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795
Nonlinear Neural Networks: Principles, Mechanisms, and Architectures
, 1988
"... An historical discussion is provided of the intellectual trends that caused nineteenth century interdisciplinary studies of physics and psychobiology by leading scientists such as Helmholtz, Maxwell, and Mach to splinter into separate twentiethcentury scientific movements. The nonlinear, nonstatio ..."
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Cited by 262 (21 self)
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Schuster models. A Liapunov functional method is described for proving global limit or oscillation theorems for nonlinear competitive systems when their decision schemes are globally consistent or inconsistent, respectively. The former case is illustrated by a model of a globally stable economic market
Mechanical Theorem Proving in Geometry
, 2012
"... Mechanical theorem proving in geometry plays an important role in the research of automated reasoning. In this paper, we introduce three kinds of computerized methods for geometrical theorem proving: the first is Wu ’ s method in the international community, the second is elimination point method an ..."
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Mechanical theorem proving in geometry plays an important role in the research of automated reasoning. In this paper, we introduce three kinds of computerized methods for geometrical theorem proving: the first is Wu ’ s method in the international community, the second is elimination point method
Mechanical Theorem Proving in Projective Geometry
, 1993
"... We present an algorithm that is able to confirm projective incidence statements by carrying out calculations in the ring of all formal determinants (brackets) of a configuration. We will describe an implementation of this prover and present a series of examples treated by the prover, including Pappo ..."
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Cited by 14 (3 self)
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Pappos' and Desargues' Theorems, the Sixteen Point Theorem, Saam's Theorem, the Bundle Condition, the uniqueness of a harmonic Point and Pascal's Theorem.
Qualitative Theorem Proving in Linear Constraints
 In International Symposium on Artificial Intelligence and Mathematics. Long version to appear in the Annals of Mathematics and Artificial Intelligence
, 2000
"... We know, from the classical work of Tarski on real closed fields, that elimination is, in principle, a fundamental engine for mechanized deduction. But, in practice, the high complexity of elimination algorithms has limited their use in the realization of mechanical theorem proving. We advocate q ..."
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Cited by 8 (0 self)
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We know, from the classical work of Tarski on real closed fields, that elimination is, in principle, a fundamental engine for mechanized deduction. But, in practice, the high complexity of elimination algorithms has limited their use in the realization of mechanical theorem proving. We advocate
Mechanical Theorem Proving in Tarski’s Geometry
"... Abstract. This paper describes the mechanization of the proofs of the first height chapters of Schwabäuser, Szmielew and Tarski’s book: Metamathematische Methoden in der Geometrie. The proofs are checked formally using the Coq proof assistant. The goal of this development is to provide foundations f ..."
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Cited by 10 (3 self)
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Abstract. This paper describes the mechanization of the proofs of the first height chapters of Schwabäuser, Szmielew and Tarski’s book: Metamathematische Methoden in der Geometrie. The proofs are checked formally using the Coq proof assistant. The goal of this development is to provide foundations
Clifford Algebra and Mechanical Geometry Theorem Proving
"... It is a difficult problem which is left since the Euclid times to find a mechanical method to prove difficult geometry theorems to make learning and teaching of geometry easy. In history, many mathematicians, such as Leibniz, Hilbert, and etc., have tried on this field. Modern computer technology a ..."
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It is a difficult problem which is left since the Euclid times to find a mechanical method to prove difficult geometry theorems to make learning and teaching of geometry easy. In history, many mathematicians, such as Leibniz, Hilbert, and etc., have tried on this field. Modern computer technology
A Method for Proving Theorems in Differential Geometry and Mechanics
, 1995
"... A zero decomposition algorithm is presented and used to devise a method for proving theorems automatically in differential geometry and mechanics. The method has been implemented and its practical efficiency is demonstrated by several nontrivial examples including Bertrand's theorem, Schell&ap ..."
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A zero decomposition algorithm is presented and used to devise a method for proving theorems automatically in differential geometry and mechanics. The method has been implemented and its practical efficiency is demonstrated by several nontrivial examples including Bertrand's theorem, Schell
Multisymplectic geometry, variational integrators, and nonlinear PDEs
 Comm. Math. Phys
, 1998
"... Abstract: This paper presents a geometricvariational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fundamental geometric structures as well as their preservation along solutions can be obtained directly from the v ..."
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Cited by 126 (24 self)
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the variational principle. In particular, we prove that a unique multisymplectic structure is obtained by taking the derivative of an action function, and use this structure to prove covariant generalizations of conservation of symplecticity and Noether’s theorem. Natural discretization schemes for PDEs, which
Entanglement of Formation of an Arbitrary State of Two Qubits
, 1998
"... The entanglement of a pure state of a pair of quantum systems is defined as the entropy of either member of the pair. The entanglement of formation of a mixed state ρ is defined as the minimum average entanglement of a set of pure states constituting a decomposition of ρ. An earlier paper [Phys. Rev ..."
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Cited by 200 (0 self)
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states of this system and shows how to construct entanglementminimizing purestate decompositions. PACS numbers: 03.65.Bz, 89.70.+c 1 Entanglement is the peculiar feature of quantum mechanics that allows, in principle, feats such as teleportation [1] and dense coding [2] and is what Schrödinger called
Interactive Theorem Proving in Twelf
"... In recent work, we showed how to implement tacticstyle theorem proving in Twelf [2]. Tactics and tacticals are a mechanism used in a variety of theorem provers such as LCF [5], HOL [4], and Coq [8]. They provide
exible control for goaldirected proof search. Tactics provide the basic search proced ..."
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In recent work, we showed how to implement tacticstyle theorem proving in Twelf [2]. Tactics and tacticals are a mechanism used in a variety of theorem provers such as LCF [5], HOL [4], and Coq [8]. They provide
exible control for goaldirected proof search. Tactics provide the basic search
Results 1  10
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