Refinements of Yu. V. Prokhorov's theorems on the asymptotic behavior of the binomial distribution

One finds the asymptotic behavior of the minimax distance between the binomial and its approximating normal or Poisson distributions, taken with the second terms of their expansions.Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 4–19, 1986.     

Uncertainty principle and the horizon size of our universe

Quantum uncertainties prevent simultaneous measurement of the expansion factor S(t) and its time derivative . Consequently the Hubble size has an inherent uncertainty in the quantum state that describes the semiclassical evolution of the universe. We show that the quantum uncertainty in the Hubble size of the universe is amplified to unacceptably large values in any inflationary process.This essay received an honorable mention from the Gravity Research Foundation, 1986-Ed.     

Continuity equation constraint in the transverse quadrupole electric-type form factors

The analysis of nuclear convection-current contributions to the transverseE 2 isoscalar and isovector form factors in¹²C initiated by Flanz et al. has been extended. It is shown that the continuity equation of the nuclear electromagnetic current provides the constraint needed to explain the behaviour of the form factors studied in the range 0<q<2fm^–1.     

Optical studies of pulsed-laser fragmentation of biliary calculi

The fragmentation of gallstones and kidney stones using pulsed visible laser radiation has recently been demonstrated; however, the fragmentation mechanism is not well understood. The temporal and spectral characteristics of the bright flash of light accompanying fragmentation of gallstones were studied using 0.8 and 360-s-long, 690-nm-wavelength, dye-laser pulses. Time-resolved visible emission spectra show a broad continuum upon which line spectra are superimposed. The continuum emission is due to free-free and free-bound electron transitions indicative of a plasma and the line spectra are due to neutral and ionized calcium. Initiation of this plasma is fluence rather than intensity dependent. A model is proposed in which laser energy is coupled to the plasma, which then impulsively expands, generating intense acoustic transients which fracture the stone.     

Hyperfine structure and isotope shift investigations in202–222Rn for the study of nuclear structure beyond Z=82

The hyperfine structure (hfs) and isotope shift (IS) in the isotopic chain of the radioactive element radon have been studied for the first time. The measurements were carried out by collinear fast-beam laser spectroscopy at the mass separator facility ISOLDE at CERN. The IS between 16 isotopes in the mass range 202A222 and the hfs of 7 odd-A isotopes were determined in the transitions 7s [3/2]₂-7p [5/2]₃ (745 nm) of Rn I. The nuclear spins and moments, as well as the observed inversion of the odd-even staggering for^218–222Rn, can be associated with the effects of octupole instability around N=134.This work was supported by the Bundesministerium für Forschung und Technologie and the Deutsche Forschungsgemeinschaft.     

160Tb nuclear orientation in yttrium single crystal

First experimental results of¹⁶⁰Tb nuclear orientation in yttrium single crystal matrix are described. The influence of external magnetic field in combination with the crystal field interaction is discussed.     

Spanning tree formulas and chebyshev polynomials

The Kirchhoff Matrix Tree Theorem provides an efficient algorithm for determiningt(G), the number of spanning trees of any graphG, in terms of a determinant. However for many special classes of graphs, one can avoid the evaluation of a determinant, as there are simple, explicit formulas that give the value oft(G). In this work we show that many of these formulas can be simply derived from known properties of Chebyshev polynomials. This is demonstrated for wheels, fans, ladders, Moebius ladders, and squares of cycles. The method is then used to derive a new spanning tree formula for the complete prismR _n (m) =K _m ×C _n . It is shown that $$2^{\left( {\begin{array}{*{20}c} n \\ 2 \\ \end{array} } \right)\left( {1 - \frac{1}{{r - 1}} + o\left( 1 \right)} \right)} $$ whereT _n (x) is then ^th order Chebyshev polynomial of the first kind.     

Critical behavior of the two-dimensional first passage time

We study the two-dimensional first passage problem in which bonds have zero and unit passage times with probabilityp and 1–p, respectively. We prove that as the zero-time bonds approach the percolation thresholdp _c, the first passage time exhibits the same critical behavior as the correlation function of the underlying percolation problem. In particular, if the correlation length obeys(p) ¦p–p _c¦^–v, then the first passage time constant satisfies(p)¦p–p _c¦^v. At p_c, where it has been asserted that the first passage time from 0 tox scales as ¦x¦ to a power with 0<<1, we show that the passage times grow like log ¦x¦, i.e., the fluid spreads exponentially rapidly.