27429660
Automatic determination of dynamical symmetries of ordinary differential equations
We describe the application of a computer program CRACKSTAR for the exact analytic solution of overdetermined systems of differential equations which result in determining point-, contact- and dynamical symmetries of ordinary differential equations. Examples are discussed.ZusammenfassungWir beschreiben die Anwendung des Computerprogramms CRACKSTAR zur exakten Lösung überbestimmter Differentialgleichungssysteme, die von der Bestimmung von Punkt- und Berührungssymmetrien sowie dynamischer Symmetrien gewöhnlicher Differentialgleichungen herrühren.
9140187
The integration of systems of linear PDEs using conservation laws of syzygies
A new integration technique is presented for systems of linear partial differential equations (PDEs) for which syzygies can be formulated that obey conservation laws. These syzygies come for free as a by-product of the differential Grobner basis computation. Compared with the more obvious way of integrating a single equation and substituting the result in other equations the new technique integrates more than one equation simultaneously and therefore introduces temporarily fewer new functions of integration that in addition depend on fewer variables. Especially for high order PDE systems in many variables the conventional integration technique may lead to an explosion of the number of functions of integration which is avoided with the new method. A further benefit is that redundant free functions in the solution are either prevented or that their number is at least reduced.
1220
A comparison of four approaches to the calculation of conservation laws
The paper compares computational aspects of four approaches to compute conservation laws of single differential equations or systems of them, ODEs and PDEs. The only restriction, required by two of the four corresponding computer algebra programs, is that each DE has to be solvable for a leading derivative. Extra constraints may be given. Examples of new conservation laws include non-polynomial expressions, an explicit variable dependence and conservation laws involving arbitrary functions. Examples involve the following equations: Ito, Liouville, Burgers, Kadomtsev-Petviashvili, Karney-Sen-Chu-Verheest, Boussinesq, Tzetzeica, Benney.
3233905
Programs for applying symmetries
In this paper the programs APPLYSYM, QUASILINPDE and DETRAFO are described which aim at the utilization of infinitesimal symmetries of differential equations. The purpose of QUASILINPDE is the general solution of quasilinear PDEs. This procedure isusedby APPLYSYM fortheapplication of point symmetries for either Q calculating simila,rity variables toperform a point transformation which lowers the order of an ODEoreffectiveiy reduces the number of explicitly occuringindependent variablesin aPDE(-system) or for . generalizing given special solutions of ODEs/PDEs with new constant parameters. The program DETRAFO performs arbitrary pointand contact transformations of ODEs/PDEs and is applied if similarity and symmetry variables have been found. The program APPLYSYM is used in connection with the program LIEPDE for formulating and solving the conditions for pointand cent act symmetries which is described in [4]. The actual problem solving is done in all these programs through a call to the package CRACK for solving overdetermined PDE systems.
45184054
A package for the analytic investigation and exact solution of differential equations
To find exact solutions of differential equations fDEs) one usually performs a variety of tests and ansaetze as e.g. the symmetry ansatz, separation ansatz, ansaetze for first integrals. When carrying through these ideas one h a s to solve overdetermined systems of partial DEs fPDEs). Whereas the formulation of the overdetermined system f o r each ansatz is achieved by different programs we use one program to investigate the overdetermined sys~. This program CRAOKSTAR contains three basic modules for the deooupling of DEs, for the integration of exact DEs and f o r separation. They are explained by examples. With these new a b i l i t i e s i t becomes poss ib le f o r CRACKSTAR to so lve systems of DEs which are sore difficult, i.e. the ansatz to be carried through ma y be less restrictive. An example shows that in this way not only point s y m m e t r i e s b u t a l s o m o r e g e n e r a l d y n a m i c a l s y m m e t r i e s o f o r d i n a r y DEs ( O D E s ) c a n b e d e t e r m i n e d . F o r t h e I n v e s t i g a t i o n o f L l e s ~ t r i e s o f systems of PDEs an interval strategy is applied which reduces the effort f o r GKACKSTM~ c o n s i d e r a b l y . F u r t h e r t w o new c o n c e p t s , a n i n t e g r a l a n s a t z f o r ODEs and a generalized separation ansatz f o r PDEs are described as w e l l a s t h e p r o g r a m s w h i c h g e n e r a t e o v e r d e t e r m i n e d s y s t e m s for e a c h ansatz.
