This work is a survey of results for ill-posed Cauchy problems for PDEs of the author with co-authors starting from 1991. A universal method of the regularization of these problems is presented here. Even though the idea of this method was previously discussed for specific problems, a universal approach of this paper was not discussed, at least in detail. This approach consists in constructing of such Tikhonov functionals which are generated by unbounded linear operators of those PDEs. The approach is quite general one, since it is applicable to all PDE operators for which Carleman estimates are valid. Three main types of operators of the second order are among them: elliptic, parabolic and hyperbolic ones. The key idea is that convergence rates of minimizers are established using Carleman estimates. Generalizations to nonlinear inverse problems, such as problems of reconstructions of obstacles and coefficient inverse problems are also feasible. 相似文献
The attributes of vehicle routing problems are additional characteristics or constraints that aim to better take into account the specificities of real applications. The variants thus formed are supported by a well-developed literature, including a large variety of heuristics. This article first reviews the main classes of attributes, providing a survey of heuristics and meta-heuristics for Multi-Attribute Vehicle Routing Problems (MAVRP). It then takes a closer look at the concepts of 64 remarkable meta-heuristics, selected objectively for their outstanding performance on 15 classic MAVRP with different attributes. This cross-analysis leads to the identification of “winning strategies” in designing effective heuristics for MAVRP. This is an important step in the development of general and efficient solution methods for dealing with the large range of vehicle routing variants. 相似文献
We report on ideas, problems and results, which occupied us during the past decade and which seem to extend the frontiers of information theory in several directions. The main contributions concern information transfer by channels. There are also new questions and some answers in new models of source coding. While many of our investigations are in an explorative state, there are also hard cores of mathematical theories. In particular we present a unified theory of information transfer, which naturally incorporates Shannon's theory of information transmission and the theory of identification in the presence of noise as extremal cases. It provides several novel coding theorems. On the source coding side we introduce data compression for identification. Finally we are led beyond information theory to new concepts of solutions for probabilistic algorithms.
The original paper [R. Ahlswede, General theory of information transfer, Preprint 97-118, SFB 343 Diskrete Strukturen in der Mathematik, Universität Bielefeld, 1997] gave to and received from the ZIF-project essential stimulations which resulted in contributions added as GTIT-Supplements “Search and channels with feedback” and “Noiseless coding for multiple purposes: a combinatorial model”.
Other contributions—also to areas initiated—are published in the recent book [R. Ahlswede et al. (Eds.), General Theory of Information Transfer and Combinatorics, Lecture Notes in Computer Science, vol. 4123, Springer, Berlin, 2006].
The readers are advised to study always the pioneering papers in a field—in this case the papers [R. Ahlswede, G. Dueck, Identification via channels, IEEE Trans. Inform. Theory 35 (1989) 15–29; R. Ahlswede, G. Dueck, Identification in the presence of feedback—a discovery of new capacity formulas, IEEE Trans. Inform. Theory 35 (1989) 30–39] on identification. It is not only the most rewarding way to come to new ideas, but it also helps to more quickly grasp the more advanced formalisms without going through too many technicalities. Perhaps also the recent Shannon Lecture [R. Ahlswede, Towards a General Theory of Information Transfer, Shannon Lecture at ISIT in Seattle 13th July 2006, IEEE Information Theory Society Newsletter, 2007], aiming at an even wider scope, gives further impetus. 相似文献
A recent editorial reviewed several definitions of quality. The limitations of these definitions are discussed here, with
a simple suggestion to define quality as meeting a specified error rate whereby the required elements for an error rate are
listed.
Papers published in this section do not necessarily reflect the opinion of the Editors, the Editorial Board and the Publisher. 相似文献
In this survey, the history of the subject from 1776 until 1960 is presented. A brief biographical sketch of Vilfredo Pareto is given first. Then, the more or less simultaneous development of the concepts of utility, preference, and welfare theory follows, with results which go back to Hausdorff and Cantor. A brief discussion of the work of Borel and von Neumann as initiators of game theory is included. Each of these areas has developed enough to warrant its own survey; hence, they are reviewed here only insofar as they provide necessary foundations. Thereafter, the concepts of efficiency, vector maximum problem, and Pareto optimality are reviewed in connection with production theory, programming, and economics. The survey is presented within a unified mathematical framework, and the emphasis is on mathematical results, rather than psychological or socio-economic discussion. To enable the reader to draw conclusions without having to obtain each article himself, the results have been presented in somewhat more detail than usual. 相似文献
Nanotechnology will be an increasing part of the everyday lives of most people in the world. There is a general recognition
that few people understand the implications of the technology, the technology itself or even the definition of the word. This
lack of understanding stems from a lack of knowledge about science in general but more specifically difficulty in grasping
the size scale and symbolism of nanotechnology. A potential key to informing the general public is establishing the ability
to comprehend the scale of nanotechnology. Transitioning from the macro to the nanoscale seems to require an ability to comprehend
scales of one-billion. Scaling is a skill not common in most individuals and tests of their ability to extrapolate size based
upon scaling a common object demonstrates that most individuals cannot scale to the extent needed to make the transition to
nanoscale. Symbolism is another important vehicle to providing the general public with a basis to understand the concepts
of nanotechnology. With increasing age, individuals are able to draw representations of atomic scale objects, but these tend
to be iconic and the different representations not easily translated. Ball and stick models are most recognized by the public,
which provides an opportunity to present not only useful symbolism but also a reference point for the atomic scale. 相似文献