Instability analysis of saddle points by a local minimax method

The objective of this work is to develop some tools for local instability analysis of multiple critical points, which can be computationally carried out. The Morse index can be used to measure local instability of a nondegenerate saddle point. However, it is very expensive to compute numerically and is ineffective for degenerate critical points. A local (weak) linking index can also be defined to measure local instability of a (degenerate) saddle point. But it is still too difficult to compute. In this paper, a local instability index, called a local minimax index, is defined by using a local minimax method. This new instability index is known beforehand and can help in finding a saddle point numerically. Relations between the local minimax index and other local instability indices are established. Those relations also provide ways to numerically compute the Morse, local linking indices. In particular, the local minimax index can be used to define a local instability index of a saddle point relative to a reference (trivial) critical point even in a Banach space while others failed to do so.

     

Antiderivatives and potentials of local differential operators

A necessary and sufficient condition for the antiderivative of a local differential operator to be local is derived. A formula is given which explicitly exhibits the antiderivative as a local operator when this condition is met. The analogous problem for local vector differential operators is treated. A decomposition of an arbitrary local differential operator in terms of the derivative of a local operator and the gradient of a functional is given.     

局部C线性算子群

本文定义了一种局部C群，讨论了局部C群与局部C半群的关系及一些基本性质，并建立了局部C群的生成定理．     

Self-intersection local times and collision local times of bifractional Brownian motions

In this paper, we consider the local time and the self-intersection local time for a bifractional Brownian motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the existence and smoothness of the self-intersection local time and the collision local time, through the strong local nondeterminism of bifractional Brownian motion, L2 convergence and Chaos expansion.     

Multistart method with estimation scheme for global satisfycing problems

We present a multistart method for solving global satisfycing problems. The method uses data generated by linearly converging local algorithms to estimate the cost value at the local minimum to which the local search is converging. When the estimate indicates that the local search is converging to a value higher than the satisfycing value, the local search is interrupted and a new local search is initiated from a randomly generated point. When the satisfycing problem is difficult and the estimation scheme is fairly accurate, the new method is superior over a straightforward adaptation of classical multistart methods.     

地方政府决策绩效评价研究

地方政府决策是为解决地方特定社会问题而作出的决策和行为，其绩效对地方经济社会的发展、政府的公共管理和公共形象具有重要作用。为进一步分析地方政府决策在地区经济社会发展中的重要作用，本文构建了符合科学发展观和社会主义和谐社会要求，且具备系统、完整、可操作性的地方政府决策绩效评价体系，并对宁波政府决策绩效进行实证研究。     

一种基于局部回归的多尺度碳市场价格预测模型研究

碳市场价格呈现非线性、非平稳的复杂特性,准确预测具有较大的挑战。基于“分而治之”的思想,提出了一种基于局部回归的多尺度碳市场价格预测模型。提出的模型利用集成经验模态分解(EEMD)对碳市场价格时间序列进行分解。启发于EEMD局部特征分解的特点,对分解后的分量采用局部回归方法进行预测,然后将分量预测结果进行集成。采用的局部回归方法包括局部线性回归(LLP)、局部多项式回归、局部岭回归、局部主成分回归、局部偏最小二乘回归和局部套索回归。实验结果表明基于局部回归的多尺度预测模型具有优异的预测性能。在提出的模型中,EEMD-LLP结构简单且性能更为突出,进一步对EEMD-LLP参数的适应性进行探讨。与新近提出模型的对比结果表明了EEMD-LLP在碳市场价格预测中的有效性。     

On Local Descent to Metaplectic Groups and Local Theta Correspondence

Let F be a p-adic field of characteristic 0.We study a twisted local descent construction for the metaplectic groups Sp_(2 n)(F),and also its relation to the corresponding local descent construction for odd special orthogonal groups via local theta correspondence.In consequence,we show that this descent construction gives irreducible supercuspidal genuine representations of Sp_(2n)(-F) parametrized by a simple local L-parameter φ_τ corresponding to an irreducible supercuspidal representation τ of GL_(2n)(F) of symplectic type,and the genericity of the representations constructed can be indicated by a local epsilon factor condition.In particular,this local descent construction recovers the local Shimura correspondence for supercuspidal representations.     

On the Local Time of the Weighted Bootstrap and Compound Empirical Processes

This article is mainly concerned with the local times of the weighted bootstrap process. We prove a strong approximation theorem for the local time of the weighted bootstrap process by the local time of a Brownian bridge. We consider also the local time of the compound empirical processes that can be seen, asymptotically, as the local time of the convolution of two independent Gaussian processes.     

LOCAL C-SEMIGROUPS AND LOCAL C-COSINE FUNCTIONS

0IntroductionLetB(X)betheBanachspaceofallboundedlinearoperatorsonaBanachspaceX.CEB(X)isinjective.Alloperatorsarelinear.D(A),Im(A),andP(A)denotethedomain,theimage,andtheresolventsetofoperatorA,respectivelyNandRdenotethesetofallnaturalnumbersandthesetofallrealnumbers.TheconceptoflocalC-sernigroupsalldlocalC-cosinefunctionwereintroducedbyTanakaandOkazawain[1]tF.HuangandT.Huangin[21,respectively.Aspointedoutin[3]and[2]thatnotalllocalC-sendgroups(C--cosinefunctions)canbeextendedtobeC-se…     

On characterization of maximal independent sets via quadratic optimization

This article investigates the local maxima properties of a box-constrained quadratic optimization formulation of the maximum independent set problem in graphs. Theoretical results characterizing binary local maxima in terms of certain induced subgraphs of the given graph are developed. We also consider relations between continuous local maxima of the quadratic formulation and binary local maxima in the Hamming distance-1 and distance-2 neighborhoods. These results are then used to develop an efficient local search algorithm that provides considerable speed-up over a typical local search algorithm for the binary Hamming distance-2 neighborhood.     

