A Frontend Dublin Core Database for Zentralblatt MATH

Table of Contents

1. Executive Summary
2. Introduction
3. Description of Zentralblatt MATH
4. Description of Method Used / Work Done
5. Analysis and Findings
6. Conclusions
7. Recommendations
8. References
A. Annexes

1. Executive Summary

2. Introduction

The deliverable is both an outline description of the work done in the bibliographic database adaptation task and a guideline for the purpose of future partners. It is not intended to be a detailed manual. E.g. for detailed instructions to set up a Zebra Z39.50 server one should be referred to the Zebra related documentation.
 
 

3. Description of Zentralblatt MATH

The name Zentralblatt MATH stands equally for the conventional printed service as well as for the three online services. The central service consists in the online database with WWW-access, further services are made via the host system of STN International, and the CD-ROM version for off-line use. The total amount of information stored in the databases corresponds to more than 1.700.000 documents. The online databases are updated monthly along with the production scheme of the printed version of Zentralblatt.

Searches can be made using a variety of fields: authors, titles, classification, basic index, source, language etc. A search can be formulated in logical combinations of these terms. The databases can be queried with a command language or through a graphical user interface. The information is available in the AMSTeX source code, but tools for a convenient formula display are available. Download of the hit list at the users site is possible, and links to the full text of the corresponding article will be provided, if this is available electronically.

Getting the full text of an article through central document delivery services is an additional option. Buttons are provided in the search menu to enable connection and to see  if the corresponding article available there. Document delivery can be arranged by these services electronically or by sending copies by ordinary mail on a cost basis.

Improvements of Zetralblatt services are ongoing in several areas, the most important being:
Aspects of cooperation - Zentralblatt as a European activity:
The overall goal is to improve the facilities of the "European Database in Mathematics" with Zentralblatt MATH as its core, to transform Zentralblatt within this framework to a distributed European activity, and to improve and widen the access to Zentralblatt for European countries by providing structures for a better distribution on the technical and on the economical level. Initial steps into the direction of the European extension have been initiated through a bilateral German-French co-operation (CNRS/Université Grenoble) on software development and support, distribution of the database in France, and by a series of co-operations between German and Middle/East-European academic institutions (Hungary, Czech Republic, Russia, Ukraine et al.). About 60 servers of various types currently exist. Broader and improved access to the database via national access nodes and new data distribution methods are currently under discussion. In particular, improvements of access are planned for isolated universities in regions under economic difficulties and in associated states of Central and Eastern Europe where a mathematical tradition of excellence is under economic threat. Stimulation of usage for all kinds of research as well as for funding organisations before decision making is achieved by initial trial accounts. Improved coverage and evaluation of European research literature is planned via nationally distributed editorial units, and the development of new technologies for efficient database production. These activities are supervised by a European advisory board (under the auspices of the EMS), in close coordination with other European information activities (like FIZ, VINITI, European publishers etc.).
 
 

4. Description of Method Used / Work Done

A conversion program was written to transform data from the internal MATH production database export format to the DC-based EULER format. The specification and implementation of the converter needed to be done in coordination with the specification of the DC-based EULER format (Task 3.1 and other Workpackage 2 Tasks).

Also in connection with Task 3.1, requirements for enriching the data were specified. E.g. full serials names instead of abbreviations, connection to online accessible document delivery services.

The mapping (as of January 2000) from MATH fields to EULER DC records is schematically given in the following table. See Annex A.1 for a more complete explanation of MATH fields and Annex A.2 for some sample records.
 
