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.     

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.     

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.     

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.     

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,     

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.     

Compatibility and Schur Complements of Operators on Hilbert C*-Module

Let E be a Hilbert C*-module,and ■ be an orthogonally complemented closed submodule of E.The authors generalize the definitions of ■-complementability and ■-compatibility for general(adjointable) operators from Hilbert space to Hilbert C*-module,and discuss the relationship between each other.Several equivalent statements about ■-complementability and ■-compatibility,and several representations of Schur complements of ■-complementable operators(especially,of ■-compatible operators and of positive ■-compatib...     

复杂非线性系统的控制综合与动态分析

随着当代科学和技术的发展,复杂非线性系统和控制理论研究不断深入,应用领域不断扩大,已影响了科技和社会领域的许多方面.针对当今该领域的研究难点和重点,本文集中讨论了复杂非线性系统控制研究中的3个关键问题,包括非光滑系统控制、网络化系统控制、临界态分析与控制.一方面是对在相关研究领域中的部分科研成果做一个简要的总结;另一方面,想借此机会在自动化学会控制理论专业委员会成立50周年之际向专业委员会表示感谢和祝贺.     

县域工旅农产业协同度测度研究——以河北省典型县域为例

在全域旅游的背景下,基于产业协同理论,利用工业、旅游业、农业产业系统有序度、协同度模型,从规模、结构、绩效三方面建立其协同度测度指标体系,依据2003-2014年的数据,定性和定量的分析评价了河北典型县域——涞水县、宽城满族自治县、抚宁县、蔚县的工旅农产业协同度.研究表明,县域工旅农产业协同度低,波动明显,且县域工业与旅游业协同变化趋势对其作用显著;县域旅游业与工业或农业普遍处于不协同状态,且前者协同度高于后者.     

中国煤层气的产业化进程与发展建议

煤层气产业在中国能源建设中具有重要战略地位。中国煤层气勘探开发历经矿井瓦斯抽排利用、现代煤层气理论技术的引进发展与成功应用、商业化开发试验及产业化发展（初期）4个阶段。由于在煤层气地质基础理论、勘探技术方法、开发工艺技术、集输利用与管理制度等方面的发展创新、系统集成,我国已有能力大规模发展煤层气产业,这在我国能源发展战略上是非常难得的历史机遇。当前,为了加快煤层气产业的发展,必须加强统筹规划,发挥多种积极性;加强煤层气地质研究、提高对区域勘探的指导与目标评价水平;开展高效低成本开发工艺技术攻关;发展煤层气产品集输和加工利用;继续跟踪国外煤层气前沿理论技术,加强技术交流与合作研究。     

基于“动态生成”的大学数学课堂教学

"动态生成"教学观的建立旨在摆脱课堂教学中以教师为中心、强调知识传授的传统教学模式的缺陷,从根本上正确理解课堂教学的复杂性和动态性,构建充满生命活力的大学数学课堂教学生态环境.在用动态生成的视角审视当前大学数学课堂教学中存在的问题的基础上,文章对在课堂教学中如何有效地进行动态生成提出了一些具体的策略:更新教学观念,精心预设弹性化的数学课堂教学方案;根据学生课堂反馈情况及时调整预设,并及时捕捉可利用的动态资源,为学生的生成创造可能的机会;加强教学研究,不断提高课堂教学智慧.     

Time-linearized,compact methods for the inviscid GRLW equation subject to initial Gaussian conditions

The objective of this paper is three-fold. First, four time-linearization methods that are second- and fourth-order accurate in time and space, respectively, are presented and used to study the dynamics of the modified and generalized regularized-long wave equations (mRLW and GRLW equations, respectively). Two of the methods use the conservation-law form of the equations and treat the wave amplitude and its second-order spatial derivative and the linear and nonlinear advection fluxes as unknowns, whereas the other two employ the non-conservation-law form of the equations and consider the wave amplitude and its first- and second-order spatial derivatives as unknowns. The methods employ three-point fourth-order accurate Padé discretizations for the first- and second-order derivatives, are second-order accurate in time, and yield linear systems of blocktridiagonal matrices. Second, the accuracy of these methods is assessed by comparing their results with those of the exact solution of the mRLW equation. It is reported that the four methods predict nearly the same values of the three invariants and have the same accuracy, and that an accurate prediction of the invariants may not correspond to small errors in space and time. Third, the dynamics of the inviscid GRLW equation is studied first qualitatively in terms of length and time scales and then numerically as a function of the linear advection speed, the exponent of the nonlinear advection flux, the dispersion coefficient and the amplitude and width of the initial bell-shaped or Gaussian conditions. It is shown that wide initial conditions result in wave steepening and breakup and the formation of solitary waves whose amplitude and speed decrease as the time for their formation increases. For narrow initial conditions, it is shown that only a single solitary wave may form. Behind this wave and depending on the parameters that characterized the inviscid GRLW equation, rarefaction or negative amplitude waves that propagate towards the upstream boundary or a train of localized oscillatory waves that do not emerge from the trailing edge of the leading solitary wave may be formed. These oscillatory waves exhibit the characteristics of, but are not dispersive shock waves and their amplitude and frequency increases as the width of the initial conditions is decreased. The results presented here do not only complement previous work by the authors, they also show that the dynamics of the inviscid GRLW equation undergoes new and interesting phenomena as the width of the initial conditions is decreased.     

