集合的$\varOmega$-凸性及其基础性质[英文]

作为集合凸性概念的一种推广以及统一凸性与近似（nearly）凸性等概念的一种尝试, 本文引入集合$\varOmega$-凸性的概念, 并对$\varOmega$-凸集合的性质进行初步的研究. 另外, 本文还研究了一些常见变换与集合运算的保$\varOmega$-凸性质.     

L—fuzzy几乎良紧性的若干性质

进一步研究Ｌ－ｆｕｚｚｙ几乎良紧性的特征及其与良紧性，近似良紧性，几乎Ｆ紧性，可数良紧性和ＮＳ闭性等概念之间的关系。证明了Ｌ－ｆｕｚｚｙ几乎良紧性的是Ｌ－ｆｕｚｚｙ θ－闭遗传的拓扑不变的等重要性质。     

经验似然的冗余性

提出经验似然的冗余性和偏冗余性的概念,讨论了相应的冗余性等价条件,将GMM的冗余性结果推广到经验似然估计,同时模拟实验结果也证实了经验似然的冗余性和偏冗余性对估计的影响.     

Fuzzy序列紧性,可数Fuzzy紧性和Fuzzy列紧性

本文引进了Fuzzy序列紧性、可数Fuzzy紧性和Fuzzy列紧性,它们是一般拓扑学中相应概念的“良扩张”(R. Lowen意义下),文中讨论了这些fts的主要性质,以及它们之间的联系。     

L—Fuzzy拓扑空间中局部F紧性的可乘性

在文[9]中,作者提出了六种L—Fuzzy拓扑空间中的局部F紧性。即,强局部F紧性、星强局部F紧性,局部F紧性,星局部F紧性,弱局部F紧性和星弱局部F紧性。本文讨论了L-Fuzzy拓扑空间族的乘积空间(L~x,δ)的六种局部F紧性与其因子空间的相应局部F紧性之间的关系。证明了前四种局部F紧性是有限可乘性质,后两种局部F紧性是积稀有限可乘性质。最后给出了一类特殊空间是星局部F紧空间或星弱局部F紧空间的充要条件。     

滞后控制系统的完全能控性、毕竟能控性、最终能控性和拟能控性

讨论时滞控制系统的能控性 .指出与无时滞系统不同的是 ,该类系统的能控性与终点时刻有一定的关系 .由此给出一系列与终点时刻有关的能控性 ,即完全能控性、毕竟能控性、最终能控性等 ,并得到一些判定定理 .     

边值系统的能控性与能观测性问题

把抽象系统的能控性和能观测性推广到由强连续双半群描述的抽象边值系统,给出了相应的边值系统能控性的充要条件,并研究了能观测性与能控性之间的对偶关系.最后作为例子,研究了双曲系统能控性.文中所得的结果可用于讨论现代物理系统中出现一类边值系统的能控性与能观测性问题.     

平均跟踪性与双曲线性同胚

本文研究了双曲线性自同胚的平均跟踪性,利用双曲线性映射的性质和压缩映射定理,得到了在有界的Banach空间上的双曲线性自同胚具有平均跟踪性.另外,证明了在一般的度量空间上的压缩映射也具有平均跟踪性.     

具有突变率的广义生-灭过程——随机单调性、Feller性及可配称性

本文给出了具有突变率的广义生－灭过程的随机单调性、Feller性及可配称性的充要条件。     

半参数方差误差模型的估计

本文综合近邻权函数法及最小二乘法，用两阶段最小二乘估计的方法得到了半参数EV模型中参数的估计量及其强相合性，渐近正态性。同时也得到了非参数函数的估计量及其强相合性，一致强相合性。     

城市老旧居住小区交通环境评价指标与评价方法

定量的评判城市老旧居住小区整体交通环境质量并进而科学有效的提出老旧小区交通环境更新与改善措施,对城市老旧居住小区交通环境进行了调查,明确了老旧居住小区存在的突出交通问题,并提出了城市老旧居住小区交通环境评价的指标体系,包括行人跨路出行指数、无人行道路段长度占比、停车泊位供需比、路内非法停车占比、平均停车步行距离、泊位数量户数比、人均步行空间、无障碍通道、盲道设置比例、非机动车泊位供需比、地面停放车辆数小区面积比、外部穿行交通周转量小区面积比等。并给出了具体指标的计算方法与获得办法。以长沙市四个典型老旧居住小区为例,对评价方法进行了论证,并得到城市老旧居住小区存在的一般问题,包括人车混杂、人车交织现象严重,停车泊位短缺、车辆乱停乱放,交通设施、特别是弱势群体交通设施缺乏。给出的评价指标、评价方法与结论可为城市老旧小区改造更新,特别是其中很重要的交通环境更新提供决策依据。     

The generalized hierarchical product of graphs

A generalization of both the hierarchical product and the Cartesian product of graphs is introduced and some of its properties are studied. We call it the generalized hierarchical product. In fact, the obtained graphs turn out to be subgraphs of the Cartesian product of the corresponding factors. Thus, some well-known properties of this product, such as a good connectivity, reduced mean distance, radius and diameter, simple routing algorithms and some optimal communication protocols, are inherited by the generalized hierarchical product. Besides some of these properties, in this paper we study the spectrum, the existence of Hamiltonian cycles, the chromatic number and index, and the connectivity of the generalized hierarchical product.     