 

MATH field	Dublin Core	EULER field
AN	EULER.Record.Source & ..ident	RS, OI, DI, DID
AU	DC.Creator	CR
AR	DC.Creator	CR
TI	DC.Title, DC.Title.Alternative	TI, TIA
LA	DC.Language	LA
SO, contains:  Series/Journal Title  Publisher/Location  ISBN  ISSN  URL  volume, issue, pages  price (only for books),etc.	splitted:  DC.Identifier (free)  DC.Publisher  DC.Identifier (ISBN)  DC.Identifier (ISSN)  DC.Identifier (URL)  DC.Identifier (free)  n/a	splitted:  IDF  PU  IDB  IDS  IDL  IDF  -
PY	DC.Date	DA
DT	DC.Type (mapped to DC resource types)	TY
CC	DC.Subject (MSC91)	SUM
UT	DC.Subject (free)	SU
BR	n/a	-
AB	DC.Description	DE
RV	EULER.Record.Creator	RC
CI	n/a	-

EULER fields not applicable:
all SU* fields (except for SU and SUM), DC.Creator.CorporateName - CA, DC.Contributor.PersonalName - COP, DC.Contributor.CorporateName - COC, EULER.Fulltext - FT, FO, FOP, EL, ED, EN, TC, FT

Unused MATH fields: BR, CI, SO (price)
 

Implementation of the converter required database field splitting and merging techniques for MATH database fields that have no direct correspondence in the DC-based format, and adaptation of data encoding schemes. The conversion and adaptation program was written in the Perl programming language.

After the conversion from the production database export format to the standard EULER record format, the records are post processed by the ISO tool, and then indexed by Zebra using the `one large file' method.

A first test installation of the DC-based frontend database for the EULER Engine relied entirely on the results from Task 3.1 (and the starting phase of Task 3.2). The database machine proposed by those tasks (Zebra version 1.0b1, see Deliverable D.3.1) was installed and tested with a small set of test-data (provided by NetLab) at FIZ in October 1998 without major problems. Configuration files (provided by NetLab as part of Tasks 3.1/3.2) were tested and adapted to local settings, the test data were loaded into that database. The resulting database was made available to a early version of the central EULER Engine via Z39.50.

Subsequently, the EULER Engine (alpha version) and its interaction with the converted excerpts from MATH database was tested publicly. Necessary changes on the side of  MATH (correction of fields appearing in wrong places etc.) were applied. This work was done in parallel with the intermediate service evaluation Task 3.3.

The data set from MATH that was finally available in the EULER demonstrator service was specified. It consists of 264176 records, namely the full Zentralblatt MATH production of the period January 1996 - March 1999 (196406 records) plus all monographs (67770 records, including dissertations and similar publications) that are referenced earlier in Zentralblatt MATH since its beginning (1931). In the table in Annex A.3 the distribution of the EULER fields among the records is shown. The procedures for conversion and loading that have been developed above were applied to the large data set. Those data represent the contribution of Zentralblatt MATH to the EULER demonstrator.

Last minute changes and fine-tuning of the procedures will streamline the process. This includes also the development of a concept for dynamic updates of new entries in MATH.
 
 

5. Analysis and Findings

It was observed that not all entries from Zentralblatt are reported by the EULER Engine. Various comments stated that a search in the original Zentralblatt MATH database on WWW yielded substantially more hits than an equivalent query in the EULER service, restricted to Zentralblatt MATH entries. The reason for this problem was of course that only a small fraction of test data was available in EULER during the tests of the alpha version. Zentralblatt MATH is a paid service that is normally available with the full functionality only to subscribing institutions. Within the project, Zentralblatt has successfully demonstrated that the EULER methodology is viable for integrating Zentralblatt data (a test set) with other resources. The question of full access to all Zentralblatt data within a future full service, and conditions for such a type of access will be addressed in the Technology Implementation Plan (Deliverable: D5.2 "Recommendations for the continuation of EULER services").

