In this paper, we investigate more relations between the symmetric residuated lattices $L$ with their corresponding intuitionistic fuzzy residuated lattice $tilde{L}$. It is shown that some algebraic structures of $L$ such as Heyting algebra, Glivenko residuated lattice and strict residuated lattice are preserved for $tilde{L}$. Examples are given for those structures that do not remain the sam...

These notes concentrate on the paradigm of spherical functions on Riemannian symmetric spaces. This paradigm has led to the notion of special functions associated with root systems. The first sections deal with older work on the interaction between spherical functions on rank one symmetric spaces and special functions (q=1) in one variable. The (spectacular) developments in the higher rank case...

We study the three point genus zero Gromov-Witten invariants on the Grassmannians which parametrize non-maximal isotropic subspaces in a vector space equipped with a nondegenerate symmetric or skew-symmetric form. We establish Pieri rules for the classical cohomology and the small quantum cohomology ring of these varieties, which give a combinatorial formula for the product of any Schubert clas...

The pseudo-perturbative shifted l expansion technique PSLET is shown applicable in the non-Hermitian PT symmetric context. The construction of bound states for several PT symmetric potentials is presented, with special attention paid to V (r) = ir3 − α √ ir oscillators.

Periodic or symmetric extensions are commonly used for processing images and other finitelength signals with a paraunitary Alter bank (PUFB). Unlike infinite-length signals, PUFBs applied to finite-length signals will not necessarily lead to an orthogonal system. We show that for symmetric extensions, orthogonality is only possible for special PUFBs based on linearphase Alters. We also discuss ...

A branch and bound algorithm for finding the minimal cost symmetric assignment is discussed. The matching problem in graph theory and the Chinese postman puzzle are all special cases of the symmetric assignment problem, and hence this algorithm can be applied to solve them.

The pseudo-perturbative shifted l expansion technique PSLET is shown applicable in the non-Hermitian PT symmetric context. The construction of bound states for several PT symmetric potentials is presented, with special attention paid to V (r) = ir3 − α √ ir oscillators.

For each skew shape we define a nonhomogeneous symmetric function, generalizing a construction of Pak and Postnikov [9]. In two special cases, we show that the coefficients of this function when expanded in the complete homogeneous basis are given in terms of the (reduced) type of k-divisible noncrossing partitions. Our work extends Haiman’s notion of a parking function symmetric function [5, 10].

In this paper, a pair of Wolfe type nondifferentiable second order symmetric minimax mixed integer dual problems is formulated. Symmetric and self-duality theorems are established under η1bonvexity/η2-boncavity assumptions. Several known results are obtained as special cases. Examples of such primal and dual problems are also given.

We establish the formula for multiplication by the class of a special Schubert variety in the integral cohomology ring of the flag manifold. This formula also describes the multiplication of a Schubert polynomial by either an elementary symmetric polynomial or a complete homogeneous symmetric polynomial. Thus, we generalize the classical Pieri’s rule for symmetric polynomials/Grassmann varietie...