Real solutions of the equation ϕ(X)=1/nJ n

For ann x n real matrixX, let ?(X)=X ο (X ^?1) ^T , where ο stands for the Hadamard (entrywise) product. SupposeA, B, C andD aren x n real nonsingular matrices, and among them there are at least one solutions to the equation ?(X)=1/nJ _n . An equivalent condition which enable $M = \left( {\begin{array}{*{20}c} A & B \\ C & D \\ \end{array} } \right)$ become a real solution to the equation ?(X)=1/2nJ _2n , is given. As applications, we get new real solutions to the matrix equation ?(X)-1/2nJ _2n by applying the results of Zhang, Yang and Cao [SIAM. J. Matrix Anal. Appl, 21 (1999), pp: 642–645] and Chen [SIAM. J. Matrix Anal. Appl, 22 (2001), pp:965–970]. At the same time, all solutions of the matrix equation ?(X)=1/4J ₄ are also given.     

New Deformation of Para-Bose Statistics

We propose commutation relations for a single mode -deformed para-Bose oscillator. In this new deformation of para-Bose statistics the distribution function has the same form as in the para-Bose statistics. Furthermore, we show analogies between the coherent states of -deformed and q-deformed para-Bose statistics.     

A controllable synthetic route to Cu,Cu2O,and CuO nanotubes and nanorods

Reducing Cu(OH)4(2-) with hydrazine hydrate and glucose in the presence of a structure-directing surfactant at room temperature gave Cu and Cu2O nanotubes/nanorods, respectively, whereas facile hydrothermal treatment of Cu(OH)4(2-) precursor resulted in CuO nanotubes/nanorods.     

Titanium dipyrrolylmethane derivatives: rapid intermolecular alkyne hydroamination

Alkynes are rapidly hydroaminated by primary amines using titanium dipyrrolylmethane derivatives as catalyst.     

The asymptotic behaviour of the ground state solutions for Hénon equation

The main purpose of this paper is to analyze the asymptotic behaviour of the ground state solution of Hénon equation −Δu=|x|^αu^p−1 in Ω, u=0 on ∂Ω (Ω⊂Rn is a ball centered at the origin). It proved that for p close to 2∗=2n/(n−2)(n?3), the ground state solution u_p has a unique maximum point x_p and as p→2∗. The asymptotic behaviour of u_p is also given, which deduces that the ground state solution is non-radial.     

A note on the sign-changing solutions to elliptic problems with critical Sobolev and Hardy terms

Let be a bounded domain such that . We obtain existence of sign-changing solutions for the Dirichlet problem on Ω,u=0 on ∂Ω for suitable positive numbers μ and λ.     

Analysis of planar waveguides with index discontinuity or index slope discontinuity

In this paper, we propose a novel analytic transfer matrix method (ATMM) to the analysis of planar waveguides with index discontinuity or index slope discontinuity, for the cases when the conventional WKB method is no longer valid. We also analyze the physical insight of the approximations in WKB theory, and according to our research, the phase shift at the turning point is not /2, but exactly . Test calculations are done for an index profile with a known solution and the comparison shows that our method gives extremely accurate propagation constant.     

The Near-Infrared Transition of CuCl Observed by Intracavity Laser Spectroscopy

The near-infrared electronic transition of CuCl, occurring in the region of 745 nm, was recorded using intracavity laser absorption spectroscopy. The (0, 0), (1, 1), and (2, 2) vibronic bands were analyzed, and from this the molecular constants for the two electronic states were derived. Originally assigned as A' (3)Sigma(+)-X(1)Sigma(+), we have confirmed that this transition does not connect to the ground state, but occurs between two unknown excited states. The excited CuCl molecules were produced in a copper hollow cathode, operated using argon and a small amount of CCl(4). Line positions were referenced to iodine spectra observed from a heated extracavity cell using the broadband spectral output of the intracavity laser as the light source. Copyright 2000 Academic Press.