模糊正则文法的逼近性

为了扩大现有研究的应用范围,基于max-min型模糊正则文法引入了max-*型模糊正则文法(其中*为特定t-模)的概念,讨论了max-*型模糊正则文法可以通过max-min型模糊正则文法在任意给定的逼近精度来逼近.研究表明,当t-模*满足一定的条件时,max-*型模糊正则文法与max-min型模糊正则文法在生成模糊语言能力方面是等价的.     

Homeomorphs and amallamorphs of the Petersen graph

Let P be the Petersen graph. The main results of this paper are the discovery of infinite families of chromatically equivalent pairs of P homeomorphs and the discovery of infinite families of flow equivalent pairs of P amallamorphs. In particular, three families of P homeomorphs with 8 parameters, five families with 7 parameters and many families with fewer parameters are obtained. Also one family of P amallamorphs with 9 parameters, three families with 7 parameters, seven families with 6 parameters and many families with fewer parameters are obtained.     

多元整系数多项式因式分解的一种理论和算法

本文将ｔ（ｔ是大于２的整数）元整系数多项式看成为系数为ｔ－２元整系数多项式的二元多项式，建立了多元整系数多项式因式分解的一种新理论，进而得到了分解多元整系数多项式的一个有力的算法。     

带两个服务等级的三台机最优在线算法

研究了带服务等级约束的三台平行机在线排序问题.每台机器和每个工件的服务等级为1或者2,工件只能在等级不高于它的机器上加工,即等级为1的工件只能在等级为1的机器上加工,等级为2的工件可在所有机器上加工.每个工件的加工时间为一个单位,目标是极小化所有工件的总完工时间.考虑两种情形:当一台机器等级为1,两台机器等级为2时,给出了竞争比为17/14的最优在线算法;当两台机器等级为1,一台机器等级为2时,给出了竞争比为43/36的最优在线算法.     

变厚度圆薄板非对称非线性弯曲问题

首先将直角坐标系中的横向变厚度薄板的大挠度方程,转化到极坐标系中的变厚度圆薄板的非对称大挠度方程·　此方程和极坐标系中径向、切向两个平衡方程联立求解·　将物理方程和中面应变非线性变形方程,代入3个平衡方程,可得用3个变形位移表示的3个非对称非线性方程·　用Fourier级数表示的解代入基本方程,获得相应的基本方程·　在周边夹紧边界条件下,用修正迭代法求解·　作为算例,研究了余弦形式载荷作用下的问题,还给出了载荷与挠度的特征曲线,曲线依据变厚度参数变化而变化,其结果和物理概念完全吻合·     

M/G/1一般减量服务单重休假排队系统的随机分解

本文讨论了M/G/1型一般减量服务单重休假排队模型,运用结构分析法得到稳态队长和服务时间的随机分解的母函数和拉式变换,并给出稳态分布成立的条件及其概率含义．     

Optimal regulation of the service rate for a queue with finite waiting space

The optimal control for the service rate of a single-server queue with limited waiting space is derived. Costs are associated with providing the service and with waiting. A comparison with the traditional steady-state result is made.     

A generalized model for data envelopment analysis with interval data

Data envelopment analysis (DEA) is a method to estimate the relative efficiency of decision-making units (DMUs) performing similar tasks in a production system that consumes multiple inputs to produce multiple outputs. So far, a number of DEA models with interval data have been developed. The CCR model with interval data, the BCC model with interval data and the FDH model with interval data are well known as basic DEA models with interval data. In this study, we suggest a model with interval data called interval generalized DEA (IGDEA) model, which can treat the stated basic DEA models with interval data in a unified way. In addition, by establishing the theoretical properties of the relationships among the IGDEA model and those DEA models with interval data, we prove that the IGDEA model makes it possible to calculate the efficiency of DMUs incorporating various preference structures of decision makers.     

Four equivalent lot-sizing models

We study the following lot-sizing models that recently appeared in the literature: a lot-sizing model with a remanufacturing option, a lot-sizing model with production time windows, and a lot-sizing model with cumulative capacities. We show the equivalence of these models with a classical model: the lot-sizing model with inventory bounds.     

Arithmetical and specular self-reference

Arithmetical self-reference through diagonalization is compared with self-recognition in a mirror, in a series of diagrams that show the structure and main stages of construction of self-referential sentences. A Gödel code is compared with a mirror, Gödel numbers with mirror images, numerical reference to arithmetical formulas with using a mirror to see things indirectly, self-reference with looking at one’s own image, and arithmetical provability of self-reference with recognition of the mirror image. The comparison turns arithmetical self-reference into an idealized model of self-recognition and the conception(s) of self based on that capacity.     

