In this paper, we consider an optimal control problem governed by linear parabolic differential equations with memory. Under the assumption that the corresponding linear parabolic differential equation without memory term ...

We consider two sequences 𝑎¹𝑛ºand𝑏¹𝑛º, 𝑛1, generated by Dirichlet series ∑︁𝑛=1𝑎¹𝑛º𝜆𝑠𝑛 and ∑︁𝑛=1𝑏¹𝑛º𝜇𝑠𝑛 satisfying a familiar functional equation involving the gamma function Γ¹𝑠º. Two general identities ...

The scattering problem of a bottom-mounted surface-piercing compound porous cylinder located on a porous sea-bed is theoretically investigated under the assumption of small amplitude wave theory. The compound cylinder is ...

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 ...

We consider L-functions L1,..., Lk from the Selberg class which have polynomial Euler product and satisfy Selberg's orthonormality condition. We show that on every vertical line s = σ + it with σ ∈ (1/2, 1), these L-functions ...

A submonoid of ℕd is of maximal projective dimension (MPD) if the associated affinesemigroup ring has the maximum possible projective dimension. Such submonoids have a nontrivial set of pseudo-Frobenius elements. We ...

In this paper, we carry out a fairly comprehensive study of two special classes of numerical semigroups, one generated by the sequence of partial sums of an arithmetic progression and the other one generated by a shifted ...

We consider two sequences 𝑎¹𝑛ºand𝑏¹𝑛º, 𝑛1, generated by Dirichlet series ∑︁𝑛=1𝑎¹𝑛º𝜆𝑠𝑛 and ∑︁𝑛=1𝑏¹𝑛º𝜇𝑠𝑛 satisfying a familiar functional equation involving the gamma function Γ¹𝑠º. Two general identities ...

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 ...