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     

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.     

Optimal Harvesting in an Age-Structured Predator–Prey Model

We investigate optimal harvesting control in a predator–prey model in which the prey population is represented by a first-order partial differential equation with age-structure and the predator population is represented by an ordinary differential equation in time. The controls are the proportions of the populations to be harvested, and the objective functional represents the profit from harvesting. The existence and uniqueness of the optimal control pair are established.     

Structural and electronic properties of graphite layers grown on SiC(0 0 0 1)

Photoelectron spectroscopy, low-energy electron diffraction, and scanning probe microscopy were used to investigate the electronic and structural properties of graphite layers grown by solid state graphitization of SiC(0 0 0 1) surfaces. The process leads to well-ordered graphite layers which are rotated against the substrate lattice by 30°. On on-axis 6H-SiC(0 0 0 1) substrates we observe graphitic layers with up to several 100 nm wide terraces. ARUPS spectra of the graphite layers grown on on-axis 6H-SiC(0 0 0 1) surfaces are indicative of a well-developed band structure. For the graphite/n-type 6H-SiC(0 0 0 1) layer system we observe a Schottky barrier height of ?_B,n = 0.3 ± 0.1 eV. ARUPS spectra of graphite layers grown on 8° off-axis oriented 4H-SiC(0 0 0 1) show unique replicas which are explained by a carpet-like growth mode combined with a step bunching of the substrate.     

Wavelength and power monitoring of DWDM systems using scanning F–P filter calibrated with a F–P laser

A novel technique to overcome the long-term drift and hysteresis of a scanning Fabry–Perot filter was developed and applied to wavelength and power monitoring of DWDM system. By using the comb peaks generated by a temperature-stabilized, near threshold-biased Fabry–Perot diode laser as wavelength reference for the scanning Fabry–Perot filter, wavelength and power measurement accuracy of better than ±10 pm and 0.2 dB, respectively, were achieved.     

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.     

To-and-fro motion of W5Si3 on a beta-Si3N4 substrate at elevated temperatures.

Behavior of fine crystalline particles of W5Si3 on a beta-Si3N4 substrate at high temperatures was observed by an in situ heating experiment in a transmission electron microscope. Some of the fine particles of W5Si3 moved in a to-and-fro manner.     

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     

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