算子代数的斜积

引入了算子代数的一种新运算"斜积",证明了在这个新定义的斜积运算下算子代数的自反性保持不变.研究发现,斜积运算对应的子空间格是拓扑意义下的格的直积关系.这个新发现的重要意义在于由此可从已知的自反子空间格生成更多更复杂的新自反格,从而得到新的自反代数.在此基础上,本文对KS-代数保持性等其他非自伴代数类的性质也作了相应研究.     

一类非Hopf 代数的双Frobenius 代数

本文构造了一类非Hopf 代数的双Frobenius 代数. 特别地, 在某些特殊的情形下, 这里构造的双Frobenius 代数是整体维数为3 的阶1 生成的Artin-Schelter 正则代数的Yoneda 代数.     

Fuzzy蕴涵代数与MV代数

本文讨论Ｆｕｚｚｙ蕴涵代数与ＭＶ代数之间的关系，并证明了在一定的条件下Ｆｕｚｚｙ蕴函代数是剩余格。     

正整数集上的闭包函数

解答了P.C.Hammer于1960年提出的问题:设h是在正整数集M的幂集上以集乘积来定义的闭包函数,c是幂集上的补余函数,问可否在集M中找出子集A,使A在h与c的任意作用下,恰可衍生出14个不同的集合?并给出各种不同的例子.     

一类商代数上的双-Frobenius代数结构

设C[X]为复数域上的一元多项式代数,I为n+1次Dickson多项式E_(n+1)(X)生成的C[X]的理想,C[X]/I为商代数.证明了商代数C[X]/I既是Frobenius代数,又是Frobenius余代数.进一步,该商代数在恒等对极下还是双-Frobenius代数.     

Fuzzy锁代数

众所周知,论域X上的全体Fuzzy子集[0,1]~x,在L. A. Zadeh的∪,∩,C(余运算)意义下,由于排中律不成立,而只能构成“软”代数。可是我们还注意到了Giles. R在1976年提出的算子(?),(?)及C运算所构成的代数系统,确定非分配的“硬”代数结构。本文从这一类算子出发,抽象出一个新的代数系统——Fuzzy锁代数。并研究了它的代数结构。     

BCYB代数的常个体及ZY3代数的简化刻画

证明了在等价意义下,BCYB代数有常个体,同时还简化了ZY3代数的刻画规则。     

泊松着色代数

首先,给出了泊松着色代数的定义及构造泊松着色代数的一种方法,其次,证明了在张量积的运算下泊松着色代数是封闭的,最后,通过容许泊松着色代数及其上的非结合二元运算等价定义了泊松着色代数.     

(3,1)-维李2-代数的分类（英文）

当V₀的维数是3,V₁的维数是1时,我们称李2-代数(V₁ ■V₀,l₂,l₃)为一个(3,1)-维李2-代数.我们分别给出了(3,1)-维李2-代数在等价、同构、线性同构三种关系下的分类.有趣的是,在这种情况下,等价和同构下的分类是一致的.     

一般扭算子李代数g(G,l)[σ]的结构

扭算子李代数在研究李代数的结构中有着广泛的应用,因而讨论扭算子李代数的结构具有很重要的意义.讨论了随着G,l的选取,在各种情形下扭算子李代数g(G,l)[σ]所具有的代数结构.     

Nonparametric Density Estimation for a Long-Range Dependent Linear Process

We estimate the marginal density function of a long-range dependent linear process by the kernel estimator. We assume the innovations are i.i.d. Then it is known that the term of the sample mean is dominant in the MISE of the kernel density estimator when the dependence is beyond some level which depends on the bandwidth and that the MISE has asymptotically the same form as for i.i.d. observations when the dependence is below the level. We call the latter the case where the dependence is not very strong and focus on it in this paper. We show that the asymptotic distribution of the kernel density estimator is the same as for i.i.d. observations and the effect of long-range dependence does not appear. In addition we describe some results for weakly dependent linear processes.     

制造业行业收入差距的影响因素及解决路径分析——以浙江省宁波市为例

本文以浙江省宁波市制造业的行业小类为研究对象,以第一、二次经济普查数据为来源,细分以特征及影响因素两大角度展开实证分析。研究发现:宁波市行业收入差距明显,各经济指标差异显著;同时,石油石化及烟草这两大行业凭借其强大的垄断性独占鳌头,而工艺品及其制造业则一直位列末端;福利性支出扩大了行业间的收入差距;且2004年到2008年,浙江省宁波市行业间的福利性收入差距在不断扩大,但行业间工资性收入差距却逐步缩小,总体上来看,该市人均收入差距缩小明显;两次经济普查中,影响因素的排序皆为:行业盈利能力,行业资本密度,行业垄断和行业技术效率,各因素的影响程度均在加强,以后两者最为明显;四因素对不同收入水平的群体影响程度不同。     

General binomial-type coefficients in the sequence of Bernstein operators

In this paper we study the sequence of Bernstein operators in the case when the binomial coefficients are substituted by general ones satisfying a similar recursive rule. Besides the characterization of the convergence and the approximation properties of the sequence of operators obtained in this manner, the main application regards the approximation of the solutions of suitable second-order parabolic problems. Work performed under the auspices of G. N. A. F. A. (C. N. R.) and M. U. R. S. T.     

