Bootstrapping a weighted linear estimator of the ARCH parameters

Abstract.  A standard assumption while deriving the asymptotic distribution of the quasi maximum likelihood estimator in ARCH models is that all ARCH parameters must be strictly positive. This assumption is also crucial in deriving the limit distribution of appropriate linear estimators (LE). We propose a weighted linear estimator (WLE) of the ARCH parameters in the classical ARCH model and show that its limit distribution is multivariate normal even when some of the ARCH coefficients are zero. The asymptotic dispersion matrix involves unknown quantities. We consider appropriate bootstrapped version of this WLE and prove that it is asymptotically valid in the sense that the bootstrapped distribution (given the data) is a consistent estimate (in probability) of the distribution of the WLE. Although we do not show theoretically that the bootstrap outperforms the normal approximation, our simulations demonstrate that it yields better approximations than the limiting normal.     

On-line search based pulsating torque compensation of a fault modesingle-phase variable frequency induction motor drive

Improved reliability and fault tolerant operation of inverter-fed variable frequency AC motor drives are very important for critical industrial applications. The paper describes variable frequency, variable voltage operation of a three-phase induction motor drive in single-phase mode for inverter fault conditions, such as open base drive and device short circuit. The detailed mathematical analysis of the machine in single-phase mode indicates that odd harmonic voltages of appropriate magnitude and phase can be injected at the machine terminal to neutralize the large low-frequency pulsating torques so as to permit smooth drive operation. The magnitude and phase angle of the desired harmonic voltages have been derived theoretically. However, to eliminate the parameter variation effect and operating point dependencies, a general purpose search algorithm has been proposed in the paper which fabricates the desired harmonic voltages on a real time basis. The search algorithm was initially exercised manually on a simulated drive system to prove its validity, and than tested extensively on a volts/hertz controlled 3-hp drive system in the laboratory     

Fenton and Electro-Fenton Methods for Oxidation of H-Acid and Reactive Black 5

Oxidative treatment of H-acid (HA) and Reactive Black 5 (RB5) using Fenton reagent (Fe2+/H2O2) and the electro-Fenton (EF) method is reported. Optimization of doses of ferrous iron and hydrogen peroxide was carried out in each case using HA; and the oxidation of RB5 was also carried out under the optimized conditions. Approximately 71% chemical oxygen demand (COD) was removed in 2 h using the conventional Fenton method at optimized doses: Fe2+ = 0.3?g/L (5.37 mM), H2O2 = 6?mL/L (53.0 mM), H2O2/Fe2+ = 10. In contrast, more than 92% COD was removed in 15 min using the EF method with an optimized Fe2+ dose of 0.130?g/L (2.34 mM) and 8?ml/L (70.6 mM) of H2O2. The pseudo-first-order rate constants (k) for the Fenton reagent and EF method were 0.054 and 0.38?min?1. The COD removal through the EF method was seven times faster. The calculated energy requirement of the EF method was 0.82?kg?COD/kW?h at the minimum applied current (0.25 A) when approximately 92.5% COD was removed. In the case of RB5, about 67 and 87% COD was removed under optimized Fenton and electro-Fenton conditions, respectively. The higher efficiency of the EF method was attributed to incremental addition of Fe2+ and accompanying higher H2O2/Fe2+ molar ratio. The results are discussed in the light of the mechanism for Fenton’s oxidation.     

Thermal properties of MoSi2 and SiC whisker-reinforced MoSi2

The heat capacity, thermal conductivity and coefficient of thermal expansion of MoSi₂ and 18 vol % SiC whisker-reinforced MoSi₂ were investigated as a function of temperature. The materials were prepared by hot isostatic pressing between 1650 and 1700 °C, the hold time at temperature being 4 h. The heat capacity of MoSi₂ showed an increase from about 0.44 Wsg^–11K^–1 at room temperature to 0.53 at 700 °C. Whisker reinforcement increased heat capacity by about 10%. Thermal conductivity exhibited a decreasing trend from 0.63 Wcm^–1 K^–1 at room temperature to 0.28 Wem^–1 K^–1 at 1400°C. Whiskers reduced conductivity by about 10%. The thermal expansion coefficient increased from 7.42 °C^–1 between room temperature and 200 °C to 9.13 °C^–1 between room temperature and 1200 °C. There was a 10% decrease resulting from the whiskers. The measured data are compared with literature values. The trends in the data and their potential implications for high-temperature aerospace applications of MoSi₂ are discussed.     

A method to determine whether two polynomials are relatively prime

In this paper, it is established that a necessary and sufficient condition for two monic polynomialsf(lambda)andg(lambda)to have a common root is thatdet [f(B)] = 0ordet [g(A)] = 0, whereAandBare, respectively, the companion matrices associated withf(lambda)andg(lambda). The simplicity of this method is illustrated by examples.     

Estimation of hole conductivity of AgI through tarnishing studies of silver in iodine vapour at about room temperature

This work reports the hole conductivity data of growing AgI film on silver both for the thicker (5500 to 30 000 Å) and thinner (<6000 Å) ranges at about room temperature. Hole conductivity has been estimated through tarnishing studies of silver in iodine atmosphere and estimation has been based on the fundamental equation of Wagner relating the rate constant and the conductivity of the film. It is revealed that the thinner films show a higher hole conductivity than that of the thicker films under similar temperature and iodine pressure.     

Editorial

Editorial Commentary

Editorial     

High-frequency, depressing inhibition facilitates synchronization in globally inhibitory networks

Motivated by the study of sharp wave-associated ripples, high-frequency (approximately 200 Hz) extracellular field oscillations observed in the CA1 region of the rat hippocampus during slow-wave sleep and periods of behavioural immobility, we consider a single inhibitory neuron synapsing onto a network of uncoupled, excitatory neurons. The inhibitory synapse is depressing and has a small synaptic delay. Each excitatory cell provides instantaneous, positive feedback to the inhibitory cell. We show that the interneuron can rapidly synchronize the action potentials of the pyramidal cells if the frequency of inhibitory input is increased in a ramp-like manner as occurs during the ripple. We show that the basin of attraction of the synchronous solution is larger when the inhibition frequency is gradually increased as opposed to remaining constant.     

An efficient algorithm for superresolution in medium field imaging

In this paper, we study the problem of reconstruction of a high-resolution (HR) image from several blurred low-resolution (LR) image frames in medium field. The image frames consist of blurred, decimated, and noisy versions of a HR image. The HR image is modeled as a Markov random field (MRF), and a maximum a posteriori (MAP) estimation technique is used for the restoration. We show that with the periodic boundary condition, a HR image can be restored efficiently by using fast Fourier transforms. We also apply the preconditioned conjugate gradient method to restore HR images in the aperiodic boundary condition. Computer simulations are given to illustrate the effectiveness of the proposed approach. This research was conducted with support from the Army Research Office Grant DAAD 19-03-1-0261 and the National Science Foundation Grant CCF-0429481. Research supported in part by RGC Grant Nos. 7130/02P, 7046/03P, 7035/04P and 7035/04P and FRG/04-05/II-51.