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Results 1 - 10
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7,298
On Solving Systems of Autonomous Ordinary Differential Equations by Reduction to a Variable of an Algebra
"... A new technique for solving a certain class of systems of autonomous ordinary differential equations over K n is introduced K being the real or complex field . The technique is based on two observations: 1 , if K n has the structure of certain normed, associative, commutative, and with a unit, alge ..."
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A new technique for solving a certain class of systems of autonomous ordinary differential equations over K n is introduced K being the real or complex field . The technique is based on two observations: 1 , if K n has the structure of certain normed, associative, commutative, and with a unit
A Further Result on the Instability of Solutions to a Class of Non-Autonomous Ordinary Differential Equations of Sixth Order
, 2007
"... The aim of the present paper is to establish a new result, which guarantees the instability of zero solution to a certain class of non-autonomous ordinary differential equations of sixth order. Our result includes and improves some well-known results in the literature. ..."
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The aim of the present paper is to establish a new result, which guarantees the instability of zero solution to a certain class of non-autonomous ordinary differential equations of sixth order. Our result includes and improves some well-known results in the literature.
Rational General Solution of 1-Dimensional Systems of Autonomous Ordinary Differential Equations
"... An algebro-geometric method for determining the rational solvability of autonomous algebraic ordinary differential equations is extended from single equations of order 1 to systems of equations of arbitrary order but dimension 1. We provide necessary conditions, for the existence of rational solutio ..."
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An algebro-geometric method for determining the rational solvability of autonomous algebraic ordinary differential equations is extended from single equations of order 1 to systems of equations of arbitrary order but dimension 1. We provide necessary conditions, for the existence of rational
Rational General Solutions of Systems of Autonomous Ordinary Differential Equations of Algebro-Geometric Dimension One
"... An algebro-geometric method for determining the rational solvability of au-tonomous algebraic ordinary differential equations is extended from single equa-tions of order 1 to systems of equations of arbitrary order but dimension 1 in the algebro-geometric sense. We provide necessary conditions, for ..."
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An algebro-geometric method for determining the rational solvability of au-tonomous algebraic ordinary differential equations is extended from single equa-tions of order 1 to systems of equations of arbitrary order but dimension 1 in the algebro-geometric sense. We provide necessary conditions
J. Differential Equations 189 (2003) 440–460 Non-autonomous systems: asymptotic behaviour and weak invariance principles$
, 2001
"... Results pertaining to asymptotic behaviour of solutions of non-autonomous ordinary differential equations with locally integrably bounded right-hand sides are presented. Ramifications for weakly asymptotically autonomous systems and adaptively controlled systems are highlighted. ..."
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Results pertaining to asymptotic behaviour of solutions of non-autonomous ordinary differential equations with locally integrably bounded right-hand sides are presented. Ramifications for weakly asymptotically autonomous systems and adaptively controlled systems are highlighted.
Modeling and simulation of genetic regulatory systems: A literature review
- JOURNAL OF COMPUTATIONAL BIOLOGY
, 2002
"... In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between ..."
Abstract
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Cited by 738 (14 self)
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, ordinary and partial differential equations, qualitative differential equations, stochastic equations, and rule-based formalisms. In addition, the paper discusses how these formalisms have been used in the simulation of the behavior of actual regulatory systems.
Elastically deformable models
- Computer Graphics
, 1987
"... The goal of visual modeling research is to develop mathematical models and associated algorithms for the analysis and synthesis of visual information. Image analysis and synthesis characterize the domains of computer vision and computer graphics, respectively. For nearly three decades, the vision an ..."
Abstract
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Cited by 883 (20 self)
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to control the creation and evolution of models. Mathematically, the approach prescribes systems of dynamic (ordinary and partial) differential equations to govern model behavior. These equations of motion may be
Grounding in communication
- In
, 1991
"... We give a general analysis of a class of pairs of positive self-adjoint operators A and B for which A + XB has a limit (in strong resolvent sense) as h-10 which is an operator A, # A! Recently, Klauder [4] has discussed the following example: Let A be the operator-(d2/A2) + x2 on L2(R, dx) and let ..."
Abstract
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Cited by 1122 (20 self)
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B = 1 x 1-s. The eigenvectors and eigenvalues of A are, of course, well known to be the Hermite functions, H,(x), n = 0, l,... and E, = 2n + 1. Klauder then considers the eigenvectors of A + XB (A> 0) by manipulations with the ordinary differential equation (we consider the domain questions
AUTO97: Continuation and bifurcation software for ordinary differential equations (with HomCont)
, 1998
"... ..."
The Bifurcation of One or More Closed Orbits from an Equilibrium Point of an Autonomous Differential System*
, 1967
"... In the present paper we will consider an autonomous ordinary differential equation of the form 2 = P(E) x + X(x, E), (*> where x and X are real n-vectors in the Euclidean space ZP(n> 2), E> 0 ..."
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In the present paper we will consider an autonomous ordinary differential equation of the form 2 = P(E) x + X(x, E), (*> where x and X are real n-vectors in the Euclidean space ZP(n> 2), E> 0
Results 1 - 10
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