In this paper, we establish the existence of a positive solution to
{−M+λ,Λ(D2u)=μk(x)f(u)uα−ηh(x)uqu=0in Ωon ∂Ω,
{−Mλ,Λ+(D2u)=μk(x)f(u)uα−ηh(x)uqin Ωu=0on ∂Ω,
where ΩΩ is a smooth bounded domain in Rn, n≥1.Rn, n≥1. ...
Dixit, Atul; Glasser, M. Lawrence; Moll, Victor H.; Vignat, Christophe(SpringerOpen, 2017-07)
In 1998 Don Zagier introduced the modified Bernoulli numbers B∗nBn∗ and showed that they satisfy amusing variants of some properties of Bernoulli numbers. In particular, he studied the asymptotic behavior of B∗2nB2n∗, and ...
Berndt, Bruce C..; Dixit, Atul; Kim, Sun; Zaharescu, Alexandru(American Mathematical Society, 2017-04)
Let $ r_k(n)$ denote the number of representations of the positive integer $ n$ as the sum of $ k$ squares. In 1934, the Russian mathematician A. I. Popov stated, but did not rigorously prove, a beautiful series transformation ...
Kour, Surjeet(Cornell University Library, 2017-01)
Let G be a finite group and M,N be two normal subgroups of G. Let AutMN(G) denote the group of all automorphisms of G which fix N element wise and act trivially on G/M. Let n be a positive integer. In this article we have ...
Pahlajani, Chetan D.(American Institute of Mathematical Sciences, 2017-03)
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 ...
Sengupta, Indranath; Saha, Joydip; Tripathi, Gaurab(Cornell University Library, 2016-11)
In this paper we compute the Betti numbers for ideals of the form I1(XY)+J, where X and Y are matrices and J is the ideal generated by the 2×2 minors of the matrix consisting of any two rows of X.
Sengupta, Indranath; Tripathi, Gaurab; Saha, Joydip(Cornell University Library, 2016-10)
In this paper we prove the primality of certain ideals which
are generated by homogeneous degree 2 polynomials and occur naturally
from determinantal conditions
Dixit, Atul; Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru(Cornell University Library, 2016-10)
Let rk(n) denote the number of representations of the positive integer n as the sum of k squares. In 1934, the Russian mathematician A. I. Popov stated, but did not rigorously prove, a beautiful series transformation ...