On a class of operators related to second-order differential equations

In the present paper, we find a class of linear homogeneous differential equations of order n + 1 (n > 1) whose fundamental system of solutions is constructed from the fundamental system of solutions of a second-order differential equation. The spectral properties of differential operators generated by these differential expressions are investigated. In particular, sufficient conditions are obtained for the coefficients of a second-order differential equation under which the case of maximal deficiency indices is realized. Dedicated to the memory of B. M. Levitan     

Advances in micro-perforated panel absorbers

Theoretical and experimental investigations on the performance of micro-perforated -panel absorbers are reviewed in this paper. By reviewing recent research work, this paper reveals a relationship between the maximum absorption coefficient and the limit of the absorption frequency bandwidth. It has been demonstrated that the absorption frequency bandwidth can be extended up to 3 or 4 octaves as the diameters of the micro-holes decrease. This has become possible with the development of the technologies for manufacturing micro-perforated panels, such as laser drilling, powder metallurgy, welded meshing and electro-etching to form micrometer order holes. In this paper, absorption characteristics of such absorbers in random fields and in high sound intensity are discussed both theoretically and experimentally. A new absorbing structure based on micro-perforated-panel absorbers demonstrate experimentally high sound absorption capability. This review shows that the micro-perforated-panel absorber has potentials to be one of ideal absorbing materials in the 21st century.     

High pressure X-ray diffraction study of CdAl2Se4 and Raman study of AAl2Se4 (A=Hg, Zn) and CdAl2X4 (X=Se, S)

We report the results of an X-ray diffraction study of CdAl₂Se₄ and of Raman studies of HgAl₂Se₄ and ZnAl₂Se₄ at room temperature, and of CdAl₂S₄ and CdAl₂Se₄ at 80 K at high pressure. The ambient pressure phase of CdAl₂Se₄ is stable up to a pressure of 9.1 GPa above which a phase transition to a disordered rock salt phase is observed. A fit of the volume pressure data to a Birch-Murnaghan type equation of state yields a bulk modulus of 52.1 GPa. The relative volume change at the phase transition at ∼9 GPa is about 10%. The analysis of the Raman data of HgAl₂Se₄ and ZnAl₂Se₄ reveals a general trend observed for different defect chalcopyrite materials. The line widths of the Raman peaks change at intermediate pressures between 4 and 6 GPa as an indication of the pressure induced two stage order-disorder transition observed in these materials. In addition, we include results of a low temperature Raman study of CdAl₂S₄ and CdAl₂Se₄, which shows a very weak temperature dependence of the Raman-active phonon modes.     

Effects of sputter deposition parameters and post-deposition annealing on the electrical characteristics of LaAlO3 dielectric films on Si

The influence of processing parameters on the electrical characteristics of RuO₂/LaAlO₃/Si metal-oxide-semiconductor structures was investigated. In particular, the sputtering regime during deposition of LaAlO₃ on Si and the atmosphere used in the post-deposition annealing step were addressed by determining capacitance-voltage and gate current-voltage characteristics. These results were correlated with compositional information obtained by Rutherford backscattering spectrometry and nuclear reaction analysis. A post-deposition annealing step in oxygen at 600 °C resulted in better electrical characteristics of the final structure as compared to the same treatment performed in nitrogen. This result is explained by oxygen ability to heal oxygen vacancies in the LaAlO₃ film, especially at the dielectric/semiconductor interface region. A thermalized sputtering regime during deposition of LaAlO₃ on Si leads to capacitors with electrical characteristics superior to those deposited in ballistic regime. PACS 77.84.Dy; 81.15.Cd; 81.40.Gh; 73.40.Qv; 82.80.Yc     

Smart Geodesic Tracing in GRworkbench

We have developed a new tool for numerical work in General Relativity: GRworkbench. We discuss how GRworkbench's implementation of a numerically-amenable analogue to Differential Geometry facilitates the development of robust and chart-independent numerical algorithms. We consider, as an example, geodesic tracing on two charts covering the exterior Schwarzschild space-time.     

On the Reality of the Eigenvalues for a Class of -Symmetric Oscillators

 We study the eigenvalue problem with the boundary conditions that decays to zero as z tends to infinity along the rays , where is a real polynomial and . We prove that if for some we have for all , then the eigenvalues are all positive real. We then sharpen this to a larger class of polynomial potentials. In particular, this implies that the eigenvalues are all positive real for the potentials when with , and with the boundary conditions that decays to zero as z tends to infinity along the positive and negative real axes. This verifies a conjecture of Bessis and Zinn-Justin. Received: 16 January 2002 / Accepted: 1 May 2002 Published online: 6 August 2002     

Eigenvalue distributions of random unitary matrices

 Let U be an n × n random matrix chosen from Haar measure on the unitary group. For a fixed arc of the unit circle, let X be the number of eigenvalues of M which lie in the specified arc. We study this random variable as the dimension n grows, using the connection between Toeplitz matrices and random unitary matrices, and show that (X -E [X])/(\Var (X))^1/2 is asymptotically normally distributed. In addition, we show that for several fixed arcs I ₁ , ..., I _m , the corresponding random variables are jointly normal in the large n limit. Received: 15 November 2000 / Revised version: 27 September 2001 / Published online: 17 May 2002     

Some Estimates for the Derivative of a Quasiconformal Reflection Spiral-Shaped Domains

Some estimates of derivatives are sharpened for quasiconformal reflections of a special class of simply connected plane domains. Bibliography: 2 titles.     

A primer on perfect simulation for spatial point processes

This primer provides a self-contained exposition of the case where spatial birth-and-death processes are used for perfect simulation of locally stable point processes. Particularly, a simple dominating coupling from the past (CFTP) algorithm and the CFTP algorithms introduced in [13], [14], and [5] are studied. Some empirical results for the algorithms are discussed. Received: 30 June 2002     

Every diassociative A-loop is Moufang

An A-loop is a loop in which every inner mapping is an automorphism. A problem which had been open since 1956 is settled by showing that every diassociative A-loop is Moufang.