In this paper, we establish exact solutions for nonlinear evolution equations. The homogeneous balance method is used to construct exact travelling wave solutions of the CalogeroDegasperis (CD) and Potential Kadomstev-Petviashvili (PKP) equations, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation. Many new f...

Under the travelling wave transformation, Calogero-Degasperis-Focas equation was reduced to an ordinary differential equation. Using a symmetry group of one-parameter, this ODE was reduced to a second order linear inhomogeneous ODE. Furthermore, we applied the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classific...

Using a technique based on the Yangian Gelfand-Zetlin algebra and the associated Yangian Gelfand-Zetlin bases we construct an orthogonal basis of eigenvectors in the Calogero-Sutherland Model with spin, and derive product-type formulas for norms of these eigenvectors. 1 e-mail: [email protected] 2 e-mail: [email protected]

Heckman-Opdam system of differential equations is holonomic , with regular singularities and has locally |W |-dimensional space of solutions ( cf. corollary 3.9 of [12]), where |W | is the cardinality of the Weyl group W . The system is a generalization of radial parts of Laplace-Casimir operators on symmetric Riemannian spaces of nonpositive curvature and is isomorphic to Calogero-Sutherland m...

We find a complete set of supertraces on the algebras H W (R) (ν), the algebra of observables of the rational Calogero model with harmonic interaction based on the classical root systems R of B N , C N and D N types. These results extend the results known for the case A N −1. It is shown that H W (R) (ν) admits q(R) independent supertraces where q(B N) = q(C N) is a number of partitions of N in...

We study properties of coefficients of a linear form, originating from a multiple integral. As a corollary, we prove Vasilyev's conjecture, connected with the problem of irrationality of the Riemann zeta function at odd integers.

In 1957, H. Hadwiger conjectured that a convex body K in a Euclidean d-space, d 1, can always be covered by 2 smaller homothetic copies of K. We verify this conjecture when K is the polar of a cyclic d-polytope. Mathematics Subject Classifications (1991): 52A15, 52A20.

We review some recent results on quasi-exactly solvable spin models presenting near-neighbors interactions. These systems can be understood as cyclic generalizations of the usual Calogero–Sutherland models. A nontrivial modification of the exchange operator formalism is used to obtain several infinite families of eigenfunctions of these models in closed form.

We prove an equivariant version of the fact that word-hyperbolic groups have finite asymptotic dimension. This is important in connection with our forthcoming proof of the Farrell-Jones conjecture for K∗(RG) for every word-hyperbolic group G and every coefficient ring R.

A robust method for the reconstruction of 3D object shape is described based on the inverse perspective method [1,2], which uses a single camera mounted on a commercial manipulator arm for accurate 3D positioning and orientation of the sensor head in 3D space. Preliminary measurements are presented and the reconstruction theory used by the technique.