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• 1990-1994  (760,496)
Material
Years
Year
Language
• 1
Electronic Resource
Amsterdam : Elsevier
Physics Letters B 294 (1992), S. 466-478
ISSN: 0370-2693
Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
Topics: Physics
Type of Medium: Electronic Resource
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• 2
Electronic Resource
Amsterdam : Elsevier
Physics Letters B 317 (1993), S. 474-484
ISSN: 0370-2693
Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
Topics: Physics
Type of Medium: Electronic Resource
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• 3
Book
Wien [u.a.] :Springer, ; 1.1977 - 16.2003; damit Ersch. eingest.
Title: Computing : archives for informatics and numerical computation; Supplementum
Publisher: Wien [u.a.] :Springer,
Year of publication: 1977-2003
Dates of Publication: 1.1977 - 16.2003; damit Ersch. eingest.
Type of Medium: Book
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• 4
Journal/Serial
New York, NY :ACM, ; 1.1969 - 7.1975/76; N.S. 1.1976 - 21.2001,1; damit Ersch. eingest.
Author: Association for Computing Machinery / Special Interest Group on Biomedical Computing
Publisher: New York, NY :ACM,
Year of publication: 1969-2001
Dates of Publication: 1.1969 - 7.1975/76; N.S. 1.1976 - 21.2001,1; damit Ersch. eingest.
ISSN: 0163-5697
Type of Medium: Journal/Serial
Language: Undetermined
Parallel Title: Internetausg. ---〉:Biomedical computing
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• 5
Journal/Serial
New York, NY :North-Holland, ; 1.1984 - 46.2000
Title: ¬The¬ journal of logic programming
Publisher: New York, NY :North-Holland,
Year of publication: 1984-2000
Dates of Publication: 1.1984 - 46.2000
ISSN: 0743-1066
Type of Medium: Journal/Serial
Language: Undetermined
Subsequent Title: Forts. ---〉:¬The¬ journal of logic and algebraic programming
Parallel Title: Internetausg. ---〉:¬The¬ journal of logic and algebraic programming
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• 6
Book
New York, NY :ACM, ; Nachgewiesen 2.1971 - 20.1999,4; damit Ersch. eingest.
Title: Computer personnel : a quarterly publ. of the Special Interest Group on Computer Personnel Research, SIGCPR
Publisher: New York, NY :ACM,
Year of publication: 1971-1999
Dates of Publication: Nachgewiesen 2.1971 - 20.1999,4; damit Ersch. eingest.
ISSN: 0160-2497
Type of Medium: Book
Parallel Title: Internetausg. ---〉:Computer personnel
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• 7
Journal/Serial
Amsterdam :CWI, ; 1.1988 - 12.1999; damit Ersch. eingest.
Title: CWI quarterly
Author: Centrum voor Wiskunde en Informatica 〈Amsterdam〉
Publisher: Amsterdam :CWI,
Year of publication: 1988-1999
Dates of Publication: 1.1988 - 12.1999; damit Ersch. eingest.
ISSN: 0168-826X , 0922-5366
Type of Medium: Journal/Serial
Language: Undetermined
Former Title: Vorg. ---〉:Centrum voor Wiskunde en Informatica 〈Amsterdam〉: CWI newsletter
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• 8
Journal/Serial
San Francisco, Calif. :Miller Freeman, ; 1.1983 - 16.1998,3
Title: Unix review : the publication for the Unix community
Publisher: San Francisco, Calif. :Miller Freeman,
Year of publication: 1983-1998
Dates of Publication: 1.1983 - 16.1998,3
ISSN: 0742-3136
Type of Medium: Journal/Serial
Language: Undetermined
Subsequent Title: Forts. ---〉:Unix review's performance computing
Parallel Title: Internetausg. ---〉:Unix review.com
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• 9
Journal/Serial
New York, NY :ACM, ; 1.1990 - 9.1998
Title: SIGART bulletin : a quarterly publ. of the Special Interest Group on Artificial Intelligence
Author: Association for Computing Machinery / Special Interest Group on Artificial Intelligence
Publisher: New York, NY :ACM,
Year of publication: 1990-1998
Dates of Publication: 1.1990 - 9.1998
ISSN: 1053-4830
Type of Medium: Journal/Serial
Language: Undetermined
Former Title: Vorg. ---〉:Association for Computing Machinery / Special Interest Group on Artificial Intelligence: SIGART newsletter
Subsequent Title: Forts. ---〉:Intelligence
Parallel Title: Internetausg. ---〉:Artificial intelligence
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• 10
Journal/Serial
Amsterdam [u.a.] :Elsevier [u.a.], ; 9.1985 - 30.1998
Title: Computer networks and ISDN systems : the international journal of computer and telecommunications networking
Publisher: Amsterdam [u.a.] :Elsevier [u.a.],
Year of publication: 1985-1998
Dates of Publication: 9.1985 - 30.1998
ISSN: 0169-7552 , 0376-5075
Type of Medium: Journal/Serial
Language: Undetermined
Subsequent Title: Vorg. u. Forts. ---〉:Computer networks
Note: Computer networks for research in Europe
Additional Information: In 14,1=15 von:Networkshop: Conference report
Additional Information: 16,1/2=4; 17,4/5=5 von:European Networkshop: European Networkshop
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• 11