Mathematical formulae are coded in the TeX typesetting language in the original Zentralblatt. They appear in large quantities in the text of the reviews and abstracts, and also in titles. Within the EULER project, no efforts were undertaken by Zentralblatt to recode them in another way, since no internationally accepted standard was available for this purpose. Two problems connected with the coding of mathematical formulae should be mentioned here:
1) Searching:
Searching databases for mathematical formulae is generally an unsolved problem. Within every coding scheme/typesetting language there are always different ways to denote equivalent or even identical formulae. Very complex algorithms would be needed to solve this problem. Within the EULER project, these questions have not been addressed. It is therefore only possible to search for textual fragments of TeX code in EULER.
2) Display:
Displaying mathematics on the web is another (yet) unsolved problem. Standard practice used for mathematical research papers is to distribute DVI, Postscript or PDF versions, which contain graphical representations of the formulae. This option is not easily applicable in HTML based services like EULER. Genuine WWW based coding schemes are still not available, although draft specifications of MathML, an application of XML, exist. However, MathML enabled browsers are largely unavailable or have very restricted functionality. For these reasons, display of mathematical formulae from Zentralblatt in EULER is in TeX coding, which is not a severe problem since most mathematicians are able to read TeX easily. For very complicated TeX encoded formulae, it is possible to get DVI, Postscript or PDF rendered pages from the original Zentralblatt MATH database: each Zentralblatt entry in EULER has a link to the corresponding original entry, where these output formats can be generated automatically on request.

It was remarked that the display field named "Record Creator" should better be changed to "Reviewer" for Zentralblatt MATH records. Because of the homogeneous layout of the EULER service pages, the field name "Record Creator" was kept for now.

The display of book series and conference proceedings, is inhomogeneous: That a book belongs, e.g., to a series does appear in the category "Alternative Title", or sometimes in the category "Publisher", while it should appear in the field "Bibliographic Info". The reason for this confusion is, that the original "Source" field of the Zentralblatt MATH database does not have a sufficiently fine and fixed substructure. During the several periods of production of Zentralblatt MATH, the internal structure has changed. In the EULER conversion process, the "Source" field of MATH is being split into several EULER fields, and the current conversion program is not able to handle all cases of different formats of the Source field. Further improvements of the respective conversion routines can be expected later, as part of the implementation of the final Demonstrator.

It was observed that Zentralblatt MATH appears to be the main source of data (one evaluator remarked for example that only 4 out of 200 articles came from other databases). This is of course not a problem of Zentralblatt MATH but originates from the nearly complete coverage of all mathematical research literature, including more than 2000 journals on the article level. In the current EULER settings, Zentralblatt MATH is just one data provider on the same level as all others. It might be worthwhile to rethink the EULER architecture so that database providers with a vast coverage of the field would be handled differently than other collections of limited size.

The editors of Mathematical Reviews and Zentralblatt MATH have initiated the process of revising the 1991 Mathematics Subject Classification, which is used by both services as their classification system. MSC2000 is the result of a collaborative effort by the editors of Zentralblatt MATH and Mathematical Reviews to update the classification. Both services have started using the new classification MSC2000 in January of the year 2000. While the introduction of the new classification system has lead to no special new requirements on the side of EULER conversion routines, it is clear that the EULER service (equally as all other services using MSC) might be confusing to the user (as far as the mathematical subject classification is concerned) during the transition period, when both - old and new - classification systems are in use. However, the EULER MSC browsing tool combines both classification systems in a user friendly way, by highlighting deleted old and newly inserted classifications, and giving correspondences between both of these. The MSC browsing tool is developed as part of the EULER Engine by NetLab, the combined MSC91 - MSC2000 specifications were developed by MDC.

Additional data from the "Jahrbuch über die Fortschritte der Mathematik" may be included in the conversion process if resources permit. "Jahrbuch" covers the most important literature in mathematics from 1868-1943. A first set of "Jahrbuch"-data is available as an electronic database (about 180.000 entries).

Some facts about Jahrbuch:

Jahrbuch der Fortschritte der Mathematik (JFM)
1869 --- 1943
Edited by: Preussische Akademie der Wissenschaften
Publisher: de Gruyter, Berlin
Frequency: One volume for every year, reporting on all the mathematical literature which has appeared in the corresponding year.
Coverage 1868: 800 documents, 50% from journals,
50% from other sources,
total number of journals: 80.

