The quadratic embedding constant (QEC) of a finite, simple, connected graph G is the maximum of the quadratic form of the distance matrix of G on the subset of the unit sphere orthogonal to the all-ones vector. The study ...

Generalized digamma functions ψk(x), studied by Ramanujan, Deninger, Dilcher, Kanemitsu, Ishibashi etc., appear as the Laurent series coefficients of the zeta function associated to an indefinite quadratic form. In this ...

In this paper we propose a generalization of the Grothendieck inequality for pairs of Banach spaces E and F with E being finite dimensional and investigate the behaviour of the Grothendieck constant KG(E,F) implicit in ...

In this paper, we study the class of affine semigroup generated by integral vectors, whose components are in generalised arithmetic progression and we observe that the defining ideal is determinantal. We also give a ...

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.

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 ...

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. ...

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 ...

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 ...

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 ...