Continuity properties of the normal cone to the level sets of a quasiconvex function

Two main properties of the subgradient mapping of convex functions are transposed for quasiconvex ones. The continuity of the functionxf(x)^–1f(x) on the domain where it is defined is deduced from some continuity properties of the normal coneN to the level sets of the quasiconvex functionf. We also prove that, under a pseudoconvexity-type condition, the normal coneN(x) to the set {x:f(x)f(x)} can be expressed as the convex hull of the limits of type {N(x _n)}, where {x _n} is a sequence converging tox and contained in a dense subsetD. In particular, whenf is pseudoconvex,D can be taken equal to the set of points wheref is differentiable.This research was completed while the second author was on a sabbatical leave at the University of Montreal and was supported by a NSERC grant. It has its origin in the doctoral thesis of the first author (Ref. 1), prepared under the direction of the second author.The authors are grateful to an anonymous referee and C. Zalinescu for their helpful remarks on a previous version of this paper.     

Partially Strictly Monotone and Nonlinear Penalty Functions for Constrained Mathematical Programs

We introduce the concept of partially strictly monotone functions and apply it to construct a class of nonlinear penalty functions for a constrained optimization problem. This class of nonlinear penalty functions includes some (nonlinear) penalty functions currently used in the literature as special cases. Assuming that the perturbation function is lower semi-continuous, we prove that the sequence of optimal values of nonlinear penalty problems converges to that of the original constrained optimization problem. First-order and second-order necessary optimality conditions of nonlinear penalty problems are derived by converting the optimality of penalty problems into that of a smooth constrained vector optimization problem. This approach allows for a concise derivation of optimality conditions of nonlinear penalty problems. Finally, we prove that each limit point of the second-order stationary points of the nonlinear penalty problems is a second-order stationary point of the original constrained optimization problem.     

Speeding up the FMMR perfect sampling algorithm: A case study revisited

In a previous paper by the second author, two Markov chain Monte Carlo perfect sampling algorithms—one called coupling from the past (CFTP) and the other (FMMR) based on rejection sampling—are compared using as a case study the move‐to‐front (MTF) self‐organizing list chain. Here we revisit that case study and, in particular, exploit the dependence of FMMR on the user‐chosen initial state. We give a stochastic monotonicity result for the running time of FMMR applied to MTF and thus identify the initial state that gives the stochastically smallest running time; by contrast, the initial state used in the previous study gives the stochastically largest running time. By changing from worst choice to best choice of initial state we achieve remarkable speedup of FMMR for MTF; for example, we reduce the running time (as measured in Markov chain steps) from exponential in the length n of the list nearly down to n when the items in the list are requested according to a geometric distribution. For this same example, the running time for CFTP grows exponentially in n. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2003     

H-矩阵的实用判定

H-矩阵在许多领域中都发挥着重要作用，但在实用中要判别H-矩阵却是很困难的．本文中，我们获得了H-矩阵判别的新的实用充分条件，所得结果包含了[1]的一个主要结果，并用例子说明了文中结果的有效性.     

Generalizations of Slater's constraint qualification for infinite convex programs

In this paper we study constraint qualifications and duality results for infinite convex programs (P) = inf{f(x): g(x) – S, x C}, whereg = (g ₁,g ₂) andS = S ₁ ×S ₂,S _i are convex cones,i = 1, 2,C is a convex subset of a vector spaceX, andf andg _i are, respectively, convex andS _i -convex,i = 1, 2. In particular, we consider the special case whenS ₂ is in afinite dimensional space,g ₂ is affine andS ₂ is polyhedral. We show that a recently introduced simple constraint qualification, and the so-called quasi relative interior constraint qualification both extend to (P), from the special case thatg = g ₂ is affine andS = S ₂ is polyhedral in a finite dimensional space (the so-called partially finite program). This provides generalized Slater type conditions for (P) which are much weaker than the standard Slater condition. We exhibit the relationship between these two constraint qualifications and show how to replace the affine assumption ong ₂ and the finite dimensionality assumption onS ₂, by a local compactness assumption. We then introduce the notion of strong quasi relative interior to get parallel results for more general infinite dimensional programs without the local compactness assumption. Our basic tool reduces to guaranteeing the closure of the sum of two closed convex cones.     

Extracting the low-energy constant ${L}_{0}^{r}$ at three flavors from pion-kaon scattering

Based on our analysis of the contributions from the connected and disconnected contraction diagrams to the pion-kaon scattering amplitude, we provide the first determination of the only free low-energy constant at ${ \mathcal O }({p}^{4})$, known as ${L}_{0}^{r}$, in SU (4∣1) Partially-Quenched Chiral Perturbation theory using the data from the Extended Twisted Mass collaboration, ${L}_{0}^{r}(\mu ={M}_{\rho })=0.77(20)(25)(7)(7)(2)\cdot {10}^{-3}$. The theory uncertainties originate from the unphysical scattering length, the physical low-energy constants, the higher-order chiral corrections, the (lattice) meson masses and the pion decay constant, respectively.     

广义凸集的切锥

本文讨论作者在〔16〕中提出的广义凸集的各种切锥之间的关系,切锥与正则锥的关系以及切锥的一些代数性质和拓朴性质。     

杨氏双缝干涉实验中的光谱奇异现象

基于部分相干光的传输理论,研究了杨氏双缝干涉实验中的光谱奇异现象。发现在杨氏双缝干涉实验干涉场区中的某个点的光谱奇异现象,它会随着某些参量(如源光谱宽度Γ′,缝宽参量ε,相对空间相干度Δ0)的变化而改变,指出该现象可应用于信息的编码及自由空间的信息传输。     

A comparison of different approaches to integrate flamelet tables with presumed-shape PDF in flamelet models for turbulent flames

Flamelet models for turbulent combustion modelling make use of presumed-shape probability density functions (PDFs) for integrating laminar flamelet solutions to obtain an integrated flamelet table that can readily be used for turbulent flame calculations. The existence of non-unique approaches for such an integration has rarely been investigated before. For the first time, this work studies systematically the non-uniqueness of the flamelet table integration approaches. A flamelet model called the flamelet/progress variable model is used in the study, although the issue exists generally in many other flamelet models. Two classes of table integration approaches are investigated, one preserving the laminar flamelet structures during integration and the other not. Three different table integration approaches are examined and compared in detail to provide a thorough understanding of the different approaches. A partially stirred reactor is used as a test case for examining the different approaches. A method based on the transported PDF method is also employed to provide a reference for the assessment of the different flamelet table integration approaches. It is found in general that the flamelet preserving integration approach yields a more reasonable joint PDF of the mixture fraction and the progress variable, and the prediction results are closer to the referenced transported PDF results.