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Rational Solution of the KZ equation (example)
, 2006
"... We investigate the KnizhnikZamolodchikov linear differential system. The coefficients of this system are rational functions. We prove that the solution of the KZ system is rational when k is equal to two and n is equal to three. While doing so, we found the coefficients of expansion in a neighborho ..."
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We investigate the KnizhnikZamolodchikov linear differential system. The coefficients of this system are rational functions. We prove that the solution of the KZ system is rational when k is equal to two and n is equal to three. While doing so, we found the coefficients of expansion in a
Rational solutions of firstorder differential equations
 Annales Acad. Sci. Fennicae., Math
, 1998
"... We prove that degrees of rational solutions of an algebraic differential equation F(dw/dz, w, z) = 0 are bounded. For given F an upper bound for degrees can be determined explicitly. This implies that one can find all rational solutions by solving algebraic equations. Consider the differential equa ..."
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Cited by 4 (0 self)
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We prove that degrees of rational solutions of an algebraic differential equation F(dw/dz, w, z) = 0 are bounded. For given F an upper bound for degrees can be determined explicitly. This implies that one can find all rational solutions by solving algebraic equations. Consider the differential
Rational solutions of Riccatilike partial differential equations
 J. Symbolic Comput
, 2001
"... Abstract. When factoring linear partial differential systems with a finitedimensional solution space or analyzing symmetries of nonlinear ode’s, we need to look for rational solutions of certain nonlinear pde’s. The nonlinear pde’s are called Riccatilike because they arise in a similar way as Ricc ..."
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Cited by 12 (2 self)
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Abstract. When factoring linear partial differential systems with a finitedimensional solution space or analyzing symmetries of nonlinear ode’s, we need to look for rational solutions of certain nonlinear pde’s. The nonlinear pde’s are called Riccatilike because they arise in a similar way
A FOURPARAMETRIC RATIONAL SOLUTION TO PAINLEVÉ VI
, 2008
"... The seminal paper by Okamoto [3] showed how to get a sequence of rational solutions to Painlevé VI if you start with a rational seed solution. But Okamoto did not even write down the Bäcklund transformation. This is understandable since its denominator is of degree 6 in p and q. Today we have Maple ..."
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The seminal paper by Okamoto [3] showed how to get a sequence of rational solutions to Painlevé VI if you start with a rational seed solution. But Okamoto did not even write down the Bäcklund transformation. This is understandable since its denominator is of degree 6 in p and q. Today we have Maple to
THE RATIONAL SOLUTIONS OF THE MIXED NONLINEAR SCHRÖDINGER EQUATION
"... Abstract. The mixed nonlinear Schrödinger (MNLS) equation is a model for the propagation of the Alfvén wave in plasmas and the ultrashort light pulse in optical fibers with two nonlinear effects of selfsteepening and self phasemodulation(SPM), which is also the first nontrivial flow of the inte ..."
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and determinant representation. Starting from a periodic seed(plane wave), rational solutions with two parameters a and b of the MNLS equation are constructed by the DT and the Taylor expansion. Two parameters denote the contributions of two nonlinear effects in solutions. We show an unusual result: for a given
Rational Solutions of the Sasano System of Type A (2)
, 2010
"... doi:10.3842/SIGMA.2011.030 Abstract. In this paper, we completely classify the rational solutions of the Sasano system, which is given by the coupled Painlevé III system. This system of differential of type A (2) 5 equations has the affine Weyl group symmetry of type A (2) ..."
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doi:10.3842/SIGMA.2011.030 Abstract. In this paper, we completely classify the rational solutions of the Sasano system, which is given by the coupled Painlevé III system. This system of differential of type A (2) 5 equations has the affine Weyl group symmetry of type A (2)
Plans And ResourceBounded Practical Reasoning
 COMPUTATIONAL INTELLIGENCE, 4(4):349355, 1988
, 1988
"... An architecture for a rational agent must allow for meansend reasoning, for the weighing of competing alternatives, and for interactions between these two forms of reasoning. Such an architecture must also address the problem of resource boundedness. We sketch a solution of the first problem that p ..."
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Cited by 488 (19 self)
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An architecture for a rational agent must allow for meansend reasoning, for the weighing of competing alternatives, and for interactions between these two forms of reasoning. Such an architecture must also address the problem of resource boundedness. We sketch a solution of the first problem
Computing rational solutions of linear matrix inequalities
 ISSAC'13
, 2013
"... Consider a (D × D) symmetric matrix A whose entries are linear forms in Q[X1,..., Xk] with coefficients of bit size ≤ τ. We provide an algorithm which decides the existence of rational solutions to the linear matrix inequality A ≽ 0 and outputs such a rational solution if it exists. This problem is ..."
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Cited by 3 (2 self)
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Consider a (D × D) symmetric matrix A whose entries are linear forms in Q[X1,..., Xk] with coefficients of bit size ≤ τ. We provide an algorithm which decides the existence of rational solutions to the linear matrix inequality A ≽ 0 and outputs such a rational solution if it exists. This problem
Hankel Determinant structure of the Rational Solutions for Painlevé Five
, 904
"... In this paper, we construct the Hankel determinant representation of the rational solutions for the fifth Painlevé equation through the Umemura polynomials. Our construction gives an explicit form of the Umemura polynomials σn for n ≥ 0 in terms of the Hankel Determinant formula. Besides, this resul ..."
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In this paper, we construct the Hankel determinant representation of the rational solutions for the fifth Painlevé equation through the Umemura polynomials. Our construction gives an explicit form of the Umemura polynomials σn for n ≥ 0 in terms of the Hankel Determinant formula. Besides
Results 11  20
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