Combinatorial optimization under uncertainty

In this paper, the general problem of Euclidean combinatorial optimization under uncertainty is formulated for the first time and the concepts of a stochastic multiset, a multiset of fuzzy numbers, a stochastic Euclidean combinatorial set, and general Euclidean combinatorial set of fuzzy stochastic numbers that combines the properties of both types of uncertainty are introduced. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 35–44, September–October 2008.     

Some Statistical-Estimation Methods for Stochastic Finite-State Transducers

Formal translations constitute a suitable framework for dealing with many problems in pattern recognition and computational linguistics. The application of formal transducers to these areas requires a stochastic extension for dealing with noisy, distorted patterns with high variability. In this paper, some estimation criteria are proposed and developed for the parameter estimation of regular syntax-directed translation schemata. These criteria are: maximum likelihood estimation, minimum conditional entropy estimation and conditional maximum likelihood estimation. The last two criteria were proposed in order to deal with situations when training data is sparse. These criteria take into account the possibility of ambiguity in the translations: i.e., there can be different output strings for a single input string. In this case, the final goal of the stochastic framework is to find the highest probability translation of a given input string. These criteria were tested on a translation task which has a high degree of ambiguity.     

State Observation and Diagnosis of Discrete-Event Systems Described by Stochastic Automata

The problems ofstate observation and diagnosis are solved for discrete–eventsystems, which are described by stochastic automata. As manysystems are not observable in the sense that it is possible toreconstruct the state unambiguously, the observation problemis set up as the problem of determining the smallest possibleset of states that are compatible with the measured input andoutput sequences. The diagnostic problem is shown to be, in principle,an observation problem. Conditions for the observability anddiagnosability of stochastic automata are presented. The resultsare illustrated by examples.     

A FORMULA FOR THE INVERSE AUTOCORRELATION FUNCTION OF AN AUTOREGRESSIVE PROCESS

Abstract. The determination of the inverse autocorrelation function of a weakly stationary autoregressive process using the autocorrelation function is considered. Usually this is carried out either by using frequency domain methods or by solving first the parameters of the process and then using them. In this paper we give a simple formula by which the inverse autocorrelation function can be determined directly from the autocorrelation function.     

Stochastic Models for Pad Structure and Pad Conditioning Used in Chemical-Mechanical Polishing

Stochastic models are presented for the structure and conditioning of pads used in chemical-mechanical polishing of wafers. First the one-dimensional distribution function of surface depth in the case of a conditioned solid pad is described. Then, for characterizing the structure of a foamed pad, the theory of random closed sets is applied. An important distributional characteristic of a random closed set, the linear contact distribution function, yields the contribution to surface depth resulting from pores. As a special example the Boolean model is considered. This leads to a formula that describes the variability of the surface of a conditioned foamed pad after a certain time. Simulations and experimental data show a good agreement between theory and reality.     

The generalized Riemann problem method for the shallow water equations with bottom topography

This paper extends the generalized Riemann problem method (GRP) to the system of shallow water equations with bottom topography. The main contribution is that the generalized Riemann problem method (J. Comput. Phys. 1984; 55 (1):1–32) is used to evaluate the midpoint values of solutions at each cell interface so that the bottom topography effect is included in numerical fluxes, and at the same step the source term is discretized with an interface method in which only mid‐point values are plugged in. This scheme is well balanced between the flux gradient and bottom topography when incorporating the surface gradient method (SGM) (J. Comput. Phys. 2001; 168 (1):1–25) into data reconstruction step, and it is also suitable for both steady and unsteady flow simulations. We illustrate the accuracy of this scheme by several 1‐D and 2‐D numerical experiments. Copyright © 2005 John Wiley & Sons, Ltd.     

A finite element method for poro mechanical modelling of geotechnical problems using local second gradient models

In this paper, a new finite element method is described and applied. It is based on a theory developed to model poromechanical problems where the mechanical part is obeying a second gradient theory. The aim of such a work is to properly model the post localized behaviour of soils and rocks saturated with a pore fluid. Beside the development of this new coupled theory, a corresponding finite element method has been developed. The elements used are based on a weak form of the relation between the deformation gradient and the second gradient, using a field of Lagrange multipliers. The global problem is solved by a system of equations where the kinematic variables are fully coupled with the pore pressure. Some numerical experiments showing the effectiveness of the method ends the paper. Copyright © 2005 John Wiley & Sons, Ltd.     

中间夹层材料和保护气体对不锈钢-碳钢复合效果的影响

提出了利用中间夹层材料促进不锈钢与碳钢复合的新工艺。研究了中间夹层材料和保护气体对不锈钢与碳钢复合效果的影响规律。结果表明，采用自制的银基中间夹层材料可以使两种母材在较低的压力下实现良好的复合；加热过程中采用氩气保护能够有效地去除不锈钢表面致密的氧化膜。     

Starting solutions for some unsteady unidirectional flows of a second grade fluid

Exact solutions corresponding to the motions of a second grade fluid, due to the cosine and sine oscillations of an infinite flat plate as well as those induced by an oscillating pressure gradient are determined by means of the Fourier sine transforms. These solutions, presented as sum of the steady-state and transient solutions, satisfy both the governing equations and all associate initial and boundary conditions. In the special case when α₁ → 0, they reduce to those for a Navier-Stokes fluid.     

Stochastic stabilization of differential systems with general decay rate

Some sufficient conditions concerning stability of solutions of stochastic differential evolution equations with general decay rate are first proved. Then, these results are interpreted as suitable stabilization ones for deterministic and stochastic systems. Also, they permit us to construct appropriate linear stabilizers in some particular situations.