Abstracts

Use of modern computing technology, in particular, of WWW-servers and hypertext systems allows to pose and solve problems of concentration, systematization, usage, and development of ill-posed problems’ solution methods on quantitative new level. Hypertext systems allow to elaborate multilevel material structurization that is inaccessible or accessible with a lot of input on paper mediums. The simpliest example of such structurization is a diversity on different levels of theorems’ statements and their proofs. Of course, deeper structurization is also possible: the diversity of the main ideas of the proofs and technical details; separation of the most important special cases or generalizations, etc. For research that are basic to create some algorithms, very important and useful is the opportunity of elaboration of demonstrative programs corresponding to stated methods and algorithms. Existing of such programs allows comparing different methods in various situations of their usage. Mentioned above properties of electronic publications in the form of hypertext pages which are complemented by executive programs may be used both on CD-ROM and specialized servers. Creation of such systems in the form of specialized servers allows to provide dynamic material modification that is very important for research being intensively led in many scientific centers. In present time in the Institute of Mathematics of Siberian Branch of Russian Academy of Sciences (SB RAS) and in the Institute of Automation and Electrometry SB RAS with support of Russian Foundation of Basic Research (RFBR) the server «Ill-Posed Problems» is being created. Addresses of the Server are the following:

http://www.iae.nsk.su/~trofimov/IPP/main.htm 
http://a-server.math.nsc.ru/IPP/main.htm 
http://cs.nstu.ru/ipp/

• General concepts of ill-posed problems.
• Base papers. A. Tikhonov's, M. Lavrentiev's, W. Ivanov's papers are included in this topic, and also well-known Adamar's example.
• Monographs. In this step, in general, monographs of Russian scientists are included.
• Tomography. In present time in this topic there exists theoretical basis for computer tomography methods. Distinguishing of the class of ill-posed problems connected with Tomography problems is cased by actuality of corresponding questions. Demonstrative version of computerized 2D-Tomography program accessible for INTERNET users exists on the Server. Analogous programs for 3-D Tomography are elaborated in present time.
• References. This section includes references to Web-pages in close themes.
• Conferences. The topic contains the information about future and past conferences. In particular, there is information about tomographic symposiums that were led in Russia, Ukraine and Uzbekistan during 10 years.
• Search. There exists the system that allows searching information on the server using keywords.

Note. Abstracts are published in author's edition

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