概率生成函数及其在随机微分方程中的应用

由于概率生成函数和分布函数一一对应,分布函数唯一确定概率生成函数;概率生成函数也唯一确定分布函数,并且使用概率生成函数做为取整数值的离散随机变量的研究工具比用分布函数在许多方面显得更加简便,因此,概率生成函数已成为概率论的重要分析工具之一。     

自由树的端点数问题(英文)

本文研究具有 n 个节点的、所有结构不同的自由树的端点总数,得到了关于这些数的计算公式,给出了其生成函数与 n 节点有向树个数的生成函数和 n 节点有向数总叶数生成函数之间的一个简明关系.主要结果是:定理 设 E_n为具有 n 个节点的、所有结构不同的自由树的端点总数,则 E_n 的生成函数E(z)=sum from n=1 to ∞ E_n~z~n 满足E(z)=L(z)+zA(z)-A(z)L(z)+L(z~2),其中 A(z)和 L(z)分别是 n 节点有向树的个数 a_n 和总叶数 L_n 的生成函数.此外,E_n=(?)计算结果如正文中的数表所示.     

有限集合的部分映射生成的格

本文研究了有限集合[n]={1,2,···,n}的部分映射生成的格.利用秩函数和M¨obius函数,讨论了这类格的几何性,得到了它们的特征多项式.推广了有限集合生成格的相关性质.     

有限集合的部分映射生成的格（英文）

本文研究了有限集合[n]={1,2,···,n}的部分映射生成的格.利用秩函数和M¨obius函数,讨论了这类格的几何性,得到了它们的特征多项式.推广了有限集合生成格的相关性质.     

依概率收敛与依分布收敛的关系

本文探讨了随机变量序列依概率收敛与依分布收敛的关系 ,并给出了一个依分布收敛能保证依概率收敛的最弱的条件 ,即 :设分布函数列 { Fn(x) }弱收敛于连续的分布函数 F(x) ,则存在随机变量序列{ξn}和随机变量ξ,它们分别以 { Fn(x) }和 F(x)为其对应的分布函数列和分布函数 ,且 {ξn}依概率收敛于ξ.     

关于数列{Γ(n+1/2)/√nΓ(n/2)}+∞n=1的极限

用单调有界定理证明了数列{Γ(n+1/2)/√nΓ(n/2)}+∞n=1的奇子列和偶子列极限的存在性,并给出了该数列的极限为1/√2.本文所得结果对帮助学生更好理解概率统计论中t分布密度函数的极限函数的证明有一定指导作用.     

关于Lucas多项式平方和的恒等式

利用广义Lucas多项式L n(x,y)的性质,通过构造组合和式T n(x,y;tx2),结合Bernoulli多项式的生成函数和Euler多项式的生成函数,采用分析学中的方法,得到两个有关L2n(x,y)的恒等式.并从这一结果出发,得到了两个推论,推广了相关文献的一些结果.     

书本图与齿轮图的子树计数及渐进密度特性分析

图的子树数拓扑指标对指导可靠性网络设计和分析化合物的物理与化学性质均具有重要意义.本文基于生成函数、结构分析及矩阵映射的方法给出书本图B_(n,2)(n≥2)和齿轮图G_(n,1)(n≥3)的子树数生成函数,并分析了B_(n,2)(n≥2)和G_(n,1)(n≥3)的子树密度的渐进特性,本研究为探索复杂圈图和分子的结构新特性提供了新的视角和方法.     

划分格中的Mbius函数和秩生成函数

设S={1,2,…,n},P(n)是由S的所有划分组成的集合.对于π,σ∈P(n),如果π中的每个块包含在σ的一个块里,就定义π≤σ,那么P(n)作成一个格.如果M(n,k)是由S的所有k部划分组成的集合,而L(n,k)是由M(n,k)生成的格.在P(n)和L(n,k)中,给出M(o|¨)bius函数,并且确定了特征多项式和秩生成函数的表示式.     

