A Shifted-Barrier Primal-Dual Algorithm Model for Linearly Constrained Optimization Problems

In this paper we describe a Newton-type algorithm model for solving smooth constrained optimization problems with nonlinear objective function, general linear constraints and bounded variables. The algorithm model is based on the definition of a continuously differentiable exact merit function that follows an exact penalty approach for the box constraints and an exact augmented Lagrangian approach for the general linear constraints. Under very mild assumptions and without requiring the strict complementarity assumption, the algorithm model produces a sequence of pairs converging quadratically to a pair where satisfies the first order necessary conditions and is a KKT multipliers vector associated to the linear constraints. As regards the behaviour of the sequence x ^k alone, it is guaranteed that it converges at least superlinearly. At each iteration, the algorithm requires only the solution of a linear system that can be performed by means of conjugate gradient methods. Numerical experiments and comparison are reported.     

On the Selection of Random Numbers in the EIGamal Algorithm

The EIGamal algorithm, which can be used for both signature and encryption, is of importance in public-key cryptosystems. However, there has arisen an issue that different criteria of selecting a random number are used for the same algorithm. In the aspects of the sufficiency, necessity, security and computational overhead of parameter selection, this paper analyzes these criteria in a comparative manner and points out the insecurities in some textbook cryptographic schemes. Meanwhile, in order to enhance security a novel generalization of the EIGamal signature scheme is made by expanding the range of selecting random numbers at an acceptable cost of additional computation, and its feasibility is demonstrated.     

Derivation of a new class of distributions for the microcanonical ensemble

A new class of distributions for the microcanonical ensemble, which are shown to be stable laws, are derived by applying the central limit theorem to the canonical ensemble. This opens up a whole new host of phenomena that can be treated from a unified thermodynamic point of view. Pressure broadening of line shapes is used as an illustration.1. Work supported, in part, by contributions from the Consiglio Nazionale di Ricerche and the Ministero dell'Università e della Ricerca Scientifica e Tecnologica.2. The interaction parameterC is proportional to the mean square dipole moment. As an order of magnitude of the dipole moment, we can take it as the product of the electric charge and a typical atomic radius for a moderately excited state, which is several times the Bohr radius. Multiplication by the fine structure constant converts the Bohr radius into the Compton wavelength, thereby reducing the magnitude of the interaction by 1/137.     

A preconditioned conjugate gradient Uzawa-type method for the solution of the stokes problem by mixed Q1–P0 stabilized finite elements

We study the behaviour of a conjugate gradient Uzawa-type method for a stabilized finite element approximation of the Stokes problem. Many variants of the Uzawa algorithm have been described for different finite elements satisfying the well-known Inf-Sup condition of Babu?ka and Brezzi, but it is surprising that developments for unstable ‘low-order’ discretizations with stabilization procedures are still missing. Our paper is presented in this context for the popular (so-called) Q1–P0 element. First we show that a simple stabilization technique for this element permits us to retain the property of a convergence factor bounded independently of the discretization mesh size. The second contribution of this work deals with the construction of a less costly preconditioner taking full advantages of the block diagonal structure of the stabilization matrix. Its efficiency is supported by 2D and. 3D numerical results.     

Two-Dimensional Numerical Simulations of Photon Scanning Tunneling Microscopy: Fourier Modal Method and R-Matrix Algorithm

Numerical simulation of a two-dimensional probe–object system for photon scanning tunneling microscope is presented. The R-matrix propagation algorithm incorporated into the Fourier modal method was used to achieve an extended capability for modeling of a realistic system consisting of both a probe and a sample. The type of the mode guided through the dielectric probe and the coupling of the near-field to fundamental guiding mode in the probe are discussed. The influence of the probe parameters on the near-field images is investigated. Three different probe shapes were simulated in the constant height scanning mode. The transmitted flux intensity through the probe was found to be strongly dependent on the tip shape. The analysis shows a good agreement of the obtained results with the available theoretical works and confirming experimental results. The proposed numerical scheme can find applications for near-field probe characterization and provides an understanding of the degree of perturbation introduced by a probe tip in the experiment.     

Neighboring extremals of dynamic optimization problems with path equality constraints

Neighboring extremals of dynamic optimization problems with path equality constraints and with an unknown parameter vector are considered in this paper. With some simplifications, the problem is reduced to solving a linear, time-varying two-point boundary-value problem with integral path equality constraints. A modified backward sweep method is used to solve this problem. Two example problems are solved to illustrate the validity and usefulness of the solution technique. This research was supported in part by the National Aeronautics and Space Administration under NASA Grant No. NCC-2-106. The author is indebted to Professor A. E. Bryson, Jr., Department of Aeronautics and Astronautics, Stanford University, for many stimulating discussions.     

Fourier acceleration of iterative processes in disordered systems

Technical details are given on how to use Fourier acceleration with iterative processes such as relaxation and conjugate gradient methods. These methods are often used to solve large linear systems of equations, but become hopelessly slow very rapidly as the size of the set of equations to be solved increases. Fourier acceleration is a method designed to alleviate these problems and result in a very fast algorithm. The method is explained for the Jacobi relaxation and conjugate gradient methods and is applied to two models: the random resistor network and the random central-force network. In the first model, acceleration works very well; in the second, little is gained. We discuss reasons for this. We also include a discussion of stopping criteria.     

A simple version of Karzanov's blocking flow algorithm

Dinic has shown that the classic maximum flow problem on a graph of n vertices and m edges can be reduced to a sequence of at most n ? 1 so-called ‘blocking flow’ problems on acyclic graphs. For dense graphs, the best time bound known for the blocking flow problems is O(n²). Karzanov devised the first O(n²)-time blocking flow algorithm, which unfortunately is rather complicated. Later Malhotra, Kumar and Maheshwari devise another O(n²)-time algorithm, which is conceptually very simple but has some other drawbacks. In this paper we propose a simplification of Karzanov's algorithm that is easier to implement than Malhotra, Kumar and Maheshwari's method.     

Mathematical modeling of a steam generator for sensor fault detection

A dynamic model for a nuclear power plant steam generator (vertical, preheated, U-tube recirculation-type) is formulated as a sixth-order nonlinear system. The model integrates nodal mass and energy balances for the primary water, the U-tube metal and the secondary water and steam. The downcomer flow is determined by a static balance of momentum. The mathematical system is solved using transient input data from the Philippsburg 2 (FRG) nuclear power plant. The results of the calculation are compared with actual measured values. The proposed model provides a low-cost tool for the automatic control and simulation of the steam generating process. The “parity-space” algorithm is used to demonstrate the applicability of the mathematical model for sensor fault detection and identification purposes. This technique provides a powerful means of generating temporal analytic redundancy between sensor signals. It demonstrates good detection rates of sensor errors using relatively few steps of scanning time and allows the reconfiguration of faulty signals.     

HC112市内电话维护管理系统

本文介绍了市内电话维护管理系统体系结构的层次模型，讨论了各组成部分的关键技术及层间关系，给出了一种基于局域网和广域网的ＨＣ１１２（Ｈｙｐｏ Ｃｅｎｔｒａｌｉｚｅｄ１１２）的实现。