Journal/Serial
Woodbury, NY :AIP, ; 1.1987,1(Nov./Dez.); 2.1988 - 12.1998
Title: Computers in physics /
Publisher: Woodbury, NY :AIP,
Year of publication: 1987-1998
Dates of Publication: 1.1987,1(Nov./Dez.); 2.1988 - 12.1998
ISSN: 0894-1866
Type of Medium: Journal/Serial
Language: Undetermined
Subsequent Title: Forts. ---〉:Computing in science & engineering
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• 12
Journal/Serial
New York, NY :ACM, ; 4.1969 - 33.1998,2; damit Ersch. eingest
Author: Association for Computing Machinery / Special Interest Group on Numerical Mathematics
Publisher: New York, NY :ACM,
Year of publication: 1969-1998
Dates of Publication: 4.1969 - 33.1998,2; damit Ersch. eingest
ISSN: 0163-5778
Type of Medium: Journal/Serial
Former Title: Vorg. ---〉:Association for Computing Machinery / Special Interest Committee on Numerical Mathematics: SICNUM newsletter
Additional Information: 16,3=3,2 von:Association for Computing Machinery / Technical Committee on Fortran: FORTEC forum
Parallel Title: Internetausg. ---〉:Numerical mathematics
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• 13
Journal/Serial
Basel :Baltzer, ; 1.1994 - 4.1997; damit Ersch. eingest
Title: Annals of numerical mathematics : journal edition
Publisher: Basel :Baltzer,
Year of publication: 1994-1997
Dates of Publication: 1.1994 - 4.1997; damit Ersch. eingest
ISSN: 1021-2655
Type of Medium: Journal/Serial
Language: Undetermined
Parallel Title: Internetausg. : Annals of numerical algorithms
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• 14
Journal/Serial
Thousand Oaks, Calif. :Sage Science Press, ; 1.1987 - 11.1997
Title: ¬The¬ international journal of supercomputer applications and high performance computing
Publisher: Thousand Oaks, Calif. :Sage Science Press,
Year of publication: 1987-1997
Dates of Publication: 1.1987 - 11.1997
ISSN: 1078-3482 , 0890-2720
Type of Medium: Journal/Serial
Subsequent Title: Forts. ---〉:¬The¬ international journal of high performance computing applications
Parallel Title: Internetausg. ---〉:¬The¬ international journal of high performance computing applications
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• 15
Book
Bergheim :DATACOM-Zeitschriften-Verl., | Köln Müller -1993,9 ; 11.1973 - 14.1976; 19.1981 - 20.1982; 1983 - 1994; 32.1995 - 34.1997,10
Title: Online : erfolgreiches Informationsmanagement, ADI-Nachrichten, ÖVD ; Organ d. ADI - Anwenderverband Deutscher Informationsverarbeiter e.V
Publisher: Bergheim :DATACOM-Zeitschriften-Verl., , Köln Müller -1993,9
Year of publication: 1973-1997
Dates of Publication: 11.1973 - 14.1976; 19.1981 - 20.1982; 1983 - 1994; 32.1995 - 34.1997,10
ISSN: 0340-1545 , 0179-6623 , 0342-9393
Type of Medium: Book
Language: Undetermined
Former Title: Vorg. ---〉:Zeitschrift für Datenverarbeitung
Subsequent Title: Aufgeg. in ---〉:Information week
Note: Später ohne Zählung
Additional Information: Beil. ---〉:Online / special
Parallel Title: 19.1981 auch in ---〉:Öffentliche Verwaltung und Datenverarbeitung
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• 16
Journal/Serial
New York, NY :ACM, ; 19.1993/94,3(1994) - 23.1997/98,2(1997); damit Ersch. eingest.
Title: SIGICE bulletin : a monthly publication of the ACM Special Interest Group on Individual Computing Environments
Author: Association for Computing Machinery / Special Interest Group on Individual Computing Environments
Publisher: New York, NY :ACM,
Year of publication: 1994-1997
Dates of Publication: 19.1993/94,3(1994) - 23.1997/98,2(1997); damit Ersch. eingest.
Type of Medium: Journal/Serial
Language: Undetermined
Former Title: Vorg. ---〉:Association for Computing Machinery / Special Interest Group on Small and Personal Computing Systems and Applications: SIGSMALL - PC notes
Parallel Title: Internetausg. ---〉:Association for Computing Machinery / Special Interest Group on Individual Computing Environments: ACM SIGICE bulletin
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• 17
E-Resource
Chichester [u.a.] :Wiley, ; 1/20.1971/90(1994) - 21/25.1991/95(1997); damit Ersch. eingest.
Title: Software 〈Chichester〉 : practice & experience ; SP & E ; SP & E archive
Publisher: Chichester [u.a.] :Wiley,
Year of publication: 1994-1997
Dates of Publication: 1/20.1971/90(1994) - 21/25.1991/95(1997); damit Ersch. eingest.
ISSN: 0038-0644
Type of Medium: Electronic Resource
Language: Undetermined
Additional Information: 1/20=3; 21/25=5 von:Software 〈Chichester〉 / Special
Parallel Title: Druckausg. ---〉:Software 〈Chichester〉
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• 18
Journal/Serial
Amsterdam :Amsterdam Universities Computing Centre, ; Nr. 1.1984 - 69.1997; damit Ersch. eingest.
Title: Supercomputer : bimonthly magazine on supercomputing in the Netherlands
Publisher: Amsterdam :Amsterdam Universities Computing Centre,
Year of publication: 1984-1997
Dates of Publication: Nr. 1.1984 - 69.1997; damit Ersch. eingest.
