Orderings and Probability Functionals Consistent with Preferences

This paper unifies the classical theory of stochastic dominance and investor preferences with the recent literature on risk measures applied to the choice problem faced by investors. First, we summarize the main stochastic dominance rules used in the finance literature. Then we discuss the connection with the theory of integral stochastic orders and we introduce orderings consistent with investors' preferences. Thus, we classify them, distinguishing several categories of orderings associated with different classes of investors. Finally, we show how we can use risk measures and orderings consistent with some preferences to determine the investors' optimal choices.     

Positive solutions for ratio-dependent predator-prey interaction systems

In this paper, we study the dynamics of predator-prey interaction systems between two species with ratio-dependent functional responses. First we provide sufficient and necessary conditions for positive steady-state solutions, and then we investigate the relationships between positive equilibria and positive solutions of the system over a large domain. Furthermore, we deal with the uniqueness and the stability of positive steady-states solutions with some assumptions. In addition, we discuss the extinction and the persistence results of time-dependent positive solutions to the system.     

修正的IPA算法的建立及在不等式约束凸优化问题中的应用

本文首先对IPA算法进行了修正，并证明了修正IPA算法的收敛性，然后将修正后的IPA应用到不等式约束凸优化问题中得到新的内点算法，并与传统的障碍函数法作了比较，从理论上体现了新算法的优势，并给出了其工程解求解法以及收敛性的证明．     

机械臂运动路径设计

采用D-H方法推导出了机械臂角度姿态与指尖空间位置的关系,以距离偏差为目标,建立了给定位置求机械臂参数的优化模型,并提出了二分步长接近式搜索算法求解该模型.进一步从实际工程精度要求出发,提出了确定精度求指令的方法.针对按照确定曲线运行的问题,采取了离散曲线而且相邻离散点之间一条指令可达的方法,并用改进的二分步长接近式搜索算法来求解.提出了解决避障问题的启发式算法和位姿空间变换法.还对机械臂结构进行了理论分析及论证,根据分析结果,针对旋转角度范围、角度量化、杆长选择等方面提出了一些建议.     

On the Theoretical and Numerical Control of a One-Dimensional Nonlinear Parabolic Partial Differential Equation

This paper deals with the analysis of the internal and boundary control of a one-dimensional parabolic partial differential equation with nonlinear diffusion. First, we prove a local null controllability result with distributed controls, locally supported in space. The proof relies on local inversion (more precisely, we use Liusternik’s Inverse Function Theorem), together with some appropriate specific estimates. We also establish a similar result with controls on one side of the boundary. Then, we consider an iterative algorithm for the computation of null controls, we prove the convergence of the iterates, and we perform some numerical experiments.     

General construction of symmetric parabolic structures

First we introduce a generalization of symmetric spaces to parabolic geometries. We provide construction of such parabolic geometries starting with classical symmetric spaces and we show that all regular parabolic geometries with smooth systems of involutive symmetries can be obtained in this way. Further, we investigate the case of parabolic contact geometries in great detail and we provide the full classification of those with semisimple groups of symmetries without complex factors. Finally, we explicitly construct all non-trivial contact geometries with non-complex simple groups of symmetries. We also indicate geometric interpretations of some of them.     

The catwalk task: Reflections and synthesis: Part 2

In this article we recount our experiences with a series of encounters with the catwalk task and reflect on the professional growth that these opportunities afforded. First, we individually reflect on our own mathematical work on the catwalk task. Second, we reflect on our experiences working with a group of community college students on the catwalk task and our interpretations of their mathematical thinking. In so doing we also detail a number of innovative and novel student-generated representations of the catwalk photos. Finally, we each individually reflect on the entire experience with the catwalk problem, as mathematics learners, as teachers, and as professionals.     

Qualitative Properties of Eigenvectors Related to Multivalued Operators and some Existence Results

In this work, we study a class of nonlinear eigenvalue problems related to fully discontinuous operators. In particular, we prove the existence of a critical point for two distinct problems. Connected with this problem, we also study a minimization problem with constraint, and we investigate the existence of solutions for a resonant case near zero. Moreover, we give some estimates and qualitative properties of solutions by using the relative rearrangement theory.     

Constructing few-weight linear codes and strongly regular graphs

Linear codes with few weights have applications in data storage systems, secret sharing schemes, graph theory and so on. In this paper, we construct a class of few-weight linear codes by choosing defining sets from cyclotomic classes and we also establish few-weight linear codes by employing weakly regular bent functions. Notably, we get some codes that are minimal and we also obtain a class of two-weight optimal punctured codes with respect to the Griesmer bound. Finally, we get a class of strongly regular graphs with new parameters by using the obtained two-weight linear codes.     

Constraint Qualifications for Nonsmooth Mathematical Programs with Equilibrium Constraints

We study nonsmooth mathematical programs with equilibrium constraints. First we consider a general disjunctive program which embeds a large class of problems with equilibrium constraints. Then, we establish several constraint qualifications for these optimization problems. In particular, we generalize the Abadie and Guignard-type constraint qualifications. Subsequently, we specialize these results to mathematical program with equilibrium constraints. In our investigation, we show that a local minimum results in a so-called M-stationary point under a very weak constraint qualification.      

