Electrical breakdown of anodic aluminum oxide

Results are presented from a study of electrical breakdown of anodic aluminum oxide in a constant field with a platinum pressure electrode. Statistical breakdown parameters and their dependence on the magnitude and polarity of the applied voltage are obtained. Field and temperature dependences of breakdown delay time over the interval 10^–6–10³ sec are determined. It is shown that the experimental (E) curves can be rectified (in two segments) in the coordinates log E^–1. This indicates a possible contribution to the breakdown mechanism by both tunnel injection of electrons from the cathode and subsequent avalanche multiplication of electrons within the dielectric.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 25–29, April, 1990.In conclusion, the authors thank T. V. Shmidt and E. Ya. Khanin for assistance in the study.     

Operator stable laws: Series representations and domains of normal attraction

LetX,X ₁,X ₂,... be i.i.d. random vectors in ^d. The limit laws that can arise by suitable affine normalizations of the partial sums,S _n=X ₁+...+X _n, are calledoperator-stable laws. These laws are a natural extension to ^d of the stable laws on. Thegeneralized domain of attraction of [GDOA()] is comprised of all random vectorsX whose partial sums can be affinely normalized to converge to . If the linear part of the affine transformation is restricted to take the formn ^–B for some exponent operatorB naturally associated to thenX is in thegeneralized domain of normal attraction of [GDONA()]. This paper extends the theory of operator-stable laws and their domains of attraction and normal attraction.     

Discrimination of frequency transitions by human infants

Difference limens (DLs) for linear frequency transitions using a 1.0-kHz pulsed-tone standard were obtained from 6- to 9-month-old human infants in a series of three experiments. A repeating standard "yes-no" operant headturning technique and an adaptive staircase (tracking) procedure were used to obtain difference limens from a total of 71 infants. The DLs for 300-ms upward and downward linear frequency sweeps were approximately 3%-4% when the repeating standard was an unmodulated 1.0-kHz pulsed tone of 300-ms duration. These DLs for frequency sweeps were not significantly different from DLs for frequency increments and decrements using 330-ms pulsed tones [J. M. Sinnott and R. N. Aslin, J. Acoust. Soc. Am. 78, 1986-1992 (1985)]. The DLs for frequency sweeps of 50 ms appended to the beginning or the end of a 250-ms unmodulated 1.0-kHz tone were approximately 6%-7%. This greater DL for brief frequency sweeps was confirmed by varying the duration but not the extent of the sweep. Finally, DLs were greater than 50% when the repeating standard was a 50-ms rising or falling frequency sweep appended to the beginning of a 250-ms unmodulated 1.0-kHz tone. These results suggest that rapid frequency transitions are much more difficult to discriminate from frequency transitions of the same category (rising or falling) than from either a frequency transition of the opposite category (falling or rising) or an unmodulated tone.(ABSTRACT TRUNCATED AT 250 WORDS)     

Lower bound of overall exponential sums for polynomialsϕ(x d )

LetS ⁽¹⁾ (n, Q) denote the maximum module of exponential sums for polynomials of degree n over the Galois fieldF _Q . In a previous paper the transition to the multiple exponential sums allowed us to obtain a good lower bound of the valueS ⁽¹⁾ (n, Q), which coincides with Weil's bound whenn = q ^(m-1)/2 + 1, whereq, m are odd andm 3. Here the same approach is used for the estimation of the valueS ^(d) (n, Q), which corresponds to polynomials(x ^d ) overF _Q , whered is any divisor ofq – 1.     

The influence of final-syllable position on the vowel and word duration of deaf talkers

Hearing talkers produce shorter vowel and word durations in multisyllabic contexts than in monosyllabic contexts. This investigation determined whether a similar effect occurs for deaf talkers, a population often characterized as lacking coarticulation in their speech. Four prelingually deafened adults and two hearing controls produced three sets of word sequences. Each set included a kernel word and six derived forms (e.g., "speed," "speedy," "speeding," etc.). The derived forms were created by adding unstressed and stressed syllables to the kernel form. A spectrographic analysis indicated that the deaf subjects did not always decrease word and vowel durations for the derivatives. Unlike hearing speakers, they often did not reduce vowel segments more than consonant segments. Three explanations are forwarded for the shortening effects. One relates to the implementation of temporal rules, the second concerns the organization imposed upon the articulators to produce speech, and the third suggests a language-independent vocal tract characteristic. The role of auditory information in developing the shortening effects is also considered.     

Circles through two points that always enclose many points

This paper proves that any set of n points in the plane contains two points such that any circle through those two points encloses at least points of the set. The main ingredients used in the proof of this result are edge counting formulas for k-order Voronoi diagrams and a lower bound on the minimum number of semispaces of size at most k.Work on this paper by the first author has been supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and by the National Science Foundation under Grant CCR-8714565, by the second author has been partially supported by the Digital Equipment Corporation, by the fourth author has been partially supported by the Office of Naval Research under Grant N00014-86K-0416.     

Symmetries and conservation laws of Kadomtsev-Pogutse equations

Kadomtsev-Pogutse equations are of great interest from the viewpoint of the theory of symmetries and conservation laws and, in particular, enable us to demonstrate their potentials in action. This paper presents, firstly, the results of computations of symmetries and conservation laws for these equations and the methods of obtaining these results. Apparently, all the local symmetries and conservation laws admitted by the considered equations are exhausted by those enumerated in this paper. Secondly, we point out some reductions of Kadomtsev-Pogutse equations to more simpler forms which have less independent variables and which, in some cases, allow us to construct exact solutions. Finally, the technique of solution deformation by symmetries and their physical interpretation are demonstrated.     

Scaling function for the velocity correlator in the theory of isotropic developed turbulence

The scaling function is calculated in the framework of the renormalization group approach to the theory of developed turbulence for the velocity correlator to the second order in the -expansion.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 164, pp. 3–9, 1987.The author thanks L. Ts. Adzhemyan, A. N. Vasil'ev, and M. Gnatich for helpful discussions.     

Elliptic bundle and generating operators

A hierarchy of Poisson Hamiltonian structures connected with an elliptic spectral problem is constructed. Generating operators connected with the Landau-Lifshits equations and asymmetric chiral 0(3)-field are found.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 161, pp. 76–87, 1987.The author is profoundly grateful to P. P. Kulish, A. G. Reiman, and M. A. Semenov-Tyan-Shanskii for interest in the present paper and helpful comments.     

Spectrum of the algebra of pseudodifferential operators in a halfspace

One considers C*-algebras, generated by pseudodifferential operators in a halfspace. The operators act in functional spaces with weighted norms. One describes the set of all classes of equivalent irreducible representations of algebras and reveals the topology on the spectrum. One investigates, in particular, the dependence of the spectrum on the choice of the weighted functional space.Translated from Problemy Matematicheskogo Analiza, No. 10, pp. 160–180, 1986.