ISSN: 0168-7875
Type of Medium: Journal/Serial
Language: Undetermined
Note: Teils auch mit Jg.-Zählung
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• 19
Journal/Serial
Dordrecht [u.a.] :Kluwer Acad. Publ., ; 1.1988 - 10.1997
Title: LISP and symbolic computation : an internat. journal ; a forum for current and envolving symbolic computing, focusing on LISP and object-oriented programming
Publisher: Dordrecht [u.a.] :Kluwer Acad. Publ.,
Year of publication: 1988-1997
Dates of Publication: 1.1988 - 10.1997
ISSN: 0892-4635
Type of Medium: Journal/Serial
Language: Undetermined
Subsequent Title: Forts. ---〉:Higher order and symbolic computation
Parallel Title: Internetausg. ---〉:Higher-order and symbolic computation
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• 20
Journal/Serial
München :Hanser, ; 1.1983 - 14.1996,6
Title: Unix mail : Europas erster Informationsdienst für Unix-Hersteller und -Anwender
Publisher: München :Hanser,
Year of publication: 1983-1996
Dates of Publication: 1.1983 - 14.1996,6
ISSN: 0176-8654
Type of Medium: Journal/Serial
Language: Undetermined
Subsequent Title: Forts. ---〉:¬Die¬ blauen Blätter
Parallel Title: CD-ROM-Ausg. ---〉:Unix mail, die blauen Blätter
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• 21
Journal/Serial
Minneapolis, Minn. :Cray Research, Inc., ; Nachgewiesen 6.1984 - 18.1996,2; damit Ersch. eingest.
Title: Cray channels : a Cray Research, Inc. publication
Publisher: Minneapolis, Minn. :Cray Research, Inc.,
Year of publication: 1984-1996
Dates of Publication: Nachgewiesen 6.1984 - 18.1996,2; damit Ersch. eingest.
Type of Medium: Journal/Serial
Language: Undetermined
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• 22
Journal/Serial
Sebastopol, Calif. :O'Reilly, ; 0.1991[Probeh.]; Nr. 1.1992 - 17.1996; damit Ersch. eingest.
Title: ¬The¬ X resource : a practical journal of the X window system
Publisher: Sebastopol, Calif. :O'Reilly,
Year of publication: 1991-1996
Dates of Publication: 0.1991[Probeh.]; Nr. 1.1992 - 17.1996; damit Ersch. eingest.
ISSN: 1058-5591
Type of Medium: Journal/Serial
Language: Undetermined
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• 23
Journal/Serial
Berlin :VDE-Verl., ; 8.1955,10 - 40.1987,2; 40.1987,6 - 48.1995,2
Title: Nachrichtentechnische Zeitschrift : NTZ ; Zeitschrift für Informationstechnik u. Telekommunikation ; Organ der Nachrichtentechnischen Gesellschaft im VDE
Publisher: Berlin :VDE-Verl.,
Year of publication: 1955-1995
Dates of Publication: 8.1955,10 - 40.1987,2; 40.1987,6 - 48.1995,2
ISSN: 0027-707X
Type of Medium: Journal/Serial
Language: Undetermined
Former Title: Vorg. ---〉:Fernmeldetechnische Zeitschrift
Subsequent Title: 40.1987,3-5 u. Forts. ---〉:NTZ
Note: Mikro-Elektronik
Additional Information: Index 1/10=11 von:Nachrichtentechnische Fachberichte
Parallel Title: CD-ROM-Ausg. 1994 - 1995 ---〉:Elektronisches Zeitschriftenarchiv
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• 24
Journal/Serial
New York, NY :ACM Inc., ; 1.1987/88 - 4.1990/91; 5.1992; 6.1992/93; 7.1994 - 8.1995,2; damit Ersch. eingest.
Title: LISP pointers /
Publisher: New York, NY :ACM Inc.,
Year of publication: 1987-1995
Dates of Publication: 1.1987/88 - 4.1990/91; 5.1992; 6.1992/93; 7.1994 - 8.1995,2; damit Ersch. eingest.
ISSN: 1045-3563
Type of Medium: Journal/Serial
Note: Special Interest Group on Programming Languages (SIGPLAN)
Parallel Title: Internetausg. ---〉:Association for Computing Machinery / Special Interest Group on Programming Languages: ACM SIGPLAN LISP pointers
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• 25
Journal/Serial
New York, NY :ACM, ; 2.1971/72 - 16.1985; 19.1988 - 26.1995; damit Ersch. eingest.
Title: SIGMICRO newsletter : a quarterly publ. of the Special Interest Group on Microprogramming
Author: Association for Computing Machinery / Special Interest Group on Microprogramming
Publisher: New York, NY :ACM,
Year of publication: 1971-1995
Dates of Publication: 2.1971/72 - 16.1985; 19.1988 - 26.1995; damit Ersch. eingest.