Weighted estimates for commutators of higher dimensional Hardy operators

得到了由加权Lipschitz函数(或加权CMO函数)和n维Hardy算子生成的交换子在一些函数空间的有界性,例如加权Lebesgue空间,加权Herz型空间.     

颤振分析中的特征值排序问题

颤振分析中判断颤振临界速度的重要依据是系统V-g和V-f图,即系统特征值随参数的变化曲线.在几乎所有商用软件及自编程序的输出结果中,有时会出现所谓的"窜支"现象,这给颤振临界速度和颤振穿越分支及耦合形式的判断带来很大不便.通过隐函数定理可以证明,除重特征值点以外,系统特征值连续依赖于系统参数变化.依据多元向量值函数连续性,建立对特征值的排列算法,给出系统特征根轨迹的正确曲线,再输出V-g和V-f图数据,从而避免"窜支"现象.编制应用程序,通过几个典型算例对算法进行了验证.该工作能够有效简化颤振分析的后处理工作,提高分析效率.     

Creep of polymer concrete in the nonlinear region

Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference in their porosity. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.) Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000.     

A model for predicting the shear bearing capacity of FRP-strengthened beams

The shear failure of reinforced concrete beams needs more attention than the bending failure since no or only small warning precedes the failure. For this reason, it is of utmost importance to understand the shear bearing capacity and also to be able to undertake significant rehabilitation work if necessary. In this paper, a design model for the shear strengthening of concrete beams by using fiber-reinforced polymers (FRP) is presented, and the limitations of the truss model analogy are highlighted. The fracture mechanics approach is used in analyzing the bond behavior between the FRP composites and concrete. The fracture energy of concrete and the axial rigidity of the FRP are considered to be the most important parameters. The effective strain in the FRP when the debonding occurs is determined. The limitations of the anchorage length over the cross section are analyzed. A simple iterative design method for the shear debonding is finally proposed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 357–372, May–June, 2008.     

Variation of the structure and permeability of tensioned fiber layers during impregnation with a thermoplastic polymer melt

The influence of displacements of tensioned fibers on the impregnation of fibrous layers with a polymer melt and on the final composite structure is studied. Using computer simulation, it is shown that, during impregnation, the structure of tensioned fibrous layers changes considerably depending on the initial arrangement and tensioning of fibers. The consolidated regions formed under the melt front move inside the impregnated layer with the advancing melt front. Displacement of the tensioned fibers as well as the formation of “washouts” favors the impregnation of internal layers, but cause significant inhomogeneity of the polymer structure. The surface (on the side of the melt flow) regions are more saturated with the polymer than the internal ones. A difference in the melt percolation mechanisms at various impregnation regimes is revealed. The effective permeability coefficients of a tensioned fiber layer are not constant but depend on the conditions and regimes of impregnation. Submitted to the 11th Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 259–270, March–April, 2000.     

Exact and stable least squares solution to the linear programming problem

A linear programming problem is transformed to the finding an element of polyhedron with the minimal norm. According to A. Cline [6], the problem is equivalent to the least squares problem on positive ortant. An orthogonal method for solving the problem is used. This method was presented earlier by the author and it is based on the highly developed least squares technique. First of all, the method is meant for solving unstable and degenerate problems. A new version of the artifical basis method (M-method) is presented. Also, the solving of linear inequality systems is considered.     

Testing Ten Theories

Using the most comprehensive data set now available, this investigation tests the precision of all exchange theories that now contend. Beyond precision, the investigation focuses on broad issues of effectiveness including consistency, parsimony, and whether the theories can be applied to structures larger than normally studied in the lab. Seeking greater parsimony, this investigation introduces a new model by combining parts of two contending theories. We find that all ten theories have scientific merit for all can predict with some effectiveness for the exchange structures experimentally investigated. Nevertheless, the ten vary in precision. Elementary Theory is the most precise. The new Expected-value Resistance model ranks second in precision and is the simplest. Both apply to large networks as well as the best of the other theories.     

