High-voltage field-controlled integrated thyristor

The design and technology of powerful field-controlled integrated thyristors, new energy-saving devices intended for converter equipment, are considered. The turn-on and turn-off current and voltage waveforms of the n+p′N-n′p ⁺ microthyristor chip are presented, and turn-on and turn-off mechanisms are discussed. The development of local dynamic breakdown at turn-off is experimentally studied. The respective waveforms for this process are given, and the type of breakdown at a current density of about 150 A/cm² is demonstrated. The current-voltage characteristics in the on state at room temperature and at 125°C indicate the temperature dependence changes sign at a current density above 60 A/cm², becoming positive. This is significant for parallel operation of microthyristor chips in a module. It is shown that the static and dynamic characteristics of simple-in-design field-controlled integrated thyristors are highly competitive with those of insulated-gate bipolar transistors-basic devices of advanced high-power converter equipment.     

Brondsted order in a metric space and generalizations of Caristi theorem

Fixed point and coincidence theorems for mappings of ordered sets and their metric counterparts generalizing the well-known Caristi fixed point theorem are presented.     

High-voltage fast diode with “soft” recovery

High-voltage fast silicon p ⁺ Nn ⁺ diodes used in almost all modern electrical energy converters must have a low residual voltage in the conducting state, but can simultaneously be rapidly switched to the off state with low commutation losses without producing a surge overvoltage. Such a combination of parameters is usually ensured by producing the profile concentration distribution for recombination centers in the N base with a peak of the p ⁺ N junctions. Such a distribution is produced by irradiating the p ⁺ Nn ⁺ diode in vacuum by protons or α particles on the side of the p ⁺ N junctions. We report on the results of testing of diodes in which profile distribution for the centers is obtained using a simpler and more productive method by electron bombardment in a certain energy range in air. It is shown using the specially designed devices with a blocked voltage up to 5 kV that all dynamic characteristics of the diodes correspond to the world standard, and the residual voltage in the conducting state for the working current density is approximately 30% lower.     

Fractional moments of automorhic L-FUNCTIONS. II

Asymptotics for fractional moments of automorphic L-functions are found. Bibliography: 11 titles.     

A general formula of the solutions of the Peterson-Codazzi equations on a hypersphere

Translated from Ukrainskii Geometricheskii Sbornik, No. 32, pp. 124–126, 1989.     

Distribution of values of Fourier coefficients for modular forms of weight 1

For modular forms of weight, 1, the distribution of values of their Fourier coefficients over polynomial sequences of natural numbers is considered. A new proof of Bernays' theorem is given. It is proved that the error term in the well-known Rankin-Selberg asymptotic formula can be improved for cusp forms associated with binary theta series. Bibliography: 52 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 196–227.     

Mathematical statistics and problems of ancient chronology. A new approach

New methods of processing statistically quantitative textual information of a narrative character are introduced. The methods can be used to recognize dependent and independent texts among large collections of texts. The methods are applied to the problem of correct dating of the events in ancient chronology. These results induce conjecture on the redating of some historical events.     

Sum of squares in imaginary quadratic fields

One obtains results related with the representation of integers as sums of three squares in imaginary quadratic fields.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 125, pp. 184–197, 1983.     

Identity between the fourth-degree Riemann theta-constant of genus 2 and the Eisenstein series

One proves the identity between the Siegel theta-series of genus 2 associated with the 4×4 identity matrix and the corresponding Eisenstein-Siegel series.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 91, pp. 158–168, 1979.The author dedicates this paper to Askol'd Ivanovich Vinogradov on the occasion of his 50th birthday.