This study reports the validity of the modified Shanks’ conjecture on the planar least squares inverse (PLSI) method of stabilizing two-dimensional (2-D) recursive digital filters. A theoretical procedure proposed based on the Lagrange multiplier method of mathematical optimization. The results indicate that the modified Shanks’ conjecture reported by Jury was valid for special classes of 2-D p...

In this paper we determine upper bounds for the number of control sets on flag manifolds of a real non-compact simple Lie group whose Lie algebra is a real form of a complex simple Lie algebra. The estimates for the number of control sets are based on the results of San Martin and Tonelli [6]. They are determined by computing the orbits of a subgroup of the Weyl Group.

In this work, we show how to obtain for non-compact manifolds the results that have already been done for Monge Transport Problem for costs coming from Tonelli Lagrangians on compact manifolds. In particular, the already known results for a cost of the type dr , r > 1, where d is the Riemannian distance of a complete Riemannian manifold, hold without any curvature restriction.

This paper studies properties of Tonelli Hamiltonian systems that possess n independent but not necessarily involutive constants of motion. We obtain results reminiscent of the Liouville-Arnol′d theorem under a suitable hypothesis on the regular set of these constants of motion. This work continues the work in [30] by the second author.

Daniel Shanks was born on January 17, 1917, in the city of Chicago, where he was raised and where in 1937 he received his B.S. in physics from the University of Chicago. In 1940 he worked as a physicist at the Aberdeen Proving Grounds, moving the following year to the position of physicist at the Naval Ordinance Laboratory, a position he retained until 1950. In 1951 his post at the NOL changed ...

We present a detailed analysis of SQUFOF, Daniel Shanks’ Square Form Factorization algorithm. We give the average time and space requirements for SQUFOF. We analyze the effect of multipliers, either used for a single factorization or when racing the algorithm in parallel.

88 © 2014 Guilford Publications, Inc. We thank Adam Harris, Magda Osman, Danny Oppenheimer, and Piotr Winkielman for many helpful discussions. Preparation of this paper was supported in part by an Australian Research Council Future Fellowship (FT110100151) awarded to Ben Newell. Address correspondence to David R. Shanks, Division of Psychology and Language Sciences, University College London, 2...

For integers a and b we deene the Shanks chain p 1 ; p 2 ; : : : ; p k of length k to be a sequence of k primes such that p i+1 = ap i 2 ? b for i = 1; 2; : : : ; k ? 1. While for Cunningham chains it is conjectured that innnitely long chains exist, this is, in general, not true for Shanks chains. In fact, with s = ab we show that for all but 56 values of s 1000 any corresponding Shanks chain m...