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Results 1 - 10
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204
Integral Quartic Cayley Graphs on Abelian Groups
"... A graph is called integral, if its adjacency eigenvalues are integers. In this paper we determine integral quartic Cayley graphs on finite abelian groups. As a side result we show that there are exactly 27 connected integral Cayley graphs up to 11 vertices. 1 ..."
Abstract
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Cited by 3 (2 self)
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A graph is called integral, if its adjacency eigenvalues are integers. In this paper we determine integral quartic Cayley graphs on finite abelian groups. As a side result we show that there are exactly 27 connected integral Cayley graphs up to 11 vertices. 1
On integrable system on S 2 with the second integral quartic in the momenta.
, 2004
"... We consider integrable system on the sphere S 2 with an additional integral of fourth order in the momenta. At the special values of parameters this system coincides with the Kowalevski-Goryachev-Chaplygin system. 1 ..."
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We consider integrable system on the sphere S 2 with an additional integral of fourth order in the momenta. At the special values of parameters this system coincides with the Kowalevski-Goryachev-Chaplygin system. 1
Integrable Quartic Potentials and Coupled KdV Equations
, 2008
"... We show a surprising connection between known integrable Hamiltonian systems with quartic potential and the stationary flows of some coupled KdV systems related to fourth order Lax operators. In particular, we present a connection between the Hirota-Satsuma coupled KdV system and (a generalisation o ..."
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We show a surprising connection between known integrable Hamiltonian systems with quartic potential and the stationary flows of some coupled KdV systems related to fourth order Lax operators. In particular, we present a connection between the Hirota-Satsuma coupled KdV system and (a generalisation
Computation of an Integral Basis of Quartic
, 907
"... In this paper, based on techniques of Newton polygons, a result which allows the computation of a p integral basis of every quartic number field is given. For each prime integer p, this result allows to compute a p-integral basis of a quartic number field K defined by an irreducible polynomial P(X) ..."
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In this paper, based on techniques of Newton polygons, a result which allows the computation of a p integral basis of every quartic number field is given. For each prime integer p, this result allows to compute a p-integral basis of a quartic number field K defined by an irreducible polynomial P
Quartic Thue Equations Quartic Thue Equations
"... Abstract We will give upper bounds upon the number of integral solutions to binary quartic Thue equations. We will also study the geometric properties of a specific family of binary quartic Thue equations to establish sharper upper bounds. ..."
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Abstract We will give upper bounds upon the number of integral solutions to binary quartic Thue equations. We will also study the geometric properties of a specific family of binary quartic Thue equations to establish sharper upper bounds.
Integrable systems of quartic oscillators. II
, 2004
"... Several completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion (“acceleration equal force”), with linear and cubic forces, in N-dimensional space (N being an arbitrary positive integer, with special attention to N = 2, nam ..."
Abstract
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Cited by 1 (1 self)
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Several completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion (“acceleration equal force”), with linear and cubic forces, in N-dimensional space (N being an arbitrary positive integer, with special attention to N = 2
Quasi-exactly solvable quartic: elementary integrals and asymptotics
, 2011
"... Littlewood, when he makes use of an algebraic identity, always saves himself the trouble of proving it; he maintains that an identity, if true, can be verified in few lines by anybody obtuse enough to feel the need of verification. Freeman Dyson [7] We study elementary eigenfunctions y = pe h of ope ..."
Abstract
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Cited by 6 (6 self)
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of operators L(y) = y ′ ′ + Py, where p, h and P are polynomials in one variable. For the case when h is an odd cubic polynomial, we investigate the real level crossing points and asymptotics of eigenvalues. This study leads to an interesting identity with elementary integrals.
Connected Quartic Bipartite Cayley Integral Graphs
"... Here, for the first time, all connected quartic bi-partite Cayley integral graphs are given includ-ing all non-obvious * isomorphisms. Computations used previous results showing that all connected quartic bipartite integral graphs have one of 43 possible values for the number of vertices, all fallin ..."
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Here, for the first time, all connected quartic bi-partite Cayley integral graphs are given includ-ing all non-obvious * isomorphisms. Computations used previous results showing that all connected quartic bipartite integral graphs have one of 43 possible values for the number of vertices, all
Results 1 - 10
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204