Periodic Solutions for Second Order Differential Inclusions with Nonconvex and Unbounded Multifunction

In this paper we consider a second order multivalued periodic boundary value problem with a nonconvex and unbounded orientor field (set-valued vector field). Using a directionally continuous selector, through its Filippov regularization we produce a convex-valued, bounded multifunction and with this as orientor field we introduce a new multivalued periodic problem. Using the Leray-Schauder principle, we solve the convex problem and then we show that its solutions also solve the original nonconvex problem.     

Viscosity solutions for second order integro-differential equations without monotonicity condition: the probabilistic approach

In this paper, we establish a new existence and uniqueness result of a continuous viscosity solution for integro-partial differential equation (IPDE in short). The novelty is that we relax the so-called monotonicity assumption on the driver which is classically assumed in the literature of viscosity solutions of equation with non-local terms. Our method strongly relies on the link between IPDEs and backward stochastic differential equations with jumps for which we already know that the solution exists and is unique for general drivers. In the second part of the paper, we deal with the IPDE with obstacle and we obtain similar results.     

On subtractive varieties II: General properties

As a sequel to [23] we investigate ideal properties focusing on subtractive varieties. After having listed a few basic results, we give several characterizations of the commutator of ideals and prove, for example, that it commutes with finite direct products. We deal with the ideal extension property (IEP) and with related commutator properties, showing for instance that IEP implies that the commutator commutes with restriction to subalgebras. Then we characterize varieties with distributive ideal lattices and relate this property with (a form of) equationally definable principal ideals and with IEP. Then, at the other extreme, we deal with Abelian and Hamiltonian properties (of ideals and congruences), giving for example a purely ideal theoretic characterization of varieties of Abelian groups with linear operations. To finish with, we present a few examples aiming at vindicating our work.Presented by A. F. Pixley.     

Approximation of Markov semigroups in total variation distance under an irregular setting: An application to the CIR process

In this paper, we propose a method to prove the total variation convergence of approximation of Markov semigroups with singularities. In particular our approach is adapted to the study of numerical schemes for Stochastic Differential Equation (SDE) with simply locally smooth coefficients. First we present this method and then, we apply it to the CIR process. In particular, we consider the weak second order scheme introduced in Alfonsi (2010) and we prove that it also converges towards the CIR diffusion process for the total variation distance. This convergence occurs with almost order two.     

T-QBD过程水平和位相的独立性

研究了三对角无限位相拟生灭过程(T-QBD过程)平稳分布水平与位相的独立性.首先,给出了水平和位相相互独立并且两个边缘分布都为几何分布的充要条件,得到了过程平稳分布的解析形式;其次,提出了验证水平和位相独立性条件的具体方法,说明了如何把得到的结果应用于实际模型,最后,讨论了一种广义独立性,并对水平和位相独立时率算子的性质做了某些讨论.     

Backward heat equation with time dependent variable coefficient

Backward heat equation with time dependent variable coefficient is severely ill‐posed in the sense of Hadamard, so we need regularization. In this paper, we consider Backward heat equation with time dependent variable coefficient, and by small perturbing, we obtain an approximation problem. We show this approximation problem is well‐posed with small parameter. Also, we show this approximation system converges to the original problem when parameter goes to zero. Here, we use modified‐quasi boundary value method to regularize this problem. Copyright © 2016 John Wiley & Sons, Ltd.     

Time complexity of single- and identical parallel-machine scheduling with GERT network precedence constraints

In this paper we deal with the time complexity of single- and identical parallel-machine scheduling problems in which the durations and precedence constraints of the activities are stochastic. The stochastic precedence constraints are given by GERT networks. First, we sketch the basic concepts of GERT networks and machine scheduling with GERT network precedence constraints. Second, we discuss the time complexity of some open single-machine scheduling problems with GERT network precedence constraints. Third, we investigate the time complexity of identical parallel-machine scheduling problems with GERT network precedence constraints. Finally, we present an efficient reduction algorithm for the problem of computing the expected makespan for the latter type of scheduling problem.     

关于有1模格的等价定义

进一步讨论有1模格的等价定义问题,得到并证明了一个(2,2,0)型代数成为有1模格的一个充分必要条件.这样大大简化了有1模格的等价定义.     

New Algorithms for Three-Partitioning Containing Kernels

1.IntroductionGivenasetRofmketnelitems(wecallthemkernels),R={ri2o,i=1,2,...,tn}andasetPofn52mnonkernelitems(wecallthemitems),P={Pj2o,j=1,2,...tn}.WewanttopartitionT=RUPintomsubsetssuchthatrjEMjandlMj153.DenoteCj=Zx,callittheloadofMj,Thendefinethemin-maxproblemastominimizethe2eMmaximumloadofthesemsubsets,andthemax-minproblemastomaximizetheminimumloadofthesemsubset.TheseproblemsareNP-complete[1],meantimeaHeuristicalgorithmKLPTisgivenforthemin-maxproblem,andtheworst-caseboundis:-C'thebo…