We establish the asymptotic behaviour of the least energy solutions of the following nonlocal Neumann problem:d(-∆)su + u = |u|p-1 u in Ω, Nsu = 0 in Rn \ Ω, u > 0 in Ω,where Ω ⊂ Rn is a bounded domain of class C1,1, 1 < ...

Conca and Varbaro (Invent. Math. 221 (2020), no. 3) showed the equality of depth of a graded ideal and its initial ideal in a polynomial ring when the initial ideal is square-free. In this paper, we give some beautiful ...

A modular relation of the form F(α,w)=F(β,iw), where i=√−1and αβ=1, is obtained. It involves the generalized digamma function ψw(a) which was recently studied by the authors in their work on developing the theory of the ...

Let Ω⊆Cm be a bounded connected open set and H⊆O(Ω) be an analytic Hilbert module, i.e., the Hilbert space H possesses a reproducing kernel K, the polynomial ring C[z]⊆H is dense and the point-wise multiplication induced ...

In this paper, we give the necessary and sufficient conditions for the Cohen-Macaulayness of the associated graded ring of a simplicial affine semigroups using Gröbner basis. We generalize the concept of homogeneous numerical ...

General summation formulas have been proved to be very useful in number theory and other branches of mathematics. The Lipschitz summation formula is one of them. In this paper, we give its application by providing a new ...

Let a and d be two linearly independent vectors in N2, over the field of rational numbers.For a positive integer k ≥2, consider the sequencea, a+d, . . . , a+kdsuch that the affine semigroupSa,d,k=〈a, a+d, . . . , a+kd〉is ...

Bhoria, Eyyunni and Maji recently obtained a four-parameter q-series identity which gives as special cases not only all five entries of Ramanujan on pages 354 and 355 of his second notebook but also allows them to obtain ...

We consider a nonlinear differential equation under the combined influence of small state-dependent Brownian perturbations of size ε, and fast periodic sampling with period δ; 0<ε,δ≪1. Thus, state samples (measurements) ...

Fix a Dedekind domain O and a non-zero prime p in it along with a uniformizer π. In the first part of the paper, we construct m-shifted π-typical Witt vectors Wmn(B) for any O algebra B of length m+n+1. They are a ...