Dixit, Atul; Kesarwani, Aashita; Kumar, Rahul(Cornell University Library, 2020-12)
An exact transformation, which we call a \emph{master identity}, is obtained for the series ??n=1?a(n)e?ny for a?C and Re(y)>0. As corollaries when a is an odd integer, we derive the well-known transformations of the ...
Gupta, Rajat; Kumar, Rahul(Cornell University Library, 2020-12)
n this article, a q-series examined by Kluyver and Uchimura is generalized. This allows us to find generalization of the identities in the random acyclic digraph studied by Simon, Crippa, and Collenberg in 1993. As one of ...
We recount and discuss some of the most important methods and blow-up criteria for analyzing solutions of Keller-Segel chemotaxis models. First, we discuss the results concerning the global existence, boundedness and blow-up ...
We establish Lyapunov?type inequalities for a class of singular elliptic partial differential equations. As an application of Lyapunov?type inequalities, we obtain lower bounds for the first eigenvalue of the associated ...
We establish the existence of nonnegative weak solutions to time fractional Keller�Segel system with Dirichlet boundary condition in a bounded domain with smooth boundary. Since the considered system has a cross?diffusion ...
J. R. Wilton obtained an expression for the product of two Riemann zeta functions. This expression played a crucial role to find the approximate functional equation for the product of two Riemann zeta functions in the ...
Closed-form evaluations of certain integrals of J0(?), the Bessel function of the first kind, have been crucial in the studies on the electromagnetic field of alternating current in a circuit with two groundings, as can ...
In this paper, we give a construction of the moduli space of filtered representations of a given quiver of fixed dimension vector with the appropriate notion of stability. The construction of the moduli of filtered ...