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E-print Articles: Recent submissions

  • Hilbert-Kunz multiplicity of powers of ideals in dimension two 
    Stefani, Alessandro De; Masuti, Shreedevi K.; Rossi, Maria Evelina; Verma, Jugal K. (Cornell University Library, 2024-12)
    We study the behavior of the Hilbert-Kunz multiplicity of powers of an ideal in a local ring. In dimension two, we provide answers to some problems raised by Smirnov, and give a criterion to answer one of his questions in ...
  • The Rogers-Ramanujan dissection of a theta function 
    Dixit, Atul; Kumar, Gaurav (Cornell University Library, 2024-11)
    Page 27 of Ramanujan's Lost Notebook contains a beautiful identity which not only gives, as a special case, a famous modular relation between the Rogers-Ramanujan functions G(q) and H(q) but also a relation between two ...
  • Fundamental groupoid schemes and semi-finite bundles 
    Adroja, Pavan; Amrutiya, Sanjay (Cornell University Library, 2024-11)
    In this article, we study the various fundamental groupoid schemes and semi-finite bundles on complex tori and Riemann surfaces. We have computed fundamental groupoid of anisotropic conic, Klein bottle and abelian varieties. ...
  • Voronoi summation formulas, oscillations of Riesz sums, and Ramanujan-Guinand and Cohen type identities 
    Chorge, Shashank; Dixit, Atul (Cornell University Library, 2024-10)
    We derive Vorono\"{\dotlessi} summation formulas for the Liouville function λ(n), the Möbius function μ(n), and for d2(n), where d(n) is the divisor function. The formula for λ(n) requires explicit evaluation of certain ...
  • Microlocal inversion of a restricted mixed ray transform for second-order tensor fields in R3 
    Thakkar, Chandni (Cornell University Library, 2024-09)
    In this article, we study a restricted mixed ray transform acting on second-order tensor fields in 3-dimensional Euclidean space and prove the invertibility of this integral transform using microlocal techniques. Here, the ...
  • Sign regularity preserving linear operators 
    Choudhury, Projesh Nath; Yadav, Shivangi (Cornell University Library, 2027-07)
    A matrix A∈Rm×n is strictly sign regular/SSR (or sign regular/SR) if for each 1≤k≤min{m,n}, all k×k minors of A (or non-zero k×k minors of A) have the same sign. This class of matrices contains the totally positive matrices, ...
  • Inverse boundary value problem for the convection-diffusion equation with local data 
    Kumar, Pranav; Purohit, Anamika (Cornell University Library, 2024-07)
    We study a local data inverse problem for the time-dependent Convection-Diffusion Equation (CDE) in a bounded domain where a part of the boundary is treated to be inaccessible. Up on assuming the inaccessible part to be ...
  • Topological invariance of quantum homogeneous spaces of type B and D 
    Bhuva, Akshay; Biswas, Surajit; Saurabh, Bipul (Cornell University Library, 2024-06)
    In this article, we study two families of quantum homogeneous spaces, namely, SOq(2n+1)/SOq(2n−1), and SOq(2n)/SOq(2n−2). By applying a two-step Zhelobenko branching rule, we show that the C∗-algebras C(SOq(2n+1)/SOq(2n−1)), ...
  • Spectral dimension of p-adic integers 
    Biswas, Surajit; Saurabh, Bipul (Cornell University Library, 2024-06)
    The notion of spectral dimension was introduced by Chakraborty and Pal in \cite{cp}. In this paper, we show that the spectral dimension of the ring of p-adic integers, Zp, is equal to its manifold dimension, which is 0. ...
  • Hodge decomposition theorem on compact d-Kähler manifolds 
    Amrutiya, Sanjay; Jaiswal, Ayush (Cornell University Library, 2024-06)
    In this article, we will explore the fundamental concepts, including various basic concepts on d-complex manifolds, along with several differential operators and examine the relationships between them. A d-Kähler manifold ...
  • Projective closure of semigroup algebras 
    Saha, Joydip; Sengupta, Indranath; Srivastava, Pranjal (Cornell University Library, 2024-05)
    This paper investigates the projective closure of simplicial affine semigroups in Nd, d≥2. We present a characterization of the Cohen-Macaulay property for the projective closure of these semigroups using Gröbner bases. ...
  • V-line tensor tomography: numerical results 
    Ambartsoumian, Gaik; Mishra, Rohit Kumar; Zamindar, Indrani (Cornell University Library, 2024-05)
    This article presents the numerical verification and validation of several inversion algorithms for V-line transforms (VLTs) acting on symmetric 2-tensor fields in the plane. The analysis of these transforms and the ...
  • Inversion of generalized V-line transforms of vector fields in R2 
    Bhardwaj, Rahul; Mishra, Rohit Kumar; Vashisth, Manmohan (Cornell University Library, 2024-04)
    This article studies the inverse problem of recovering a vector field supported in DR, the disk of radius R centered at the origin, through a set of generalized broken ray/V-line transforms, namely longitudinal and transverse ...
  • Inversion formula, unique continuation property, and range characterization of the mixed ray transform in R2 
    Mishra, Rohit Kumar; Sahoo, Suman Kumar; Thakkar, Chandni (Cornell University Library, 2024-04)
    In this article, we study various aspects of the mixed ray transform of (k+ℓ)-tensor fields that are symmetric in its first k and last ℓ indices. As a first result, we derive an inversion algorithm to recover the solenoidal ...
  • Inversion of a restricted transverse ray transform with sources on a curve 
    Mishra, Rohit Kumar; Thakkar, Chandni (Cornell University Library, 2024-02)
    In this paper, a restricted transverse ray transform acting on vector and symmetric m-tensor fields is studied. We developed inversion algorithms using restricted transverse ray transform data to recover symmetric m-tensor ...
  • Mackey Imprimitivity and commuting tuples of homogeneous normal operators 
    Misra, Gadadhar; Narayanan, E. K.; Varughese, Cherian (Cornell University Library, 2024-02)
    In this semi-expository article, we investigate the relationship between the imprimitivity introduced by Mackey several decades ago and commuting d- tuples of homogeneous normal operators. The Hahn-Hellinger theorem gives ...
  • Gersten-type conjecture for henselian local rings of normal crossing varieties 
    Sakagaito, Makoto (Cornell University Library, 2024-02)
    Let n≥0 be an integer. For a normal crossing variety Y over the spectrum of a field k of positive characteristic p>0, K.Sato defined an étale logarithmic Hodge-Witt sheaf λnY,r on the étale site Ye´t which agrees with ...
  • Determining time-dependent convection and density terms in convection-diffusion equation using partial data 
    Purohit, Anamika (Cornell University Library, 2024-01)
    In this article, we study an inverse boundary value problem for the time-dependent convection-diffusion equation. We use the nonlinear Carleman weight to recover the time-dependent convection term and time-dependent density ...
  • An example for Kuznetsov-Shinder conjecture 
    Srivastava, Tanya Kaushal (Cornell University Library, 2024-01)
    We give an example for the Kuznetsov-Shinder conjecture, with infinitely many non-isomorphic D-equivalent and L-equivalent varieties.
  • Recent developments pertaining to Ramanujan's formula for odd zeta values 
    Dixit, Atul (Cornell University Library, 2023-12)

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