Estimation of density functions by order statistics

The properties of the empirical density function,f _n(x) = k/n( _j ⁺ – _j-1 ⁺ ) if _j-1 ⁺ < x ⁺ where _j-1 ⁺ and _j ⁺ are sample elements and there are exactlyk – 1 sample elements between them, are studied in that practical point of view how to choose a suitablek for a good estimation. A bound is given for the expected value of the absolute value of difference between the empirical and theoretical density functions.     

Fields as Kolmogzrov flows

It is widely recognized that for highly unstable dynamical systems there exists a fundamental limitation on predictability and determinism. An important class of such highly unstable systems is the class of K-flow, which is further characterized by the existence of time-asymmetric objects in the form of K-partition. Our recent approach to the problem of irreversibility has shown that when the implications of the limitation on determinism arising from strong form of instability and those of the existence of K-partition are consistently taken into account, one is naturally led from the physically unrealizable deterministic evolution of phase points to an entropy-increasing stochastic Markovian evolution. Furthermore, this transition is not the result of extraneously imposed coarse graining and/or approximation schemes, but can be brought about by an invertible transformation whose existence and construction are determined by the nature of the instability of the dynamical system itself. After a brief review of this theory which also contains some relatively new remarks, we prove that classical Klein-Gordon field (both massive and massless) possess the structure of K-flow. This seems to provide the first examples of relativistic systems that are K-flows. Some of the implications of this result are briefly discussed. From a mathematical point of view, this seems to be a first step toward an ergodic theory of partial differential equations. In the process, we also provide an independant group-theoretic proof of the existence of incoming and outgoing subspaces of the scattering theory of Lax and Phillips for the wave equation.     

Growth of Ni2Si by rapid thermal annealing: Kinetics and moving species

The growth kinetics is characterized and the moving species is identified for the formation of Ni₂Si by Rapid Thermal Annealing (RTA) of sequentially deposited Si and Ni films on a 100 Si substrate. The interfacial Ni₂Si layer grows as the square root of time, indicating that the suicide growth process is diffusion-limited. The activation energy is 1.25±0.2 eV in the RTA temperature range of 350–450° C. The results extend those of conventional steady-state furnace annealing quite fittingly, and a common activation energy of 1.3±0.2 eV is deduced from 225° to 450° C. The marker experiment shows that Ni is the dominant moving species during Ni₂Si formation by RTA, as is the case for furnace annealing. It is concluded that the two annealing techniques induce the same growth mechanisms in Ni₂Si formation.     

Strong-coupling effects in high-T c superconductors

It is conceivable that the high-T _c superconducting perovskites are conventional electronphonon superconductors. In this case one expects significant strong-coupling effects because of the unusually high ratiok _B T _c / of the order 0.1 and greater. We use a set of reasonable models for the Eliashberg function ² F() (which takes into account available information on the phonon spectra and which fit the measuredT _c 's) and calculate strong-coupling effects in the specific heatc _s (T)/T _c , the ratio ₀/k _B T _c , the critical fieldsH _c (T) andH _c2 (T) including Pauli limiting, and other measurable quantities. Strongcoupling corrections turn out to be in the range of 0 to about 100%, depending on the quantity of interest. We discuss the perspectives of using strong-coupling effects as indicators for conventional electron-phonon superconductivity in the new materials.     

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.     

Baryons as rotating excitations of the chiral soliton

We show that the usual ansatz used for quantizing the collective coordinates corresponding to a rotation of chiral soliton does not satisfy the equations of motion. We suggest a more general ansatz that admits the separation of rotational degrees of freedom and does not contradict the equations of motion.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.     

Hyperfine anomalies and nuclear γ-factors of56Co,57Co and60Co isotopes studied by NMR/ON

The results of NMR/ON measurements on^56,57,60Co isotopes in iron are presented in the paper. To avoid the uncertainties caused by local demagnetizing field inhomogeneities the measurements on two cobalt isotopes in one sample have been carried out. The values of nuclear-factors ratios ⁵⁷/ ⁶⁰=1·805(20), ⁶⁰/ ⁵⁶ = 0·761(20), ⁵⁶/ ⁵⁷ = 0·726(20) and hyperfme anomalies^{56 60} = –0·036(10),^{60 57} = 0·017(10) and^{57 56} = 0·018(10) have been calculated from the experimental results.Dedicated to the 30th anniversary of the Joint Institute for Nuclear Research.