ISSN: 0163-5751 , 1050-916X
Type of Medium: Journal/Serial
Language: Undetermined
Former Title: Vorg. ---〉:Association for Computing Machinery / Special Interest Committee on Microprocessing: SICMICRO newsletter
Subsequent Title: 17.1986 - 18.1987 ---〉:Association for Computing Machinery / Special Interest Group on Microprogramming: SIGMICRO TCMICRO newsletter
Additional Information: 9,4=11; 12,4=14; 13,4=15 von:Micro
Additional Information: 20,3=22 von:International Workshop on Microprogramming and Microarchitecture: Annual International Workshop on Microprogramming and Microarchitecture
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• 26
Journal/Serial
Heidelberg :Physica-Verl., ; 16.1972 - 42.1995
Title: Zeitschrift für Operations-Research : ZOR ; mathematical methods of operations research
Publisher: Heidelberg :Physica-Verl.,
Year of publication: 1972-1995
Dates of Publication: 16.1972 - 42.1995
ISSN: 0340-9422
Type of Medium: Journal/Serial
Language: Undetermined
Former Title: Vorg. ---〉:Ablauf- und Planungsforschung
Subsequent Title: Forts. ---〉:Mathematical methods of operations research
Note: Ser. A, Theorie = H. 1,3,5,7 d. Jg.; Ser. B, Praxis = H. 2,4,6,8 d. Jg. , Deutsche Gesellschaft für Operations-Research
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• 27
Journal/Serial
Oxford [u.a.] :Pergamon Press, ; 1.1960 - 19.1995
Title: Annual review in automatic programming
Publisher: Oxford [u.a.] :Pergamon Press,
Year of publication: 1960-1995
Dates of Publication: 1.1960 - 19.1995
ISSN: 0066-4138
Type of Medium: Journal/Serial
Language: Undetermined
Subsequent Title: Forts. ---〉:Annual reviews in control
Additional Information: 1=3; 2=6, 3=11, 4=12; 5=13,2 von:International tracts in computer science and technology and their application
Additional Information: 8=7; 9,2/3=8; 10=10; 11=11; 13,1=13; 14,1=15 von:Real time programming
Additional Information: 12,1-12,2=2 von:Systems analysis and simulation
Additional Information: 13,2=5 von:Control applications of nonlinear programming and optimization
Parallel Title: Internetausg. ---〉:Annual reviews in control
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• 28
Journal/Serial
Baltimore, Md., ; 1.1989 - 7.1995
Title: ORSA journal on computing /
Author: Operations Research Society of America
Publisher: Baltimore, Md.,
Year of publication: 1989-1995
Dates of Publication: 1.1989 - 7.1995
ISSN: 0899-1499
Type of Medium: Journal/Serial
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• 29
Journal/Serial
Stuttgart :IBM, ; 22.1972,Apr. - 45.1995 = Nr. 210-323; damit Ersch. eingest.
Title: IBM-Nachrichten /
Author: IBM Deutschland GmbH 〈Stuttgart〉
Publisher: Stuttgart :IBM,
Year of publication: 1972-1995
Dates of Publication: 22.1972,Apr. - 45.1995 = Nr. 210-323; damit Ersch. eingest.
ISSN: 0018-8662
Type of Medium: Journal/Serial
Language: Undetermined
Former Title: Vorg. ---〉:Internationale Büro-Maschinen-Gesellschaft Deutschland 〈Sindelfingen〉: IBM-Nachrichten
Parallel Title: CD-ROM-Ausg. ---〉:IBM Deutschland GmbH 〈Stuttgart〉: IBM-Nachrichten
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• 30
Publication Date: 2014-02-26
Description: The paper's main result is a simple derivation rule for the Jacobi polynomials with respect to their parameters, i.e. for $\partial_{\alpha} P_n^{\alpha,\beta}$, and $\partial_{\beta} P_n^{\alpha,\beta}$. It is obtained via relations for the Gaussian hypergeometric function concerning parameter derivatives and integer shifts in the first two arguments. These have an interest on their own for further applications to continuous and discrete orthogonal polynomials. The study is motivated by a Galerkin method with moving weight, presents all proofs in detail, and terminates in a brief discussion of the generated polynomials.
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/postscript
Format: application/pdf
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• 31
Publication Date: 2014-02-26
Description: We derive a simple accuracy matching strategy for inexact Gauss Newton methods and apply it to the numerical solution of boundary value problems of ordinary differential equations by collocation. The matching strategy is based on an affine contravariant convergence theorem, i. e. , the characteristic constants are invariant under affine transformations of the domain. The inexact Gauss Newton method is applied to an integral formulation of the BVP. As discretization for the arising linear subproblems we employ adaptive collocation at Gaussian nodes with varying local orders and stepsizes. The grids are chosen via adaptive refinement and order selection.
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/postscript
Format: application/pdf
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• 32
Publication Date: 2015-06-01
Description: In this article we present a method to implement orthogonal polynomials and many other special functions in Computer Algebra systems enabling the user to work with those functions appropriately, and in particular to verify different types of identities for those functions. Some of these identities like differential equations, power series representations, and hypergeometric representations can even dealt with algorithmically, i.\ e.\ they can be computed by the Computer Algebra system, rather than only verified. The types of functions that can be treated by the given technique cover the generalized hypergeometric functions, and therefore most of the special functions that can be found in mathematical dictionaries. The types of identities for which we present verification algorithms cover differential equations, power series representations, identities of the Rodrigues type, hypergeometric representations, and algorithms containing symbolic sums. The current implementations of special functions in existing Computer Algebra systems do not meet these high standards as we shall show in examples. They should be modified, and we show results of our implementations.
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/postscript
Format: application/pdf
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• 33
Publication Date: 2014-02-26
Description: {\newcommand{\R} {{\rm {\mbox{\protect\makebox[.15em][l]{I}R}}}} Given a list of $n$ numbers in $\R$, one wants to decide wether every number in the list occurs at least $k$ times. I will show that $(1-\epsilon)n\log_3(n/k)$ is a lower bound for the depth of a linear decision tree determining this problem. This is done by using the Björner-Lov\'asz method, which turns the problem into one of estimating the Möbius function for a certain partition lattice. I will also calculate the exponential generating function for the Möbius function of a partition poset with restricted block sizes in general.}
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/postscript
Format: application/pdf
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• 34
Unknown
Publication Date: 2014-02-26
Description: Die Autoren sind sich dar{ü}ber im klaren, daß zahlreiche Imponderabilien die Ergebnisse der vorgelegten Modellrechnungen beeinflussen k{ö}nnen. Immerhin repräsentiert jedoch das vorgelegte mathematische Modell die Summe unserer derzeitigen Kenntnisse zur Fragestellung AIDS--Epidemie; neu hinzukommende Erkenntnisse lassen sich rasch einarbeiten und in ihren Konsequenzen überschauen. Die Entwicklung neuer effizienter numerischer Methoden spielte eine Schlüsselrolle bei der tatsächlichen Simulation dieses umfangreichen realitätsnahen mathematischen Modells.
Keywords: ddc:000
Language: German
Type: reportzib , doc-type:preprint
Format: application/postscript
Format: application/pdf
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• 35
Publication Date: 2014-02-26
Description: We present an adaptive Rothe method for two--dimensional problems combining an embedded Runge--Kutta scheme in time and a multilevel finite element discretization in space. The spatial discretization error is controlled by a posteriori error estimates based on interpolation techniques. A computational example for a thermodiffusive flame propagation model illustrates the high accuracy that is possible with the proposed method.
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/postscript
Format: application/pdf
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• 36
Publication Date: 2014-02-26
Description: The multicommodity linear formulation of the Fixed Charge Network Flow Design problem is known to have significantly sharp linear relaxation lower bounds. However the tradeoff is the introduction of a large amount of artificial variables. We exhibit a class of special instances for which the lower bound is tight. Further we completly describe the polyhedron in the space of the natural variables.
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/postscript
Format: application/pdf
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• 37
Unknown
Publication Date: 2020-03-09
Description: Die von der DMV-Fachgruppe Scientific Computing in Kooperation mit dem gleichnamigen GAMM-Fachausschuss organisierte Tagung \glqq Scientific Computing in der Theoretischen Physik\grqq~fand vom 16. - 18. März 1994 am Fachbereich Mathematik und Informatik der Freien Universität Berlin statt. Ziel des Workshops war, die Kontakte zwischen den Fachleuten der Gebiete {\em Computational Physics} und {\em Scientific Computing} zu intensivieren. Schwerpunkte des Workshops waren numerische Simulation von Transportmodellen der Astrophysik und Halbleiterphysik, Multilevel-Methoden für partielle Differentialgleichungen sowie Monte-Carlo-Methoden und molekulardynamische Verfahren für Probleme der Statistischen Physik und Quantenfeldtheorie. Der Workshop fand ein äusserst positives Echo und führte über 70 Teilnehmer der verschiedenen Teilgebiete der Theoretischen Physik und ca. 50 Teilnehmer aus dem Bereich der Numerischen Mathematik zusammen. \originalTeX
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/postscript
Format: application/pdf
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• 38
Publication Date: 2015-06-01
Description: We give an overview of an approach on special functions due to Truesdell, and show how it can be used to develop certain type of identities for special functions. Once obtained, these identities may be verified by an independent algorithmic method for which we give some examples.
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/postscript
Format: application/pdf
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• 39
Publication Date: 2015-06-01
Description: {\newcommand{\N} {{\rm {\mbox{\protect\makebox[.15em][l]{I}N}}}} In several publications the first author published an algorithm for the conversion of analytic functions for which derivative rules are given into their representing power series $\sum\limits_{k=0}^{\infty}a_{k}z^{k}$ at the origin and vice versa, implementations of which exist in {\sc Mathematica}, {\sc Maple} and {\sc Reduce}. One main part of this procedure is an algorithm to derive a homogeneous linear differential equation with polynomial coefficients for the given function. We call this type of ordinary differential equations {\sl simple}. Whereas the opposite question to find functions satisfying given differential equations is studied in great detail, our question to find differential equations that are satisfied by given functions seems to be rarely posed. In this paper we consider the family $F$ of functions satisfying a simple differential equation generated by the rational, the algebraic, and certain transcendental functions. It turns out that $F$ forms a linear space of transcendental functions. % with polynomial function coefficients. Further $F$ is closed under multiplication and under the composition with rational functions and rational powers. These results had been published by Stanley who had proved them by theoretical algebraic considerations. In contrast our treatment is purely algorithmically oriented. We present algorithms that generate simple differential equation for $f+g$, $f\cdot g$, $f\circ r$ ($r$ rational), and $f\circ x^{p/q}$ ($p,q\in\N_0$), given simple differential equations for $f$, and $g$, and give a priori estimates for the order of the resulting differential equations. We show that all order estimates are sharp. After finishing this article we realized that in independent work Salvy and Zimmermann published similar algorithms. Our treatment gives a detailed description of those algorithms and their validity.}
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• 40
Publication Date: 2020-11-17
Description: The power of the symbolic math system {\small REDUCE} for solving large and difficult problems in science and engineering is demonstrated by a set of model problems. These include algebraic equation solving, formal variable elimination, formal power series, symbolic treatment of differential equations and applications from theoretical physics.
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• 41
Publication Date: 2014-02-26
Description: Results from finite-element-calculations are usually visualized by colored surface- and contour-line-plots or polygonal patches or simply displaced lines and grids. In computer graphics however more advanced techniques like texture-mapping and NURBS are well established and there exist efficient algorithms and implementations. We show that these techniques are not only easy to use, but form a very natural and far more efficient approach for visualization of higher order finite-element's solutions like in $p$- and $h$-$p$-version. Texture-mapping is useful for displaying vector-valued data, too.