Electronic version of JFM:
Coverage: All the documents contained in Jahrbuch der Fortschritte der Mathematik
Availability: This is an ongoing DFG project.
Jahrbuch-project: Joint enterprise of Keith Dennis (editor-in-chief of MR)  under the supervision of the AMS and Bernd Wegner (editor-in-chief of Zbl) under the supervision of the EMS.
Technical procedure: Scanning and keyboarding of the text.
Editorial procedure: Classification and keywords, verification of journals' names, verification of authors' names, references for the acquisition of literature, translations, comments, cross-references.
 
 

6. Conclusions

It is expected that the EULER system will be able to incorporate other scientific literature database resources, as long as conversion and adaptation routines are in conformity with the EULER format specifications.
 
 

7. Recommendations

Additional data from the "Jahrbuch über die Fortschritte der Mathematik" should be included in the conversion process if resources permit. "Jahrbuch" covers the most important literature in mathematics from 1868-1943.
 
 

8. References

• Fachinformationszentrum Karlsruhe, Dept. of Mathematics and Computer Science (Berlin, Germany): http://www.zblmath.fiz-karlsruhe.de/
• Zentralblatt MATH WWW database: http://www.emis.de/ZMATH/
• Journals and Serials covered by Zentralblatt MATH: http://www.emis.de/ZMATH/serials/index.html
• The Jahrbuch-project (Electronic Research Archive for  Mathematics: http://www.emis.de/projects/JFM/

A. Annexes

 A.1 List of Categories kept in the Zentralblatt-Data

 

Flag	Fields	Subfields, Explanations	Occurr.
AN	Accession Number	Zbl-Volume Number Zbl-Review Number	single
AU	AUthor(s) Editor(s) Compiler(s)	Last Name First Name(s)/Initial(s)	mult.
AR	Author References (Spelling etc.) Author(s) of additions	Last Name First Name(s)/Initial(s)	mult.
TI	TItle	Original Title Translation Title	single
LA	LAnguage	Language(s) Language of original Language(s) of Author's Summary	single
SO	SOurce Source of Orig./Transl. Source of Addenda/Errata	Series / Journal Corporate Editor Publisher Publication Place ISBN ISSN URL Volume Issue Pages Price (only books)	single
PY	Publication Year		single
DT	Document Type		mult.
CC	Classification Code	Prim. Classification Sec. Classification(s) Subject Fields from MSC'91	mult.
UT	Uncontrolled Terms	Index Terms Keywords (in English)	single
BR	Biographical References	Last Name First Name(s)/Initial(s) (same format as AU)	mult.
AB	ABstract Review Introduction Summary	Text with math.signs and formulas	single
RV	ReViewer	Name Town	mult.
CI	CItations Zbl.-Reference Numbers	Reviewed Citation Author's References (not yet)	mult.

All Text (special signs, formulas, etc.)  is TeX-coded.

A.2 Sample records from the MATH Database

Some features could be subject of change in the www-database in the future.This concerns the following:

• German Umlaute and other Special Characters (\TeX-coded/HTML-coded),
• Accents (\TeX-coded/HTML-coded)
• Separate fields for ISSN and ISBN and URL

---

Books

AN  859.00025
AU  Voiculescu, Dan-Virgil (ed.)
TI  Free probability theory. Papers from a workshop on random matrices and 
    operator algebra free products, Toronto, Canada, Mars 1995.
LA  English
SO  Fields Institute Communications. 12. Providence, RI: American Mathematical
    Society,   vii, 312 p. \$ 79.00 (1997). [ISSN 1069-5265] [ISBN 0-8218-
    0675-0/hbk]
PY  1997
DT  B
CC  00B25 60-06 46-06 15-02 15A52
UT  Free probability theory; Workshop; Proceedings; Toronto (Canada); Random 
    matrices; Operator algebra; Free products
AB  The articles of this volume will be reviewed individually.

