Coincidence Wecken Property for Nilmanifolds

Let f, g: X → Y be maps from a compact infra-nilmanifold X to a compact nilmanifold Y with dim X ≥ dim Y. In this note, we show that a certain Wecken type property holds, i.e., if the Nielsen number N(f, g) vanishes then f and g are deformable to be coincidence free. We also show that if X is a connected finite complex X and the Reidemeister coincidence number R(f, g) = ∞ then f ～ f' so that C(f', g) = {x ∈ X | f'(x) = g(x)} is empty.     

Uniform Asymptotic Expansions for Meixner Polynomials

Meixner polynomials m _n (x;β,c) form a postive-definite orthogonal system on the positive real line x > 0 with respect to a distribution step function whose jumps are Unlike classical orthogonal polynomials, they do not satisfy a second-order linear differential equation. In this paper, we derive two infinite asymptotic expansions for m _n (nα;β,c) as . One holds uniformly for , and the other holds uniformly for , where a and b are two small positive quantities. Both expansions involve the parabolic cylinder function and its derivative. Our results include all five asymptotic formulas recently given by W. M. Y. Goh as special cases. April 16, 1996. Date revised: October 30, 1996.     

Pyroelectric properties of BiFeO3 ceramics prepared by a modified solid-state-reaction method

BiFeO₃ (BFO) ceramics were prepared by a modified solid-state-reaction method which adopts a higher heating/cooling rate during the sintering process than usually used. It was found that the calcination temperature T _cal (from 400 to 750°C) does not influence the BFO phase formation, while the sintering temperature T _sin (from 815 to 845°C) dominates the phase purity. The optimum sintering temperature was in the range from 825 to 835°C. The optimized samples exhibit saturated ferroelectric hysteresis loops with a remnant polarization of 13.2 μC/cm². The measured piezoelectric coefficient d ₃₃ was 45 pC/N. No remnant magnetization was observed in all of the samples. The pyroelectric properties were studied as a function of temperature and frequency. A pyroelectric coefficient as high as 90 μC/m² K was obtained at room temperature in the optimized sample. An abrupt decrease of the pyroelectric coefficient was observed at temperatures between 70 and 80°C. On the basis of our results, BFO may have the potential for pyroelectric applications.     

Neighbor Distinguishing Edge Colorings Via the Combinatorial Nullstellensatz Revisited

Consider a simple graph and its proper edge coloring c with the elements of the set . We say that c is neighbor set distinguishing (or adjacent strong) if for every edge , the set of colors incident with u is distinct from the set of colors incident with v. Let us then consider a stronger requirement and suppose we wish to distinguishing adjacent vertices by sums of their incident colors. In both problems the challenging conjectures presume that such colorings exist for any graph G containing no isolated edges if only . We prove that in both problems is sufficient. The proof is based on the Combinatorial Nullstellensatz, applied in the “sum environment.” In fact the identical bound also holds if we use any set of k real numbers instead of as edge colors, and the same is true in list versions of the both concepts. In particular, we therefore obtain that lists of length ( in fact) are sufficient for planar graphs.     

A brief review of co-doping

Dopants and defects are important in semiconductor and magnetic devices. Strategies for controlling doping and defects have been the focus of semiconductor physics research during the past decades and remain critical even today. Co-doping is a promising strategy that can be used for effectively tuning the dopant populations, electronic properties, and magnetic properties. It can enhance the solubility of dopants and improve the stability of desired defects. During the past 20 years, significant experimental and theoretical efforts have been devoted to studying the characteristics of co-doping. In this article, we first review the historical development of co-doping. Then, we review a variety of research performed on co-doping, based on the compensating nature of co-dopants. Finally, we review the effects of contamination and surfactants that can explain the general mechanisms of co-doping.     

Sub-Rayleigh imaging via N-photon detection

The Rayleigh diffraction bound sets the minimum separation for two point objects to be distinguishable in a conventional imaging system. We demonstrate sub-Rayleigh resolution by scanning a focused beam--in an arbitrary, object-covering pattern that is unknown to the imager--and using N-photon photodetection implemented with a single-photon avalanche detector array. Experiments show resolution improvement by a factor ～(N-N(max))(?) beyond the Rayleigh bound, where N(max) is the maximum average detected photon number in the image, in good agreement with theory.     

On impulsive control for synchronization and its application to the nuclear spin generator system

The issue of impulsive control theory for the synchronization of the nuclear spin generator (NSG) chaotic systems is developed. We propose an impulsive control scheme for the complete synchronization of the NSG system including chaotic systems. A sufficient condition for the impulsive control is derived, with an easily calculated maximum impulsive interval. The proposed impulsive control scheme is applied to the NSG system and the simulation result demonstrates the effectiveness of the method.     

Ultralow power continuous-wave frequency conversion in hydrogenated amorphous silicon waveguides

We demonstrate wavelength conversion through nonlinear parametric processes in hydrogenated amorphous silicon (a-Si:H) with maximum conversion efficiency of -13 dB at telecommunication data rates (10 GHz) using only 15 mW of pump peak power. Conversion bandwidths as large as 150 nm (20 THz) are measured in continuous-wave regime at telecommunication wavelengths. The nonlinear refractive index of the material is determined by four-wave mixing (FWM) to be n(2)=7.43×10(-13) cm(2)/W, approximately an order of magnitude larger than that of single crystal silicon.     

The effects of binaural spectral resolution mismatch on Mandarin speech perception in simulated electric hearing

This study assessed the effects of binaural spectral resolution mismatch on the intelligibility of Mandarin speech in noise using bilateral cochlear implant simulations. Noise-vocoded Mandarin speech, corrupted by speech-shaped noise at 0 and 5?dB signal-to-noise ratios, were presented unilaterally or bilaterally to normal-hearing listeners with mismatched spectral resolution between ears. Significant binaural benefits for Mandarin speech recognition were observed only with matched spectral resolution between ears. In addition, the performance of tone identification was more robust to noise than that of sentence recognition, suggesting factors other than tone identification might account more for the degraded sentence recognition in noise.     

The analysis of a finite element method for the three-species Lotka–Volterra competition-diffusion with Dirichlet boundary conditions

A Galerkin finite element method is developed for the two dimensional/three dimensional nonlinear time-dependent three-species Lotka–Volterra competition-diffusion equations on a bounded domain. The existence and uniqueness of the solution to the numerical formulation are proved. An error estimate for the numerical solution is obtained. Numerical computations are carried out to examine the expected orders of accuracy in the error estimates.