In this paper, we present some fixed point theorems for single valued mappings on $K$-complete, $M$-complete and Symth complete quasi metric spaces. Here, for contractive condition, we consider some altering distance functions together with functions belonging to $C$-class and $A$-class. At the same time, we will consider two different type $M$ functions in contractive conditions because the qu...

In this article, we propose a few sufficient conditions on polynomials having integer coefficients all of whose zeros lie outside closed disk centered at the origin in complex plane and deduce irreducibility over ring integers.

In this paper we investigate a new family of multivariable polynomials. These polynomials, denoted Rλ(z1, . . . , zn; r), depend on a parameter r and are indexed by a partition λ of length n. Up to a scalar, Rλ is characterized by the following elementary properties: • Rλ is symmetric in the odd variables z1, z3, z5, . . . as well as in the even variables z2, z4, z6, . . .. Polynomials having t...

We observe that the Poincaré duality isomorphism for a string manifold is an isomorphism of modules over the subalgebra A(2) of the modulo 2 Steenrod algebra. In particular, the pattern of the operations Sq, Sq, and Sq on the cohomology of a string manifold has a symmetry around the middle dimension. We characterize this kind of cohomology operation duality in term of the annihilator of the Tho...