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Mathematics: Recent submissions

  • On Cohen-Macaulay posets of dimension two and permutation graphs 
    Jahangir, Rizwan; Veer, Dharm (Cornell University Library, 2023-05)
    We characterize Cohen-Macaulay posets of dimension two; they are precisely the shellable and strongly connected posets of dimension two. We also give a combinatorial description of these posets. Using the fact that ...
  • On the Möbius invariant principal functions of Pincus 
    Ghosh, Sagar; Misra, Gadadhar (Cornell University Library, 2023-04)
    In this semi-expository short note, we prove that the only homogeneous \textit{pure} hyponormal operator T with rank(T∗T−TT∗)=1, modulo unitary equivalence, is the unilateral shift.
  • On the associated graded ring of semigroup algebras 
    Saha, Joydip; Sengupta, Indranath; Srivastava, Pranjal (Taylor and Francis, 2023-10)
    In this paper, we give a necessary and sufficient condition for the Cohen-Macaulayness of the associated graded ring of a simplicial affine semigroup using Grobner basis. We generalize the concept of homogeneous numerical ...
  • The v-number of binomial edge ideals 
    Balu, Ambhore Siddhi; Saha, Kamalesh; Sengupta, Indranath (Cornell University Library, 2023-04)
    The invariant v-number was introduced very recently in the study of Reed-Muller-type codes. Jaramillo and Villarreal (J Combin. Theory Ser. A 177:105310, 2021) initiated the study of the v-number of edge ideals. Inspired ...
  • Group inverses of weighted trees 
    Nandi, Raju (Cornell University Library, 2023-04)
    Let (G,w) be an undirected weighted graph. The group inverse of (G,w) is the weighted graph with the adjacency matrix A#, where A is the adjacency matrix of (G,w). We study the group inverse of singular weighted trees. It ...
  • Explicit transformations for generalized Lambert series associated with the divisor function σ(N)a(n) and their applications 
    Banerjee, Soumyarup; Dixit, Atul; Gupta, Shivajee (Cornell University Library, 2023-04)
    Let σ(N)a(n)=∑dN|nda. An explicit transformation is obtained for the generalized Lambert series ∑∞n=1σ(N)a(n)e-ny for Re(a)>-1 using the recently established Voronoï summation formula for σ(N)a(n), and is extended to a ...
  • A product formula for homogeneous characteristic functions 
    Bagchi, Bhaska; Hazra, Somnath; Misra, Gadadhar (Springer, 2023-06)
    A bounded linear operator T on a Hilbert space is said to be homogeneous if φ(T) is unitarily equivalent to T for all φ in the group Möb of bi-holomorphic automorphisms of the unit disc. A projective unitary representation ...
  • Unboundedness of the first Betti number and the last Betti number of numerical semigroups generated by concatenation 
    Mehta, Ranjana; Saha, Joydip; Sengupta, Indranath (Springer, 2023-03)
    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.
  • Canonical witt formal scheme extensions and p-torsion groups 
    Bertapelle, Alessandra; Mazzari, Nicola; Saha, Arnab (Springer, 2023-03)
    We study the nth arithmetic jet space of the p-torsion subgroup attached to a smooth commutative formal group scheme. We show that the nth jet space above fits in the middle of a canonical short exact sequence between a ...
  • Transversal intersection and sum of polynomial ideals 
    Saha, Joydip; Sengupta, Indranath; Tripathi, Gaurab (RMS Publications, 2023-03)
    In this paper we derive some conditions for transversal intersection of polynomial ideals and present some examples. Finally, as an application of the results proved, we compute the Betti numbers of ideals of the form ...
  • Fully nonlinear degenerate equations with applications to grad equations 
    Oza, Priyank (Cornell University Library, 2023-03)
    We consider a class of degenerate elliptic fully nonlinear equations with applications to Grad equations:(|Du|γM+λ,ΛD2u(x) = f|u ≥ u(x)| in Ωu = g on ∂,where γ≥1 is a constant, Ω is a bounded domain in RN with C1,1 boundary. ...
  • Fluctuation analysis for a class of nonlinear systems with fast periodic sampling and small state-dependent white noise 
    Dhama, Shivam; Pahlajani, Chetan D. (Elsevier, 2023-07)
    We consider a nonlinear differential equation under the combined influence of small state-dependent rownian perturbations of size ε, and fast periodic sampling with period δ; 0 < ε, δ 1. State samples (measurements) are ...
  • Voronoi summation formula for the generalized divisor function σ(k)z(n 
    Dixit, Atul; Maji, Bibekananda; Vatwani, Akshaa (Cornell University Library,, 2023-03)
    For a fixed z∈C and a fixed k∈N, let σ(k)z(n) denote the sum of z-th powers of those divisors d of n whose k-th powers also divide n. This arithmetic function is a simultaneous generalization of the well-known divisor ...
  • Cauchy problem for impulsive fractional differential equations with almost sectorial operators 
    Jaiswal, Anjali; Tyagi, Jagmohan (EMS Press, 2023-03)
    We study a class of non-instantaneous impulsive fractional differential equations in a Banach space. We consider the Cauchy problem with Caputo derivative having variable lower limits and almost sectorial operators. We ...
  • Arithmetic jet spaces 
    Bertapelle, Alessandra; Previato, Emma; Saha, Arnab (Elsevier, 2023-06)
    One of the primary objectives of this paper is to establish compatibility between two different jet space functors in the most general context. We first show an adjunction between the jet and the Witt functor on algebras. ...
  • Betti sequence of the projective closure of affine monomial curves 
    Saha, Joydip; Sengupta, Indranath; Srivastava, Pranjal (Elsevier, 2023-11)
    We introduce the notion of star gluing of numerical semigroups and show that this preserves the arithmetically Cohen-Macaulay and Gorenstein properties of the projective closure. Next, we give a sufficient condition involving ...
  • Modified Bessel functions in analytic number theory 
    Berndt, Bruce C.; Dixit, Atul; Gupta, Rajat; Zaharescu, Alexandru (Cornell University Library, 2023-03)
    The modified Bessel functions Kν(z), or, for brevity, K-Bessel functions, arise at key places in analytic number theory. In particular, they appear in beautiful arithmetic identities. A survey of these arithmetical identities ...
  • Delta characters and crystalline cohomology 
    Pandit, Sudip; Saha, Arnab (Cornell University Library, 2023-02)
    The first part of the paper develops the theory of m-shifted π-typical Witt vectors which can be viewed as subobjects of the usual π-typical Witt vectors. We show that the shifted Witt vectors admit a delta structure that ...
  • Regularity of solutions to variable-exponent degenerate mixed fully nonlinear local and nonlocal equations 
    Oza, Priyank; Tyagi, Jagmohan (Cornell University Library, 2023-02)
    We consider a class of variable-exponent mixed fully nonlinear local and nonlocal degenerate elliptic equations, which degenerate along the set of critical points, C:={x:Du(x)=0}. Under general conditions, first, we establish ...
  • Polyocollection ideals and primary decomposition of polyomino ideals 
    Cisto, Carmelo; Navarra, Francesco; Veer, Dharm (Cornell University Library, 2023-02)
    In this article, we study the primary decomposition of some binomial ideals. In particular, we introduce the concept of polyocollection, a combinatorial object that generalizes the definitions of collection of cells and ...

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