两个投射子组合的核空间与列空间

This paper establishes some new equalities and inequalities for the null and column spaces of combinations of two projectors P and Q. Some new necessary and sufficient conditions for P ± Q to be invertible are given by the structure of null and column space of some combinations of P and Q. In addition, the inclusion relation of N(P Q + QP) and N(P Q- QP) is discussed and necessary and sufficient conditions for them to be equal are also studied.     

Journal of Mathematical Research and Exposition Guide for Authors

Journal overview： Journal of Mathematical Research and Exposition （JMRE） was created in 1981 to promote mathematical research and to report and review theoretical and applied results in mathematics. This journal is devoted to original research articles of the highest quality in all areas of pure and applied mathematics. Short communications, survey or review articles, and articles on mathematical methodology and mathematical philosophy are welcome. In addition, introductions to new branches of mathematics, new methods for intersection fields of mathematics, unsolved open problems and state of the art of important research subjects are also included. The target audience comprises： pure and applied mathematicians, graduate students in broad fields of sciences and technology, scientists and engineers interested in mathematics.     

Journal of Mathematical Research and Exposition Guide for Authors

Journal overview： Journal of Mathematical Research and Exposition （JMRE） was created in 1981 to promote mathematical research and to report and review theoretical and applied results in mathematics. This journal is devoted to original research articles of the highest quality in all areas of pure and applied mathematics. Short communications, survey or review articles, and articles on mathematical methodology and mathematical philosophy are welcome. In addition, introductions to new branches of mathematics, new methods for intersection fields of mathematics, unsolved open problems and state of the art of important research subjects are also included. The target audience comprises： pure and applied mathematicians, graduate students in broad fields of sciences and technology, scientists and engineers interested in mathematics.     

Journal of Partial Differential Equations

Aims and Scope
The Journal of Partial Differential Equations （JPDE） publishes research papers and short commu- nications of high scientific quality in theory and applications including numerical analysis of partial differential equations. The main interest of the Journal is to encourage the research of partial differential equations, and to promote national and international exchange between partial differential equations, engineering, physics and different fields of mathematics.     

Journal of Partial Differential Equations

Aims and Scope
The Journal of Partial Differential Equations （JPDE） publishes research papers and short communications of high scientific quality in theory and applications including numerical analysis of partial differential equations. The main interest of the Journal is to encourage the research of partial differential equations, and to promote national and international exchange between partial differential equations, engineering, physics and different fields of mathematics.     

一类六角系统图的特征多项式及应用

Let Ln be the hexagonal chain graph,Fnbe the hexacyclic system graph and Mn be the M¨obius hexacyclic system graph. Derflinger and Sofer gave the spectra of Ln and Fn by using group theoretical method. Later, Gutman gave the spectra of them using a polynomial result due to Godsil and McKay. In this paper, we give a simple and direct method to determine the characteristic polynomial and spectra of Fn and Ln. By the method, we give the characteristic polynomial and spectrum of Mn that is new. Additionally, the exact values of total π-electron energy and the nullities of Ln, Fn and Mn are obtained, and the bounds for the energy of Ln and Mn are also considered.     

投影的约化极小模和空间的夹角

Let M and N be nonzero subspaces of a Hilbert space H, and PM and PN denote the orthogonal projections on M and N, respectively. In this note, an exact representation of the angle and the minimum gap of M and N is obtained. In addition, we study relations between the angle, the minimum gap of two subspaces M and N, and the reduced minimum modulus of （I - PN）PM,     

若干笛卡尔积图的邻点可区别关联染色

An adjacent vertex distinguishing incidence coloring of graph G is an incidence coloring of G such that no pair of adjacent vertices meets the same set of colors.We obtain the adjacent vertex distinguishing incidence chromatic number of the Cartesian product of a path and a path,a path and a wheel,a path and a fan,and a path and a star.     

On Global and Local Properties of the Trajectories of Gaussian Random Fields——A Look Through the Set of Limit Points

This paper studies the global and local properties of the trajectories of Gaussian random fields with stationary increments and proves sufficient conditions for Strassen's functional laws of the iterated logarithm at zero and infinity respectively.The sets of limit points of those Gaussian random fields are obtained.The main results are applied to fractional Riesz-Bessel processes and the sets of limit points of this field are obtained.     

Simultaneous optimality of LSE and ANOVA estimate in general mixed models

Problems of the simultaneous optimal estimates and the optimal tests in general mixed models are considered. A necessary and sufficient condition is presented for the least squares estimate of the fixed effects and the analysis of variance （Hendreson III＇s） estimate of variance components being uniformly minimum variance unbiased estimates simultaneously. This result can be applied to the problems of finding uniformly optimal unbiased tests and uniformly most accurate unbiased confidential interval on parameters of interest, and for finding equivalences of several common estimates of variance components.     

