The collocation method for the solution of boundary integral equations

This article is devoted to investigating the approximate solutions to a class of boundary integral equations over a closed, bounded and smooth surface found via the collocation method. This article provides sufficient conditions for the convergence of this method in the space of continuous functions.     

A method for calculating active feedback system to provide vertical position control of plasma in a tokamak

In designing tokamaks, the maintenance of vertical stability of plasma is one of the most important problems. Systems of the passive and active feedbacks are applied for this purpose. Role of the passive system consisting of a vacuum vessel and passive coils is to suppress fast MHD (magnetohydrodynamic) instabilities. The active feedback system is applied to control slow motions of plasma. The objective of the paper is to investigate two successive problems, solution of which allows to determine the possibility of controlling plasm a motions. One of these is the problem of vertical stability under the assumption of ideal conductivity of plasma and passive stabilizing elements. The problem is solved analytically and on the basis of the obtained solution a criterion of MHD-stability is formulated. The other problem is connected with the control of plasma vertical position with active feedback system. Calculation of feedback control parameters is formulated as an optimization problem and an approximate method to solve the problem is suggested. Numerical simulations are performed with parameters of the T-15M tokamak in order to justify the suggested method.      

The fine structure of the recovering auditory detection threshold.

Detection thresholds were gathered for a 2 kHz Gaussian-shaped probe (standard deviation = 0.5 ms), centered at intervals of as little as half a millisecond over 0-30 ms following a 200 ms, 97 dB SPL, 2 kHz tone. Surprisingly, there were small, sudden rises and falls superimposed on each subject's generally smooth recovery. Even more obvious were nonmonotonicities in the standard deviation of the cumulative normal fitted to each threshold's psychometric function.     

Effects of peripheral nonlinearity on psychometric functions for forward-masked tones

Psychometric functions (PFs) for forward-masked tones were obtained for conditions in which signal level was varied to estimate threshold at several masker levels (variable-signal condition), and in which masker level was varied to estimate threshold at several signal levels (variable-masker condition). The changes in PF slope across combinations of masker frequency, masker level, and signal delay were explored in three experiments. In experiment 1, a 2-kHz, 10-ms tone was masked by a 50, 70 or 90 dB SPL, 20-ms on-frequency forward masker, with signal delays of 2, 20, or 40 ms, in a variable-signal condition. PF slopes decreased in conditions where signal threshold was high. In experiments 2 and 3, the signal was a 4-kHz, 10-ms tone, and the masker was either a 4- or 2.4-kHz, 200-ms tone. In experiment 2, on-frequency maskers were presented at 30 to 90 dB SPL in 10-dB steps and off-frequency maskers were presented at 60 to 90 dB SPL in 10-dB steps, with signal delays of 0, 10, or 30 ms, in a variable-signal condition. PF slopes decreased as signal level increased, and this trend was similar for on- and off-frequency maskers. In experiment 3, variable-masker conditions with on- and off-frequency maskers and 0-ms signal delay were presented. In general, the results were consistent with the hypothesis that peripheral nonlinearity is reflected in the PF slopes. The data also indicate that masker level plays a role independent of signal level, an effect that could be accounted for by assuming greater internal noise at higher stimulus levels.