistic effect due to the competition site, other causes need to be further explored. Meanwhile, the expression levels of the estrogen receptor genes (ERα, ERβ1) and antioxidant enzyme genes (SOD, CAT, GPX) were analyzed using a quantitative real-time polymerase chain reaction in zebrafish exposure to LC₅₀ of BPZ, BPS, BPC, and BPF collected at 24, 48, 72, and 96 h. Relative expression of CAT, GPX, and ERβ1 mRNA declined significantly compared to the blank control, which might be a major cause of oxidant injury of antioxidant systems and the disruption of the endocrine systems in zebrafish.