Several completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion (" acceleration equal force "), with linear and cubic forces, in N-dimensional space (N being an arbitrary positive integer, with special attention to N = 2, namely motions in a plane, and N = 3, namely motions in ordinary three-dimensional space). All the...

The existence of almost periodic solutions of a nonlinear Volterra difference equation with infinite delay is obtained by using some restrictive conditions of the equation. AMS subject classification: 39A10, 39A11.

We present some explicit formulas for queue length and waiting time distributions of customers in the MfHE,,,/l queue. The formulas are obtained with the aid of roots of quadratic, cubic, and quartic polynomials constructed from a recurrence equation. With an example, we demonstrate that the formulas for queueing dishbutions are exhemely accurate, while the corresponding infinite history M IGII...

We consider a modiication of moment functionals for the Hahn classical polynomials of a discrete variable by adding two mass points at the ends of the interval, i.e., in x = 0 and x = N 1. We obtain the resulting orthogonal polynomials and identify them as hypergeometric functions. The corresponding three term recurrence relation and tridiagonal matrices are also studied. x1 Introduction. The s...

One usually defines the notion of a computable real number by using recursive functions. However, there is a simple way due to A. Mostowski to characterize the computable real numbers by using only primitive recursive functions. We prove Mostowski’s result differently and apply it to get other simple characterizations of this kind. For instance, a real number is shown to be computable if and on...

This study presents miscellaneous properties of pseudo-factorials, which are numbers whose recurrence relation is a twisted form of that of usual factorials. These numbers are associated with special elliptic functions, most notably, a Dixonian and a Weierstraß function, which parametrize the Fermat cubic curve and are relative to a hexagonal lattice. A continued fraction expansion of the ordin...