We prove that an excluded minor for the class of GF(q)-representable matroids cannot contain a large projective geometry over GF(q) as a minor. © 2005 Elsevier Inc. All rights reserved.

In this article, we give new proofs on the some cases on Weinstein conjecture and get some new results on Weinstein conjecture.

We show that the three body Calogero model with inverse square potentials can be interpreted as a maximally superintegrable and multiseparable system in Euclidean three-space. As such it is a special case of a family of systems involving one arbitrary function of one variable. Indexing Codes: 02.30Ik, 02.40.Ky, 02.20.Hj Electronic mail: [email protected] Electronic mail: [email protected]...

In this paper, we introduce and study the notion of a partial n-hypergroupoid, associated with a binary relation. Some important results concerning Rosenberg partial hypergroupoids, induced by relations, are generalized to the case of n-hypergroupoids. Then, n-hypergroups associated with union, intersection, products of relations and also mutually associative n-hypergroupoids are analyzed. Fina...

We identify the Bethe algebra of the Gaudin model associated to gl N acting on a suitable representation with the center of the rational Cherednik algebra and with the algebra of regular functions on the Calogero-Moser space.

Operators that intertwine representations of a degenerate version of the double affine Hecke algebra are introduced. Each of the representations is related to multivariable orthogonal polynomials associated with Calogero-Sutherland type models. As applications, raising operators and shift operators for such polynomials are constructed.

The purpose of this paper is twofold. First we derive theoretically, using appropriate transformation on x(n), the closed-form solution of the nonlinear difference equation x(n+1) = 1/(±1 + x(n)), n ∈ N_0. The form of solution of this equation, however, was first obtained in [10] but through induction principle. Then, with the solution of the above equation at hand, we prove a case ...

In this paper, we show that for any finite order entire function $f(z)$, the function of the form $f(z)^{n}[f(z+c)-f(z)]^{s}$ has no nonzero finite Picard exceptional value for all nonnegative integers $n, s$ satisfying $ngeq 3$, which can be viewed as a different result on Hayman conjecture. We also obtain some uniqueness theorems for difference polynomials of entire functions sharing one comm...

‎By the Mordell‎- ‎Weil theorem‎, ‎the group of rational points on an elliptic curve over a number field is a finitely generated abelian group‎. ‎This paper studies the rank of the family Epq:y2=x3-pqx of elliptic curves‎, ‎where p and q are distinct primes‎. ‎We give infinite families of elliptic curves of the form y2=x3-pqx with rank two‎, ‎three and four‎, ‎assuming a conjecture of Schinzel ...