Integral closure,basically full closure,and duals of nonresidual closure operations

We develop a duality for operations on nested pairs of modules that generalizes the duality between absolute interior operations and residual closure operations from [5], extending our previous results to the expanded context. We apply this duality in particular to integral and basically full closures and their respective cores to obtain integral and basically empty interiors and their respective hulls. We also dualize some of the known formulas for the core of an ideal to obtain formulas for the hull of a submodule of the injective hull of the residue field. The article concludes with illustrative examples in a numerical semigroup ring.     

Path-following interior point algorithms for the Cartesian <Emphasis Type="Italic">P</Emphasis><Subscript>*</Subscript>(κ)-LCP over symmetric cones

In this paper, we establish a theoretical framework of path-following interior point algorithms for the linear complementarity problems over symmetric cones (SCLCP) with the Cartesian P _*(κ)-property, a weaker condition than the monotonicity. Based on the Nesterov-Todd, xy and yx directions employed as commutative search directions for semidefinite programming, we extend the variants of the short-, semilong-, and long-step path-following algorithms for symmetric conic linear programming proposed by Schmieta and Alizadeh to the Cartesian P _*(κ)-SCLCP, and particularly show the global convergence and the iteration complexities of the proposed algorithms. This work was supported by National Natural Science Foundation of China (Grant Nos. 10671010, 70841008)     

Controlled remote implementation of partially unknown quantum operation

A protocol for controlled remote implementation of a partially unknown operation on an arbitrary quantum state is proposed. In this protocol, a task can be performed using a GHZ state shared among three distant parties: Alice, Bob and the controller Charlie. This protocol is also generalized to the multi-party control system based on sharing an N-qubit GHZ state. Supported by the Natural Science Youth Teacher Foundation of Xuzhou Institute of Technology, China (Grant No. XKY2007317)     

A trust-region and affine scaling algorithm for linearly constrained optimization

A new trust-region and affine scaling algorithm for linearly constrained optimization is presented in this paper. Under no nondegenerate assumption, we prove that any limit point of the sequence generated by the new algorithm satisfies the first order necessary condition and there exists at least one limit point of the sequence which satisfies the second order necessary condition. Some preliminary numerical experiments are reported. The work was done while visiting Institute of Applied Mathematics, AMSS, CAS.     

A combination of potential reduction steps and steepest descent steps for solving convex programming problems

This paper studies the possibility of combining interior point strategy with a steepest descent method when solving convex programming problems, in such a way that the convergence property of the interior point method remains valid but many iterations do not request the solution of a system of equations. Motivated by this general idea, we propose a hybrid algorithm which combines a primal–dual potential reduction algorithm with the use of the steepest descent direction of the potential function. The complexity of the potential reduction algorithm remains valid but the overall computational cost can be reduced. Our numerical experiments are also reported. Copyright © 2002 John Wiley & Sons, Ltd.     

Dynamics of implicit operations and tameness of pseudovarieties of groups

This work gives a new approach to the construction of implicit operations. By considering ``higher-dimensional' spaces of implicit operations and implicit operators between them, the projection of idempotents back to one-dimensional spaces produces implicit operations with interesting properties. Besides providing a wealth of examples of implicit operations which can be obtained by these means, it is shown how they can be used to deduce from results of Ribes and Zalesski, Margolis, Sapir and Weil, and Steinberg that the pseudovariety of -groups is tame. More generally, for a recursively enumerable extension closed pseudovariety of groups , if it can be decided whether a finitely generated subgroup of the free group with the pro- topology is dense, then is tame.

     

LD泵浦Nd:YAG 946 nm/1 064 nm双波长运转及腔内和频

用国产半导体激光二极管(LD)端面泵浦NdYAG晶体, 通过优化激光谐振腔反射膜系,调节1 064 nm谱线的线性损耗以达到与弱谱线946 nm的增益匹配,在室温下实现1 064 nm和946 nm双波长连续运转,并通过I类临界相位匹配LBO晶体腔内和频在国内首次实现500.8 nm青色激光连续输出.当泵浦注入功率为1.4W时和频青色激光最大输出达20 mW,光-光转换效率为1.4%,功率稳定性24 h内优于±3%.     

Existence and Limiting Behavior of Trajectories Associated with P0-equations

Given a continuous P₀-function F : Rⁿ Rⁿ, we describe a method of constructing trajectories associated with the P₀-equation F(x) = 0. Various well known equation-based reformulations of the nonlinear complementarity problem and the box variational inequality problem corresponding to a continuous P₀-function lead to P₀-equations. In particular, reformulations via (a) the Fischer function for the NCP, (b) the min function for the NCP, (c) the fixed point map for a BVI, and (d) the normal map for a BVI give raise to P₀-equations when the underlying function is P₀. To generate the trajectories, we perturb the given P₀-function F to a P-function F(x, ); unique solutions of F(x, ) = 0 as varies over an interval in (0, ) then define the trajectory. We prove general results on the existence and limiting behavior of such trajectories. As special cases we study the interior point trajectory, trajectories based on the fixed point map of a BVI, trajectories based on the normal map of a BVI, and a trajectory based on the aggregate function of a vertical nonlinear complementarity problem.     

On a Primal-Dual Analytic Center Cutting Plane Method for Variational Inequalities

We present an algorithm for variational inequalities VI( , Y) that uses a primal-dual version of the Analytic Center Cutting Plane Method. The point-to-set mapping is assumed to be monotone, or pseudomonotone. Each computation of a new analytic center requires at most four Newton iterations, in theory, and in practice one or sometimes two. Linear equalities that may be included in the definition of the set Y are taken explicitly into account.We report numerical experiments on several well—known variational inequality problems as well as on one where the functional results from the solution of large subproblems. The method is robust and competitive with algorithms which use the same information as this one.     

A combinatorial interior point method for network flow problems

For solving minimum cost flow problems, we develop a combinatorial interior point method based on a variant of the algorithm of Karmarkar, described in Gonzaga [3, 4]. Gonzaga proposes search directions generated by projecting certain directions onto the nullspace ofA. By the special combinatorial structure of networks any projection onto the nullspace ofA can be interpreted as a flow in the incremental graph ofG. In particular, to evaluate the new search direction, it is sufficient to choose a negative circuit subject to costs on the arcs depending on the current solution. That approach results in an O(mn ² L) algorithm wherem denotes the number of vertices,n denotes the number of arcs, andL denotes the total length of the input data.