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 ...
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 ...
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. ...
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 ...
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 ...
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 ...
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 ...
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 ...
A modular relation of the form F(α,w)=F(β,iw), where i=√−1and αβ=1, is obtained. It involves the generalized digamma function ψw(a) which was recently studied by the authors in their work on developing the theory of the ...
In the spirit of the landmark work of Granville and Soundararajan, we further develop the theory of limitations to equidistribution in arithmetic progressions for a general class of nonnegative arithmetical functions. Our ...
Dey, Sampa; Savalia, Aditi(Cornell University Library, 2023-01)
Let Fq[t] be the polynomial ring over the finite field Fq. For arithmetic functions ψ1,ψ2:Fq[t]→C, we establish that if a Bombieri-Vinogradov type equidistribution result holds for ψ1 and ψ2, then it also holds for their ...
Jaiswal, Anjali; Rani, Poonam; Tyagi, Jagmohan(American Institute of Mathematical Sciences, 2023-07)
We consider the following Keller-Segel system with gradient dependent chemotactic coefficient:ut = ∆u − χ∇ · (uf(|∇v|)∇v), 0 = ∆v − v + g(u), in smooth bounded domains Ω ⊂ Rn, n ≥ 1 with f(ξ) = (ξp-2(1+ξp) q−p/p), 1 <q ≤ ...
Let q=|q|eiπθ be a nonzero complex number such that |q|≠1 and consider the compact quantum group Uq(2). For θ∉Q∖{0,1}, we obtain the K-theory of the underlying C⁎-algebra C(Uq(2)). We construct a spectral triple on Uq(2) ...
Bhardwaj, Om Prakash; Sengupta, Indranath(Springer, 2023-02)
Let a and d be two linearly independent vectors in N2, over the field of rational numbers. For a positive integer k≥2, consider the sequence a,a+d,…,a+kd such that the affine semigroup Sa,d,k=⟨a,a+d,…,a+kd⟩ is minimally ...
Oza, Priyank; Tyagi, Jagmohan(Cornell University Library, 2023-01)
We establish the comparison principle, existence and regularity of solutions to the following problem concerning the mixed operator: (αM+λ,ΛD2HN ,Su- β- ∆HNs u = f in Ω,u = g in HN \ Ω, where M+λ,Λis the extremal Pucci's ...
Gandal, Somnath; Tyagi, Jagmohan(Cornell University Library, 2023-01)
We establish the existence of solutions to the following semilinear Neumann problem for fractional Laplacian and critical exponent:(??)su + ?u = |u|p?1 u in ?, Nsu(x) = 0 in R n \ ?, u ? 0 in ?, where ? > 0 is a constant ...
Gandal, Somnath; Tyagi, Jagmohan(Cornell University Library, 2023-01)
We establish the asymptotic behaviour of the least energy solutions of the following nonlocal Neumann problem:d(-∆)su + u = |u|p-1 u in Ω, Nsu = 0 in Rn \ Ω, u > 0 in Ω,where Ω ⊂ Rn is a bounded domain of class C1,1, 1 < ...
Let Fq[t] be the polynomial ring over the finite field Fq. For arithmetic functions ψ1,ψ2:Fq[t]→C, we establish that if a Bombieri-Vinogradov type equidistribution result holds for ψ1 and ψ2, then it also holds for their ...