Certain extremal problems for polynomials

Extensions of two classical results about polynomials, one due to W. Markov and the other due to Duffin and Schaeffer, are obtained in this paper. An interesting result of S. Bernstein, which went unnoticed until it was rediscovered by P. Erdos, years later, is also generalized. Our results are especially amenable to numerical calculations, and may, therefore, be of some practical importance.

     

Noetherian PI Hopf algebras are Gorenstein

We prove that every noetherian affine PI Hopf algebra has finite injective dimension, which answers a question of Brown (1998).

     

New type of biosensor based on magnetic nanoparticle detection

A new type of biosensor has been developed based on detection of nanosized superparamagnetic particles that serve as labels in bioreactions. The method is based on non-linear magnetic material detection by a magnetic field having components at two frequencies f₁ and f₂. The response is measured at the combinatorial frequencies f_i=mf₁+nf₂, where m and n are integers, e.g., f_i=f₁±2f₂. Several highly sensitive readers of superparamagnetic particles have been designed and used for development of various formats of immunoassays, including those compatible with immunoconcentration and magnetic enrichment of antigens.     

Preparation and characterization of a poled nanocrystal and polymer composite PbTiO3/PEKc film for electro-optic applications

Composite thin films of PbTiO₃ nanocrystals and high-transparency PEKc polymer for applications in electro-optical devices were prepared using the spin coating technique. The size of the PbTiO₃ nanocrystals was estimated to be 30–40 nm using a transmission electron microscope. The transmission technique, a simple method for measuring the electro-optic coefficients of poled composite polymer films was developed. The electro-optic coefficient γ₃₃ of poled PbTiO₃/PEKc composite polymer films was measured to be 18.34 pm  V^-1 at 633 nm under room temperature. The index at 633 nm and the dielectric constant at 100 kHz under room temperature were determined to be 1.65248 and 7.32, respectively. The figure of merit F₂=n⁷γ²/ε was estimated to be 1546, showing very good electro-optical properties. Received: 5 February 2002 / Accepted: 12 March 2002 / Published online: 19 July 2002 RID="*" ID="*"Corresponding author. Fax: +852/2788-7791, E-mail: eeytc@cityu.edu.hk     

Studies of ion energy and yield from argon clusters heated by intense femtosecond laser pulses

Using time-of-flight spectrometry, the interaction of intense femtosecond laser pulses with argon clusters has been studied by measuring the energy and yield of emitted ions. With two different supersonic nozzles, the dependence of average ion energy on cluster size in a large range of has been measured. The experimental results indicate that when the cluster size , the average ion energy Coulomb explosion is the dominant expansion mechanism. Beyond this size, the average ion energy gets saturated gradually, the clusters exhibit a mixed Coulomb-hydrodynamic expansion behavior. We also find that with the increasing gas backing pressure, there is a maximum ion yield, the ion yield decreases as the gas backing pressure is further increased.     

Quantum entanglement and chaos in kicked two-component Bose-Einstein condensates

We study two-component Bose-Einstein condensates that behave collectively as a spin system obeying the dynamics of a quantum kicked top. Depending on the nonlinear interaction between atoms in the classical limit, the kicked top exhibits both regular and chaotic dynamical behavior. The quantum entanglement is physically meaningful if the system is viewed as a bipartite system, where the subsystem is any one of the two modes. The dynamics of the entanglement between the two modes in this classical chaotic system has been investigated. The chaos leads to rapid rise and saturation of the quantum entanglement. Furthermore, the saturated values of the entanglement fall short of its maximum. The mean entanglement has been used to clearly display the close relation between quantum entanglement and underlying chaos.     

Design of interdigital transducers for crack detection in plates

Interdigital transducers (IDT) for non-destructive evaluation (NDE) of cracks in plates are designed based on an analytical model established previously. Key considerations include mode selectivity, excitation strength, collimation of wave and cost. The advantage of mode selectivity of IDT over PZT patch is presented both analytically and experimentally. Effects of parameters, namely finger spacing, width, length, number of fingers, and the size of IDT, on the excitation strength and mode selectivity are considered. This led to the design of a mobile double-sided IDT as an efficient device where excitation strength is strong and focused. The device was fabricated in-house using commercially available piezoelectric ceramics and used to develop a procedure for accurate identification of the direction and extent of cracks in plates. Three aluminum plates, one with a linear deep crack, another with a piecewise linear shallower crack and the third with a curved crack, were used to illustrate the accuracy and efficiency of both the proposed device and procedure for effective NDE.     

Observations of surface modifications induced by the multiple pulse irradiation using a soft picosecond x-ray laser beam

To study the interactions between picosecond soft x-ray laser (SXRL) beams and material surfaces, gold (Au), copper (Cu), and silicon (Si) surfaces were irradiated with SXRL pulses having a wavelength of 13.9 nm and a duration of ～7 ps. Following irradiation, the surfaces of the substrates were observed using a scanning electron microscope and an atomic force microscope. With single pulse irradiation, ripple-like structures were formed on the Au and Cu surfaces. These structures were different from previously investigated conical structures formed on an Al surface. In addition, it was confirmed that the development of modified structures, i.e., growth of hillocks on the Au and Cu surfaces, was observed after multiple SXRL pulse exposures. However, on the Si surface, deep holes that seemed to be melted structures induced by the accumulation of multiple pulses of irradiations were found. Therefore, it was concluded that SXRL beam irradiation of various material surfaces causes different types of surface modifications, and the changes in the surface behaviors are attributed to the differences in the elemental properties, such as the attenuation length of x-ray photons.     

All-solid-state continuous-wave frequency doubling Nd:LuVO4/LBO laser with 2.17 W output power at 543 nm

Efficient and compact green-yellow laser output at 543 nm is generated by intracavity frequency doubling of a CW diode-pumped Nd:LuVO₄ laser at 1086 nm under the condition of suppressing the higher gain transition near 1064 nm. With 16 W of diode pump power and the frequency-doubling crystal LBO, as high as 2.17 W of CW output power at 543 nm is achieved, corresponding to an optical-to-optical conversion efficiency of 13.6% and the output power stability over 8 hours is better than 2.86%. To the best of our knowledge, this is the highest watt-level laser at 543 nm generated by intracavity frequency doubling of a diode pumped Nd:LuVO₄ laser at 1086 nm.