Results 1  10
of
11
Homotopy hyperbolic 3manifolds are hyperbolic
 Ann. of Math
, 2003
"... This paper introduces a rigorous computerassisted procedure for analyzing hyperbolic 3manifolds. This procedure is used to complete the proof of several longstanding rigidity conjectures in 3manifold theory as well as to ..."
Abstract

Cited by 58 (4 self)
 Add to MetaCart
This paper introduces a rigorous computerassisted procedure for analyzing hyperbolic 3manifolds. This procedure is used to complete the proof of several longstanding rigidity conjectures in 3manifold theory as well as to
Combining symbolic computation and theorem proving: some problems of Ramanujan
 In A. Bundy (Ed.), Automated Deduction (CADE12
, 1994
"... One way of building more powerful theorem provers is to use techniques from symbolic computation. The challenge problems in this paper are taken from Chapter 2 of Ramanujan 's Notebooks. They were selected because they are nontrivial and require the use of symbolic computation techniques. We have d ..."
Abstract

Cited by 11 (3 self)
 Add to MetaCart
One way of building more powerful theorem provers is to use techniques from symbolic computation. The challenge problems in this paper are taken from Chapter 2 of Ramanujan 's Notebooks. They were selected because they are nontrivial and require the use of symbolic computation techniques. We have developed a theorem prover based on the symbolic computation system Mathematica that can prove all the challenge problems completely automatically. The axioms and inference rules for constructing the proofs are also briefly discussed. This research was sponsored in part by the Avionics Laboratory, Wright Research and Development Center, Aeronautical Systems Division (AFSC), U.S. Air Force, WrightPatterson AFB, Ohio 454336543 under Contract F3361590C1465, ARPA Order No. 7597, and in part by National Science Foundation under Contract Number CCR9217549. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official p...
SYMORO+: a system for the symbolic modelling of robots
 Robotica
, 1997
"... This paper presents the software package SYMORO+ for the automatic symbolic modelling of robots. This package permits to generate the direct geometric model, the inverse geometric model, the direct kinematic model, the inverse kinematic model, the dynamic model, and the inertial parameters identific ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
This paper presents the software package SYMORO+ for the automatic symbolic modelling of robots. This package permits to generate the direct geometric model, the inverse geometric model, the direct kinematic model, the inverse kinematic model, the dynamic model, and the inertial parameters identification models. The structure of the robots can be serial, tree structure or containing closed loops. The package runs on Sun stations and PC computers, it has been developed under MATHEMATICA and C language. In this paper we give an overview of the algorithms used in the different models, the computational cost of the dynamic models of the PUMA robot are given.
A construction for computer visualization of certain complex curves
 Notices of the Amer.Math.Soc
, 1994
"... Computer graphics has proven to be a very attractive tool for investigating lowdimensional algebraic manifolds and gaining intuition about their properties [9]. In principle, a computer image of any manifold described by algebraic ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
Computer graphics has proven to be a very attractive tool for investigating lowdimensional algebraic manifolds and gaining intuition about their properties [9]. In principle, a computer image of any manifold described by algebraic
Symbolic Computation of Divided Differences
, 1999
"... Divided differences are enormously useful in developing stable and accurate numerical formulas. For example, programs to compute f(x)  f(y) as might occur in integration, can be notoriously inaccurate. Such problems can be cured by approaching these computations through divided difference formulati ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Divided differences are enormously useful in developing stable and accurate numerical formulas. For example, programs to compute f(x)  f(y) as might occur in integration, can be notoriously inaccurate. Such problems can be cured by approaching these computations through divided difference formulations. This paper provides a guide to divided difference theory and practice, with a special eye toward the needs of computer algebra systems that should be programmed to deal with these oftenmessy formulas.
Model Selection for Solving Kinematic Problems
, 1991
"... There has been much interest in the area of modelbased reasoning within the Artificial Intelligence community, particularly in its application to diagnosis and trou bleshooting. The core issue in this thesis, simply put, is, modelbased reasoning is fine, but whence the model? Where do the models ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
There has been much interest in the area of modelbased reasoning within the Artificial Intelligence community, particularly in its application to diagnosis and trou bleshooting. The core issue in this thesis, simply put, is, modelbased reasoning is fine, but whence the model? Where do the models come from? How do we know we have the right models? What does the right model mean anyway? Our work has three major components. The first component deals with how we determine whether a piece of information is relevant to solving a problem. We have three ways of determining relevance: derivational, situational and an orderofrnagnitude reasoning process. The second component deals with the defining and building of models for solving problems. We identify these models, determine what we need to know about them, and importantly, determine when they are appropriate. Currently, the system has a collection of four basic models and two hybrid models. This col lection of models has been successfully tested on a set of fifteen simple kinematics problems. The third major component of our work deals with how the models are selected.
Conservation laws for the classical Toda field theories
, 1993
"... We have performed some explicit calculations of the conservation laws for classical (affine) Toda field theories, and some generalizations of these models. We show that there is a huge class of generalized models which have an infinite set of conservation laws, with their integrated charges being in ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
We have performed some explicit calculations of the conservation laws for classical (affine) Toda field theories, and some generalizations of these models. We show that there is a huge class of generalized models which have an infinite set of conservation laws, with their integrated charges being in involution. Amongst these models we find that only the Am and A (1) m (m ≥ 2) Toda field theories admit such conservation laws for spin3. We report on our explicit calculations of spin4 and spin5 conservation laws in the (affine) Toda models. Our perhaps most interesting finding is that there exist conservation laws in the Am models (m ≥ 4) which have a different origin than the exponents of the corresponding affine theory or There is an intimate connection between the integrability of a Hamiltonian system and the existence of a sufficient number of conserved quantities. Liouville
On the relation between QCD potentials in momentum and position space
"... We derive a formula which relates the QCD potentials in momentum space and in position space in terms of the fi function of the renormalizationgroup equation for the potential. This formula is used to study the theoretical uncertainties in the potential and in particular in its application to the d ..."
Abstract
 Add to MetaCart
We derive a formula which relates the QCD potentials in momentum space and in position space in terms of the fi function of the renormalizationgroup equation for the potential. This formula is used to study the theoretical uncertainties in the potential and in particular in its application to the determination of the pole mass m b when we use perturbative expansions. We demonstrate the existence of these uncertainties for the Richardson potential explicitly and then discuss the limited theoretical accuracy in the perturbative QCD potential. We conclude that a theoretical uncertainty of m b much below 100 MeV would not be achievable within perturbative QCD. PACS: 12.38.t, 12.38.Bw, 12.39.Pn On leave of absence from Department of Physics, Tohoku University, Sendai 98077, Japan. In this article we discuss a relation between the static QCD potential [1] in momentum space V (q) = \GammaC F 4ff V (q) q 2 ; (1) where for quarks C F = 4=3, and the corresponding potential in positio...
Src2tex Version 2.12
, 1996
"... One of the authors has a strong desire for combining documentation and manual with source program by using T E X's beautiful text and PostScript figures without any big literate programming tools, such as WEB system ( [8] ) or something like that ( [15] ). ..."
Abstract
 Add to MetaCart
One of the authors has a strong desire for combining documentation and manual with source program by using T E X's beautiful text and PostScript figures without any big literate programming tools, such as WEB system ( [8] ) or something like that ( [15] ).