27997406
Forward Pruning and Other Heuristic Search Techniques in Tsume Go
Abstract G o T ools is the name of a computer program to analyse life and death fights in the game of go. First, a motivation for programing go is given. General aspects of the heuristic search performed in G o T ools are discussed. The absolute strength and the effect of forward tree pruning are tested in a competition between G o T ools and dan level human players. It is found that with a speed up of a factor of 30 the program still finds for 70% of the problems of a test set the correct first move. A suggestion is made to compare intelligence between contestants (in solving fully enclosed life/death problems) by comparing their relative increase in the time to solve problems with the increase of the difficulty of the problems. The rules of go are explained in the shortest possible form in Appendix A .
23941957
Model Checking
Die Gewährleistung der korrekten
Funktionsweise von Hard- und Software ist ein entscheidender
Faktor bei der heutigen Systementwicklung. Dies trifft ganz
besonders auf das Gebiet der sog. „sicherheitskritischen“
Systeme zu, bei dem ein Systemversagen Menschenleben gefährden
kann.
196094
Integrating object-oriented programming and protected objects in Ada 95
Integrating concurrent and object-oriented programming has been an active research topic since the late 1980's. There is a now a plethora of methods for achieving this integration. The majority of approaches have taken a sequential object-oriented language and made it concurrent. A few approaches have taken a concurrent language and made it object-oriented. The most important of this latter class is the Ada 95 language, which is an extension to the object-based concurrent programming language Ada 83. Arguably, Ada 95 does not fully integrate its models of concurrency and object-oriented programming. For example, neither tasks nor protected objects are extensible. This article discusses ways in which protected objects can be made more extensible.
11330765
Transparent filtering of streams in GLADE
Note: Also available as Technical Report EPFL 97/241 Reference LGL-CONF-1997-009 Record created on 2005-09-20, modified on 2016-08-08
43214033
Ein neuer Ansatz zur Lösung der Phasenentfaltungsproblematik
Ein durch eine harmonische Intensitatsverteilung beschreibbares Streifenmuster soll ausgewertet werden. Dabei mus fur jeden Punkt des Musters die Phasenlage bestimmt werden. Mit auto-matischen Phasenauswertemethoden last sich im allgemeinen die Phase nur im sich periodisch fortsetzenden Werteintervall [−π, π] bestimmen (Sagezahnbild). Das Zusammensetzen zur Gesamtphase wird als Phasenentfaltung bezeichnet. Die Anwendung des Streifenprojektions-verfahrens [Breu93] zur Konturbestimmung von Schaumstoffoberflachen in Kombination mit der Phasenshifttechnik fuhrt zu einem Sagezahnbild, dessen automatische Entfaltung bei Anwendung von ublichen Methoden zu erheblichen Fehlern fuhrt. Oftmals ist nur eine interaktive Phasenkorrektur durch den Benutzer moglich. Mit Hilfe der Fuzzy-Logik kann man das menschliche Expertenwissen in einer vom Computer verarbeitbaren Form fur die automatische Phasenentfaltung zur Verfugung stellen.
31197886
Object-Oriented Programming and Protected Objects in Ada 95
Integrating concurrent and object-oriented programming has been an active research topic since the late 1980s. The majority of approaches have taken a sequential object-oriented language and made it concurrent. A few approaches have taken a concurrent language and made it object-oriented. The most important of this latter class is the Ada 95 language which is an extension to the object-based concurrent programming language Ada 83. Arguably, Ada 95 does not fully integrate its models of concurrency and object-oriented programming. This paper discusses ways in which protected objects can be made more extensible.