In this article, we prove that the Gelfand-Kirillov dimension of the quantized algebra of regular functions on certain homogeneous spaces of types $ A$, $ C$, and $ D$ is equal to the dimension of the homogeneous space as ...
Dixit, Atul; Maji, Bibekananda(Cambridge University Press, 2019-02)
It is pointed out that the generalized Lambert series��studied by Kanemitsu, Tanigawa and Yoshimoto can be found on page 332 of Ramanujan's Lost Notebook in a slightly more general form. We extend an important transformation ...
Gupta, Madhu; Mishra, Rohit Kumar; Roy, Souvik(Cornell University Library, 2019-03)
A new non-linear optimization approach is proposed for the sparse reconstruction of log-conductivities in current density impedance imaging. This framework comprises of minimizing an objective functional involving a least ...
In this article, we survey some results on geometric methods to study quiver representations, and applications of these results to sheaves, equivariant sheaves and parabolic bundles.
Amrutiya, Sanjay(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. ...
Tyagi, Jagmohan(European Mathematical Society (EMS), 2018-10)
In this note, we establish Leighton's variational lemma for fractional Laplace equations. We use the classical techniques to establish this variational lemma. We also point out several questions concerning the zeros of the ...
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 ...
Berndt, Bruce C.; Dixit, Atul; Kim, Sun; Zaharescu, Alexandru(Elsevier, 2018-11)
Letrk(n) denote the number of representations of the positive integernas thesum ofksquares. We rigorously prove for the first time a Vorono ?? summation formula forrk(n), k?2,proved incorrectly by A. I. Popov and later ...
Mehta, Ranjana; Saha, Joydip; Sengupta, Indranath(Association for Computing Machinery, 2018-08)
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 ...
Amrutiya, Sanjay; Dubey, Umesh(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 ...