We introduce a Laplace-Beltrami type operator on the Fock space of symmetric functions and show that the Jack symmetric functions are the only family of eigenvectors of the differential operator, thus giving a new characterization of Jack polynomials. This was achieved by explicit computation of its action on generalized homogeneous symmetric functions. Using this new method we give a combinato...

Some estimates are proved for the generalized Fourier-Bessel transform in the space (L^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.

The controllability of viscoelastic fields is a fundamental concept that defines some essential capabilities and limitations of the resulting materials. In this paper, we study the controllability of different homogeneous flow fields of viscoelastic fluids governed by the upper convected Maxwell model. The approach is largely based on the nonlinear geometric control theory. Through the analysis...

we prove the generalized hyers--ulam stability  of n--th order linear differential equation of the form $y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x)$, with condition that there exists a non--zero solution of corresponding homogeneous equation. our main results extend and improve the corresponding results obtained by many authors.

where ∆pu= div(|∇u|p−2∇u) is the p-Laplacian, 1 < p <∞. ByW1,p(Ω) we denote the usual Sobolev space with dual space (W1,p(Ω))∗, andW 0 (Ω) denotes its subspace whose elements have generalized homogeneous boundary values and whose dual space is given by W−1,p(Ω). We assume the following growth and asymptotic behaviour of the nonlinear right-hand side f of (1.1): (H1) f :Ω×R → R is a Carathéodory...

We describe presentations of the Roger-Yang generalized skein algebras for punctured spheres with an arbitrary number punctures. This algebra is a quantization decorated Teichmuller space and generalizes construction Kauffman bracket algebra. In this paper, we also obtain new interpretation homogeneous coordinate ring Grassmannian planes in terms theory.

flood frequency analysis is faced with the problem of data and information limitation in arid and semi-arid regions. particularly in these regions, the length of records is usually too short to ensure reliable quantile estimates. more than 75% of iran is located in arid and semi-arid regions and despite the low annual precipitation, often large floods occur. one way to provide more information ...