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Content

Welcome to the Zentralblatt MATH Database. This database contains records for the documents covered by

Zentralblatt Math

The present edition contains the information of those documents the reviews of which were printed in Zentralblatt für Mathematik and in addition the bibliographic information from those journals, serials, books, and proceedings that are currently under documentation.

MATH provides a comprehensive coverage of the international mathematical research published since year1931. It contains articles from about 2,000 journals and serials, book of all publishers, available proceedings of all conferences, and other research papers appearing in any language.

More than 5,000 scientists from all over the world are providing Zentralblatt with reviews. The reviews are written mainly in English, but reviews in French or German are also to be found.

Help Desk

If you need additional help on topics not covered here, you can correspond with any of the following addresses: 
         Editors of Zentralblatt für Mathematik
         c/o Fachinformationszentrum Karlsruhe
         Dept. of Mathematics and Computer Science (Berlin)
         Franklinstraße 11
         D-10589 Berlin
         Phone    (+49) 30 / 392 7026
         FAX      (+49) 30 / 392 7009
         e-mail   editor@zblmath.fiz-karlsruhe.de

Display-Fields

The DISPLAY fields which you may see in records of MATH Database are summarized below.

Search-Fields

The searchable fields of the database MATH which are displayed in the search menu are listed below.

Proximity

A simple form of proximity searching is available for this database, in the following text fields: BI, TI, SO. A group of consecutive words may be searched for by selecting "expression".

Accession Number

The accession number AN of the MATH Database is closely related to the document number as used in Zentralblatt fuer Mathematik:
  • the first 4 digits refer to the Zbl-volume number
  • the two digit behind the full stop represent the MSC field
  • the last 3 digits are consecutive numbers
Examples: 
                        0779.14002
The search can be restricted to a single volume by entering, for example 
                       779.*
in the Zbl. Nr. field.

TeX

The description of mathematical contents within the records of MATH database requires the use of a formatting language which is capable of presenting special characters, formulae and formatting instructions. The most widely used and best known language for these purposes is TeX. Therefore TeX is used in the encoding of the data for MATH. However, a TeX-implementation on your computer is not a necessary condition for MATH Database to run.

But if high output quality is asked for, if it is desired to get output in a form similar to the printed version of Zentralblatt für Mathematik, then viewers for DVI, PostScript or PDF should be available on your system.

BI - Basic Index

The Basic Index is the main tool in the subject search of MATH Database as a bibliographic text-oriented database.

This index contain all single words of the fields describing the contents of the document.

The following fields are included in the Basic Index:

AU - Author(s), Editors, Author References

Author names have been implemented in a form common to all STN databases, i.e. last name, first name, middle name. First and middle names can or cannot be abbreviated. When searching for an author's name, it is recommended to use only the first initial. You will get all forms of the first names, because the system adds automatically a truncation symbol. Thus, the following forms of implementation are possible: Examples: 
  Friedrich Wilhelm Mahle    as    Mahle, F.
                                   Mahle, F. W.
                                   Mahle, Friedrich
                                   Mahle, Friedrich W.
                                   Mahle, Friedrich Wilhelm
  and as an Editor (e.g.)          Mahle, Friedrich W. (ed.)
The recommended search form is: 
                                   Mahle, F
The system will automatically search for 
                                   Mahle, F*
Names containing a preposition (von, van), article (le), combination of article and preposition (du, vander), relationships or attributes (Fitz, Mac, Jun., III) have the format common to their country of origin. It is therefore recommended to search for names with the supplements placed in front of the name and after the name. 
     Document                            Database Record
     
     Peter von der Muehl         as      Muehl, Peter von der
     Fritz von Heyden (DE)       as      Heyden, Fritz von
     Fritz Von Heyden (US)       as      Von Heyden, Fritz
     A. De L'Aigle               as      L'Aigle, A de
     C. M. Di Bari               as      Di Bari, C.M.
     Michel Del Pedro            as      Del Pedro, Michel
     L. C. MacLean               as      MacLean, L.C.
     John Fitz Gerald            as      Fitz Gerald, John
     A. Miller jun.              as      Miller, A.jun.
The publisher is also given in the AU field, and is listed with the supplement (ed.). 
     Edited by H. Waadeland      as     Waadeland, H.(ed.)
     Editor Anita K. Jones       as     Jones, Anita K.(ed.)
Names in kyrillic letters have been transcribed according to the ISO standard. In some cases this transliteration will differ from that one on the translated document or in the western journal. In that case we include the different form of spelling as an author reference displayed in braces in the author field.

