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385
The knowledge complexity of interactive proof systems

, 1989
"... Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/nonHamiltonian. In th ..."
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Cited by 1246 (39 self)
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Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/nonHamiltonian
On Diagonal Elliptic and Parabolic Systems with SuperQuadratic Hamiltonians
"... gemeinschaft getragenen Sonderforschungsbereichs 611 an der Universität ..."
Abstract

Cited by 15 (1 self)
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gemeinschaft getragenen Sonderforschungsbereichs 611 an der Universität
PATHINTEGRAL FOR QUADRATIC HAMILTONIAN SYSTEMS AND BOUNDARY CONDITIONS
, 1998
"... A pathintegral representation for the kernel of the evolution operator of general Hamiltonian systems is reviewed. We study the models with bosonic and fermionic degrees of freedom. A general scheme for introducing boundary conditions in the pathintegral is given. We calculate the pathintegral fo ..."
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integral for the systems with quadratic first class constraints and present an explicit formula for the heat kernel (HK) in this case. These results may be applied to many quantum systems which can be reduced to the Hamiltonian systems with quadratic constraints (confined quarks, Calogero type models, string and p
The Cyclicity of Period Annulus of Degenerate Quadratic Hamiltonian System with Elliptic Segment
"... We study the cyclicity of period annuli (or annulus) for general degenerate quadratic Hamiltonian systems with an elliptic segment or a saddle loop, under quadratic perturbations. By using geometrical arguments and studying the respective Abelian integral based on the PicardFuchs equation, it is sh ..."
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Cited by 2 (1 self)
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We study the cyclicity of period annuli (or annulus) for general degenerate quadratic Hamiltonian systems with an elliptic segment or a saddle loop, under quadratic perturbations. By using geometrical arguments and studying the respective Abelian integral based on the PicardFuchs equation
On the Number of Limit Cycles of a Piecewise Quadratic NearHamiltonian System
"... This paper is concerned with the problem for the maximal number of limit cycles for a quadratic piecewise nearHamiltonian system. By using the method of the first order Melnikov function, we find that it can have 8 limit cycles. ..."
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This paper is concerned with the problem for the maximal number of limit cycles for a quadratic piecewise nearHamiltonian system. By using the method of the first order Melnikov function, we find that it can have 8 limit cycles.
Tomography of multimode quantum systems with quadratic Hamiltonians and multivariable Hermite polynomials
, 2001
"... The systems with multimode nonstationary Hamiltonians quadratic in position and momentum operators are reviewed. The tomographic probability distributions (tomograms) for the Fock states and Gaussian states of the quadratic systems are discussed. The tomograms for the Fock states are expressed in te ..."
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The systems with multimode nonstationary Hamiltonians quadratic in position and momentum operators are reviewed. The tomographic probability distributions (tomograms) for the Fock states and Gaussian states of the quadratic systems are discussed. The tomograms for the Fock states are expressed
Gaussian Stochastic Linearization for Open Quantum Systems Using Quadratic Approximation of Hamiltonians∗
"... Abstract This paper extends the energybased version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential equations with nonquadratic Hamiltonians. The linear ..."
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Abstract This paper extends the energybased version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential equations with nonquadratic Hamiltonians
The cyclicity of the period annulus of the quadratic Hamiltonian systems with nonMorsean point
 J. Differential Equations
"... ar ..."
Definiteness of quadratic functionals for Hamiltonian and symplectic systems: A survey
, 2009
"... Abstract In this paper we provide a survey of characterizations of the nonnegativity and positivity of quadratic functionals arising in the theory of linear Hamiltonian and symplectic systems. We study these functionals on traditional continuous time domain (under and without controllability), on d ..."
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Abstract In this paper we provide a survey of characterizations of the nonnegativity and positivity of quadratic functionals arising in the theory of linear Hamiltonian and symplectic systems. We study these functionals on traditional continuous time domain (under and without controllability
Secondorder analysis in polynomially perturbed reversible quadratic Hamiltonian systems
, 1999
"... Abstract. We study degree n polynomial perturbations of quadratic reversible Hamiltonian vector fields with one center and one saddle point. It was recently proved that if the first Poincaré–Pontryagin integral is not identically zero, then the exact upper bound for the number of limit cycles on th ..."
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Cited by 1 (1 self)
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Abstract. We study degree n polynomial perturbations of quadratic reversible Hamiltonian vector fields with one center and one saddle point. It was recently proved that if the first Poincaré–Pontryagin integral is not identically zero, then the exact upper bound for the number of limit cycles
Results 1  10
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385