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 ...
Let m = (m0, m1, m2, n) be an almost arithmetic sequence, i.e., a sequence of positive integers with gcd(m0, m1, m2, n) = 1, such that m0 < m1 < m2 form an arithmetic progression, n is arbitrary and they minimally generate ...
Berndt, Bruce C.; Dixit, Atul; Roy, Arindam; Zaharescu, Alexandru(Cornell University Library, 2016-08)
We focus on three pages in Ramanujan's lost notebook, pages 336, 335, and 332, in decreasing order of attention. On page 336, Ramanujan proposes two identities, but the formulas are wrong -- each is vitiated by divergent ...
Srivastava, Akanksha(Springer International Publishing, 2016-08)
In this article, a modification of Newton’s method with fifteenth-order convergence is presented. The modification of Newton’s method is based on the method of fifth-order convergence of Hu et al. First, we present theoretical ...
Banerjee, Koustav; Dixit, Atul(Cornell University Library, 2016-07)
Two new representations for Ramanujan's function σ(q) are obtained. The proof of the first one uses the three-variable reciprocity theorem due to Soon-Yi Kang and a transformation due to R.P. Agarwal while that of the ...
Dixit, Atul; Glasser, M. Lawrence; Moll, Victor H.; Vignat, Christophe(Springer, 2016-12)
In 1998 Don Zagier introduced the modified Bernoulli numbers B∗n and showed that they satisfy amusing variants of some properties of Bernoulli numbers. In particular, he studied the asymptotic behavior of B∗2n, and also ...