Markov partition in non-hyperbolic interval dynamics

We considerC ² unimodal mapsf such that all periodic points are hyperbolic, the critical point is non-degenerated and non-recurrent, and the Julia set does not contain intervals. We construct a Markov partition for a big part of the Julia set. Then we use it to estimate the limit capacity and Hausdorff dimension of the Julia set.Partially supported by CNPq, S.C.T.-Brazil     

Measurement of the dynamic elastic constants of short isotropic cylinders

A method based on a single test is proposed to characterize the elasticity of an isotropic homogeneous material in the shape of a cylinder of any slenderness (length-diameter) ratio. Firstly, the Rayleigh-Ritz method is used to determine the natural frequencies of the cylinders vibrating axisymmetrically. The study is focused on cylindrical samples with diameter and length of similar magnitude so that the shear modulus and the Poisson ratio can be calculated simultaneously. Subsequently, the theoretical results for cylinders of slenderness ratio between 0.1 and 3 are analyzed in order to obtain the data required to determine the elastic constants from one of the two lowest measured natural frequencies and their quotient. The analysis of the results demonstrates that any slenderness ratio is useful in the calculation of the elastic constants, although in some cases the third natural frequency should be used. Furthermore, the influence of the length-diameter quotient on the sensitivity of the method is analyzed by evaluating the systematic uncertainties for both dynamic elastic constants. Finally, the method is experimentally tested by characterizing two steel cylinders with slenderness ratios 0.1 and 1, respectively. The results demonstrate that uncertainties for both Poisson ratio and the shear modulus are smaller when the slenderness ratio is 1.     

Hydrophilic and hydrophobic copolymer systems based on acrylic derivatives of pyrrolidone and pyrrolidine

This article deals with the synthesis of hydrophilic methacrylic monomers derived from ethyl pyrrolidone [2‐ethyl‐(2‐pyrrolidone) methacrylate (EPM)] and ethyl pyrrolidine [2‐ethyl‐(2‐pyrrolidine) methacrylate (EPyM)] and their respective homopolymers. For the determination of their reactivity in radical copolymerization reactions, both monomers were copolymerized with methyl methacrylate (MMA), the reactivity ratios being calculated by the application of linear and nonlinear mathematical methods. EPM and MMA had ratios of r_EPM = 1.11 and r_MMA = 0.76, and this indicated that EPM with MMA had a higher reactivity in radical copolymerization processes than vinyl pyrrolidone (VP; r_VP = 0.005 and r_MMA = 4.7). EPyM and MMA had reactivity ratios of r_EPyM = 1.31 and r_MMA = 0.92, and this implied, as for the EPM–MMA copolymers, a tendency to form random or Bernoullian copolymers. The glass‐transition temperatures of the prepared copolymers were determined by differential scanning calorimetry (DSC) and were found to adjust to the Fox equation. Total‐conversion copolymers were prepared, and their behavior in aqueous media was found to be dependent on the copolymer composition. The swelling kinetics of the copolymers followed water transport mechanism case II, which is the most desirable kinetic behavior for a swelling controlled‐release material. Finally, the different states of water in the hydrogels—nonfreezing water, freezing bound water, and unbound freezing water—were determined by DSC and found to be dependent on the hydrophilic and hydrophobic units of the copolymers. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 395–407, 2003     

Birefringent filter with amplitude beats

In this work, we show a very simple birefringent filter useful to modulate a broadband light spectrum. We first show the generation of various oscillating spectra using two identical multiple-order waveplates. In particular a sinusoidal broadband spectrum with a rapid oscillation is obtained. This spectrum is amplitude modulated by adding another waveplate to the system. This waveplate has a small phase shift, and with the proper orientation generates amplitude beats on the broadband spectrum. Finally, we show how this system can be voltage controlled by means of a ferroelectric liquid crystal modulator. We experimentally demonstrate this behavior with the aid of a portable spectrophotometer, and we provide a theoretical explanation on the basis of the Jones matrix formalism.     

Constants of Motion for Several One-Dimensional Systems and Problems Associated with Getting Their Hamiltonians

The constants of motion of the following systems are deduced: a relativistic particle with linear dissipation; a no-relativistic particle with a time explicitly depending force; a no-relativistic particle with a constant force and time depending mass; and a relativistic particle under a conservative force with position depending mass. The Hamiltonian for these systems, which is determined by getting the velocity as a function of position and generalized linear momentum, can be found explicitly at first approximation for the first system. The Hamiltonians for the other systems are kept implicitly in their expressions for their constants of motion.     

Annealing effects on the magnetization of Co–Ni–B amorphous nanoparticles

Chemically prepared (Co_xNi_1−x)_1−yB_y (x=0.5, 0.75, 1; y≈0.4) amorphous fine particles were characterized by X-ray diffraction, DTA and TGA, and in situ magnetic measurement as a function of annealing temperature in an inert atmosphere. Magnetic measurement performed in as-prepared and 150°C annealed samples shows an increase of the saturation magnetization and magnetic moment after thermal treatment. Room temperature magnetization increases by factors of 3.5, 1.8, and 1.5, for x=0.5, 0.75, and 1, respectively. These measurements may indicate a local re-ordering of the amorphous phase at temperatures much lower than the full crystallization temperature.     

Entropy and ergodic probability for differentiable dynamical systems and their bundle extensions

We answer a problem of Liao [S.T. Liao, Standard systems of differential equations and obstruction sets—from linearity to perturbations, in: System Researches, Proceedings Dedicated to the 85th Anniversary of Qian Xue-Sen, Zhejiang Education Press, Hangzhou, China, 1996, pp. 279-290 (in Chinese)]: A C¹ vector field or a C¹ diffeomorphism on an n-dimensional manifold has equal entropy with that of its bundle extensions. We also prove that each ergodic probability with simple Lyapunov spectrum has at most n²n! covering probabilities on each bundle extension.