Characterization of isolated homogeneous hypersurface singularities in ℂ4

Let V be a hypersurface with an isolated singularity at the origin in ? ⁿ⁺¹. It is a natural question to ask when V is defined by weighted homogeneous polynomial or homogeneous polynomial up to biholomorphic change of coordinates. In 1971, a beautiful theorem of Saito gives a necessary and sufficient condition for V to be defined by a weighted homogeneous polynomial. For a two-dimensional isolated hypersurface signularity V, Xu and Yau found a coordinate free characterization for V to be defined by a homogeneous polynomial. Recently Lin and Yau gave necessary and sufficient conditions for a 3-dimensional isolated hypersurface singularity with geometric genus bigger than zero to be defined by a homogeneous polynomial. The purpose of this paper is to prove that Lin-Yau’s theorem remains true for singularities with geometric genus equal to zero.     

On decomposition of continuity

Summary The main purpose of this paper is to introduce the concepts of η-sets, ηζ-sets,η-continuity and ηζ-continuity and to obtain a decomposition of continuity.     

Addendum to "On the L1-Condition Number of the Univariate Bernstein Basis"

The paper mentioned above is a contribution of the authors to Volume 18 (2002) of this journal, see . Recently, J. Domsta pointed out to us that the proof of Theorem 4.2 in that paper contains an error. The purpose of this addendum is to present a correct argument for it.     

Stability testing in an integrated scheme

ISO Guide 35 deals with RM stability issues and scrutinizes the evaluation of stability testing results under the assumption that either there is no trend at all (a rather rare situation), or any observed deterministic change is insignificant and thus can be neglected. However, market demands for reliable reference materials are obviously not limited to stable or at least seemingly stable materials. In many analytical applications, analytes and measurands under consideration are known, or at least suspected, to be unstable on time scales that may vary widely from measurand to measurand. The Federal Institute for Materials Research and Testing (BAM) has developed (and successfully uses) an integrated approach in its certification practice. The approach is based on an initial stability study and subsequent post-certification monitoring. Data evaluation is model-based and takes advantage of all information collected in the stability testing scheme(s). It thus allows one to deal with any kind of instability observed, to assess limiting time intervals at any stress condition in the range tested, to estimate a final expiry date for materials with detected instabilities or the maximum admissible re-testing interval for seemingly stable materials, and to assess maximum admissible stress loads during delivery of the material to the customer. The article describes (and exemplifies) typical study layout, the model selection, and the integrated data assessment.     

Electrochemical Recovery of Silver from Lead Alloys in Chloride Melts

Electrochemical separation of lead-silver alloys into the constituents by thin-layer electrolysis in molten electrolytes, with bismuth as metal separator, is studied. It is proposed to determine the extent of component recovery by potentiometry.     

Electroactive conducting polymers for corrosion control

There is an intensive effort underway to develop new corrosion control coatings for structural metals. In part, this effort has been motivated by the desire to replace chromium(VI)-containing coatings currently used for corrosion control of iron and aluminum alloys. Cr(VI) has been shown to be hazardous to the environmental and to human health, and its use in many countries will be sharply curtailed in the coming years. Electroactive conducting polymers (ECPs) represent a class of interesting materials currently being explored for use in corrosion control coating systems, possibly as a replacement for Cr(VI)-based coatings. The electroactivity and the electronic conductivity (or semiconductivity) of ECPs set them apart from traditional organic coatings. As with chromate, interesting and potentially beneficial interactions of ECPs with active metal alloys such as steel and aluminum are anticipated, with concomitant alteration of their corrosion behavior. A review of this active research area will be presented in two parts. Here in Part 1, a general introduction to the topic of corrosion control by ECPs will be presented, including an overview of corrosion and its control by traditional methods, an introduction to ECPs and their properties, and a discussion of the processing issues surrounding the use of ECPs as coatings. Part 1 also includes a review of the literature on the use of ECPs as coatings (or components of coatings) on non-ferrous active metals, principally aluminum and aluminum alloys, although some work on zinc, copper, silver, titanium and silicon will also be described. In Part 2 of this review (to be published in the next issue of this journal), the rather extensive literature on the use of ECPs for the corrosion control of ferrous alloys (steels) will be reviewed. Electronic Publication     

Multicriteria decision making under uncertainty

Formalization for problems of multicriteria decision making under uncertainty is constructed in terms of guaranteed and weak estimates. A relevant definition of the vector maximinimax value is given. Parameterization and approximation of maximum, minimax, and maximinimax values based on the inverse logical convolution are suggested. An application for multicommodity networks is considered. Received: December 13, 2000 / Accepted: August 21, 2001?Published online May 8, 2002     

BoneRoute: An Adaptive Memory-Based Method for Effective Fleet Management

This paper presents an adaptive memory-based method for solving the Capacitated Vehicle Routing Problem (CVRP), called BoneRoute. The CVRP deals with the problem of finding the optimal sequence of deliveries conducted by a fleet of homogeneous vehicles, based at one depot, to serve a set of customers. The computational performance of the BoneRoute was found to be very efficient, producing high quality solutions over two sets of well known case studies examined.     

Quadratic data envelopment analysis

Data Envelopment Analysis (DEA) offers a piece-wise linear approximation of the production frontier. The approximation tends to be poor if the true frontier is not concave, eg in case of economies of scale or of specialisation. To improve the flexibility of the DEA frontier and to gain in empirical fit, we propose to extend DEA towards a more general piece-wise quadratic approximation, called Quadratic Data Envelopment Analysis (QDEA). We show that QDEA gives statistically consistent estimates for all production frontiers with bounded Hessian eigenvalues. Our Monte-Carlo simulations suggest that QDEA can substantially improve efficiency estimation in finite samples relative to standard DEA models.