AN  859.93002
AU  Chentsov, A.G.
AR  Tschenzow, A.G.
TI  Asymptotic attainability. Transl. from an orig. Russian manuscript.
LA  English. Russian original
SO  Mathematics and its Applications (Dordrecht). 383. Dordrecht: Kluwer 
    Academic Publishers,   xiv, 322 p. Dfl. 240.00; \$ 156.00; \sterling 
    106.00 (1997). [ISSN 0921-3791] [ISBN 0-7923-4302-6]
PY  1997
DT  B
CC  93-02 93B05 93C05 93B03
UT  regularizations of extremal problems; relaxations; perturbations; finite 
    additive measure; weak absolute continuity; well-posed extensions; 
    asymptotic attainability
AB  In this monograph, questions of extensions and relaxations are considered.
    These questions arise in many applied problems in connection with the 
    operation of perturbations. Asymptotic behaviour of the attainability sets
    for different kinds of dynamical control systems with integral constraints
    are considered. The prediction of random events is also discussed. Special
    attention is paid to finite additive measure with the property of weak 
    absolute continuity. Nonlinear control problems with impulse control are 
    discussed. \par Regularizations of extremal problems on the basis of well-
    posed extensions are considered. The general problem of the asymptotic 
    optimization in a preordered topological space is investigated. Moreover, 
    the asymptotic nonsensitivity property of the optimization problem under 
    some restricted perturbations is analyzed. Several remarks and comments on
    the asymptotic attainability under perturbation are presented. Connections
    with classical control theory are explained and discussed.
RV  J.Klamka (Katowice)

Conference Article in a Proceedings Volume

AN  829.14001
AU  Nowicki, A.
TI  Richman's proof of the Abhyankar-Moh theorem.
LA  Polish. English summary
SO  16th educational conference on the theory of complex analysis and 
    geometry, Bronislawow, Poland, 9-13 January, 1995. Proceedings. Lodz: 
    Wydawnictwo Uniwersytetu Lodzkiego, 49-71 (1995).
    [ISBN 83-7016-822-1/pbk]
PY  1995
DT  CA
CC  14A05 13F20 12E05
UT  degree of polynomial; Abhyankar-Moh theorem; polynomial automorphism
AB  The Abhyankar-Moh theorem states that for any polynomial embedding $F : k 
    \mapsto k\sp 2$ (char $k = 0)$ there exists a polynomial automorphism $A :
    k\sp 2 \mapsto k\sp 2$ such that $A \circ F$ is the standard embedding $x 
    \mapsto (0,x)$. In the algebraic setting it is equivalent to the fact: if 
    $f,g \in k[t] \backslash k$ and $k[f,g] = k[t]$, then $\deg f \vert \deg 
    g$ or $\deg g \vert \deg f$.\par The author proves this last theorem after
    the idea of {\it D. R. Richman} [J. Algebra 103, 1-17 (1986; Zbl. 
    599.12026)] filling a gap in his proof. This gap was also filled by {\it 
    M. Kang} [Am. J. Math. 113, No. 3, 399-421 (1991; Zbl. 759.14009)].
RV  T.Krasinski (Lodz)
CI  Zbl.599.12026; Zbl.759.14009

