We address the parameterized complexity of Max Colorable Induced Subgraph on perfect graphs. The problem asks for a maximum sized q-colorable induced subgraph of an input graph G. Yannakakis and Gavril (Inf Process Lett ...

The generating function of partitions with repeated (resp. distinct) parts such that each odd part is less than twice the smallest part is shown to be the third order mock theta function ω(q) (resp. ν(−q)). Similar results ...

In this paper, we establish a nonlinear analogue of Picone’s identity for biharmonic operators on Heisenberg group. As an applications of Picone’s identity, we obtain Hardy-Rellich type inequality, Morse index, Caccioppoli ...

In this article, we study the Piltz divisor problem, which is sometimes called the generalized Dirichlet divisor problem, over number fields. We establish an identity akin to Vorono�'s formula concerning the error term in ...

In this article, we study the existence of positive solutions for the coupled elliptic system -Δu = λ (f(u; v) + h1(x)) in Ω -Δv = λ (g(u; v) + h2(x)) in Ω u = v = 0 on ∂Ω; under certain conditions on f; g and allowing h1; ...

In this paper we propose a model for computing a minimal free resolution for ideals of the form I1(XnYn), where Xn is an n n skew-symmetric matrix with indeterminate entries xij and Yn is a generic column matrix with ...

In this article, we survey some results on geometric methods to study quiver representations, and applications of these results to sheaves, equivariant sheaves and parabolic bundles.

In this paper, we study the effect of small Brownian noise on a switching dynamical system which models a first-order DC/DC buck converter. The state vector of this system comprises a continuous component whose dynamics ...

In this article, we obtain several remarks on the qualitative questions such as Picone’s identity, Morse index and Hardy-Rellich type inequality for biharmonic operators.