The study of the dynamic behavior of a rigid body with one fixed point (gyroscope) has a long history. A number of famous mathematicians and mechanical engineers have devoted enormous time and effort to clarify the role of dynamic effects on its movement (behavior) – stable, periodic, quasi-periodic or chaotic. The main objectives of this review are: 1) to outline the characteristic features of...

Shapiro syndrome and periodic hypothermia have been reported approximately fifty times in the literature. Shapiro syndrome is defined as the constellation of periodic hypothermia and hyperhidrosis along with agenesis of the corpus callosum by Shapiro et al. in 1969. Periodic hypothermia is a more broad diagnosis with a number of proposed mechanisms; it occurs in patients without structural brai...

Familial periodic fever syndromes, otherwise known as hereditary autoinflammatory syndromes, are inherited disorders characterized by recurrent episodes of fever and inflammation. The general hypothesis is that the innate immune response in these patients is wrongly tuned, being either too sensitive to very minor stimuli or turned off too late. The genetic background of the major familial perio...

This paper reviews evidence from April, 1998 through April 2002 for the dopaminergic treatment of the restless legs syndrome (RLS) and periodic limb movement disorder (PLMD). There has been increased study of dopaminergic agents for the treatment of these conditions since publication of a review paper and practice parameters that covered all types of medical treatment of RLS and PLMD in 1999. F...

We review the major ideas involved in the control of chaos by considering higher dimensional dynamics. We present the Ott-Grebogi-Yorke (OGY) method of controlling chaos to achieve time periodic motion by utilizing only small feedback control. The time periodic motion results from the stabilization of unstable periodic orbits embedded in the chaotic attractor. We demonstrate that the OGY method...

Periodic travelling waves (wavetrains) are an important solution type for many partial differential equations. In this paper I review the use of numerical continuation for studying these solutions. I discuss the calculation of the form and stability of a given periodic travelling wave, and the calculation of boundaries in a two-dimensional parameter plane for wave existence and stability. I als...

The goal of this lecture is to describe how homogenization theory can be applied to numerical computations of partial differential equations in highly heterogeneous media. In the first chapter we briefly review the classical numerical method for periodic media. It amounts to the separate computation of the cell and homogenized problems. We also give some indications about correctors and boundar...

We review the current status of one dimensional periodic potentials and also present several new results. It is shown that using the formalism of supersymmetric quantum mechanics, one can considerably enlarge the limited class of analytically solvable one-dimensional periodic potentials. Further, using the Landen transformations as well as cyclic identities for Jacobi elliptic functions discove...

We consider some Boussinesq systems of water wave theory, which are of coupled KdV type. After a brief review of the theory of existence-uniqueness of solutions of the associated initial-value problems, we turn to the numerical solution of their initialand periodic boundary-value problems by unconditionally stable, highly accurate methods that use Galerkin/finite element type schemes with perio...