• Affine monomial curves 

  Sengupta, Indranath (Springer, 2022-06)

  This article is an expository survey on affine monomial curves, where we discuss some research problems from the perspective of computation.
• Explicit transformations of certain Lambert series 

  Dixit, Atul; Kesarwani, Aashita; Kumar, Rahul (Springer, 2022-06)

  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 ...
• Fluctuation analysis for a class of nonlinear systems with fast periodic sampling and small state-dependent white noise 

  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) ...
• Lambert series of logarithm, the derivative of deninger's function R(z) and a mean value theorem for ζ(12−it) ζ′(12+it) 

  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). ...
• Approximation of linear controlled dynamical systems with small random noise and fast periodic sampling 

  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 ...
• A trace inequality for commuting d-tuples of operators 

  Misra, Gadadhar; Pramanick, Paramita; Sinha, Kalyan B. (Springer, 2022-06)

  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]] ...
• Kernel of arithmetic jet spaces 

  Saha, Arnab (Cornell University Library, 2022-04)

  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 ...
• Two general series identities involving modified bessel functions and a class of arithmetical functions 

  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. ...
• Asymptotics and sign patterns for coefficients in expansions of Habiro elements 

  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 ...
• Extended higher Herglotz function \textup{II} 

  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 ...
• Raj Chandra Bose: universal mathematician 

  Frisinger, H. Howard; Sengupta, Indranath (Bhavana Trust, 2022-02)
• The generalized Saint Venant operator and integral moment transforms 

  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 ...
• The C?-isomorphism property for a class of singularly-weighted X-ray transforms 

  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 ...
• Cohen-macaulay binomial edge ideals in terms of blocks with whiskers 

  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. ...
• Derivation modules for sum and gluing 

  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.
• Unboundedness of the first and the last Betti numbers of numerical semigroups segnerated by concatenation 

  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.
• A gauge theoretic aspects of parabolic bundles over Klein surfaces 

  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 ...
• Asymptotic analysis of discrete-time models for linear control systems with fast random sampling 

  Dhama, Shivam; Pahlajani, Chetan D. (2021-12-20)
• On a conjecture of sun about sums of restricted squares 

  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 ...
• The relationship of the Gaussian curvature with the curvature of a Cowen-Douglas operator 

  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, ...

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