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• 42
Publication Date: 2014-02-27
Description: In Quantum Chemistry the field of Laser--Assisted Molecular Control'' has received a considerable amount of attention recently. One key problem in this new field is the simulation of the dynamical reaction of a molecule subjected to external radiation. This problem is described by the Schrödinger equation, which, after eigenfunction expansion, can be written in the form of a large system of ordinary differential equations, the solutions of which show a highly oscillatory behaviour. The oscillations with high frequencies and small amplitudes confine the stepsizes of any numerical integrator -- an effect, which, in turn, blows up the simulation time. Larger stepsizes can be expected by averaging these fast oscillations, thus smoothing the trajectories. Standard smoothing techniques (averaging, filtering) would kill the whole process and thus, lead to wrong numerical results. To avoid this unwanted effect and nevertheless speed up computations, this paper presents a quasiresonant smoothing algorithm (QRS). In QRS, a natural splitting parameter $\delta$ controls the smoothing properties. An adaptive QRS--version (AQRS) is presented which includes an error estimation scheme for choosing this parameter $\delta$ in order to meet a given accuracy requirement. In AQRS $\delta$ is permanently adapted to the solution properties for computing the chemically necessary information'' only. The performance of AQRS is demonstrated in several test problems from the field Laser--Assisted Selective Excitation of Molecules'' in which the external radiation is a picosecond laser pulse. In comparison with standard methods speedup factors of the order of $10^2$ are observed.
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Type: doctoralthesis , doc-type:doctoralThesis
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• 43
Publication Date: 2015-06-01
Description: This article describes the REDUCE package ZEILBERG implemented by Gregor Stölting and the author. The REDUCE package ZEILBERG is a careful implementation of the Gosper (The sum package contains also a partial implementation of the Gosper algorithm.) and Zeilberger algorithms for indefinite, and definite summation of hypergeometric terms, respectively. An expression $a_k$ is called a {\sl hypergeometric term} (or {\sl closed form}), if $a_{k}/a_{k-1}$ is a rational function with respect to $k$. Typical hypergeometric terms are ratios of products of powers, factorials, $\Gamma$ function terms, binomial coefficients, and shifted factorials (Pochhammer symbols) that are integer-linear in their arguments.
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• 44
Publication Date: 2020-03-06
Language: English
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• 45
Publication Date: 2020-03-09
Language: English
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• 46
Publication Date: 2020-03-09
Language: English
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• 47
Unknown
Publication Date: 2020-03-06
Language: English
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• 48
Unknown
Publication Date: 2020-11-17
Language: English
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• 49
Unknown
Publication Date: 2020-08-05
Language: English
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• 50
Publication Date: 2020-08-05
Language: English
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• 51
Unknown
Publication Date: 2020-08-05
Language: English
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• 52
Publication Date: 2014-02-26
Description: We test the performance of the multicanonical approach for biological molecules. The simulated molecules are frustrated systems with a complicated energy landscape. The resulting slowing down in simulations is alleviated by our ansatz. We perform a multicanonical simulation of nonpolar amino acids and study their $\alpha$-helix propensities. The results are shown to be in agreement with recent experimental results.
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• 53
Unknown
Publication Date: 2014-02-26
Description: In an array of coupled oscillators {\em synchronous chaos} may occur in the sense that all the oscillators behave identically although the corresponding motion is chaotic. When a parameter is varied this fully symmetric dynamical state can lose its stability, and the main purpose of this paper is to investigate which type of dynamical behavior is expected to be observed once the loss of stability has occurred. The essential tool is a classification of Lyapunov exponents based on the symmetry of the underlying problem. This classification is crucial in the derivation of the analytical results but it also allows an efficient computation of the dominant Lyapunov exponent associated with each symmetry type. We show how these dominant exponents determine the stability of invariant sets possessing various instantaneous symmetries and this leads to the idea of {\em symmetry breaking bifurcations of chaotic attractors}. Finally the results and ideas are illustrated for several systems of coupled oscillators.
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• 54
Unknown
Publication Date: 2020-12-15
Description: We present new Monte Carlo results in non-compact lattice QED with staggered fermions down to $m_0 = 0.005$. This extends our previous investigations on the nature of the continuum limit of QED.
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• 55
Publication Date: 2015-06-01
Description: The celebrated Zeilberger algorithm which finds holonomic recurrence equations for definite sums of hypergeometric terms $F(n,k)$ is extended to certain nonhypergeometric terms. An expression $F(n,k)$ is called hypergeometric term if both $F(n+1,k)/F(n,k)$ and $F(n,k+1)/F(n,k)$ are rational functions. Typical examples are ratios of products of exponentials, factorials, $\Gamma$ function terms, binomial coefficients, and Pochhammer symbols that are integer-linear with respect to $n$ and $k$ in their arguments. We consider the more general case of ratios of products of exponentials, factorials, $\Gamma$ function terms, binomial coefficients, and Pochhammer symbols that are rational-linear with respect to $n$ and $k$ in their arguments, and present an extended version of Zeilberger's algorithm for this case, using an extended version of Gosper's algorithm for indefinite summation. In a similar way the Wilf-Zeilberger method of rational function certification of integer-linear hypergeometric identities is extended to rational-linear hypergeometric identities. The given algorithms on definite summation apply to many cases in the literature to which neither the Zeilberger approach nor the Wilf-Zeilberger method is applicable. Examples of this type are given by theorems of Watson and Whipple, and a large list of identities (Strange evaluations of hypergeometric series'') that were studied by Gessel and Stanton. It turns out that with our extended algorithms practically all hypergeometric identities in the literature can be verified. Finally we show how the algorithms can be used to generate new identities. REDUCE and MAPLE implementations of the given algorithms can be obtained from the author, many results of which are presented in the paper.
