We argue that the giant graviton configurations known from the literature have a complementary, microscopical description in terms of multiple gravitational waves undergoing a dielectric (or magnetic moment) effect. We present a non-Abelian effective action for these gravitational waves with dielectric couplings and show that stable dielectric solutions exist. These solutions agree in the large...

The class of complex modified Korteweg-de Vries (CMKdV) equations has many applications. One form of the CMKdV equation has been used to create models for the nonlinear evolution of plasma waves , for the propagation of transverse waves in a molecular chain, and for a generalized elastic solid. Another form of the CMKdV equation has been used for the traveling-wave and for a double homoclinic o...

In this communication, we use a compact split step Padé scheme (CSSPS) to solve the scalar higher-order nonlinear Schrödinger equation (HNLS) with higher-order linear and nonlinear effects. The second part, consisting of two sections, the first section is dedicated to the study numerically the stabilization of high-order solitons dynamic in optical fibers by compensation or by the interplay of ...

We presen a secure direct communication protocol by using step-split Einstein-Podolsky-Rosen (EPR) pair. In this communication protocol, Alice first sends one qubit of an EPR pair to Bob. Bob sends a receipt signal to Alice through public channel when he receives Alice’s first qubit. Alice performs her encoding operations on the second qubit and sends this qubit to Bob. Bob performs a Bell-basi...

Split-step procedures have previously been used successfully in a number of situations, e.g. for Hamiltonian systems, such as certain nonlinear wave equations. In this study, we note that one particular way to write the 3-D Maxwell’s equations separates these into two parts, requiring in all only the solution of six uncoupled 1-D wave equations. The approach allows arbitrary orders of accuracy ...

The purpose of the study was to determine the timing of a split-step in three categories of tennis players in four groups of strokes. Subjects were divided into three groups: male and female junior, and male professional tennis players. During two tournaments, all matches were recorded with two fixed video cameras. For every stroke, the timing of the split-step between the opponent's impact poi...

This paper presents a likelihood approach to population samples of microsatellite alleles. A Markov chain recursion method previously published by GRIFFITHS and TAVARE is applied to estimate the likelihood function under different models of microsatellite evolution. The method presented can be applied to estimate a fundamental population genetics parameter theta as well as parameters of the mut...

Asymptotic linear stability is studied for stochastic differential equations (SDEs) that incorporate Poisson-driven jumps and their numerical simulation using theta-method discretisations. The property is shown to have a simple explicit characterisation for the SDE, whereas for the discretisation a condition is found that is amenable to numerical evaluation. This allows us to evaluate the asymp...

We consider a long fiber-optical link consisting of alternating dispersive and nonlinear segments, i.e., a split-step model (SSM), in which the dispersion and nonlinearity are completely separated. Passage of a soliton (localized pulse) through one cell of the link is described by an analytically derived map. Multiple numerical iterations of the map reveal that, at values of the system’s stepsi...

BACKGROUND AND OBJECTIVE Previous studies suggest that error augmentation may be used as a strategy to achieve longer-term changes in gait deficits after stroke. The purpose of this study was to determine whether longer-term improvements in step length asymmetry could be achieved with repeated split-belt treadmill walking practice using an error augmentation strategy. METHODS 13 persons with ...