TI - Title

The title of the original document is not only contained in the basic index, but also in a special field TI. This is useful in those cases in which users want to limit his search to title words. The list of Stopwords is available.

The language of the title is English, French, or German. In case of French and German there is also given an English translation.

LA - Language

The complete English word for each language can be searched.

List of occuring languages 

  Afrikaans     Azerbaijani   Arabic
  Bulgarian     Byelorussian
  Catalan       Chinese       Croatian      Czech
  Danish        Dutch  
  English       Esperanto     Estonian
  Finnish       French
  Georgian      German        Greek
  Hungarian
  Italian
  Japanese
  Korean
  Latin         Latvian       Lithuanian
  Macedonian    Malay
  Norwegian
  Persian       Polish        Portuguese
  Romanian      Russian
  Serbian       Serbo-Croat   Slovak        Slovenian     Spanish
  Swedish
  Turkish
  Ukrainian
  Vietnamese

SO - Source

This field contains a great part of the bibliographic information and information about meetings.

The source field contains the following searchable data:

  • the journal title, volume, and pages
  • the title of conference volumes etc.
  • title of book series
  • the name and the place of the publisher
  • conference title and place
  • publication year (see also the index PY)
The database also contains references to papers accepted for publication but not yet printed (previews). These entries are marked "to appear" using the title as source only.

All data are parsed into single words and can be searched as text.

Examples: 

  Journal volume        Source contains the expression : ANN INST FOURIER 45
  Books of a publisher  Source contains the expression : SPRINGER VERLAG 
  Document of an ISBN   Source contains the expression : ISBN 3 540 53342 7

PY - Publication Year

The publication year is always written in 4 digits.

You may specify a period from 1 to 5 years entering the first and last year of the period. The second box may stay empty if only one year is specified. No entry is necessary for the whole period of the database.

DT - Document type

By means of document type it is possible to separate the main types of publication: Journal article, book, conference article, etc.

CC - Classification Code and Text

All Documents in Zentralblatt-MATH are indexed by codes from the

Mathematics Subject Classification (MSC) 1991

which was prepared jointly by the editorial offices of Mathematical Reviews and Zentralblatt fuer Mathematik/Mathematics Abstracts.

A list of codes and the corresponding text is available.

The corresponding text is included in the Basic Index.

It is also possible to search for the main fields (higher levels) of the classification if you use the first two digits or the first two digits followed by a character in combination with the truncation symbol.

Examples: 

      35J10   searches all papers to  "Schroedinger operator"
      35J*    searches all papers to  "elliptic equations"
      35*     searches all papers to  "partial differential equations"

UT - English Keywords

In all cases where the classification is not specific enough there are added English keywords for a detailed description of the topics (starting 1970). Since we index all literature with English keywords, it is possible to search only in English for the selection of non-English papers and reviews.

The display field UT is only searchable in the Basic Index.

AB - Review / Abstracts

The description of a document by a review should
  • contain a description of the mathematical content and eventually give applications
  • outline references to thematically related work and,
  • if necessary and possible, pronounce criticism of positive as well as negative kind.
The reviews are compiled by about 5000 reviewers from all over the world who cover the whole mathematics and all the occuring languages. If the result of a check of the summary of a document by the editors of Zentralblatt fuer Mathematik is that it is informative and of good quality, then it may be used for the printed version and the databases as well.

The preferred language for the reviews is English, but reviews in French and German will also be accepted.

The author of a review is mentioned at the end of it, as long as it is not compiled from the summary, from the text, or so from one of the editors of Zentralblatt fuer Mathematik.

Does a paper remain without a review, this indicates in general that it rather crosses the borderlines of the scope of our printed product. However, to make it as complete as we can, we include those documents in MATH Database. Also those papers which are under documentation and whose bibliographic data are given, are without a review.

