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CLP(R) and Some Electrical Engineering Problems
 Journal of Automated Reasoning
, 1991
"... The Constraint Logic Programming Scheme defines a class of languages designed for programming with constraints using a logic programming approach. These languages are soundly based on a unified framework of formal semantics. In particular, as an instance of this scheme with real arithmetic constrain ..."
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Cited by 35 (5 self)
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The Constraint Logic Programming Scheme defines a class of languages designed for programming with constraints using a logic programming approach. These languages are soundly based on a unified framework of formal semantics. In particular, as an instance of this scheme with real arithmetic constraints, the CLP(R) language facilitates and encourages a concise and declarative style of programming for problems involving a mix of numeric and nonnumeric computation. In this paper we illustrate the practical applicability of CLP(R) with examples of programs to solve electrical engineering problems. This field is particularly rich in problems that are complex and largely numeric, enabling us to demonstrate a number of the unique features of CLP(R). A detailed look at some of the more important programming techniques highlights the ability of CLP(R) to support wellknown, powerful techniques from constraint programming. Our thesis is that CLP(R) is an embodiment of these techniques in a langu...
The Painlevé Analysis and Special Solutions for Nonintegrable Systems
, 203
"... The Hénon–Heiles system in the general form is studied. In a nonintegrable case new solutions have been found as formal Laurent series, depending on three parameters. One of parameters determines a location of the singularity point, other parameters determine coefficients of the Laurent series. For ..."
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Cited by 3 (0 self)
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The Hénon–Heiles system in the general form is studied. In a nonintegrable case new solutions have been found as formal Laurent series, depending on three parameters. One of parameters determines a location of the singularity point, other parameters determine coefficients of the Laurent series. For some values of these two parameters the obtained Laurent series coincide with the Laurent series of the known exact solutions. 1 The Hénon–Heiles Hamiltonian Let us consider a threedimensional galaxy with an axialsymmetric and timeindependent potential function. The equations of galactic motion admit two wellknown integrals: energy and angular momentum. If we know also the third integral of motion, then we can solve the motion equations by the method of quadratures. Due to the symmetry of the potential the considered system is equivalent to twodimensional one. However, for many polynomial potentials the obtained system has not the second integral as a polynomial function. In the 1960s numerical [1] and asymptotic methods [2, 3] have been developed to show either existence or absence of the third integral for some polynomial potentials. To answer the question about the existence of the third integral Hénon and Heiles [1] considered the behavior of numerically integrated trajectories. They wrote [1]: ”In order to have more freedom of experimentation, we forgot momentarily the astronomical origin of the problem and consider its general form: does an axisymmetrical potential admit a third isolating integral of motion?”. They have proposed the following Hamiltonian:
Symbolic Algebra And PhysicalModelBased Control
 Computing and Control Journal
, 1996
"... this paper concentrates on a nonlinear system for the purposes of illustration. Precisely because each control algorithm has to be specially constructed for each system, it is essential to provide software to help in this process. The use of computer algebra is a vital part of such software. The pu ..."
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Cited by 2 (2 self)
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this paper concentrates on a nonlinear system for the purposes of illustration. Precisely because each control algorithm has to be specially constructed for each system, it is essential to provide software to help in this process. The use of computer algebra is a vital part of such software. The purpose of this paper is to present the computer algebra aspects of PhysicalModel Based Control; the control theory aspects covered in detail elsewhere by Gawthrop [14]. 2 PHYSICALMODELBASED CONTROL
HPGP: HighPerformance Generic Programming for Computational Mathematics by CompileTime Instantiation of Higher Order Functors
, 1997
"... A functor is a parameterized program module i.e. a function that takes modules as arguments and returns a module as its result. A higherorder functor deals in the same way with modules whose components are functors themselves. We propose to develop a generic compilation system for the construction ..."
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A functor is a parameterized program module i.e. a function that takes modules as arguments and returns a module as its result. A higherorder functor deals in the same way with modules whose components are functors themselves. We propose to develop a generic compilation system for the construction of highperformance mathematical software libraries for scientific and technical application domains. This system has the following features: 1. It is based on a powerful higherorder functor language. 2. It is an open library that can be retargeted to any core language. 3. It is able to resolve functor instantiation at compiletime. The functor language is expressive enough to build all types and type constructors without referring to the core language (thus maximizing flexibility) and to express all interactions between modules by parameterization (thus maximizing reusability). By compiletime instantiation, genericity does not cause any execution overhead; by automatically sharing instant...
Lectures on Reduce and Maple at UAMI, Mexico
, 1999
"... These lectures give a brief introduction to the Computer Algebra systems Reduce and Maple. The aim is to provide a systematic survey of most important commands and concepts. In particular, this includes a discussion of simplification schemes and the handling of simplification and substitution rules ..."
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These lectures give a brief introduction to the Computer Algebra systems Reduce and Maple. The aim is to provide a systematic survey of most important commands and concepts. In particular, this includes a discussion of simplification schemes and the handling of simplification and substitution rules (e.g., a Lie Algebra is implemented in Reduce by means of simplification rules). Another emphasis is on the different implementations of tensor calculi and the exterior calculus by Reduce and Maple and their application in Gravitation theory and Differential Geometry. I held the lectures at the Universidad Autonoma MetropolitanaIztapalapa, Departamento de Fisica, Mexico, in November 1999.
motion?”. They chose Hamiltonian
, 2002
"... The Hénon–Heiles system in the general form are studied. In a nonintegrable case new solution has been found as formal Laurent series, depending on three parameters. This asymptotic solution with some values of two parameters coincides with known exact solution. 1 The Hénon–Heiles Hamiltonian Let us ..."
Abstract
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The Hénon–Heiles system in the general form are studied. In a nonintegrable case new solution has been found as formal Laurent series, depending on three parameters. This asymptotic solution with some values of two parameters coincides with known exact solution. 1 The Hénon–Heiles Hamiltonian Let us consider a threedimensional galaxy with an axial symmetric and timeindependent potential function. The equations of galactic motion admit of two wellknown integrals: energy and angular momentum. If we know also the third integral of motion then we can solve the motion equations by the method of quadratures. However, the third integral as polynomial function does not exist in the general case. In the 1960s, numerical [1] and asymptotic methods [2, 3] have been developed to show existence or absence of the third integral for some polynomial potentials. In [1] (1964) Hénon and Heiles wrote: ”In order to have more freedom of experimentation, we forgot momentarily the astronomical origin of the problem and consider its general form: does an axisymmetrical potential admit a third isolating integral of
and
, 2000
"... Doubly periodic (periodic both in time and in space) solutions for the Lagrange–Euler equation of the (1 + 1)–dimensional scalar ϕ 4 theory are considered. The nonlinear term is assumed to be small, and the Poincaré– Lindstedt method is used to find asymptotic solutions in the standing wave form. Th ..."
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Doubly periodic (periodic both in time and in space) solutions for the Lagrange–Euler equation of the (1 + 1)–dimensional scalar ϕ 4 theory are considered. The nonlinear term is assumed to be small, and the Poincaré– Lindstedt method is used to find asymptotic solutions in the standing wave form. The principal resonance problem, which arises for zero mass, is solved if the leadingorder term is taken in the form of a Jacobi elliptic function. It have been proved that the choice of elliptic cosine with fixed value of module k (k ≈ 0.451075598811) as the leadingorder term puts the principal resonance to zero and allows us to construct (with accuracy to third order of small parameter) the asymptotic solution in the standing wave form. To obtain this leadingorder term the computer algebra system REDUCE have been used. 1.1 Periodic solutions of nonlinear equations Recently, periodic solutions of the nonlinear wave equation: