An efficient construction of period-2 bulbs in the cubic Mandelbrot set with parametric boundaries

A parametric boundary equation is established for the principal period-2 bulb in the cubic Mandelbrot set. Using its geometry, an efficient escape-time algorithm which reduces the construction time for the period-2 bulbs in the cubic Mandelbrot set is introduced and the implementation graphic results display the fascinating fractal beauty     

Synchronization of Genesio chaotic system via backstepping approach

Backstepping design is proposed for synchronization of Genesio chaotic system. Firstly, the control problem for the chaos synchronization of nominal Genesio systems without unknown parameters is considered. Next, an adaptive backstepping control law is derived to make the error signals between drive Genesio system and response Genesio system with an uncertain parameter asymptotically synchronized. Finally, the approach is extended to the synchronization problem for the system with three unknown parameters. The stability analysis in this article is proved by using a well-known Lyapunov stability theorem. Note that the approach provided here needs only a single controller to realize the synchronization. Two numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.     

In situ observations of domain wall motion in Mn–Zn and Ni–Zn ferrites by Lorentz microscopy and electron holography

Domain wall motion in Mn–Zn and Ni–Zn ferrites with applied magnetic fields is investigated by in situ observations with Lorentz microscopy and electron holography. It is found that both Mn–Zn and Ni–Zn ferrites have a mean grain size of approximately 10 μm and several pores with sizes ranging from 0.2 to 1.1 μm. In situ observations by Lorentz microscopy with an applied magnetic field reveals that in Mn–Zn ferrite, the domain walls move easily across the grain boundary, while in Ni–Zn ferrite, the domain walls move along the grain boundary but are pinned at the grain boundary and pores. From in situ observations of Ni–Zn ferrite by electron holography, it is clarified that domain wall pinning at the grain boundary retards a sensitive increase in magnetic flux parallel to the applied field direction, which is considered to result in high hysteresis loss.     

Locating and counting bifurcation points of satellite components from the main component in the degree-n bifurcation set

The bifurcation point where a satellite component buds from another component is characterized by the existence of the common tangent line between the two osculating components appearing in the degree-n bifurcation set. We investigate the existence, location and number of bifurcation points for satellite components budding from the main component in the degree-n bifurcation set as well as a parametric boundary equation of the main component of the degree-n bifurcation set. Cusp points are also located on the boundary of the main component. Typical degree-n bifurcation sets and their components are illustrated with some computational results.     

Analysis of the manufacturing lead time in a production system with non-renewal batch input,threshold policy and post-operation

In this paper, we analyze the manufacturing lead time in a production system with BMAP (Batch Markovian Arrival process) input and post-operation operated under the N-policy. We use the factorization principle to derive the waiting time distribution (hence the manufacturing lead time) and the mean performance measures. A numerical example is provided.     

Synthesis and electrical characteristics of polyaniline nanoparticles and their polymeric composite

Monodisperse polyaniline nanoparticles (PAPSSA) were synthesized from an oxidative dispersion polymerization using poly(sodium 4-styrenesulfonate) (PSSA) as both a polymeric stabilizer and a dopant agent due to its acidity. The nanoparticles were being stabilized with two different molecular weight of PSSA. Size effect of PAPSSA particles were examined by scanning electron microscopy (SEM), transmission electron microscopy (TEM) and dynamic light scattering (DLS). The d.c. electrical conductivity of composite films on the glass substrate was measured by a four-probe method. It was found that the electrical properties of the composite films are affected by the content of nano-sized polyaniline and different molecular weights of stabilizer in the poly(vinyl alcohol) (PVA) matrix.     

Logarithmic Sobolev trace inequality

A logarithmic Sobolev trace inequality is derived. Bounds on the best constant for this inequality from above and below are investigated using the sharp Sobolev inequality and the sharp logarithmic Sobolev inequality.

     

Influence of support properties on the sound radiated from the vibrations of rectangular plates

The control of the forced vibration response of structures through the optimal tuning of its supports is desirable in many applications. Tuning may enhance the dissipation of vibration energy within the supports, thereby reducing fatigue and structure-borne noise. Two different models were developed to calculate the optimal support stiffness that minimizes the velocity response of homogeneous plates. The first model, based on the wave propagation at the edge, yields a good first cut approximation of the optimal properties. The optimal viscous and viscoelastic support stiffness for minimal reflection at the edge was calculated. Maximum absorption of the incident waves occurs when the viscous support stiffness matches the characteristic mechanical impedances of the plate. The second model, based on the Rayleigh-Ritz method, yields more accurate estimates of the optimal support stiffness required to minimize the forced velocity response of the finite rectangular plate. The optimal support properties calculated from the two different methods were in good agreement. This suggested that the modal response of the plate is strongly influenced by the wave reflections at the edges. Finally, the effects of support properties on the sound radiated from the plate were investigated. The optimal support stiffness that minimizes the radiated sound power was found to be smaller than the value that minimizes the velocity response. The results show that both the velocity response and sound radiation are strongly influenced by dissipation of vibration energy at the edges, and demonstrate that support tuning can yield significant noise and vibration reduction.     

Metallization of U3O8via catalytic electrochemical reduction with Li2O in LiCl molten salt

The concept of a novel electrochemical reduction process for the treatment of spent nuclear fuels in Li₂O-LiCl molten salt was proposed and fresh tests using U₃O₈ powder were carried out to elucidate the reaction mechanism and verify the feasibility of the process. Electrolysis of Li₂O and reduction of U₃O₈ powder took place simultaneously at the cathode part of the electrolysis cell via a catalytic EC mechanism and the conversion of U₃O₈ to U metal was more than 99%. This revised version was published online in June 2006 with corrections to the Cover Date.