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• 56
Publication Date: 2014-02-26
Description: We present a set of C++ classes that realize an abstract inexact Gauss Newton method in combination with a continuation process for the solution of parameter dependent nonlinear problems. The object oriented approach allows the continuation of different types of solutions within the same framework. \\{\bf Abstract: }We present a set of C++ classes that realize an abstract inexact Gauss Newton method in combination with a continuation process for the solution of parameter dependent nonlinear problems. The object oriented approach allows the continuation of different types of solutions within the same framework.
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• 57
Unknown
Publication Date: 2014-02-26
Description: We investigate the behavior of randomized simplex algorithms on special linear programs. For this, we develop combinatorial models for the Klee-Minty cubes and similar linear programs with exponential decreasing paths. The analysis of two randomized pivot rules on the Klee-Minty cubes leads to (nearly) quadratic lower bounds for the complexity of linear programming with random pivots. Thus we disprove two bounds conjectured in the literature. At the same time, we establish quadratic upper bounds for random pivots on the linear programs under investigation. This motivates the question whether some randomized pivot rules possibly have quadratic worst-case behavior on general linear programs.
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• 58
Publication Date: 2014-02-26
Description: We consider nested iterations, in which the multigrid method is replaced by some simple basic iteration procedure, and call them {\em cascadic iterations}. They were introduced by Deuflhard, who used the conjugate gradient method as basic iteration (CCG method). He demonstrated by numerical experiments that the CCG method works within a few iterations if the linear systems on coarser triangulations are solved accurately enough. Shaidurov subsequently proved multigrid complexity for the CCG method in the case of $H^2$-regular two-dimensional problems with quasi-uniform triangulations. We show that his result still holds true for a large class of smoothing iterations as basic iteration procedure in the case of two- and three-dimensional $H^{1+\alpha}$-regular problems. Moreover we show how to use cascadic iterations in adaptive codes and give in particular a new termination criterion for the CCG method.
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• 59
Publication Date: 2014-02-26
Description: The results from invariant theory and the results for semi-invariants and equivariants are summarized in a way suitable for the combination with Gröbner basis computation. An algorithm for the determination of fundamental equivariants using projections and a Poincar\'{e} series is described. Secondly, an algorithm is given for the representation of an equivariant in terms of the fundamental equivariants. Several ways for the exact determination of zeros of equivariant systems are discussed
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• 60
Unknown
Publication Date: 2021-03-16
Description: We investigate the problem of partitioning the nodes of a graph under capacity restriction on the sum of the node weights in each subset of the partition. The objective is to minimize the sum of the costs of the edges between the subsets of the partition. This problem has a variety of applications, for instance in the design of electronic circuits and devices. We present alternative integer programming formulations for this problem and discuss the links between these formulations. Having chosen to work in the space of edges of the multicut, we investigate the convex hull of incidence vectors of feasible multicuts. In particular, several classes of inequalities are introduced, and their strength and robustness are analyzed as various problem parameters change.
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• 61
Unknown
Publication Date: 2021-03-16
Description: In this paper we consider the problem of $k$-partitioning the nodes of a graph with capacity restrictions on the sum of the node weights in each subset of the partition, and the objective of minimizing the sum of the costs of the edges between the subsets of the partition. Based on a study of valid inequalities, we present a variety of separation heuristics for so-called cycle, cycle with ears, knapsack tree and path-block-cycle inequalities. The separation heuristics, plus primal heuristics, have been implemented in a branch-and-cut routine using a formulation including the edges with nonzero costs and node variables. Results are presented for three classes of problems: equipartitioning problems arising in finite element methods and partitioning problems associated with electronic circuit layout and compiler design.
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• 62
Publication Date: 2014-02-26
Description: {\def\N{{\mbox{{\rm I\kern-0.22emN}}}} Let a set $N$ of items, a capacity $F \in \N$ and weights $a_i \in \N$, $i \in N$ be given. The 0/1 knapsack polytope is the convex hull of all 0/1 vectors that satisfy the inequality $$\sum_{i \in N} a_i x_i \leq F.$$ In this paper we present a linear description of the 0/1 knapsack polytope for the special case where $a_i \in \{\mu,\lambda\}$ for all items $i \in N$ and $1 \leq \mu 〈 \lambda \leq b$ are two natural numbers. The inequalities needed for this description involve elements of the Hilbert basis of a certain cone. The principle of generating inequalities based on elements of a Hilbert basis suggests further extensions.}
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• 63
Publication Date: 2014-02-26
Description: We compare a few variants of the recently proposed multicanonical method with the well known simulated annealing for the effectiveness in search of the energy global minimum of a biomolecular system. For this we study in detail Met-enkephalin, one of the simplest peptides. We show that the new method not only outperforms simulated annealing in the search of the energy groundstate but also provides more statistical-mechanical information about the system.
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• 64
Publication Date: 2014-02-26
Description: We demonstrate the effectiveness of the multicanonical algorithm for the tertiary structure prediction of peptides and proteins. Unlike to simulated annealing the relationship to the canonical ensemble remains exactly controlled. Hence, the new method allows not only the prediction of the lowest-energy conformation, but also the calculation of thermodynamic quantities at various temperature from one run.