The review text is searchable in the Basic Index (BI).

RV - Reviewer

There are more than 5,000 scientists from all over the world who provide Zentralblatt fuer Mathematik with about 50,000 reviews per year. They cover all areas of mathematics and its applications and all languages in which mathematical research papers are usually written. The name of the reviewer and his home town are searchable.

CI - Citations

The Reviews of MATH Database contain citations to relevant papers for different reasons. These references are provided with the MATH Database accession number (Zbl.-number).

By a mouse click on this accession number you can display directly the cited record.

Moreover there is a link on the accession number of each displayed document which provides you with all reviews citing the displayed one.

Truncation

The (right) truncation symbol * is used to retrieve various forms of your search terms. In the author search the truncation is used automatically.

Left truncation is not available.

Advanced search

Introduction

In this mode, automatic truncation of author names is not available.
The form fields can contain a boolean expression buitl with the following operators: & (and), ^ (and not), these two operators having equal priority (highest), | (or) (lower priority). 

    a | b & c ==> a | (b & c)
The evaluation order may be changed by using parentheses.

Inter-field operators (selected through the form's menus) are evaluated from left to right without any priority.
The expression: 

 Field_A * Field_B * Field_C * Field_D
is always evaluated as: 
 ((Field_A * Field_B) * Field_C) * Field_D
"*" being one the operators and, or, and not.

Examples
Author : Wiles,*
or Author : Taylor,*
and Title : Fermat

will find items:

  1. having in the Author field Taylor or Wiles
  2. having the word Fermat in the title field.
But:
Title : Fermat
and Author : Wiles,*
or Author : Taylor,*

will find :

  1. items with the word Fermat in the title field and authored by Wiles
  2. plus items authored by Taylor.
The first request may also be entered as follows:
Author : Wiles,* | Taylor,*
and Title : Fermat

The command language allows more complex queries.

Command language

This mode allows complex boolean queries.

The searchable field names are (lowercase):
Name Description
an Accession number: Zentralblatt-MATH item number
au Author name
bi Basic index
cc Mathematical subject classification code
dt Document type
la Language
py Publication year
rv Reviewer's name
so Source (Journal, Publisher...)
ti Title words

Examples
cc = 58g* & an = 885* All about section "58G" in volume 885
cc = 58g* & py = 1996:1998 All about section "58G" for years 1996 to 1998
au = (bender,* ^ canfield,*) The author is Bender, without Canfield
au = (bender,* ^ canfield,*) | au = (canfield,* ^ bender,*) The author is Bender or Canfield, but not both
au = ((bender,* ^ canfield,*) | (canfield,* ^ bender,*)) same query as above
au = ((bender,* ^ canfield,*) | (canfield,* ^ bender,*)) & py >= 1997 same query, but the item has been published after 1996
ti = (riemann* & (manifold* | variete*)) 
ti = riemann* & manifold*  Syntax error. The correct query is: ti = (riemann* & manifold*)
ti = riemann* manifold*  Expression search: will find "riemannian manifold", "riemannian manifolds", etc...
bi = (bose einstein | einstein bose)  ...
ti = (fermi dirac ^ bose einstein)  ...

Formal Syntax 

   find_expression ::= field_expression
                   ::= find_expression bool_op field_expression

   bool_op ::= '&' | '|' | '^'

   field_expression ::= name '=' '(' bool_expr ')'
                    ::= name rel_op string
                    ::= name '=' string ':' string
                    ::= '(' find_expression ')'

   rel_op ::= '<' | '<=' | '>' | '>='

   bool_expr ::= term
             ::= bool_expr '|' term

   term ::= factor
        ::= term '&' factor
        ::= term '^' factor

   factor ::= string
          ::= '(' bool_expr ')'

Examples:
  au = berard*
  au = (berard* & besson*)
  au = (berard* | (besson* & gallot*))
  au = (berard* | webb*) ^ ti = rieman* manifold*
Copyright Zentralblatt MATH : © European Mathematical Society, FIZ Karlsruhe & Springer-Verlag.
[edbm/w3] Retrieval & display software : © Cellule MathDoc, UJF & CNRS.