扁球壳在热-机械荷载作用下的稳定性分析

基于扁壳几何非线性理论,应用虚功原理和变分法推导了均匀变温场中圆底扁薄球壳在均布外侧压力作用下的位移型几何非线性控制方程.考虑周边不可移简支边界条件,运用打靶法计算获得了不同几何参数的扁球壳轴对称弯曲变形的数值结果.定义了壳体临界几何参数.考察了壳体几何参数对平衡路径和临界荷载的影响.当壳体几何参数大于壳体临界几何参数时,上临界荷载随几何参数的增加单调增加,下临界荷载在很小范围内随几何参数的增加而增加,之后随几何参数的增加而减小.给定几何参数时,考察了不同均匀温度变化对壳体临界几何参数、临界荷载和平衡构型的影响.均匀升温使上临界荷载显著增加,使下临界荷载和临界几何参数显著减小.     

Bose condensation: The viscosity critical dimension and developed turbulence

We propose a model for studying the mutual influence of critical fluctuations in the vicinity of the critical point of phase transition to a superfluid state and the velocity fluctuations in the developed turbulence regime. We demonstrate the presence of two different regimes: the turbulence regime and the equilibrium regime. We show that the standard critical behavior can break in the turbulence regime. The viscosity becomes an infrared-irrelevant parameter in the equilibrium regime. We justify the assumption that the viscosity critical dimension in this regime is determined by critical indices of the critical behavior statistical model, which are currently known with sufficient accuracy.     

Nonlinear Biharmonic Equations with Critical Potential

In this paper, we study two semilinear singular biharmonic equations： one with subcritical exponent and critical potential, another with sub-critical potential and critical exponent. By Pohozaev identity for singular solution, we prove there is no nontrivial solution for equations with critical exponent and critical potential. And by using the concentrate compactness principle and Mountain Pass theorem, respectively, we get two existence results for the two problems. Meanwhile, we have compared the changes of the critical dimensions in singular and non-singular cases, and we get an interesting result.     

Nonsmooth critical point theory and applications to the spectral graph theory

Existing critical point theories including metric and topological critical point theories are difficult to be applied directly to some concrete problems in particular polyhedral settings,because the notions of critical sets could be either very vague or too large.To overcome these difficulties,we develop the critical point theory for nonsmooth but Lipschitzian functions defined on convex polyhedrons.This yields natural extensions of classical results in the critical point theory,such as the Liusternik-Schnirelmann multiplicity theorem.More importantly,eigenvectors for some eigenvalue problems involving graph 1-Laplacian coincide with critical points of the corresponding functions on polytopes,which indicates that the critical point theory proposed in the present paper can be applied to study the nonlinear spectral graph theory.     

Topological equisingularity of hypersurfaces with 1-dimensional critical set

We focus on topological equisingularity of families of holomorphic function germs with 1-dimensional critical set. We introduce the notion of equisingularity at the critical set and prove that any family which is equisingular at the critical set is topologically equisingular. We show that if a family of germs with 1-dimensional critical set has constant generic Lê numbers then it is equisingular at the critical set, and hence topologically equisingular (answering a question of D. Massey [13]). It is worth to remark that this does not happen for higher dimensional critical set [5]. We use these topological triviality results to modify the definition of singularity stem present in the literature, introducing and characterising topological stems (being this concept closely related with Arnold?s series of singularities). We provide another sufficient condition for topological equisingularity for families whose reduced critical set is deformed flatly. Finally we study how the critical set can be deformed in a topologically equisingular family and provide examples of topologically equisingular families whose critical set is a non-flat deformation with singular special fibre and smooth generic fibre.     

扁球壳在均布压力与均匀温度场联合作用下的屈曲

根据扁壳几何非线性理论,推导了均布压力与均匀温度场联合作用下的扁球壳的位移型几何非线性控制方程.考虑夹紧边界条件,采用打靶法得到了扁球壳轴对称弯曲与屈曲的数值结果.讨论了壳体几何参数对平衡路径、临界荷载的影响.给出了壳体临界几何参数.当几何参数大于临界几何参数时,上、下临界荷载都随几何参数增加而增加.给定几何参数时,考察了不同均匀温度场对壳体上、下临界荷载、临界几何参数以及平衡构型的影响.均匀升温会使上临界荷载显著增加,会使下临界荷载略有减小.均匀变温会使临界几何参数改变.     

重复性建设项目中确定关键路线的方法研究

本文提出了一种确定重复性建设项目关键路线的新方法。借助约束线,首先给出了工序间存在各种约束条件(时间和距离约束)下潜在关键点的确定方法;为处理大规模项目,进一步提出了与图示法相对应的数值算法。以此为基础,提出了确定关键工序和关键路线的具体步骤,并定义和分析了三种不同类型的关键工序。与现有的方法相比,本文提出的确定关键路线的方法更为准确,适用性更强,而且有利于调度优化目标的实现。     

LOB中基于工期决定因素分析的资源均衡算法研究

资源均衡是重复性项目中的经典调度问题,本文提出一种新的基于平衡线法(line of balance,LOB)的资源均衡方法。首先,本文提出LOB中关键路线的确定方法,确定关键路线及关键工序类型。而后,本文分析项目总工期的决定因素,对不同类型关键工序的特性及其与总工期、资源调整之间的关系进行了研究,论证了在LOB的资源均衡问题中,由于逆关键工序、点关键工序这些特殊工序的存在,可以在保证项目总工期不变的前提下,通过同时调整关键工序和非关键工序实现资源优化。按照这一思路,论文设计了LOB中资源均衡的遗传算法。算例分析表明该资源均衡算法的优化性能。本文提出的资源均衡思路和算法能帮助项目计划人员拓展资源优化空间,达到更好的资源均衡效果。     

