Generalized binomial and negative binomial distributions of order<Emphasis Type="Italic">k</Emphasis> by the<Emphasis Type="Italic">l</Emphasis>-overlapping enumeration scheme

In this paper, we investigate the exact distribution of the waiting time for ther-th ℓ-overlapping occurrence of success-runs of a specified length in a sequence of two state Markov dependent trials. The probability generating functions are derived explicitly, and as asymptotic results, relationships of a negative binomial distribution of orderk and an extended Poisson distribution of orderk are discussed. We provide further insights into the run-related problems from the viewpoint of the ℓ-overlapping enumeration scheme. We also study the exact distribution of the number of ℓ-overlapping occurrences of success-runs in a fixed number of trials and derive the probability generating functions. The present work extends several properties of distributions of orderk and leads us a new type of geneses of the discrete distributions.     

Enhancement of the Kerr effect for a quantum dot in a cavity

Nonlinear susceptibility of a quantum dot (QD) embedded in a two-sided cavity, is studied theoretically from a weak-coupling to a strong-coupling regime. In the relevance of a quantum logic gate, the corresponding nonlinear phase shifts (Kerr effect) are estimated for coherent wavepackets including one photon on average. In the weak-coupling regime, the phase shift enhances strongly as a function of a coupling constant between the cavity photon and QD, and eventually saturates in the strong-coupling regime. We also show transmission spectra to evaluate the efficiency of the phase shift. Although the efficiency decreases monotonically in the weak-coupling regime, it rises in the strong-coupling regime.     

Observation on meta-stability of thulium nitrate crystal by using electric measurements

Frequency dependence of ac conductivity from 1 to 10⁵ Hz and time series of the conductivity at 2 kHz were measured along c-axis of thulium nitrate crystal, Tm(NO₃)₃6H₂O at temperatures from 203.15 to 293.15 K. The meta-stability was observed. The frequency spectra of the conductivity were similar to those in disorder system. Aging effect was observed. Non-periodic instability (burst) was found. Non-linear dynamical property was characterized by 1/f noise spectrum, limit cycle in return map and dependence of correlation exponent on embedding dimension.     

Shock wave diffraction over a 90 degree sharp corner — Posters presented at 18th ISSW

A special poster session was run during the 18th International Symposium on Shock Waves, held on July 21 – 26, 1991, in Sendai, Japan. The purpose of this session was to compare various CFD schemes which are useful for simulating shock wave phenomena. A 2-D planar shock wave diffraction over a 90 degree sharp corner was selected as a bench mark problem. The problem specification and the output format are described below. Experimental outputs for the close flow conditions to the computational ones were also called for. Twenty six poster presentations were made at this session and the majority of the posters reflected a standard of excellence that warrants publication in the Shock Waves journal. Therefore these results are reproduced here. However, since there is a limit on the available page numbers, it was not possible to publish all the posters that were presented at the special poster session. We express our sincere thanks to all the participants in this session.     

The q-numerical radius of weighted shift operators with periodic weights

We deal with the q-numerical radius of weighted unilateral and bilateral shift operators. In particular, the q-numerical radius of weighted shift operators with periodic weights is discussed and computed.     

Temporal analysis of products (TAP) study on oxygen storage properties over Pt−Rh/CeO2 catalyst

The oxygen storage capacity of CeO₂, Ce_0.9Pr_0.1O₂, Pt?Rh/CeO₂ and Pt?Rh/Ce_0.9Pr_0.1O₂ was investigated by conventional GC pulse method and transient pulse techniques. It is shown that incorporation of PrO_y into CeO₂ matrix strongly promotes oxygen storage capacity (OSC) measured using the transient pulse technique. The improvement of OSC at low temperature is observed in Pt?Rh loaded onto CeO₂ and Ce?Pr catalysts.     

Acoustic characteristics of Ni–Nb–Zr–H glassy alloys by ultrasonic shear waves

The propagation characteristics of shear horizontally polarized (SH) waves passing through (Ni₄₂Nb₂₈Zr₃₀)_100–x H_x (x = 0–15.2) glassy alloys were investigated as a function of hydrogen content. With an increase in hydrogen content, the propagation time and main frequency of the receiving waves show increase and decrease, respectively, indicating expan‐ sion in average atomic distance which comes from solution of hydrogen. In sharp contrast to crystalline alloys, the decrease in damping ratio and the delay in phase with increasing hydrogen suggest a strong settlement of hydrogen into four‐coordination sites surrounded tetrahedrally by four Zr atoms and the resulting increase in dynamic elasticity, respectively. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)