Period matching in modulated maps

We study discrete nonlinear maps in which the control parameter is itself “modulated” by another discrete nonlinear map. We show that for a certain class of such maps, which includes for example the logistic map, the periodicity of the modulated signal is either one, independent of the periodicity of the modulating signal, or its periodicity is an integral multiple of the periodicity of the modulating signal or it is chaotic.     

Antiplane Shear Waves in Two Contacting Ferromagnetic Half Spaces

The problem of reflection and refraction of antiplane shear (or magneto-elastic) waves at the interface between two ferromagnetic half-spaces with slipping contact (vacuum gap) is studied for waves propagating normal to the direction of the applied external magnetic field which is assumed to be parallel to the interface. We show the existence of new waves that are localized near the interface between the two ferromagnetic media and accompany the reflected and the transmitted waves. We call the new waves as accompanying surface magneto-elastic (ASME) waves; their amplitudes depend upon values of magnetoelastic parameters of the two media and the intensity of the applied magnetic field. We derive closed-form expressions for magnitudes (coefficients) of the reflected, the refracted (transmitted) and the ASME waves. We show that for a range of values of the applied magnetic field the coefficient of the reflected wave increases and that of the transmitted wave decreases with an increase in the magnitude of the applied magnetic field; these coefficients eventually approach 1 and 0, respectively. That is, the applied external magnetic field can totally eliminate the transmitted wave, and can control energies of the reflected, the refracted and the ASME waves.     

Some cyclic codes of length 2<Emphasis Type="Italic">p</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

Explicit expressions for 4n + 2 primitive idempotents in the semi-simple group ring $R_{2p^{n}}\equiv \frac{GF(q)[x]}{p and q are distinct odd primes; n ≥ 1 is an integer and q has order \fracf(2pⁿ)2{\frac{\phi(2p^{n})}{2}} modulo 2p ⁿ . The generator polynomials, the dimension, the minimum distance of the minimal cyclic codes of length 2p ⁿ generated by these 4n + 2 primitive idempotents are discussed. For n = 1, the properties of some (2p, p) cyclic codes, containing the above minimal cyclic codes are analyzed in particular. The minimum weight of some subset of each of these (2p, p) codes are observed to satisfy a square root bound.