Equality of the homogeneous and the Gabor wave front set

We prove that Hörmander’s global wave front set and Nakamura’s homogeneous wave front set of a tempered distribution coincide. In addition, we construct a tempered distribution with a given wave front set, and we develop a pseudodifferential calculus adapted to Nakamura’s homogeneous wave front set.     

Power Measures and Solutions for Games Under Precedence Constraints

Games under precedence constraints model situations, where players in a cooperative transferable utility game belong to some hierarchical structure, which is represented by an acyclic digraph (partial order). In this paper, we introduce the class of precedence power solutions for games under precedence constraints. These solutions are obtained by allocating the dividends in the game proportional to some power measure for acyclic digraphs. We show that all these solutions satisfy the desirable axiom of irrelevant player independence, which establishes that the payoffs assigned to relevant players are not affected by the presence of irrelevant players. We axiomatize these precedence power solutions using irrelevant player independence and an axiom that uses a digraph power measure. We give special attention to the hierarchical solution, which applies the hierarchical measure. We argue how this solution is related to the known precedence Shapley value, which does not satisfy irrelevant player independence, and thus is not a precedence power solution. We also axiomatize the hierarchical measure as a digraph power measure.     

Approximability of average completion time scheduling on unrelated machines

We show that minimizing the average job completion time on unrelated machines is \(\mathcal {APX}\)-hard if preemption of jobs is allowed. This provides one of the last missing pieces in the complexity classification of machine scheduling with (weighted) sum of completion times objective. The proof is based on a mixed integer linear program. This means that verification of the reduction is partly done by an ILP-solver. This gives a concise proof which is easy to verify. In addition, we give a deterministic 1.698-approximation algorithm for the weighted version of the problem. The improvement is made by modifying and combining known algorithms and by the use of new lower bounds. These results improve on the known \(\mathcal {NP}\)-hardness and 2-approximability.     

Law of Large Numbers for Branching Symmetric Hunt Processes with Measure-Valued Branching Rates

We establish weak and strong laws of large numbers for a class of branching symmetric Hunt processes with the branching rate being a smooth measure with respect to the underlying Hunt process, and the branching mechanism being general and state dependent. Our work is motivated by recent work on the strong law of large numbers for branching symmetric Markov processes by Chen and Shiozawa (J Funct Anal 250:374–399, 2007) and for branching diffusions by Engländer et al. (Ann Inst Henri Poincaré Probab Stat 46:279–298, 2010). Our results can be applied to some interesting examples that are covered by neither of these papers.     

Infinitely many non-radial solutions for fractional Nirenberg problem

In this paper, the prescribed \(\sigma \)-curvature problem

$$\begin{aligned} P_{\sigma }^{g_0} u={\tilde{K}}(x)u^{\frac{N+2\sigma }{N-2\sigma }}, x\in {\mathbb {S}}^N,u>0 \end{aligned}$$

is considered. When \({\tilde{K}}(x)\) is some axis symmetric function on \({\mathbb {S}}^N\), by using singular perturbation method, it is proved that this problem possesses infinitely many non-radial solutions for \(0<\sigma \le 1\) and \(N> 2\sigma +2\).

     

平面刚架弹塑性大位移分析的多刚体离散元法

本文基于多刚体－弹簧系统模型，给出了求解平面刚架结构弹塑性、大位移极限承载力分析的多刚体离散元法。文中首先推导了多刚体离散元法在总体坐标下的切线刚度阵，建立多刚体离散元法的增量平衡方程；而后推导了多刚体离散元的弹塑性弹簧系数矩阵，建立了多刚体离散元内力屈服面塑性铰法的增量求解格式，成功地进行了平面钢框架的弹塑性、大位移极限承载力分析。计算结果与其他数值方法或实验结果吻合良好，显示了多刚体离散元方法进行结构极限承载力分析这一复杂问题的优越性     

计算圆板大振幅非线性振动频率的平均刚度法

本文用平均刚度法研究圆板大振幅非线性振动的频率问题，导出了相应的非线性广义特征值方程，构造了一种避免发散并能加速收敛的加权平均迭代法，计算结果与Ｋａｎｔｏｒｏｖｉｃｈ时间平均法的解十分吻合。     

Dynamic characteristic analysis of a 3-D semi-submerged body as a fluid-structure interaction system

An Arnoldi‘s method with new iteration pattern, which was designed for solving a large unsymmetric eigenvalue problem introduced by displacement-pressure FE (Finite Element) pattern of a fluid-structure interaction system, was adopted here to get the dynamic characteristics of the semi-submerged body. The new iteration pattern could be used efficiently to obtain the Arnoldi‘s vectors in the shift-frequency technique, which was used for the zero-frequency problem. Numerical example showed that the fluid-structure interaction is one of the important factors to the dynamic characteristics of large semi-submerged thin-walled structures.     

求解转子系统突加不平衡响应方法的研究

本文提出并研究了用传递函数分析法求转子系统的突加不平衡响应,讨论了求这一响应的最佳数值积分方法。用本文提出的理论解方法及三种常用的数值积分法:尤拉后差法,纽马克法,及呼伯特法,对一模型转子算例进行了分析计算,结果表明;尤拉后差法最适用于求转子系统的突加不平衡响应。本文提出的传递函数分析法,可以和试验模态分析方法相结合,以求解复杂转子系统的突加不平衡响应。     

On the application of boundary layer method in the large deflection plastic buckling of a cylindrical shell

Using a cylindrical shell under axial loading as an example, we discuss the possibility of applying the membrane theory together with the boundary layer correction to analyze the large deflection plastic buckling problem. In the cases of fixed ends and simply-supported ends, the conditions to be satisfied for using the boundary layer method (also called the composite-expansion method) are given and discussed.