Journal Article

AN  834.22004
AU  Tkacenko, Michael G.
AR  Tkachenko, Mikhajl G.
TI  On group uniformities on the square of a space and extending 
    pseudometrics.
LA  English
SO  Bull. Aust. Math. Soc. 51, No.2, 309-335 (1995). [ISSN 0004-9727]
PY  1995
DT  J
CC  22A05 54H11 54E15 54G10
UT  thin subset; universal uniformity; Tychonoff space; free topological 
    group; continuous pseudometrics; continuous semi-norm
AB  For a Tychonoff space $X$, it has been proved by E. C. Nummela and by V. 
    G. Pestov that the two-sided uniformity $\sp*{\cal V}\sp*$ of the free 
    topological group $F(X)$ over $X$ induces on $X \subset F(X)$ the finest 
    uniformity (the so-called ``universal'' uniformity) compatible with its 
    topology; in the author's notation this equality takes the form $\sp*{\cal
    V}\sp* \vert X = {\cal U}\sb X$. The present paper is preliminary to the 
    author's promised forthcoming work investigating the relations between the
    uniformities $\sp*{\cal V}\sp* \vert X\sp 2$, ${\cal U}\sb X \times {\cal 
    U}\sb X$, and ${\cal U}\sb{X\sp 2}$. Here as tools for that investigation 
    he developes conditions under which, for continuous pseudometrics $d\sb 1$
    and $d\sb 2$ on $X$ and $X\sp 2$ respectively, there is a continuous semi-
    norm $N$ on $F(X)$ such that $$N(xy\sp{-1}) = d\sb 1 (x,y) \ \text {and} \
    N(xyt\sp{-1} z\sp{- 1}) \ge d\sb 2 \bigl( (x,y), (z,t) \bigr) \ \text {for
    all} \ x,y,z,t \in X.$$ The principal self-contained result of the present
    paper, proved a decade ago by the author [Math. Notes 37, 62-66 (1985); 
    translation from Mat. Zametki 37, 110-118 (1985; Zbl. 568.22001)] but by a
    different, indirect argument, is Theorem 5.3. Let $Y \subseteq X \subseteq
    F(X)$. Then $Y$ is thin in $F(X)$ (in the usual sense, that for every 
    neighborhood $U$ of $1\sb{F(X)}$ there is a neighborhood $V$ of 
    $1\sb{F(X)}$ such that $yVy\sp{-1} \subseteq U$ for each $y \in Y)$ if and
    only if there is an infinite cardinal $\tau$ such that simultaneously (a) 
    every intersection of fewer than $\tau$-many open subsets of $X$ is open 
    in $X$, and (b) of any locally finite family of open subsets of $X$, fewer
    than $\tau$-many meet $Y$.
RV  W.W.Comfort (Middletown)
CI  Zbl.568.22001

Journal Article with URL

AN  860.13002
AU  Heinzer, William; Swanson, Irena
TI  Ideals contracted from 1-dimensional overrings with an application to the 
    primary decomposition of ideals.
LA  English
SO  Proc. Am. Math. Soc. 125, No.2, 387-392 (1997). [ISSN 0002-9939] \par
    Internet: http://www.ams.org/proc/1997-125-02/
PY  1997
DT  J
CC  13B02 13H99 13E05
UT  ideal of a one-dimensional domain; equidimensional analytically unramified
    Noetherian integral domain
AB  We prove that each ideal of a locally formally equidimensional 
    analytically unramified Noetherian integral domain is the contraction of 
    an ideal of a one-dimensional semilocal birational extension domain. We 
    give an application to a problem concerning the primary decomposition of 
    powers of ideals in Noetherian rings. It is shown in an earlier paper by 
    the second author that for each ideal $I$ in a Noetherian commutative ring
    $R$ there exists a positive integer $k$ such that, for all $n\geq 1$, 
    there exists a primary decomposition $I\sp n= Q\sb 1\cap\dots\cap Q\sb s$ 
    where each $Q\sb i$ contains the $nk$-th power of its radical. We give an 
    alternative proof of this result in the special case where $R$ is locally 
    at each prime ideal formally equidimensional and analytically unramified.

Journal Article with Its Translation in One DB-Item

AN  844.54009
AU  Tkachuk, V.V.
TI  Decomposition of $C\sb p(X)$ into a countable union of subspaces with 
    ``good'' properties implies ``good'' properties of $C\sb p(X)$.
LA  English. Russian original
SO  Trans. Mosc. Math. Soc. 1994, 239-248 (1994); translation from Tr. Mosk. 
    Mat. O.-va 55, 310-322 (1994). [ISSN 0077-1554]
PY  1994
DT  J
CC  *54C35 Function spaces (general topology)
     54A25 Cardinality properties of topological spaces
UT  character; tightness; countable additivity; pointwise convergence 
    topology; Cech-completeness
AB  Let ${\cal P}$ be a topological property and suppose that the space $C\sb 
    p (X)$ of all continuous real-valued functions on $X$ with the pointwise 
    convergence topology is a union of a countable number of subspaces having 
    ${\cal P}$. Does then $C\sb p (X)$ have ${\cal P}$? The author proves that
    the answer is ``yes'' for any ${\cal P}$ from the following list: Cech-
    completeness, Frechet-Urysohn property, pseudocharacter $\le \tau$, 
    tightness $\le \tau$, hereditary $\pi$-character $\le \tau$, etc. It is 
    also shown that if $C\sb p (X)$ is homeomorphic to a retract of a 
    $G\sb{\delta, \sigma}$-subset of $\bbfR\sp \tau$, then $X$ is discrete.
RV  M.G.Tkachenko (Mexico)

