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 ...
Dixit, Atul; Kesarwani, Aashita; Moll, Victor H.(Elsevier, 2017-10)
A new generalization of the modified Bessel function of the second kind is studied. Elegant series and integral representations, a differential-difference equation and asymptotic expansions are obtained for it thereby ...
To study the su ciency of an optimization problem, one either imposes
some convexity assumptions or consider second order optimality conditions. In this
paper we establish second order optimality conditions for nonsmooth ...
Ghosh, Avirup; Mishra, Rohit(Cornell University Library, 2017-10)
The change in Holographic entanglement entropy (HEE) for small fluctuations about pure AdS are obtained by a perturbative expansion of the area functional in terms of the change in the bulk metric and the embedded extremal ...
Dwivedi, Gaurav(Indian Institute of Technology Gandhinagar, 2017)
The present work in the thesis deals with the existence and qualitative questions to biharmonic boundary value problems. More specifically, we establish the existence of solution to several type of biharmonic equations and ...
This article deals with the study of sign-changing solutions of the nonlinear singularly perturbed reaction-diffusion equation. Sign changing solutions of the nonlinear problem do not appear to have been previously studied ...
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 ...
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 ...