Local Units Versus Local Projectivity Dualisations: Corings with Local Structure Maps

We unify and generalize different notions of local units and local projectivity. We investigate the connection between these properties by constructing elementary algebras from locally projective modules. Dual versions of these constructions are discussed, leading to corings with local comultiplications, corings with local counits, and rings with local multiplications.     

Application of graph-theoretic approaches to the random landscapes of the three-dimensional assignment problem

We study local optima of combinatorial optimization problems. We show that a local search algorithm can be represented as a digraph and apply recent results for spanning forests of a diagraph. We establish a correspondence between the number of local optima and the algebraic multiplicities of eigenvalues of digraph laplacians. We apply our finding to the three-dimensional assignment problem.     

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 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.     

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.     

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.     

Algorithms for the single-source uncapacitated minimum concave-cost network flow problem

We investigate algorithms, applications, and complexity issues for the single-source uncapacitated (SSU) version of the minimum concave-cost network flow problem (MCNFP). We present applications arising from production planning, and prove complexity results for both global and local search. We formally state the local search algorithm of Gallo and Sodini [5], and present alternative local search algorithms. Computational results are provided to compare the various local search algorithms proposed and the effects of initial solution techniques.     

A new error bound result for Generalized Nash Equilibrium Problems and its algorithmic application

We present a new algorithm for the solution of Generalized Nash Equilibrium Problems. This hybrid method combines the robustness of a potential reduction algorithm and the local quadratic convergence rate of the LP-Newton method. We base our local convergence theory on a local error bound and provide a new sufficient condition for it to hold that is weaker than known ones. In particular, this condition implies neither local uniqueness of a solution nor strict complementarity. We also report promising numerical results.     

Congruence-preserving functions on Stone and Kleene algebras

We investigate local polynomial functions on Stone algebras and on Kleene algebras. We find a generating set for the clone of all local polynomial functions. We also represent local polynomial functions on a given algebra by polynomial functions of some canonical extension of this algebra.     

Local risk-minimization under the benchmark approach

We study the pricing and hedging of derivatives in incomplete financial markets by considering the local risk-minimization method in the context of the benchmark approach, which will be called benchmarked local risk-minimization. We show that the proposed benchmarked local risk-minimization allows to handle under extremely weak assumptions a much richer modeling world than the classical methodology.     

Local cohomology based on a nonclosed support defined by a pair of ideals

We introduce a generalization of the notion of local cohomology module, which we call a local cohomology module with respect to a pair of ideals (I,J), and study its various properties. Some vanishing and nonvanishing theorems are given for this generalized version of local cohomology. We also discuss its connection with ordinary local cohomology.     

Pseudolocality of the Ricci Flow Under Integral Bound of Curvature

We prove a pseudolocality type theorem for compact Ricci flows under local integral bounds on curvature. The main tool we use here is the local Ricci flow introduced by Deane Yang and the pseudolocality theorem due to Perelman. We also prove a theorem on the extension of the local Ricci flow.     

A nonmonotone filter method for nonlinear optimization

We propose a new nonmonotone filter method to promote global and fast local convergence for sequential quadratic programming algorithms. Our method uses two filters: a standard, global g-filter for global convergence, and a local nonmonotone l-filter that allows us to establish fast local convergence. We show how to switch between the two filters efficiently, and we prove global and superlinear local convergence. A special feature of the proposed method is that it does not require second-order correction steps. We present preliminary numerical results comparing our implementation with a classical filter SQP method.     

A posteriori error estimation and adaptive mesh-refinement techniques

We analyse three different a posteriori error estimators for elliptic partial differential equations. They are based on the evaluation of local residuals with respect to the strong form of the differential equation, on the solution of local problems with Neumann boundary conditions, and on the solution of local problems with Dirichlet boundary conditions. We prove that all three are equivalent and yield global upper and local lower bounds for the true error. Thus adaptive mesh-refinement techniques based on these estimators are capable to detect local singularities of the solution and to appropriately refine the grid near these singularities. Some numerical examples prove the efficiency of the error estimators and the mesh-refinement techniques.     

Trace-Based Methods for Solving Nonlinear Global Optimization and Satisfiability Problems

In this paper we present a method called NOVEL (Nonlinear Optimization via External Lead) forsolving continuous and discrete global optimization problems. NOVEL addresses the balance between global search and local search, using a trace to aid in identifying promising regions before committing to local searches. We discuss NOVEL for solving continuous constrained optimization problems and show how it can be extended to solve constrained satisfaction and discrete satisfiability problems. We first transform the problem using Lagrange multipliers into an unconstrained version. Since a stable solution in a Lagrangian formulation only guarantees a local optimum satisfying the constraints, we propose a global search phase in which an aperiodic and bounded trace function is added to the search to first identify promising regions for local search. The trace generates an information-bearing trajectory from which good starting points are identified for further local searches. Taking only a small portion of the total search time, this elegant approach significantly reduces unnecessary local searches in regions leading to the same local optimum. We demonstrate the effectiveness of NOVEL on a collection of continuous optimization benchmark problems, finding the same or better solutions while satisfying the constraints. We extend NOVEL to discrete constraint satisfaction problems (CPSs) by showing an efficient transformation method for CSPs and the associated representation in finite-difference equations in NOVEL. We apply NOVEL to solve Boolean satisfiability instances in circuit fault detection and circuit synthesis applications, and show comparable performance when compared to the best existing method.     

代数的局部完备集范畴和FS-局部dcpo范畴的笛卡儿闭性

本文引入了代数的局部完备集,FS-局部dcpo,局部稳定映射等概念．主要结果是：以局部Scott连续映射为态射的代数的局部完备集范畴,以局部稳定映射为态射的代数的局部完备集范畴以及以局部Scott连续映射为态射的FS-局部dcpo范畴都是笛卡儿闭范畴．     

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 Multigrid in H（curl）

We consider H（curl, Ω）-elliptic variational problems on bounded Lipschitz polyhedra and their finite element Galerkin discretization by means of lowest order edge elements. We assume that the underlying tetrahedral mesh has been created by successive local mesh refinement, either by local uniform refinement with hanging nodes or bisection refinement. In this setting we develop a convergence theory for the the so-called local multigrid correction scheme with hybrid smoothing. We establish that its convergence rate is uniform with respect to the number of refinement steps. The proof relies on corresponding results for local multigrid in a H^1 （Ω）-context along with local discrete Helmholtz-type decompositions of the edge element space.     

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.