# Browsing E-print Articles by Title

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• (Cornell University Library, 2016-06)
In this paper, we discuss the distributed control problem governed by the following parabolic integro-differential equation (PIDE) in the abstract form ∂y∂t+Ayy(0)==∫t0B(t,s)y(s)ds+Gu,t∈[0,T],(∗)y0∈X, where, y denotes ...
• (Cornell University Library, 2018-01)
Bresinsky defined a class of monomial curves in A4 with the property that the minimal number of generators or the first Betti number of the defining ideal is unbounded above. We prove that the same behaviour of unboundedness ...
• (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.
• (Cornell University Library, 2018-02)
Suppose e≥4 be an integer, a=e+1, b>a+(e−3)d, gcd(a,d)=1 and d∤(b−a). Let M={a,a+d,a+2d,…,a+(e−3)d,b,b+d}, which forms a minimal generating set for the numerical semigroup Γe(M), generated by the set M. We calculate the ...
• (Cornell University Library, 2018-01)
A comprehensive study of the generalized Lambert series ∑n=1∞nN−2hexp(−anNx)1−exp(−nNx),0<a≤1, x>0, N∈N and h∈Z, is undertaken. Two of the general transformations of this series that we obtain here lead to two-parameter ...
• (Cornell University Library, 2017-06)
• (Cornell University Library, 2018-10)
Recently Dixit, Kesarwani, and Moll introduced a generalization Kz,w(x) of the modified Bessel function Kz(x) and showed that it satisfies an elegant theory similar to Kz(x). In this paper, we show that while K12(x) is an ...
• (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 ...
• (Cornell University Library, 2017-06)
• (Cornell University Library, 2015-03)
Let \$\mm=(m_0,m_1,m_2,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 the ...
• (Cornell University Library, 2018-08)
In this note, we give a construction of the moduli space of filtered repre- sentations of a given quiver of fixed dimension vector with the appropriate notion of stability. The construction of the moduli of filtered ...
• (Cornell University Library, 2018-07)
• (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 ...
• (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 ...
• (Max Planck Institute for Mathematics in the Sciences, 2012)
This paper deals with the approximation of d-dimensional tensors, as discrete representations of arbitrary functions f(x1; : : : ; xd) on [0;1]d, in the so-called Tensor Chain format. The main goal of this paper is to ...
• (Cornell University Library, 2018-10)
In this note, we prove that the F-fundamental group scheme is birational invariant for smooth projective varieties. We prove that the F-fundamental group scheme is naturally a quotient of the Nori fundamental group scheme. ...
• (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 ...
• (Cornell University Library, 2015-05)
Let G=H×A be a finite group, where H is a purely non-abelian subgroup of G and A is a non-trivial abelian factor of G. Then, for n≥2, we show that there exists an isomorphism ϕ:Autγn(G)Z(G)(G)→Autγn(H)Z(H)(H) such that ...
• (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 ...
• (Cornell University Library, 2016-06)
In this paper, we consider the bifurcation problem for fractional Laplace equation (−Δ)su=λu+f(λ,x,u)in Ω,u=0in Rn∖Ω, where Ω⊂Rn,n>2s(0<s<1) is an open bounded subset with smooth boundary, (−Δ)s stands for the fractional ...