Dissertation in a Lecture Notes Series

AN  861.68042
AU  Sudan, Madhu
TI  Efficient checking of polynomials and proofs and the hardness of 
    approximation problems.
LA  English
SO  Lecture Notes in Computer Science. 1001. Berlin: Springer-Verlag,   New 
    York, NY: ACM, xiv, 87 p. DM 38.00; oeS 277.40; sFr. 38.00 (1995). [ISBN 
    3-540-60615-7]
PY  1995
DT  B, D
CC  68Q25 68T15
UT  NP-completeness problems; approximation problems; NP language
AB  The book represents the author's Ph.D. distinguished thesis at Berkely 
    (California, 1992). This dissertation describes general techniques to 
    approach the NP-completeness problems of establishing the computational 
    tractability of approximation problems. Approximation hardness is 
    established for all NP-complete problems (with P$\ne$NP) in the complexity
    class max-SNP: this includes basic problems such as the Euclidean 
    traveling salesman problem, max-2SAT, Euclidean Steiner tree, or other 
    problems related to chromatic number, set cover, and shortest vector in a 
    lattice.\par The M. Sudan's book provides a new characterization of the 
    complexity class NP, showig that any NP language admits an efficient 
    probabilistically checkable proof of membership. The membership robust 
    proofs are still polynomially long, and can be checked by probing only a 
    constant number of randomly chosen bits of the proof. Other remarkable 
    achievements within the book are: (a) a beautiful technique for creating 
    long but very robust proofs based on self-correction properties of linear 
    functions; (b) a new low-degree test that probes the value of a 
    multivariate function at only a constant number of points and verifies 
    whether it is close to some low-degree polynomial; (c) in the context of 
    coding theory, fast and randomized algorithms for error-detection and 
    error-correction of (some well-known) codes.\par In sum, a book containing
    consistent, technical, and deep results for theoretical computer science.
    P.-G.Holban (Iasi)

Dissertation in a Report Series

AN  851.35088
AU  Goebel, Dieter
TI  Viskositaetsapproximationen und schwache Loesungen fuer das System der 
    eindimensionalen nichtlinearen Elastizitaetsgleichungen. (Viscosity 
    approximations and weak solutions for the system of one-dimensional 
    nonlinear equations of elasticity).
LA  German
SO  Bonner Mathematische Schriften. Bonn: Univ. Bonn, ix, 89 S. (1993).
PY  1993
DT  R, D
CC  35L65
UT  viscosity approximations
AB  In his dissertation, the author considers initial value problems for 
    strictly hyperbolic conservation laws; as initial data interaction 
    problems are taken, i.e. a step function with three states and two 
    discontinuities as initial function. It is proved that in the vicinity of 
    a given solution of the interaction problem there exists a manifold of 
    global weak solutions of interaction problems for perturbed initial data. 
    As assumptions the author needs some smallness conditions in terms of the 
    total variation of the perturbed initial data and in terms of differences 
    of the initial states, also, finiteness conditions like those used by 
    Schochet are assumed. The structure of solutions beyond the meeting point 
    of shock waves is investigated, and the results are applied to a 4-
    dimensional hyperbolic system from elasticity theory given by 
    Antman/Malek-Madani.
RV  H.Lange (Koeln)

A.3 Distribution of EULER fields among records