Boundary-Value Problems of the Theory of Thin and Nonthin Orthotropic Shells with Account of Nonlinearly Elastic Properties and Low Shear Rigidity of Composite Materials

The basic geometric and physical relations and resolving equations of the theory of thin and nonthin orthotropic composite shells with account of nonlinear properties and low shear rigidity of their materials are presented. They are derived based on two theories, namely the theory of anisotropic shells employing the Timoshenko or Kirchhoff-Love hypothesis and the nonlinear theory of elasticity and plasticity of anisotropic media in combination with the Lagrange variational principle. The procedure and algorithm for the numerical solution of nonlinear (linear) problems are based on the method of successive approximations, the difference-variational method, and the Lagrange multiplier method. Calculations of the stress-strain state for a spherical shell with a circular opening loaded with internal pressure are presented. The effect of transverse shear strains and physical nonlinearity of the material on the distribution of maximum deflections and circumferential stresses in the shell, obtained according to two variants of the shell theories, is studied. A comparison of the results of the problem solution in linear and nonlinear statements with and without account of the shell shear strains is given. The numerical data obtained for thin and nonthin (medium thick) composite shells are analyzed.     

基于关系契约视角的农户与农产品电子商务企业合作机制演化博弈分析

本文基于关系契约的视角,运用演化博弈理论,构建有限理性特性下的农户与农产品电子商务企业合作演化博弈模型,分析双方合作策略的演进过程、稳定策略及其影响因素,并通过Matlab仿真模拟分析影响双方合作策略选择的因素,验证博弈结果正确性。研究结果表明:农户和农产品电子商务企业选择合作策略与合作投入成本、实现的超额收益密切相关,博弈初始状态、再交易成本、单方不合作获得的收益及违约罚金等因素影响系统的演化稳定结果。因此完善农户与农产品电子商务企业的合作机制,需要构建合理的利益分配机制、良好的关系治理机制、有效的监督和惩罚机制和信息共享、沟通与协调机制。     

网约车新政下平台和乘客的Stackelberg博弈模型及策略研究

近年来,滴滴和优步等网约车平台的出现给城市居民出行带来了新的选择,然而随着新政的实施以及垄断巨头的酝酿诞生,网约车平台是否会降补贴提车价成为消费者最为关心的问题。文章构建网约车平台和乘客之间的Stackelberg博弈模型,分析了网约车平台的补贴和抽成策略对乘客是否选择网约车出行的决策行为以及网约车市场均衡的影响。理论研究和仿真结果表明:网约车平台合理的补贴力度和抽成力度可以有效规避行政监管成本增加和乘客资源流失的风险,提高双方的收益,实现社会的帕累托最优。     

The application of information and communication technologies in transport

This paper examines the possibilities that are opened today and for the whole decade from the application of Information and Communication Technologies (ICTs), in the field of Transport. The various applications are examined, under the following three headings: operation and management of networks (all modes), information and guidance to the users (of the transport systems), operation and management of freight transport systems.For each of these, a concise and critical review is made of the various technologies that exist today in their final stages of development or at the stage of commercial implementation, and their applications. The review refers to various sub-categories of the above main three.The paper proceeds then to examine the prospects for the future with a medium time horizon of 2010. These prospects show that a number of areas of applications have well established technologies and are secured of commercial viability so that we can predict safely their full scale application in the course of this decade. Examples of such areas of applications are: traffic data information collection and dissemination systems, network control and traffic management strategies, vehicle control and driver assistance, systems for (Electronic or other) fee collection.And specifically for freight: freight resource management; terminal and port information and communication systems, freight and vehicle tracking and tracing, and “front” or “back-office” logistics systems.     

A 3D modeling of static and forward smoldering combustion in a packed bed of materials

A three-dimensional (3D) model based on the first principles of mass, momentum and energy was developed that numerically simulates the processes of static and forward smoldering in a porous packed bed of plant materials. The packed bed contains cellulose material or tobacco (cigarette) wrapped in a porous paper and surrounded by an ambient air. Other major characteristics of the model are including the effects of buoyancy forces in the flow field, separate treatment of solid and gas in a thermally non-equilibrium environment, and use of multi-precursor kinetic models for the pyrolysis of staring material and oxidation of char. The changes in porosity due to pyrolysis and char oxidation and the effect of porosity on the bed permeability and gas diffusivity are included. The mass, momentum, energy, and species transport equations are solved in a discretized computational domain using a commercially available computational fluid dynamics (CFD) code. The simulation results show that the model reasonably reproduces the major features of a burning cigarette during smoldering and puffing and are in a good agreement with the existing experimental results for cigarettes. Results include the velocity profiles, gas and solid temperatures, coal shape, burn rates, profile and transport of gas and vapor species throughout the packed bed, dilution through the wrapper paper and ventilation in the filter section, and the mass fraction of some pyrolysis and oxidation products in the mainstream and sidestream flows.