Harmonic distrotions under nonlinear periodic deformation of fluid polymers

Conclusions 1. It has been shown for a number of viscoelastic fluid systems that under nonlinear periodic deformation, the contribution of the third harmonic of the stress to the fundamental does not exceed 20% of the amplitude.2. In the case of clay soil and melt of filled polyethylene, the shape of the stress waves is essentially definable by the relative phase angle of the third harmonic of the stress and is practically independent of the deformation amplitude in a growing nonlinear range of deformation.3. In the case of the polyethylene melt, the amplitude dependence of the phase angles of the stress harmonics is in satisfactory agreement with the analysis of model I. With increasing deformation amplitude, the modulus vector of the first harmonic rotates counterclockwise and remains in the first trigonometric quadrant; the modulus vector of the third harmonic passes from the second to the third quadrant, and the modulus vector of the fifth harmonic passes from the second to the fourth quadrant via the third.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 893–898, September–October, 1978.     

The generalized Cauchy problem with data on two surfaces for a quasilinear analytic system

We consider the generalized Cauchy problem with data on two surfaces for a second-order quasilinear analytic system. The distinction of the generalized Cauchy problem from the traditional statement of the Cauchy problem is that the initial conditions for different unknown functions are given on different surfaces: for each unknown function we pose its own initial condition on its own coordinate axis. Earlier, the generalized Cauchy problem was considered in the works of C. Riquier, N. M. Gyunter, S. L. Sobolev, N. A. Lednev, V. M. Teshukov, and S. P. Bautin. In this article we construct a solution to the generalized Cauchy problem in the case when the system of partial differential equations additionally contains the values of the derivatives of the unknown functions (in particular outer derivatives) given on the coordinate axes. The last circumstance is a principal distinction of the problem in the present article from the generalized Cauchy problems studied earlier.     

第二类Volterra型积分方程的Chebyshev-Legendre谱配置方法

提出了一种新的求解第二类线性Volterra型积分方程的Chebyshev谱配置方法.该方法分别对方程中积分部分的核函数和未知函数在Chebyshev-Gauss-Lobatto点上进行插值,通过Chebyshev-Legendre变换,把插值多项式表示成Legendre级数形式,从而将积分转换为内积的形式,再利用Legendre多项式的正交性进行计算.利用Chebyshev插值算子在不带权范数意义下的逼近结果,对该方法在理论上给出了L∞范数意义下的误差估计,并通过数值算例验证了算法的有效性和理论分析的正确性.     

Some observations on the performance of balloons from the rate of rotation of the fan in the F-Type radiosonde

If the rate of ascent of the balloon is constant, the rate of rotation of the fan in the F-Type radiosonde should decrease with height, due to the decrease in the density of the air. It was observed from the radiosonde ascents of Minicoy that the rate of rotation of the fan remained almost unchanged up to even 100 mb. It is shown that this is due to the increase in the rate of ascent of the balloon by about 2% of the value near the ground per km. ascent. Positive evidence of turbulence in the stratosphere is provided by the large fluctuations in the rate of rotation of the fan. It is also observed that the balloon whose fabric at the 50 mb. level is about 0·014 mm. thick bursts due to the turbulence.     

Optimization of the Relaxation Parameter for S.S.O.R. and A.D.I. Preconditioning

We present and compare several approaches for the optimization of the relaxation parameter both for A.D.I. and S.S.O.R. basic iteration and preconditioning conjugate gradient method. For each kind of preconditioning a detailed link between estimates of the spectral radius of the iteration matrix and of the condition number resulting from preconditioning is proposed. It allows to choose the best approach in order to obtain the optimal relaxation parameter and the corresponding optimal estimates either of the spectral radius of the iteration matrix and of the resulting condition mumber of the S.S.O.R. and A.D.I. preconditioning.     

Time to most recent common ancestor for stationary continuous state branching processes with immigration

Motivated by sample path decomposition of the stationary continuous state branching process with immigration, a general population model is considered using the idea of immortal individual. We compute the joint distribution of the random variables： the time to the most recent common ancestor （MRCA）, the size of the current population, and the size of the population just before MRCA. We obtain the bottleneck effect as well. The distribution of the number of the oldest families is also established. These generalize the results obtained by Y. T. Chen and J. F. Delmas.     

Minimum cost spanning tree games

We consider the problem of cost allocation among users of a minimum cost spanning tree network. It is formulated as a cooperative game in characteristic function form, referred to as a minimum cost spanning tree (m.c.s.t.) game. We show that the core of a m.c.s.t. game is never empty. In fact, a point in the core can be read directly from any minimum cost spanning tree graph associated with the problem. For m.c.s.t. games with efficient coalition structures we define and construct m.c.s.t. games on the components of the structure. We show that the core and the nucleolus of the original game are the cartesian products of the cores and the nucleoli, respectively, of the induced games on the components of the efficient coalition structure.This paper is a revision of [4].