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• 65
Unknown
Publication Date: 2014-02-26
Description: Die enorme algorithmische Beschleunigung durch diskrete Galerkin-Methoden f{ü}r abz{ä}hlbare Differentialgleichungssysteme hat der Simulation von Polymerisationsprozessen neue, industriell relevante Problembereiche er{ö}ffnet, die mit den bis dahin verf{ü}gbaren Methoden nicht zug{ä}nglich waren.
Keywords: ddc:000
Language: German
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• 66
Publication Date: 2014-02-26
Description: Large chemical computations show the need for full adaptivity supporting the development of robust and highly efficient programs. For solutions possessing sharp moving spatial transitions, as travelling wavefronts or emerging boundary and internal layers, an automatic adjustment of both the space and the time stepsize is generally accepted to be more successful in efficient resolving critical regions of high spatial and temporal activity. In contrast to the widespread discretization sequence first space then time the reversed sequence first time then space is employed. Full adaptivity of the proposed algorithm is realized by combining embedded time discretization and multilevel finite element space discretization. In this paper the algorithm is described for one--dimensional problems. The numerical results show the significantly new perspectives opened by this approach.
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• 67
Unknown
Publication Date: 2019-05-10
Description: An error controlled finite elemente method (FEM) for solving stationary Schrödinger equations in three space dimensions is proposed. The method is based on an adaptive space discretization into tetrahedra and local polynomial basis functions of order $p=1$--$5$ defined on these tetrahedra. According to a local error estimator the triangulation is automatically adapted to the solution. Numerical results for standard problems appearing in vibrational motion and molecular structure calculations are presented and discussed. Relative precisions better than 1e-8 are obtained. For equilateral H$_3^{++}$ the adaptive FEM turns out to be superior to global basis set expansions in the literature. Our precise FEM results exclude in a definite manner the stability or metastability of equilateral H$_3^{++}$ in its groundstate.
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• 68
Publication Date: 2020-03-09
Description: {\def\NP{\hbox{$\cal N\kern-.1667em\cal P$}} The {\sl storage assignment problem} asks for the cost minimal assignment of containers with different sizes to storage locations with different capacities. Such problems arise, for instance, in the optimal control of automatic storage devices in flexible manufacturing systems. This problem is known to be $\NP$-hard in the strong sense. We show that the storage assignment problem is $\NP$-hard for {\sl bounded sizes and capacities}, even if the sizes have values $1$ and~$2$ and the capacities value~$2$ only, a case we encountered in practice. Moreover, we prove that no polynomial time $\epsilon$-approximation algorithm exists. This means that almost all storage assignment problems arising in practice are indeed hard.}
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• 69
Publication Date: 2014-02-26
Description: We consider the numerical treatment of Hamiltonian systems that contain a potential which grows large when the system deviates from the equilibrium value of the potential. Such systems arise, e.g., in molecular dynamics simulations and the spatial discretization of Hamiltonian partial differential equations. Since the presence of highly oscillatory terms in the solutions forces any explicit integrator to use very small step-size, the numerical integration of such systems provides a challenging task. It has been suggested before to replace the strong potential by a holonomic constraint that forces the solutions to stay at the equilibrium value of the potential. This approach has, e.g., been successfully applied to the bond stretching in molecular dynamics simulations. In other cases, such as the bond-angle bending, this methods fails due to the introduced rigidity. Here we give a careful analysis of the analytical problem by means of a smoothing operator. This will lead us to the notion of the smoothed dynamics of a highly oscillatory Hamiltonian system. Based on our analysis, we suggest a new constrained formulation that maintains the flexibility of the system while at the same time suppressing the high-frequency components in the solutions and thus allowing for larger time steps. The new constrained formulation is Hamiltonian and can be discretized by the well-known SHAKE method.
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• 70
Unknown
Publication Date: 2014-02-26
Description: We investigate the generating sets (Gröbner bases'') of integer lattices which correspond to the Gröbner bases of the associated binomial ideals. Extending results in Sturmfels and Thomas, preprint 1994, we obtain a geometric characterization of the universal Gröbner basis in terms of the vertices and edges of the associated corner polyhedra. We emphasize the special case where the lattice has finite index. In this case the corner polyhedra were studied by Gomory, and there is a close connection to the group problem in integer programming'' Schrijver, p.~363. We present exponential lower and upper bounds for the size of a reduced Gröbner basis. The initial complex of (the ideal of) a lattice is shown to be dual to the boundary of a certain simple polyhedron.
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• 71
Unknown
Publication Date: 2014-02-26
Description: We consider periodic orbits of autonomous parameter dependent ODE's. Starting from a shooting algorithm for the numerical computation of periodic orbits via an adaptive Poincar\'e-section we develop a pathfollowing algorithm for periodic solutions based on a tangential continuation method with implicit reparametrization. For ODE's equivariant w.r.t. a finite group we show that spatial as well as spatio-temporal symmetries of periodic orbits can be exploited within the (multiple) shooting context. We describe how turning points, period doubling bifurcations and Hopf points along the branch of periodic solutions can be handled. Furthermore equivariant Hopf points and generic secondary bifurcations of periodic orbits with $Z_m$-symmetry are treated. We tested the code with standard examples, e.g., the period doubling cascade in the Lorenz equations. To show the efficiency of the described methods we also used the program for an application from electronics, a ring oscillator with $n$ inverters. In this example the exploitation of symmetry reduces the amount of work for the continuation of periodic orbits from ${\cal O}(n^2)$ to ${\cal O}(n)$
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