一类渐近线性对称Hamilton方程组多个周期解的存在

本文利用对称性,将一类偶对称渐近线性Hamilton方程组归为Amann-Zehnder所建立的在∞处非共振渐近线性算子方程的约化理论框架之下,由此给出了多个非平凡周期解存在的一个充分性条件。     

一类渐近线性Neumann问题正解的存在性

利用变分法获得了一类渐近线性N eum ann问题正解的存在性结果.     

一类具有渐近线性项的奇异边值问题的正解

讨论全类具有渐近线性项的奇异边值问题,利用锥拉压不动点定理,获得了其正解的存在性。     

渐近线性碰撞振子的不变环面

利用后继映射和推广的Moser扭转定理证明了渐近线性碰撞振子的不变环面和拟周期解的存在性.     

带Hardy位势的双调和椭圆方程的正负解及变号解

本文讨论带Hardy位势的四阶渐近线性椭圆方程,应用变分方法,我们得到了正负解及变号解的存在性.     

具有无界非线性项的半线性椭圆共振问题

本文中我们研究一类在高阶特征值处共振、具有无界的非线性项的渐近线性椭圆方程的非平凡解的存在性．     

一类差分系统边值问题在渐近线性下的多解存在性

应用临界点理论,获得了一类差分系统边值问题在渐近线性下存在多个非平凡解的条件.     

求曲线的斜渐近线的泰勒展开方法

给出求曲线的斜渐近线的等价方法,指明存在斜渐近线的函数特征,并借助于函数的泰勒展开式求曲线的斜渐近线     

关于平面曲线渐近线的几个注记

针对学生在学习渐近线中出现的问题,本文对渐近线的概念、几何意义和求解思路进行了整理,并通过实例总结了求渐近线的方法与技巧,给出了无穷远处线性化方法求水平和斜渐近线方程的原理和方法.     

双曲线的渐近线

在圆锥曲线的诸多几何性质中,渐近线是双曲线特有的几何性质,因此在讨论有关双曲线的问题时,常与渐近线有关．熟悉渐近线的性质,准确把握渐近线的特殊地位,会给我们解决一些复杂的问题带来很大方便．本文遴选几例,借以说明双曲线渐近线在解题中的应用．     

Noncommutative geometry and motives: The thermodynamics of endomotives

We combine aspects of the theory of motives in algebraic geometry with noncommutative geometry and the classification of factors to obtain a cohomological interpretation of the spectral realization of zeros of L-functions. The analogue in characteristic zero of the action of the Frobenius on ?-adic cohomology is the action of the scaling group on the cyclic homology of the cokernel (in a suitable category of motives) of a restriction map of noncommutative spaces. The latter is obtained through the thermodynamics of the quantum statistical system associated to an endomotive (a noncommutative generalization of Artin motives). Semigroups of endomorphisms of algebraic varieties give rise canonically to such endomotives, with an action of the absolute Galois group. The semigroup of endomorphisms of the multiplicative group yields the Bost-Connes system, from which one obtains, through the above procedure, the desired cohomological interpretation of the zeros of the Riemann zeta function. In the last section we also give a Lefschetz formula for the archimedean local L-factors of arithmetic varieties.     

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.     

Peridynamics via finite element analysis

Peridynamics is a recently developed theory of solid mechanics that replaces the partial differential equations of the classical continuum theory with integral equations. Since the integral equations remain valid in the presence of discontinuities such as cracks, the method has the potential to model fracture and damage with great generality and without the complications of mathematical singularities that plague conventional continuum approaches. Although a discretized form of the peridynamic integral equations has been implemented in a meshless code called EMU, the objective of the present paper is to describe how the peridynamic model can also be implemented in a conventional finite element analysis (FEA) code using truss elements. Since FEA is arguably the most widely used tool for structural analysis, this implementation may hasten the verification of peridynamics and significantly broaden the range of problems that the practicing analyst might attempt. Also, the present work demonstrates that different subregions of a model can be solved with either the classical partial differential equations or the peridynamic equations in the same calculation thus combining the efficiency of FEA with the generality of peridynamics. Several example problems show the equivalency of the FEA and the meshless peridynamic approach as well as demonstrate the utility and robustness of the method for problems involving fracture, damage and penetration.     

