Vortices symmetric with respect to simultaneous parity and time reversing transformations are considered on the square lattice in the framework of the discrete nonlinear Schrödinger equation. The existence and stability of vortex configurations is analyzed in the limit of weak coupling between the lattice sites, when predictions on the elementary cell of a square lattice (i.e., a single square)...

The problem of completing partial latin squares to latin squares of the same order has been studied for many years. For instance, in 1960 Evans [9] conjectured that every partial latin square of order n containing at most n− 1 filled cells is completable to a latin square of order n. This conjecture was shown to be true by Lindner [12] and Smetaniuk [13]. Recently, Bryant and Rodger [6] establi...

Hafner and Stopple proved a conjecture of Zagier that the inverse Mellin transform symmetric square [Formula: see text]-function associated to Ramanujan tau function has an asymptotic expansion in terms nontrivial zeros Riemann zeta text]. Later, Chakraborty et al. extended this phenomenon for any Hecke eigenform over full modular group. In paper, we study Lambert series text] where is text]th ...

In this paper, we first introduce a symmetric phase type (PH) distribution, and then propose a symmetric exponential-polynomial type (EP) distribution based on the symmetric PH distribution. The class of symmetric EP distributions is illustrated to be so large that an arbitrary symmetric probability density function in L2(−∞,+∞), which is the space of square integrable functions on the real lin...