A numerical analysis of chaotic behaviour in Bianchi IX models

In this paper we investigate the chaotic behaviour of the Bianchi IX cosmological models using techniques developed in the study of dynamical systems and chaotic behaviour. We numerically calculate the Lyapunov exponent, , and show that instead of converging to a constant value, it decreases steadily. We study this effect further by studying the Lyapunov exponent using short-time averages. We show that the usual method of calculating is invalid in the case of a cosmological model.     

Effects of osmotic manipulation of intracellular hydration of HeLa S-3 cells on their proton NMR relaxation times

Pellets of HeLa from suspension cultured cells in isotonic medium (300 mosmolar) were introduced into a Bruker CXP100 NMR spectrophotometer at 80 mHz within 5 min of the start of centrifugation. T1 and T2 times were measured within a total elapsed time of 20-25 min at 80 mHz and 37 degrees C, and averaged 1430 msec and 120 msec, respectively. Extrapolation to zero extracellular space gave a corrected T1 of 1370 msec. For cells collected after 10 min in hypotonic medium (down to 30 mosmolar) increased proton density correlated well with increased cell water content, but relaxation times did not rise in proportion to that predicted for the entry of "bulk" water (T1 of 4700 msec), except when swelling approached lysis point. Cells partially dehydrated by 10 min in hypertonic medium of up to 1500 mosmolar have also been analyzed, but once again the shortening of T1 was not proportional to the loss of "free" (bulk phase) water. At the upper limit of hypertonic treatment, lacunae or vacuoles of a watery nature separated within the cytomatrix, preventing maximum dehydration. The relationship of cell water to T1 is complex over the whole range of tonicity that HeLa S-3 cells tolerate. The data indicate, however, that hypotonically induced water probably has an average T1 time considerably lower than bulk phase water. In contrast, raising the total extracellular volume with medium had precisely the predicted effect on T1 time, further strengthening the case that water taken up by cell acquires a shorter T1 time. Cells adapting to hypotonic conditions oscillated in size and water content over 2-3 hr before returning to near their initial volume. Under these circumstances, T1 oscillated in the same way but with a reduced amplitude, consistent with the above findings.     

SO(n,1) Wigner rotation as an SL(2,R) problem

We show that the composition of not only two SO(3,1) boosts, but also that of two SO(n,1) boosts for anyn 2, is basically an SO(2,1) problem and hence can be analysed completely using SL(2,R) matrices. By computing the expression for the Thomas/Wigner angle directly using SL(2,R) matrices we show that this approach results in considerable economy of algebra.     

Nonlinear properties of surface “screw” instability in symmetric semiconductor plates

For the first time we study the nonlinear properties of the surface screw instability (SSI) when waves are excited at both faces of a plate and the interaction between them must be taken into account. The nature of the SSI development and the stability of surface screw waves against modulation are examined. Diagrams of the regions where the SSI development is soft and explosive as well as the regions of modulated waves are given in the space of parameters characterizing the electro-hole plasma and external fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 30–34, April 1990.     

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.