let $p$ be a complex polynomial of the form $p(z)=zdisplaystyleprod_{k=1}^{n-1}(z-z_{k})$,where $|z_k|ge 1,1le kle n-1$ then $ p^prime(z)ne 0$. if $|z|

Assuming that every proper minor closed class of graphs contains a maximum with respect to the homomorphism order, we prove that such a maximum must be homomorphically equivalent to a complete graph. This proves that Hadwiger’s conjecture is equivalent to saying that every minor closed class of graphs contains a maximum with respect to homomorphism order. Let F be a finite set of 2-connected gr...

Let Fq be the finite field with q elements, A := Fq[T ] and F := Fq(T ). Let φ be a Drinfeld A-module over F with trivial endomorphism ring. We prove analogues of the Erdös and Halberstam Theorems for φ. If φ has rank ≥ 3, we assume the validity of the Mumford-Tate Conjecture for φ. 1

Through an h̄-expansion of the confined Calogero model with spin exchange interactions, we extract a generating function for the involutive conserved charges of the FrahmPolychronakos spin chain. The resulting conservation laws possess the spin chain yangian symmetry, although they are not expressible in terms of these yangians. 08/00 (revised: 02/01) 1 Work supported by NSERC (Canada) and FCAR ...

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]...

We demonstrate that Coxeter groups allow for complex PT -symmetric deformations across the boundaries of all Weyl chambers. We compute the explicit deformations for the A2 and G2-Coxeter group and apply these constructions to Calogero-MoserSutherland models invariant under the extended Coxeter groups. The eigenspecta for the deformed models are real and contain the spectra of the undeformed cas...

The general KdV equation (gKdV) derived by T. Chou is one of the famous (1 + 1) dimensional soliton equations with variable coefficients. It is well-known that the gKdV equation is integrable. In this paper a higher-dimensional gKdV equation, which is integrable in the sense of the Painlevé test, is presented. A transformation that links this equation to the canonical form of the Calogero–Bogoy...

We construct families of Hamiltonians extending the Calogero model and such that a finite number of eigenvectors can be computed algebraically.

It is shown that Rota’s basis conjecture follows from a similar conjecture that involves just three bases instead of n bases.