Analysis of the Stress State of the Surface Layer of a Polymeric Mass upon Filling of Bulky Compression Molds

The stress state of the surface layer of a polymeric mass during filling of bulky compression molds is analyzed. It is shown that, at particular rheological characteristics of the mass, temperature, and filling rates, cracking of the surface layer occurs, which leads to defects in the finished products. A physical analysis of this process makes it possible to conclude that the cracks arise due to the normal stresses operating in the front region of the moving polymeric mass. It is found that, under certain flow conditions, areas with a pressure lower than the atmospheric one appear on the surface of the polymer. If the tensile stresses arising in these local regions are higher than the tensile strength of the mass, the continuity of the composition is broken in the direction determined by the greatest rate of the normal deformation. To confirm the reliability of the crack-formation mechanism proposed, the distribution of the pressure and normal stresses over the free surface is calculated based on a numerical method. These calculations show that, by comparing the stress level achieved in the front region with the tensile-strength characteristics of the polymeric composition, it is possible to predict, with a sufficient accuracy, the possibility of crack formation in the surface layer of such a mass under given flow conditions and thus to solve the question on flawless manufacturing of products.     

基于综合重要度的动车组多部件系统机会维修策略研究

针对我国动车组列车现行维修方式,提出基于综合重要度序列的动车组多部件系统机会维修策略,对提高系统可靠度贡献大的关键部件进行准时优先维修。建立部件综合重要度指数计算模型,并依据其对部件维修优先级进行排序。以维修总成本最低为目标计算单部件最优维修周期及时刻,以系统维修总成本最低为目标,以关键部件的维修时刻为系统停机时刻建立考虑重要度的多部件系统机会维修模型。算例选取某型动车组四级修时更换的四部件系统为研究对象,讨论机会维修里程窗的大小及其偏移量对维修效果的影响,对比结果表明,考虑综合重要度的机会维修策略能够在维修费用基本持平的条件下,保证对系统可靠性贡献大的关键部件的可靠性,进而保证系统的整体可靠性。     

The Dirichlet divisor problem,traces and determinants for complex powers of the twisted bi-Laplacian

Estimating the counting function for the eigenvalues of the twisted bi-Laplacian leads to the Dirichlet divisor problem, which is then used to compute the trace of the heat semigroup and the Dixmier trace of the inverse of the twisted bi-Laplacian. The zeta function regularizations of the traces and determinants of complex powers of the twisted bi-Laplacian are computed. A formula for the zeta function regularizations of determinants of heat semigroups of complex powers of the twisted bi-Laplacian is given.     

Clustering Methods in Microarrays

Summary DCT Given a finite set of points in an Euclidean space the \emph{spanning tree} is a tree of minimal length having the given points as vertices. The length of the tree is the sum of the distances of all connected point pairs of the tree. The clustering tree with a given length of a given finite set of points is the spanning tree of an appropriately chosen other set of points approximating the given set of points with minimal sum of square distances among all spanning trees with the given length. DCM A matrix of real numbers is said to be column monotone orderable if there exists an ordering of columns of the matrix such that all rows of the matrix become monotone after ordering. The {\emph{monotone sum of squares of a matrix}} is the minimum of sum of squares of differences of the elements of the matrix and a column monotone orderable matrix where the minimum is taken on the set of all column monotone orderable matrices. Decomposition clusters of monotone orderings of a matrix is a clustering ofthe rows of the matrix into given number of clusters such that thesum of monotone sum of squares of the matrices formed by the rowsof the same cluster is minimal.DCP A matrix of real numbers is said to be column partitionable if there exists a partition of the columns such that the elements belonging to the same subset of the partition are equal in each row. Given a partition of the columns of a matrix the partition sum of squares of the matrix is the minimum of the sum of square of differences of the elements of the matrix and a column partitionable matrix where the minimum is taken on the set of all column partitionable matrices. Decomposition of the rows of a matrix into clusters of partitions is the minimization of the corresponding partition sum of squares given the number of clusters and the sizes of the subsets of the partitions.     

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.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

Mario Pieri’s address at the University of Catania

The contributions made by the Italian mathematician Mario Pieri (1860-1913) are well known in the field of geometry. Pieri was a member of the School of Peano at the University of Turin. There he became engaged both by the problems of logic and by the philosophical aspects of Peano’s epistemology. This article was motivated by Pieri’s address given at the University of Catania, at the inauguration of the 1906-1907 academic year. My aim is to identify Pieri’s philosophical premises as found in his works and to present them in the general framework of the historical development of the Peano School.