An exact transformation, which we call the master identity, is obtained for the first time for the series ∑∞n=1σa(n)e-ny for a∈C and Re(y)>0. New modular-type transformations when a is a nonzero even integer are obtained ...
Dhama, Shivam; Pahlajani, Chetan D.(Cornell University Library, 2022-05)
We consider a nonlinear differential equation under the combined influence of small state-dependent Brownian perturbations of size ε, and fast periodic sampling with period δ; 0<ε,δ≪1. Thus, state samples (measurements) ...
Banerjee, Soumyarup; Dixit, Atul; Gupta, Shivajee(Cornell University Library, 2022-05)
An explicit transformation for the series ∑n=1∞log(n)eny−1, Re(y)>0, which takes y to 1/y, is obtained for the first time. This series transforms into a series containing ψ1(z), the derivative of Deninger's function R(z). ...
Dhama, Shivam; Pahlajani, Chetan D.(American Institute of Mathematical Sciences (AIMS), 2022-04)
In this paper, we study the dynamics of a linear control system with given state feedback control law in the presence of fast periodic sampling at temporal frequency $ 1/\delta $ ($ 0 < \delta \II 1 $), together with small ...
For a commuting d-tuple of operators TT defined on a complex separable Hilbert space H, let [[TT∗,TT]] be the d×d block operator (([T∗j,Ti])) of the commutators [T∗j,Ti]:=T∗jTi-TiT∗j. We define the determinant of [[TT∗,TT]] ...
Fix a Dedekind domain O and a non-zero prime p in it along with a uniformizer π. In the first part of the paper, we construct m-shifted π-typical Witt vectors Wmn(B) for any O algebra B of length m+n+1. They are a ...
Berndt, Bruce C.; Dixit, Atul; Gupta, Rajat; Zaharescu, Alexandru(Cornell University Library, 2022-04)
We consider two sequences a(n) and b(n), 1≤n<∞, generated by Dirichlet series ∑n=1∞a(n)λsnand∑n=1∞b(n)μsn,satisfying a familiar functional equation involving the gamma function Γ(s). Two general identities are established. ...
Goswami, Ankush; Jha, Abhash Kumar; Kim, Byungchan; Osburn, Robert(Cornell University Library, 2022-04)
We prove asymptotics and study sign patterns for coefficients in expansions of elements in the Habiro ring which satisfy a strange identity. As an application, we prove asymptotics and discuss positivity for the generalized ...
Gupta, Rajat; Kumar, Rahul(Cornell University Library, 2022-04)
Very recently, Radchenko and Zagier revived the theory of Herglotz functions. The main goal of the article is to show that one of the formulas on page 220 of Ramanujan's Lost Notebook actually lives in the realms of this ...
Mishra, Rohit Kumar; Sahoo, Suman Kumar(Cornell University Library, 2022-03)
In this article, we work with a generalized Saint Venant operator introduced by Vladimir Sharafutdinov to describe the kernel of the integral moment transforms over symmetric m-tensor fields in n-dimensional Euclidean ...
Mishra, Rohit Kumar; Monard, Francois; Zou, Yuzhou(Cornell University Library, 2022-03)
We study various self-adjoint realizations of the X-ray transform on the Euclidean disk D, obtained by considering specific singularly weighted L2 topologies. We first recover the well-known Singular Value Decompositions ...
Saha, Kamalesh; Sengupta, Indranath(Cornell University Library, 2022-03)
For a graph G, Bolognini et al. have shown JG is strongly unmixed ? JG is Cohen-Macaulay ? G is accessible, where JG denotes the binomial edge ideals of G. Accessible and strongly unmixed properties are purely combinatorial. ...
Saha, Joydip; Sengupta, Indranath(Indian Academy of Sciences, 2022-06)
In this paper, we explicitly compute the derivation module of quotients of polynomial rings by ideals formed by the sum or by some other gluing technique. We discuss cases of monomial ideals and binomial ideals separately.
Mehta, Ranjana; Saha, Joydip; Sengupta, Indranath(Cornell University Library, 2022-02)
We show that the minimal number of generators and the Cohen-Macaulay type of a family of numerical semigroups generated by concatenation of arithmetic sequences is unbounded.
Amrutiya, Sanjay; Jaiswal, Ayush(Cornell University Library, 2022-02)
In this article, we study the gauge theoretic aspects of real and quaternionic parabolic bundles over a real curve (X,?X), where X is a compact Riemann surface and {\sigma}X is an anti-holomorphic involution. For a fixed ...
Banerjee, Soumyarup(Cornell University Library, 2022-02)
In this paper, we investigate sums of four squares of integers whose prime factorizations are restricted, making progress towards a conjecture of Sun that states that two of the integers may be restricted to the forms 2a3b ...
Ghara, Soumitra; Misra, Gadadhar(Cornell University Library, 2022-02)
It has been recently shown that if K is a sesqui-analytic scalar valued non-negative definite kernel on a domain Ω in Cm, then the function (K2∂i∂¯jlogK)mi,j=1, is also a non-negative definite kernel on Ω. In this paper, ...