Unsteady motion of a spherical bubble in a complex fluid: Mathematical modelling and simulation

The nonlinear response of an oscillatory bubble in a complex fluid is studied. The bubble is immersed in a Newtonian liquid, which may have a dilute volume fraction of anisotropic additives such as fibers or few ppm of macromolecules. The constitutive equation for the fluid is based on a Maxwell model with an extensional viscosity for the viscous contribution. The model is considered new in the study of bubble dynamics in complex fluids. The numerical computation solves a system of three first order ordinary differential equations, including the one associated with the solution of the convolution integral, using a fifth order Runge–Kutta scheme with appropriated time steps. Asymptotic solutions of governing equation are developed for small values of the pressure forcing amplitude and for small values of the elastic parameter. A study of the bubble collapse radius is also presented. We compare the results predicted by our model with other model in the literature and a good agreement is observed. The calculated asymptotic solutions are also used to test the results of the numerical simulations. In addition, the orientation of the additives is considered. The angular probability density function is assumed to be a normal distribution. The results show that the model based on the fully aligned additives with the radial direction overestimates the tendency of the additives to stabilize the bubble motion, since the effect of extensional viscosity occurs due to the particle resistance to the movement throughout its longitudinal direction.     

拍卖机制设计在区块链中的应用与挑战

区块链是新一代信息技术的重要组成部分,是分布式网络、加密技术、智能合约等多种技术集成的新型数据库软件。过去的十多年,区块链技术在全球范围内产生广泛影响。如今的区块链技术,已从最初的关注于解决货币和支付的去中心化问题,转入到解决市场的去中心化问题。智能合约的出现使得基于区块链技术的去中心化金融进入高速发展状态,也涌现出区块链环境下的各类拍卖场景。本文首次从机制设计角度,以区块链交易费机制,非同质化代币(Non-Fungible Token,NFT)拍卖和矿工可提取价值(Miner-Extractable Value,MEV)交易位置拍卖为主要对象,总结和剖析近些年来区块链上特有的拍卖机制;并针对区块链特性,提出区块链上拍卖机制设计所面临的挑战和未来亟待解决的问题。     

考虑服务和退货的双渠道供应链定价问题研究

在考虑零售服务和消费者退货情况下,运用两阶段优化方法分别探究了集中式和分散式两种双渠道供应链的最优定价策略。研究发现零售服务有助于提高零售商的渠道权力,并始终使制造商获益,但只有当服务水平小于某一临界值时,才使制造商和零售商同时得到帕累托改进。零售价格和直销价格与退货率正相关,而与服务水平的关系受渠道结构的影响。服务水平的提高加剧了供应链的“双重边际化”效应,制造商通过生产与消费者需求相匹配的产品来降低退货风险可以减弱这种效应,从而提高供应链效率。     

Gaussian Versus Optimal Integration of Analytic Functions

We consider error estimates for optimal and Gaussian quadrature formulas if the integrand is analytic and bounded in a certain complex region. First, a simple technique for the derivation of lower bounds for the optimal error constants is presented. This method is applied to Szeg?-type weight functions and ellipses as regions of analyticity. In this situation, the error constants for the Gaussian formulas are close to the obtained lower bounds, which proves the quality of the Gaussian formulas and also of the lower bounds. In the sequel, different regions of analyticity are investigated. It turns out that almost exclusively for ellipses, the Gaussian formulas are near-optimal. For classes of simply connected regions of analyticity, which are additionally symmetric to the real axis, the asymptotic of the worst ratio between the error constants of the Gaussian formulas and the optimal error constants is calculated. As a by-product, we prove explicit lower bounds for the Christoffel-function for the constant weight function and arguments outside the interval of integration. September 7, 1995. Date revised: October 25, 1996.