Dynamical Symmetry Breaking in Geometrodynamics

Using a first-order perturbative formulation, we analyze the local loss of symmetry when a source of electromagnetic and gravitational fields interacts with an agent that perturbs the original geometry associated with the source. We had proved that the local gauge groups are isomorphic to local groups of transformations of special tetrads. These tetrads define two orthogonal planes at every point in space–time such that every vector in these local planes is an eigenvector of the Einstein–Maxwell stress–energy tensor. Because the local gauge symmetry in Abelian or even non-Abelian field structures in four-dimensional Lorentzian space–times is manifested by the existence of local planes of symmetry, the loss of symmetry is manifested by a tilt of these planes under the influence of an external agent. In this strict sense, the original local symmetry is lost. We thus prove that the new planes at the same point after the tilting generated by the perturbation correspond to a new symmetry. Our goal here is to show that the geometric manifestation of local gauge symmetries is dynamical. Although the original local symmetries are lost, new symmetries arise. This is evidence for a dynamical evolution of local symmetries. We formulate a new theorem on dynamical symmetry evolution. The proposed new classical model can be useful for better understanding anomalies in quantum field theories.     

Local adaptive smoothing in kernel regression estimation

We consider nonparametric estimation of a smooth function of one variable. Global selection procedures cannot sufficiently account for local sparseness of the covariate nor can they adapt to local curvature of the regression function. We propose a new method for selecting local smoothing parameters which takes into account sparseness and adapts to local curvature. A Bayesian type argument provides an initial smoothing parameter which adapts to the local sparseness of the covariate and provides the basis for local bandwidth selection procedures which further adjust the bandwidth according to the local curvature of the regression function. Simulation evidence indicates that the proposed method can result in reduction of both pointwise mean squared error and integrated mean squared error.     

Local residual-type error estimates for adaptive boundary element methods on closed curves

Considering the Galerkin boundary element methods and mesh families with bounded local mesh ratio we derive local error estimates such that the local error is bounded by a local residual together with some global terms which can be expected to be small. If the order of the boundary operator is non-negative and at most two, these estimates show that the local residual is a local error indicator. For the operators of the negative order we obtain the same conclusion if the mesh is β-regular. Our paper improves recent results of Wendland and Yu in several respects.     

On G-Regular Local Rings

In this article, we define a G-regular local ring as a commutative, noetherian, local ring, over which all totally reflexive modules are free. We study G-regular local rings and observe that they behave similarly to regular local rings. We extend Eisenbud's matrix factorization theorem and Knörrer's periodicity theorem to G-regular local rings.     

地方总教育投资分配的博弈分析

本文采用博弈论研究地方总教育投资分配的模型 ,该模型包含两个地方政府和一个中央政府 ,并分别为地方政府提供决策 .首先 ,描述了基本模型 ,分别给出了地方政府的效用函数 ;接着分析了地方政府同时行动时的总教育投资分配 ,然后分析了地方政府顺序行动时的总教育投资分配 ;最后给出了最优解的算法并举例说明地方政府怎样去做决策     

On the local times of stationary processes with conditional local limit theorems

We investigate the connection between conditional local limit theorems and the local time of integer-valued stationary processes. We show that a conditional local limit theorem (at 0) implies the convergence of local times to Mittag-Leffler distributions, both in the weak topology of distributions and a.s. in the space of distributions.     

On multifractal of Cantor dust

We consider quasi-self-similar measures with respect to all real numbers on a Cantor dust. We define a local index function on the real numbers for each quasi-self-similar measure at each point in a Cantor dust, The value of the local index function at the real number zero for all the quasi-self-similar measures at each point is the weak local dimension of the point. We also define transformed measures of a quasi-self-similar measure which are closely related to the local index function. We compute the local dimensions of transformed measures of a quasi-self-similar measure to find the multifractal spectrum of the quasi-self-similar measure, Furthermore we give an essential example for the theorem of local dimension of transformed measure. In fact, our result is an ultimate generalization of that of a self- similar measure on a self-similar Cantor set. Furthermore the results also explain the recent results about weak local dimensions on a Cantor dust.     

Entropy in the category of perfect complexes with cohomology of finite length

Local and category-theoretical entropies associated with an endomorphism of finite length (i.e., with zero-dimensional closed fiber) of a commutative Noetherian local ring are compared. Local entropy is shown to be less than or equal to category-theoretical entropy. The two entropies are shown to be equal when the ring is regular, and also for the Frobenius endomorphism of a complete local ring of positive characteristic.Furthermore, given a flat morphism of Cohen–Macaulay local rings endowed with compatible endomorphisms of finite length, it is shown that local entropy is “additive”. Finally, over a ring that is a homomorphic image of a regular local ring, a formula for local entropy in terms of an asymptotic partial Euler characteristic is given.