In this paper, we explicitly compute the derivation module of quotients of polynomial rings by ideals formed by the sum or by some other gluing technique. We discuss cases of monomial ideals and binomial ideals separately.

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 ...

By the method of monotone iteration and Schauder fixed point theorem, we prove the existence of non-negative solutions to the system = for λ sufficiently small, where is a bounded domain in RN with smooth boundary ∂Ω and ...

In this article, we study the existence and multiplicity of nontrivial solutions to the problem    − 2F(x, D2u) = f(x, u) + ψ(Du) in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in R n, n > 2. We show ...

An exact transformation, which we call the master identity, is obtained for the first time for the series ∑∞n=1σa(n)e-ny for a∈C and Re(y)>0. New modular-type transformations when a is a nonzero even integer are obtained ...

The aim of this paper is to establish singular fractional Adams–Moser–Trudinger inequality for both bounded and unbounded domains in the Heisenberg group We first establish fractional Adams–Moser–Trudinger type inequality ...

In this article, we prove that the Gelfand-Kirillov dimension of the quantized algebra of regular functions on certain homogeneous spaces of types $ A$, $ C$, and $ D$ is equal to the dimension of the homogeneous space as ...

George Andrews and Ae Ja Yee recently established beautiful results involving bivariate generalizations of the third-order mock theta functions ω(q) and ν(q), thereby extending their earlier results with the second author. ...