A generalisation of the Cantor-Zassenhaus algorithm

We generalise the Cantor-Zassenhaus algorithm for factoring polynomials over finite fields. The generalisation yields a class of factorisation algorithms. We compute their factorisation probability and their least upper bound. We then give a simple characterisation of the algorithms reaching the least upper bound. As an example we show the Cantor-Zassenhaus and the Ben-Or algorithms have a factorisation probability equal to the least upper bound.     

Polynomial root finding by means of continuation

In this paper we deal with the problem of locating all the zeros of a given polynomialp(x) and approximating them to any degree of precision: by combining classical iterative methods with homotopy path tracking techniques, we introduce a new algorithm for polynomial root finding, prove its convergence and estimate its computational cost.     

Corrosion and deposition of ferrous alloys in molten lead-bismuth

This paper reports corrosion and deposition data from tests carried out with liquid eutectic lead-bismuth (Pb-55 at.% Bi) filled steel tubes (austenitic and martensitic) under a thermal gradient (500-280 °C) for 3000 h. For the austenitic steel, the surface exposed to Pb-55Bi exhibited a ferritic corrosion layer depleted in nickel and chromium at temperature above 450 °C. In the temperature range 450-360 °C, deposits composed of iron and chromium were found. There is a temperature effect on composition with a change from iron-rich to chromium-rich with decreasing temperature. For the martensitic steel, a corrosion without corrosion layer was observed above 480 °C. Only one type of deposit consisting of 98Fe-2Cr was found in the 400-480 °C temperature range.     

Sequence of the most informative joints (SMIJ): A new representation for human skeletal action recognition

Much of the existing work on action recognition combines simple features with complex classifiers or models to represent an action. Parameters of such models usually do not have any physical meaning nor do they provide any qualitative insight relating the action to the actual motion of the body or its parts. In this paper, we propose a new representation of human actions called sequence of the most informative joints (SMIJ), which is extremely easy to interpret. At each time instant, we automatically select a few skeletal joints that are deemed to be the most informative for performing the current action based on highly interpretable measures such as the mean or variance of joint angle trajectories. We then represent the action as a sequence of these most informative joints. Experiments on multiple databases show that the SMIJ representation is discriminative for human action recognition and performs better than several state-of-the-art algorithms.     

Effects of nitrogen on low-cycle fatigue properties of type 304L austenitic stainless steels tested with and without tensile strain hold

A quantitative analysis of the effects of nitrogen on high temperature low-cycle fatigue without and with tensile strain hold at 600 °C has been conducted for type 304L stainless steels. For better understanding of the role of nitrogen on grain boundary precipitation, the grain boundary segregation of nitrogen was analyzed by Auger electron spectroscopy. The nitrogen addition is found to give relatively better resistance to creep-fatigue than continuous low-cycle fatigue. This in turn improves the fatigue life. This is due to the retardation of the precipitation of carbides at the grain boundary and reduction in the density of grain boundary cavitation sites which are the main factor of grain boundary damage under creep-fatigue test.     

A simple and efficient boolean solver for Constraint Logic Programming

We study in this paper the use of consistency techniques and local propagation methods, originally developed for constraints over finite domains, for solving boolean constraints in Constraint Logic Programming (CLP). To this aim, we first present a boolean CLP language clp(B/FD) built upon a CLP language over finite domains clp(FD) which uses a propagation-based constraint solver. It is based on a single primitive constraint which allows the boolean solver to be encoded at a low level. The boolean solver obtained in this way is both very simple and very efficient: on average it is eight times faster than the CHIP propagation-based boolean solver, i.e. nearly an order of magnitude faster, and infinitely better than the CHIP boolean unification solver. It also performs on average several times faster than special-purpose stand-alone boolean solvers. We then present in a second time several simplifications of the above approach, leading to the design of a very simple and compact dedicated boolean solver. This solver can be implemented in a WAM-based logical engine with a minimal extension limited to four new abstract instructions. This clp(B) system provides a further factor two speedup w.r.t. clp(B/FD).     

Solution of Large Scale Algebraic Matrix Riccati Equations by Use of Hierarchical Matrices

In previous papers, a class of hierarchical matrices (ℋ-matrices) is introduced which are data-sparse and allow an approximate matrix arithmetic of almost optimal complexity. Here, we investigate a new approach to exploit the ℋ-matrix structure for the solution of large scale Lyapunov and Riccati equations as they typically arise for optimal control problems where the constraint is a partial differential equation of elliptic type. This approach leads to an algorithm of linear-logarithmic complexity in the size of the matrices. Received July 30, 2002; revised December 16, 2002 Published online: April 22, 2003     

A Numerical Study of the Xu Polynomial Interpolation Formula in Two Variables

In his paper ``Lagrange interpolation on Chebyshev points of two variables' (J. Approx. Theor. 87, 220–238, 1996), Y. Xu proposed a set of Chebyshev like points for polynomial interpolation in the square [−1,1]², and derived a compact form of the corresponding Lagrange interpolation formula. We investigate computational aspects of the Xu polynomial interpolation formula like numerical stability and efficiency, the behavior of the Lebesgue constant, and its application to the reconstruction of various test functions.     

波形智能理解及其在检针仪中的应用

波形智能理解是信号动态检测中的一种新方法。本文通过检针器的例子，介绍了传感器的测量原理，并对分离得到波形特征进行描述。     

Solution methods and computational investigations for the Linear Bottleneck Assignment Problem

The Linear Bottleneck Assignment ProblemLBAP is analyzed from a computational point of view. Beside a brief review of known algorithms new methods are developed using only sparse subgraphs for their computation. The practical behaviour of both types of algorithms is investigated. The most promising algorithm consists of computing a maximum cardinality matching with all edge costs smaller than a previously determined bound and augmenting this matching to an assignment. The methods on sparse subgraphs are useful in the case of memory restrictions and are superior if the subgraph selection can be improved by some previously generated structure. Other treated questions are how to select a suitable subgraph for the new methods, how to deal with non regular data and what connections to asymptotic results for theLBAP can be detected. Supported by the SFB F003 ‘Optimierung und Kontrolle’, Bereich Diskrete Optimierung.