Let A be an unique factorization domain containing a field k of characteristic zero and let A[X] and A[Y ] be two k-algebras. Let d1 and d2 be two generalized triangular k-derivations of A[X] and A[Y ], respectively. Denote ...

In this article, we prove that the Faltings theta functions on moduli of parabolic bundles over a smooth projective curve can be used to give an explicit scheme-theoretic projective embedding.

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 ...

We give character analogues of a generalization of a result due to Ramanujan, Hardy and Littlewood, and provide Riesz-type criteria for Riemann Hypotheses for the Riemann zeta function and Dirichlet L-functions. We also ...

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.

This paper develops a framework for analyzing the performance loss in fixed time interval decision algorithms that are based on observations of time-inhomogeneous Poisson processes, when some parameters characterizing the ...

A collection of static and mobile radiation sensors is tasked with deciding, within a fixed time interval, whether a moving target carries radioactive material. Formally, this is a problem of detecting weak time-inhomogeneous ...

In this note, we discuss an eigenvalue problem involving Hardy's potential with homogeneous Dirichlet boundary condition in a smooth bounded domain. We show that the problem possesses a continuous family of eigenvalues.

In this paper we study the existence of solutions to the following semilinear elliptic problem TeX where TeX is an open bounded subset of TeX and TeX The special feature of this problem is that it has singularity at the ...

we first show the existence of a positive solution to −Δpu−αΔu=λ(u− f(u)) inΩ, u=0 on ∂Ω, by the method of lower and upper solutions and then under certain conditions on f , we show the stability of positive solution.