Clustering of Points Randomly Distributed in \u3cem\u3en\u3c/em\u3e-Dimensional Space

We consider clusters formed by points randomly distributed in space, each point being connected to its nearest neighbor or to its nearest and next nearest neighbors. The size distribution of such clusters in n-dimensional space is presented

Unifying the Phase Diagrams of the Magnetic and Transport Properties of La_(2-x)Sr_xCuO_4, 0 < x < 0.05

An extensive experimental and theoretical effort has led to a largely complete mapping of the magnetic phase diagram of La_(2-x)Sr_xCuO_4, and a microscopic model of the spin textures produced in the x < 0.05 regime has been shown to be in agreement with this phase diagram. Here we use this same model to derive a theory of the impurity-dominated, low temperature transport. Then, we present an analysis of previously published data for two samples: x = 0.002 data from Chen et. al., and x = 0.04 data from Keimer et. al. We show that the transport mechanisms in the two systems are the same, even though they are on opposite sides of the observed insulator-to-metal transition. Our model of impurity effects on the impurity band conduction, variable-range hopping conduction, and coulomb gap conduction, is similar to that used to describe doped semiconductors. However, for La_(2-x)Sr_xCuO_4 we find that in addition to impurity-generated disorder effects, strong correlations are important and must be treated on a equal level with disorder. On the basis of this work we propose a phase diagram that is consistent with available magnetic and transport experiments, and which connects the undoped parent compound with the lowest x value for which La_(2-x)Sr_xCuO_4 is found to be superconducting, x about 0.06.Comment: 7 pages revtex with one .ps figur

Fine Structure in the Optical-Absorption Edge of Silicon

Details of the structure in the indirect optical-absorption edge of silicon were studied by measuring the dependence of the photocurrent in p−n junctions on the energy of the incident photons. The measurements were made at room and higher temperatures for photon energies 0.75 \u3c hν \u3c 1.08 eV. The sensitivity of the method enabled high-resolution measurements in the absorption tail. At room temperature, thresholds were found at ~ 0.91, 0.99, and 1.026 eV. he derivative of the response showed extensive fine structure in this tail. The TO- and LO-phonon-assisted transitions to the ground and excited state of the exciton, previously reported in the phonon emission region, were seen here with phonon absorption occurring around 1.054 and 1.065 eV. There was additional structure of unknown origin in this region

Invariance property of the determinant of a matrix whose elements are a sum of sinusoids and its application

We show that for a signal composed of a sum of m sinewaves with arbitrary frequencies, phases and amplitudes, there exists an instantaneous non-linear function of the signal, which takes on a constant magnitude anywhere on the time axis. This non-linear function is the determinant of a matrix. In the case of continuous-time signals, this matrix is composed of (2m-1) derivatives of the signal. For discrete time signals, the matrix is embedded with (2m-1) signal samples. Using this property, we show that we can determine the frequencies, phases and amplitudes of the m sinewave components. This is accomplished by adding a known auxiliary probe signal to the original signal before computing the determinant function. The nulls in the determinant function, as the frequency of the probe is varied, reveal the frequencies of the m sinewaves. The amplitudes and phases are computed using a ratio of two determinant values

On accurately tracking the harmonic components\u27 parameters in voiced-speech segments and subsequent modeling by a transfer function

We propose an improved method to model voiced speech signals. First, we describe a method to accurately model the signals using a linear combination of harmonically related sinewaves. The method fits a linear combination of sines and cosines whose frequencies are integer multiples of the unknown fundamental (pitch) frequency to the speech data in the least-square sense. The amplitudes of the sinewaves and the fundamental frequency are the unknowns and are determined simultaneously using the least-squares fit. Using our method, we show how one can obtain smoothly varying frequency and amplitude tracks for all the harmonics and thus model the speech signal parsimoniously. After obtaining the harmonic decomposition, we regard the time-varying amplitudes of the cosinusoidal and sinusoidal harmonic components as the real and imaginary parts of the complex-valued frequency responses of the slowly time-varying filter representing the vocal tract and glottal excitation pulse generator, in cascade. We then fit a sequence of all-pole/pole-zero models to the complex frequency response values

Analysis of errors in the computation of Fourier coefficients using the Arithmetic Fourier Transform (AFT) and summation by parts (SBP)

The computational complexity and the effects of quantization and sampling instant errors in the arithmetic Fourier transform (AFT) and the summation-by-parts discrete Fourier transform (SBP-DFT) algorithms are examined. The relative efficiency of the AFT and SBP-DFT algorithms is demonstrated by comparing the number of multiplications, additions, memory storage locations, and input signal samples as well as the latency time and level of parallelism of these two methods with that of more conventional single-output DFT and multiple-output fast Fourier transform (FFT) routines. The error response of the kth Fourier bin of these algorithms is analyzed as a function of increasing levels of input signal sampling errors in the AFT and coefficient quantization errors in the SBP-DFT. It is demonstrated that invalid assumptions on the bandwidth of the input signal will cause aliasing errors to occur in the AFT spectrum that are different from the aliasing errors that occur in the DFT

Instantaneous non-linear operators for tracking multicomponent signal parameters

The authors have extended the Kaiser-Teager algorithm for separating the contributions of the amplitude modulation and frequency modulation of a single sinusoid to a signal consisting of multiple components. An instantaneous nonlinear operator turns out to be the determinant of a Toeplitz matrix formed with the signal samples. Because of its instantaneously adaptive nature, this algorithm can be used to track parameter variations in the signal components, provided these variations are not too rapid. This is demonstrated using a synthetic signal containing two AM-FM components and a speech signal. The method\u27s relationship to Prony\u27s method is pointed out

1,4-Conjugate addition of allyltrimethylsilane to α,β-unsaturated ketones

α,β-Unsaturated ketones smoothly undergo conjugate addition with allyltrimethylsilane in the presence of a catalytic amount of elemental iodine under very mild and convenient conditions to afford the corresponding Michael adducts in high yields with high selectivity