by giving a representation of L(s) in terms of Hurwitz zeta functions. That representation allowed us to get some information about zeros and poles; nevertheless no functional equation could be deduced from it. In this paper following a classical argument we obtain for L(s) as above, under suitable hypothesis, a functional equation of Riemann’s type. More precisely, let us consider the Dirichle...

To depict the rule of epidemic diffusion, two different models, the Susceptible-Exposure-InfectedRecovered-Susceptible SEIRS model and the Susceptible-Exposure-Infected-Quarantine-Recovered-Susceptible SEIQRS model, are proposed and analyzed within small-world network in this paper. Firstly, the epidemic diffusionmodels are constructedwithmean-filed theory, and condition for the occurrence of d...

We study the linearised stability of the nakedly singular negative mass Schwarzschild solution against gravitational perturbations. There is a one parameter family of possible boundary conditions at the singularity. We give a precise criterion for stability depending on the boundary condition. We show that one particular boundary condition is physically preferred and show that the spacetime is ...

We establish a series of indefinite integral formulae involving the Hurwitz zeta function and other elementary and special functions related to it, such as the Bernoulli polynomials, ln sin(πq), ln (q) and the polygamma functions. Many of the results are most conveniently formulated in terms of a family of functions Ak (q) := kζ ′(1−k, q), k ∈ N, and a family of polygamma functions of negative ...

An improved linear stability theory of small-amplitude oscillations of a self-gravitating, infinitesimally thin gaseous disk of spiral galaxies has been developed. It was shown that in the differentially rotating disks for nonaxisymmetric perturbations Toomre’s modified critical Q-parameter is larger than the standard one. We use hydrodynamical simulations to test the validity of the modified l...