资源禀赋视角下政府与企业互动行为演化分析

针对政府与企业资源的异质性,从资源禀赋的视角,对政府与企业互动的不同模式(随机合作型、政策驱动型、技术推动型、协作共赢型)的界定与分析,构建政府与企业互动行为的演化博弈模型,明确政府与企业在不同模式下的互动行为演化路径。研究结果表明:政府与企业不同互动模式存在显著差异,不同类型企业与政府之间的互动对应着某种互动模式;不同互动模式的产生和演化契合政企互动关系的发展历程;协作共赢型互动模式是政府与企业互动行为演化的高级阶段,有利于政府与企业形成紧密的合作,激发政府政策资源与企业技术资源的协同效应。     

考虑桥载设备使用的机场和航空公司运行成本研究

分析了桥载设备在机场和航空公司推广所面临的问题和原因,从航空公司运行的角度讨论桥载设备的使用能否有效地节约航空公司运行成本,分析了不同机型使用桥载设备的成本优化率;然后从机场运行的角度构建了桥载设备静态投资回收周期计算模型,重点讨论了桥载设备套数和使用时间对其静态投资回收周期的影响.实践表明,使用桥载设备代替APU可实现机场、航空公司、旅客三赢:机场可收取桥载设备使用费增加收入,能在较短的时间内回收桥载设备的投资成本;航空公司可有效地节省燃油和APU维修等运行费用;使用桥载设备后可减少碳氮气体排放和噪声污染,改善旅客的航空体验.研究结果能够增强机场和航空公司使用桥载设备的信心和决心,能有效地推动民航节能减排政策在机场的实施.     

Physical entropy, information entropy and their evolution equations

Inspired by the evolution equation of nonequilibrium statistical physics entropy and the concise statistical formula of the entropy production rate, we develop a theory of the dynamic information entropy and build a nonlinear evolution equation of the information entropy density changing in time and state variable space. Its mathematical form and physical meaning are similar to the evolution equation of the physical entropy: The time rate of change of information entropy density originates together from drift, diffusion and production. The concise statistical formula of information entropy production rate is similar to that of physical entropy also. Furthermore, we study the similarity and difference between physical entropy and information entropy and the possible unification of the two statistical entropies, and discuss the relationship among the principle of entropy increase, the principle of equilibrium maximum entropy and the principle of maximum information entropy as well as the connection between them and the entropy evolution equation.     

现代化进程的测算与实证分析

论证提出了现代化的概念、内涵、涉及的领域及其主要特征;运用定性分析与定量判断相结合的方法建立了现代化的评价指标体系,科学确定出了现代化主要衡量指标的标准以及现代化实现程度的综合评价方法;并据此搜集有关数据对我国各省份及山东省各市的现代化进程进行了具体测算和实证分析.     

Primitivity and Local Primitivity of Digraphs and Nonnegative Matrices

The article surveys the main results on the primitivity and local primitivity of digraphs and matrices from the inception of this research area in 1912 by now. We review the universal and special criteria for primitivity and local primitivity as well as universal and special bounds on the exponents and local exponents of digraphs and matrices. We describe some cryptographic applications of this mathematical apparatus for analyzing the mixing properties of block ciphers and keystream generators. The new promising research directions are formulated in the study of primitivity and local primitivity of digraphs and matrices.     

Raman and infrared spectra and normal vibrations of N-methylpropionamide and N-deuterated N-methyl propionamide

Raman and infrared spectra of N-methyl-propionamide and N-deuterated N-methyl-propionamide were recorded in various states of aggregation—pure amide, in solution and vapour state—and the frequency changes of the functional groups were studied. The implane skeletal vibrations of N-methyl-propionamide and its deuterated compound were calculated treating these molecules as six-body problems. The distribution of potential energy of each normal mode among various symmetry co-ordinates was calculated and the nature of the amide I, II and III bands and the mixing up of the inplane vibrational frequencies of N-methyl-propionamide and the deuterated amide are discussed on a quantitative basis.     

用数学规划的方法优化跳台滑雪的起跳动作

本文以风洞实验、高速摄影和测力实验得到的有限的、离散的数据为依据,采用多刚体系统动力学理论和数学规划的方法,对跳台滑雪(以下简称跳雪)的起跳动作进行分析和优化,提出了跳雪起跳的最优技术动作.文中给出算例,与国内、外有关文献的结果比较,说明本文的计算与优化是合理的.     

沪深股票市场之间波动性影响关系研究

以对沪深两市波动性指标的解构分析为基础,给出了基于GRACH模型、Granger模型的综合运用,同时引入协整检验和误差纠正机制的均衡分析方法,对沪深两市的波动相关性进行实证分析和模型检验,系统性揭示了沪深两市波动性的关键特征和沪深两市波动互相影响的因果规律,为基于沪深两市金融资产的定价和风险管理奠定了基础.     

考虑农户“以次充好”行为的生鲜电商销售模式选择研究

考虑农户“以次充好”行为和电商企业抽样检测机制的基础上,运用博弈理论分别建立自营和平台两种销售模式下生鲜电商供应链的决策模型,对比研究了不同销售模式下电商企业抽样检测前后各方的最优决策及其期望收益。研究发现:(1)虽然电商企业的抽样检测将会降低农户“以次充好”的比例,提升在线销售生鲜品的品质,但却不一定带来自身和农户的收益增加;(2)无论自营模式还是平台模式,消费者的追溯赔偿和电商企业的严惩措施都会对农户“以次充好”行为起到抑制作用;(3)当农户存在“以次充好”行为时,抽检费用、内外部惩罚、信誉损失以及平台使用费等因素都将影响电商企业和农户对销售模式的选择。     

负债代理冲突下企业投融资互动行为的实物期权分析

准确分析企业投融资之间的互动关系,实现两种决策的协同,有助于提高企业决策效率和项目价值.通过把项目融资政策内生到投资决策的实物期权模型中,构建基于股东价值最大化和企业价值最大化的投融资决策互动模型,得到两种情形下的投融资决策临界点和期权价值,并借助数值分析负债代理冲突对企业投融资行为的影响.研究结果表明,负债融资既可能引发过度投资问题,也可能抑制投资.这种非效率投资将相应地提高负债融资的成本,对企业的负债融资产生抑制作用.