On time-dependent behavior of cross-ply laminated strips with viscoelastic interfaces

The two-dimensional problem of a simply supported laminated orthotropic strip with viscoelastic interfaces under static loading is studied. State-space formulations are developed based on the exact elasticity equations governing orthotropic media and the Kelvin–Voigt constitutive relation of interfaces. Since the response of the strip is time-dependent, the power series expansion technique is adopted to model the variations of elastic fields with time. Results show that the response of the laminated strip with viscoelastic interfaces changes remarkably with time, which is also significantly different from that of a plate with perfect interfaces or with viscous interfaces. Note that from the present analysis, the response for a laminated plate with spring-like interfaces or with viscous interfaces can be easily obtained because they are just two particular cases of the present Kelvin–Voigt model.     

Higher-order accurate polyspectral estimation with flat-top lag-windows

Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical estimators with second-order kernels. A simple, data-dependent algorithm for selecting the bandwidth is introduced and is shown to be consistent with estimating the optimal bandwidth. The combination of the specialized family of kernels with the new bandwidth selection algorithm yields a considerably improved polyspectral estimator surpassing the performances of existing estimators using second-order kernels. Bispectral simulations with several standard models are used to demonstrate the enhanced performance with the proposed methodology.     

直径为n-4的图的最小无号拉普拉斯谱半径

Liu Lu和Shu等在[The minimal Lapacian spectral radius of trees with a given diameter,Theoretical Computer Science,2009,410:78-83]中分别给出了直径为{1,2,3,4,n-3,n-2,n-1}的具有最小拉普拉斯谱半径的树.本文给出了直径为n-4的具有最小无号拉普拉斯谱半径的图.作为推论,给出了直径为n-4的具有最小拉普拉斯谱半径的村.     

Records with confirmation

In the present paper, the concept of records with confirmation is proposed. This new concept implies that such records cannot be contaminated with sample outliers. On determining records with confirmation, we discuss their distributional and limit properties. A test based on records with confirmation is provided in our work. We also present simulation techniques for generating record values with confirmation.     

考虑耗散效应的金属杆受扰动后的非线性动力学现象分析

研究在周期外载荷作用及Neumann边界条件下,考虑Peierls-Nabarro效应的有限长一维金属杆的运动,以位移表达杆的控制方程,是受扰动的类sine-Gordon方程．利用空间四阶精度,时间二阶精度的有限差分格式模拟系统的动力响应．对于一定特征尺寸及物理性质的金属杆,研究了初始呼吸子及周期载荷幅值对杆动力行为的影响,结果显示了4种典型的动力行为:与空间位置无关的简谐运动、单波的简谐运动、单波的准周期运动和单空间模态的时间混沌运动．通过Poincaré截面和功率谱确定系统的运动特征．     

On active redundancy allocation for coherent systems—from the viewpoint of minimal cut decomposition

This paper deals with coherent systems with one active redundancy. For systems with the subclass of minimal cuts associated with one component covering that of another, assigning the redundancy to the former component is proved to bring forth a more reliable redundant system. As for symmetric systems with lower tail permutation decreasing component lifetimes, allocating the redundancy to the less reliable component results in a longer system lifetime. Several numerical examples are also presented to illustrate the new findings.     

Hankel operators, the Segal-Bargmann space, and symmetrically-normed ideals

Starting with the Segal-Bargmann space, we investigate the Hankel operators with symbol functions in a certain linear space. Given an appropriate symbol function, we consider the associated Hankel operator together with the Hankel operator associated with that symbol function's complex conjugate. We give a necessary and sufficient condition for the simultaneous membership of these two operators in the symmetrically-normed ideal associated with any given symmetric norming function.     

Brownian motion with drift on spaces with varying dimension

Many properties of Brownian motion on spaces with varying dimension (BMVD in abbreviation) have been explored in Chen and Lou (2018). In this paper, we study Brownian motion with drift on spaces with varying dimension (BMVD with drift in abbreviation). Such a process can be conveniently defined by a regular Dirichlet form that is not necessarily symmetric. Through the method of Duhamel’s principle, it is established in this paper that the transition density of BMVD with drift has the same type of two-sided Gaussian bounds as that for BMVD (without drift). As a corollary, we derive Green function estimate for BMVD with drift.     

具有第二大基指数的本原对称带号有向图的刻画

Recently, the primitive symmetric signed digraphs on n vertices with the maximum base 2n and the primitive symmetric loop-free signed digraphs on n vertices with the maximum base 2n-1 are characterized, respectively. In this paper, the primitive symmetric signed digraphs with loops on n vertices with the base 2n-1 are characterized, and then the primitive symmetric signed digraphs on n vertices with the second maximum base 2n-1 are characterized.     

具有四条裂纹的圆形孔口问题的应力分析

利用复变函数的方法,通过构造保角映射研究了具有四条裂纹(一对非对称共线裂纹和一对对称共线裂纹)的圆形孔口的平面弹性问题,给出了裂纹尖端应力强度因子的解析解.并由此模拟出了具有三条裂纹、对称四条裂纹、非对称共线双裂纹、对称共线双裂纹的圆形孔口,以及非对称十字裂纹,十字裂纹,T形裂纹问题.