The components of chi-squared statistics for goodness-of-fit tests

One obtains a formula for the transformation of a vector with a given covariance matrix. The sum of the squares of the components of the transformed vector is equal to a chi-square type quadratic form, constructed with the aid of the initial vector. Taking into account this property, one finds the components of the Pearson statistic, Pearson-Fisher statistic, etc.Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 337–350, 1986.     

OTDM transmitter using WDM-TDM conversion with an electroabsorptionwavelength converter

An all-optical multiplexing technique using wavelength division multiplexing (WDM)-time division multiplexing (TDM) conversion with an electroabsorption wavelength converter has been proposed and demonstrated. The effectiveness of this WDM-TDM conversion technique for various pulsewidth settings was experimentally investigated. The fluctuation of the signal performance, which was inevitably caused by the coherent crosstalk between adjacent pulses in the conventional optical time division multiplexing (OTDM) technique, were successfully suppressed, even in the case of wide pulse duration. High Q-factor performance has been maintained for a wide range of duty ration from 36% to 74%. By introducing this technique to the optical time division multiplexer, a highly stable and high-quality 40-Gb/s optical signal can be effectively produced without generating the short pulse or setting two tributaries at orthogonal polarization states, and without introducing high-speed electronics for signal multiplexing. The WDM-TDM conversion with an electroabsorption wavelength converter was extended to 60-Gb/s operation by using three 20-Gb/s tributaries. A clear eye opening was confirmed for a waveform after the WDM-TDM conversion of the 60-Gb/s signal     

A study of three techniques used in the diffraction analysis ofshaped dual-reflector antennas

An examination is presented of three techniques used for the efficient computation of fields diffracted by a subreflector that has been shaped by geometrical optics synthesis. It is found that these techniques, which are based on the geometrical theory of diffraction (GTD), produce errors in the computed fields that are specific to shaped reflectors. These errors are examined for a reflector system shaped to produce maximum gain from a tapered feed illumination. The discrepancies are directly related to the caustic being located near an observation point of the GTD calculations. The errors found are localized, and they increase in magnitude as the caustic approaches the main reflector. In a general offset geometry, the location of the caustic may be located arbitrarily close to the main reflector given a prescribed output aperture distribution. For the specific case considered here-the common situation of shaping to produce maximum gain-the caustic is located near the edge of the main reflector and on the reflection shadow boundary. A local correction is derived which creates a uniform solution through the caustic and across the reflection shadow boundary. Away from this point the calculation recedes to the standard GTD solution     

Performance engineering and topological design of metro WDM opticalnetworks using computer simulation

This paper demonstrates the use of computer simulation for topological design and performance engineering of transparent wavelength-division multiplexing metropolitan-area networks. Engineering of these networks involves the study of various transport-layer impairments such as amplifier noise, component ripple, chirp/dispersion, optical crosstalk, waveform distortion due to filter concatenation, fiber nonlinearities, and polarization effects. A computer simulation methodology composed of three main simulation steps is derived and implemented. This methodology obtains performance estimations by applying efficient wavelength-domain simulations on the entire network topology, followed by time-/frequency-domain simulations on selected paths of the network and finally Q-budgeting on an identified worst case path. The above technique provides an efficient tool for topological design and network performance engineering. Accurate simulation models are presented for each of the performance impairments, and the computer simulation methodology is used for the design and engineering of a number of actual metro network architectures     

Mode coupling contribution to radiation losses in curvatures for high and low numerical aperture plastic optical fibers

We have studied the optical power losses due to multiple curvatures in polymethylmetacrylate (PMMA) plastic optical fibers (POFs) of different numerical apertures (NAs) and attenuation. The fibers were tested for several configurations in order to assess the influence of different types of curved-to-straight fiber transitions in the amount of power radiation. We found that losses are below the standards for all tested fiber types, and thus, they are a suitable choice for local area network (LAN) applications. In addition, our results revealed the presence of modal interactions as confirmed using an experimental procedure to estimate the mode coupling strength for the same fibers.     

Integrated chaos generators

This paper surveys the different design issues, from mathematical model to silicon, involved in the design of analog CMOS integrated circuits for the generation of chaotic behavior     

Numerical solutions of the shallow water equations with discontinuous bed topography

A simple scheme is developed for treatment of vertical bed topography in shallow water flows. The effect of the vertical step on flows is modelled with the shallow water equations including local energy loss terms. The bed elevation is denoted with z_b^‐ for the left and z_b⁺ for the right values at each grid point, hence exactly representing a discontinuity in the bed topography. The surface gradient method (SGM) is generalized to reconstruct water depths at cell interfaces involving a vertical step so that the fluxes at the cell interfaces can accurately be calculated with a Riemann solver. The scheme is verified by predicting a surge crossing a step, a tidal flow over a step and dam‐break flows on wet/dry beds. The results have shown good agreements compared with analytical solutions and available experimental data. The scheme is efficient, robust, and may be used for practical flow calculations. Copyright © 2002 John Wiley & Sons, Ltd.     

Whitening of sidelobe powers by pattern switching in radar array antenna

Presented here is a concept for nearly eliminating bias errors in reflectivity and velocity estimates due to power received through antenna sidelobes of pulse Doppler radars. The antenna pattern is switched from pulse to paise among specially designed patterns, with near identical main lobes, but with sidelobes having randomly distributed phases and amplitudes. The sidelobe signal then becomes incoherent without affecting the coherency of the main lobe signal. The whitened sidelobe signal does not bias the mean velocity estimate computed by Doppler processing, and an unbiased estimate of reflectivity can be computed with the knowledge of the mean whitened power level. Pattern design criteria and a method for the design of optimum patterns are developed for a linear array. The extent of sidelobe reduction by way of whitening has been studied in detail for special case of only two patterns switched randomly using a pseudonoise sequence. Pattern switching realizes an effectively low sidelobe pattern without sacrifice of main lobe resolution. A possible extension to two-dimensional arrays is suggested.     

Higher-dimensional homogeneous cosmological models as autonomous dynamical systems

The field equations for homogeneous models in an arbitrary number of dimensions form a Hamiltonian system with constraint forces. Due to the monotonic behavior of the determinant of the induced metric, the evolution of the system can be interpreted as the motion of a particle in an explicitly time-dependent potential. Considering vacuum models, we show that this explicit time-dependence can be eliminated. Using the scaling properties of the Ricci tensor we obtain an autonomous system, for which we can also find a Liapunov function in terms of the n-dimensional Ricci curvature.