ZFC的模型的上限序数的一个性质

S1 引言 Forcing方法假设存在ZFC的一个可数可传的模型M。记满足αM的最小序数α为,显然M中一切序数所成的集合即。由于M是ZFC的模型,故应具有某些性质。本文证明了它满足关系,故为ε数或1级关键数,进而证明了是H级关键数(H为任意自然数)。文中的记号等引用。     

Health shock risk,critical illness insurance,and housing services

This paper studies a consumption–investment problem involving health shock risk, perishable consumption, and consumption of housing services. Additionally to a risk-free asset and a stock index, the agent can invest in real estate. I analyze the impact of health shocks on the optimal consumption and investment decisions in model specifications with and without the possibility to buy critical illness insurance. I discuss the influence of critical illness insurance on the optimal strategy and analyze the drivers of the optimal critical illness insurance demand. The results indicate that health shock risk has potentially devastating consequences, especially for young agents. It turns out that critical illness insurance is an excellent instrument for hedging health shock risk and for consumption smoothing across different health states. Optimal critical illness insurance demand is decreasing in financial wealth and increasing in human wealth. Real estate prices have a minor influence on optimal critical illness insurance demand.     

Numerical simulation of critical dependences for symmetric two-layered Josephson junctions

Partial critical dependences of the form current-magnetic field in a two-layered symmetric Josephson junction are modeled. A numerical experiment shows that, for the zero interaction coefficient between the layers of the junction, jumps of the critical currents corresponding to different distributions of the magnetic fluxes in the layers may appear on the critical curves. This fact allows a mathematical interpretation of the results of some recent experimental results for two-layered junctions as a consequence of discontinuities of partial critical curves.     

非自发形核功与润湿角的数学模型

根据两个垂直相交平面基体上非自发形核功与润湿角数学模型,对临界形核半径和临界形核功进行了详细的推导,表明了临界形核功与润湿角的关系,完善了两个垂直相交平面基体上形核功与润湿角数学模型的研究.     

Tchebyshev Approximation by S01（△） over Some Special Triangulations

The critical point set plays a central role in the theory of Tchebyshev approximation.Generally,in multivariate Tchebyshev approximation,it is not a trivial task to determine whether a set is critical or not.In this paper,we study the characterization of the critical point set of S 0 1(△) in geometry,where is restricted to some special triangulations(bitriangular,single road and star triangulations).Such geometrical characterization is convenient to use in the determination of a critical point set.     

Level set methods for finding critical points of mountain pass type

Computing mountain passes is a standard way of finding critical points. We describe a numerical method for finding critical points that is convergent in the nonsmooth case and locally superlinearly convergent in the smooth finite dimensional case. We apply these techniques to describe a strategy for addressing the Wilkinson problem of calculating the distance from a matrix to a closest matrix with repeated eigenvalues. Finally, we relate critical points of mountain pass type to nonsmooth and metric critical point theory.     

Criticality Analysis in Activity-on-Node Networks with Minimal Time Lags

This paper is a systematic study of the critical nature of activities and relationships in AON networks with minimal time lags in the unlimited resource case, when activity splitting is not allowed. An analysis of all possible cases produces an extended and now complete classification of critical activities in six classes: normal, reverse, neutral, bicritical, increasing normal and decreasing reverse. We also present a procedure for classifying any critical task depending on the early start/finish times and on position within the critical paths.     

One-parameter families of optimization problems: Equality constraints

In this paper, we introduce generalized critical points and discuss their relationship with other concepts of critical points [resp., stationary points]. Generalized critical points play an important role in parametric optimization. Under generic regularity conditions, we study the set of generalized critical points, in particular, the change of the Morse index. We focus our attention on problems with equality constraints only and provide an indication of how the present theory can be extended to problems with inequality constraints as well.     

Nonsymmetric bifurcations of solutions of the 2D Navier–Stokes system

We consider the 2D Navier–Stokes system written for the stream function with periodic boundary conditions and construct a set of initial data such that initial critical points bifurcate from 1 to 2 and then to 3 critical points in finite time. The bifurcation takes place in a small neighborhood of the origin. Our construction does not require any symmetry assumptions or the existence of special fixed points. For another set of initial data we show that 3 critical points merge into 1 critical point in finite time. We also construct a set of initial data so that bifurcation can be generated by the Navier–Stokes flow and do not require the existence of an initial critical point.     

一类双重退化抛物方程组解的整体存在与爆破

研究一类具有非线性边界流的双重退化抛物方程组解的整体存在与爆破,通过构造自相似的上下解,得到了整体存在曲线.借助一些新的结果,获得了Fujita临界指数.其中一个有趣的现象是:整体存在曲线和Fujita临界曲线分别是由一个矩阵和线性方程组来决定.     

A local minimax characterization for computing multiple nonsmooth saddle critical points

This paper is concerned with characterizations of nonsmooth saddle critical points for numerical algorithm design. Most characterizations for nonsmooth saddle critical points in the literature focus on existence issue and are converted to solve global minimax problems. Thus they are not helpful for numerical algorithm design. Inspired by the results on computational theory and methods for finding multiple smooth saddle critical points in [14, 15, 19, 21, 23], a local minimax characterization for multiple nonsmooth saddle critical points in either a Hilbert space or a reflexive Banach space is established in this paper to provide a mathematical justification for numerical algorithm design. A local minimax algorithm for computing multiple nonsmooth saddle critical points is presented by its flow chart. Dedicated to Terry Rockafellar on his 70th birthday