On free products in varieties of associative algebras

Varieties of associative algebras over a field of characteristic zero are considered. Belov recently proved that, in any variety of this kind, the Hilbert series of a relatively free algebra of finite rank is rational. At the same time, for three important varieties, namely, those of algebras with zero multiplication, of commutative algebras, and of all associative algebras, a stronger assertion holds: for these varieties, formulas that rationally express the Hilbert series of the free product algebra via the Hilbert series of the factors are well known. In the paper, a system of counterexamples is presented which shows that there is no formula of this kind in any other variety, even in the case of two factors one of which is a free algebra. However, if we restrict ourselves to the class of graded PI-algebras generated by their components of degree one, then there exist infinitely many varieties for each of which a similar formula is valid. Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 693–702, May, 1999.     

Uniform random number generation

In typical stochastic simulations, randomness is produced by generating a sequence of independent uniform variates (usually real-valued between 0 and 1, or integer-valued in some interval) and transforming them in an appropriate way. In this paper, we examine practical ways of generating (deterministic approximations to) such uniform variates on a computer. We compare them in terms of ease of implementation, efficiency, theoretical support, and statistical robustness. We look in particular at several classes of generators, such as linear congruential, multiple recursive, digital multistep, Tausworthe, lagged-Fibonacci, generalized feedback shift register, matrix, linear congruential over fields of formal series, and combined generators, and show how all of them can be analyzed in terms of their lattice structure. We also mention other classes of generators, like non-linear generators, discuss other kinds of theoretical and empirical statistical tests, and give a bibliographic survey of recent papers on the subject.     

Complex impure systems: Sheaves,freeways, and chains

Fundamental to the approach of Complex Impure Systems is the definition of the concept of an s‐impure set as a set of perceptual beliefs or denotative significances (relative beings) of material and/or energetic real objects (absolute beings). But any Subject not only the subject S perceives objects O as significances, and he perceives the existing relations between these significances or, alternatively, he infers them. The study of these relations, conceived not as a singular relation between singular objects, but as sheaves of relations in both directions and forming relational freeways, will be studied here. In this work, we approach the structure of the system, from a synchronous point of view, as a first approach to this class of systems. © 2016 Wiley Periodicals, Inc. Complexity 21: 387–400, 2016     

基于覆盖上近似算子的拟阵结构及其关系

Covering-based rough sets,as a technique of granular computing,can be a useful tool for dealing with inexact,uncertain or vague knowledge in information systems.Matroids generalize linear independence in vector spaces,graph theory and provide well established platforms for greedy algorithm design.In this paper,we construct three types of matroidal structures of covering-based rough sets.Moreover,through these three types of matroids,we study the relationships among these matroids induced by six types of covering-based upper approximation operators.First,we construct three families of sets by indiscernible neighborhoods,neighborhoods and close friends,respectively.Moreover,we prove that they satisfy independent set axioms of matroids.In this way,three types of matroidal structures of covering-based rough sets are constructed.Secondly,we study some characteristics of the three types of matroid,such as dependent sets,circuits,rank function and closure.Finally,by comparing independent sets,we study relationships among these matroids induced by six types of covering-based upper approximation operators.     

Generalized Weyl–Wigner–Moyal–Ville Formalism and Topological Groups

Discussed are some geometric aspects of the phase space formalism in quantum mechanics in the sense of Weyl, Wigner, Moyal, and Ville. We analyze the relationship between this formalism and geometry of the Galilei group, classical momentum mapping, theory of unitary projective representations of groups, and theory of groups algebras. Later on, we present some generalization to quantum mechanics on locally compact Abelian groups. It is based on Pontryagin duality. Indicated are certain physical aspects in quantum dynamics of crystal lattices, including the phenomenon of ‘Umklapp–Prozessen’. Copyright © 2011 John Wiley & Sons, Ltd.     

众筹筑屋建设规划方案的优化

对某众筹筑屋建设规划项目方案根据国家房屋开发成本、收益、增值额、增值税、容积率、回报率等相关计算办法和要求进行了核算,对已知参筹者对各种房型的满意比例的情况下,以平均满意率最大为目标函数,建立整数线性规划模型,给出了各种房型的最优规划套数,且回报率达到建设规划执行要求.     

Utilization and maintenance in a model with scrapping

We consider a productive asset, called equipment or capital good, and we examine the properties of, as well as the interactions between, the operating policies, which are determined by its optimal utilization and maintenance, and the capital policy of scrapping, which defines the optimal time when the productive asset is retired from its current use. Starting with an abstract model and using the approach of optimal control, initially we characterize the various types of equipment by assigning to them a single total profit index, which indicates how the above policies affect the flow of operating revenues plus capital gains or losses. This index is a function of market-determined prices. So using it we then investigate how the operating and capital policies are influenced by the rate of discount, the price of new equipment, and the rise or fall of the price of new equipment relative to the value of its output. Among other interesting results, we find that the effects of these prices on the nature and interactions of optimal policies depend crucially on whether the equipment is of the usual profit making type, where output is the main source of revenue, or of the antique type, where the main source of revenue is capital gains.