On a poisson reduction for Gel'fand-Zakharevich manifolds

We formulate and discuss a reduction theorem for Poisson pencils associated with a class of integrable systems, defined on bi-Hamiltonian manifolds, recently studied by Gel'fand and Zakharevich. The reduction procedure is suggested by the bi-Hamiltonian approach to the separation of variables problem.     

Potential formation and high density plasma production on the tandem mirror GAMMA 10

GAMMA 10 experiments have advanced in high density experiments after the last EPS Workshop where we reported high density plasma production by using an ion cyclotron range of frequency heating at a high harmonic frequency and neutral beam injection in the central cell. Recently a high density plasma was obtained with much improved reproducibility than before and without degradation of diamagnetic signal. The high density plasma was attained by adjusting the spacing of the conducting plates installed in the anchor transition regions. Dependencies of particle confinement time, ion energy confinement time and plasma confining potential on plasma density were obtained for the first time in the high density region. Presented at 5th Workshop “Role of Electric Fields in Plasma Confinement and Exhaust”, Montreus, Switzerland, June 23–24, 2002.     

Discretization of the solutions to Poisson’s equation

Sharp estimates (in the power scale) are obtained for the discretization error in the solutions to Poisson’s equation whose right-hand side belongs to a Korobov class. Compared to the well-known Korobov estimate, the order is almost doubled and has an ultimate value in the power scale.     

Calibrating software reliability models when the test environment does not match the user environment

Software failures have become the major factor that brings the system down or causes a degradation in the quality of service. For many applications, estimating the software failure rate from a user's perspective helps the development team evaluate the reliability of the software and determine the release time properly. Traditionally, software reliability growth models are applied to system test data with the hope of estimating the software failure rate in the field. Given the aggressive nature by which the software is exercised during system test, as well as unavoidable differences between the test environment and the field environment, the resulting estimate of the failure rate will not typically reflect the user‐perceived failure rate in the field. The goal of this work is to quantify the mismatch between the system test environment and the field environment. A calibration factor is proposed to map the failure rate estimated from the system test data to the failure rate that will be observed in the field. Non‐homogeneous Poisson process models are utilized to estimate the software failure rate in both the system test phase and the field. For projects that have only system test data, use of the calibration factor provides an estimate of the field failure rate that would otherwise be unavailable. For projects that have both system test data and previous field data, the calibration factor can be explicitly evaluated and used to estimate the field failure rate of future releases as their system test data becomes available. Copyright © 2002 John Wiley & Sons, Ltd.     

Laguerre expansion on the Heisenberg group and Fourier-Bessel transform on C~n Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

Given a principal value convolution on the Heisenberg group Hn = Cn×R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kernel for the Laguerre expansion on the group Hn.     

Application of Hilbert＇s Projective Metric on Symmetric Cones

Let Ω be a symmetric cone. In this note, we introduce Hilbert＇s projective metric on Ω in terms of Jordan algebras and we apply it to prove that, given a linear invertible transformation g such that g（Ω） = Ω and a real number p, ｜p｜ 〉 1, there exists a unique element x ∈ Ω satisfying g（x） = x^p.     

ω-meson photoproduction on nucleons in the near-threshold region

The European Physical Journal A - The ω-meson photoproduction, γ + p→p + ω, is studied in the framework of a model, containing π-meson exchange in t-channel and...     

The pure state space of quantum mechanics as Hermitian symmetric space

The pure state space of Quantum Mechanics is investigated as Hermitian Symmetric Kähler manifold. The classical principles of quantum mechanics (Quantum Superposition Principle, Heisenberg Uncertainty Principle, Quantum Probability Principle) and Spectral Theory of observables are discussed in this non-linear geometrical context.     

On Poisson–Malcev Structures

Malcev–Poisson structure on a manifold is analogous to a Poisson structure with the Lie identity replaced by a slightly more general Malcev identity. Examples of such structures arise naturally. In the second part of the paper we study Malcev bialgebras. A theorem of characterization is proved.     

Electrical properties of neodymium doped CaBi4Ti4O15 ceramics

Neodymium doped bismuth layer structure ferroelectrics (BLSFs) ceramics CaBi_4−xNd_xTi₄O₁₅ (x=0, 0.25, 0.50, 0.75) were prepared by solid-state reaction method. X-ray diffraction pattern showed that single phase was formed when x=0-0.75. The refined lattice parameters showed that a (b) axes decrease at x=0.25 and increase with more Nd³⁺ dopant. The effects of Nd³⁺ doping on the dielectric and ferroelectric properties of CaBi₄Ti₄O₁₅ ceramics are studied. Nd³⁺ dopant decreased the Curie temperature linearly, and the dielectric loss, tan δ, as well. The remnant polarization of Nd³⁺ doped CaBi₄Ti₄O₁₅ ceramics was increased by 80% at x=0.25, while more Nd³⁺ dopant decreased the remnant polarization. CaBi_3.75Nd_0.25Ti₄O₁₅ ceramics had the largest piezoelectric constant d₃₃. The structure and properties of CaBi_4−xNd_xTi₄O₁₅ ceramics showed that Nd³⁺ may occupy different crystal locations when Nd³⁺ content x is less than 0.25 and more than 0.50.