Fabrication and characterization of a PbTe quantum dots multilayer structure

Multilayer PbTe quantum dots (QDs) and SiO₂ were grown by pulsed laser deposition (PLD) and Plasma enhanced chemical vapor deposition (PECVD) techniques. The crystalline structure, QD size and size dispersion were observed by high-resolution transmission electron microscopy (HRTEM) measurements. This technique allows one to grow PbTe QDs as small as 1.8 nm diameter and 0.6 nm size dispersion. The whole structure can be used in a Fabry–Perot cavity for an optical device operating at the mid-infrared region.     

Polarized Lidar Reflectance Measurements of Vegetation at Near-Infrared and Green Wavelengths

There is growing interest in the use of lidar for remote sensing of vegetation owing to the emergence of reliable and rugged lasers and highly sensitive detectors. Lidar remote sensing has a distinct advantage over conventional techniques in vegetation remote sensing due to its capability for three-dimensional characterization of vegetative targets. The Multiwavelength Airborne Polarimetric Lidar (MAPL) system was developed primarily for vegetation remote sensing applications from an airborne platform of up to 1,000 -m altitude. The lidar system has full waveform capture and polarimetric measurement capability at two wavelengths in the near-infrared (1064 nm) and the green (532 nm) spectral regions. This study presents preliminary ground-based lidar reflectance measurements on a variety of deciduous and coniferous trees under fully foliated conditions with a view towards tree species discrimination. Variations in the reflectance characteristics of selected deciduous trees under unfoliated and fully foliated conditions were also investigated. Our study reveals distinct differences in the reflectance characteristics of various trees.     

The Translation Invariant Massive Nelson Model: I. The Bottom of the Spectrum

In this paper we analyze the bottom of the energy-momentum spectrum of the translation invariant Nelson model, describing one electron linearly coupled to a second quantized massive scalar field. Our results are valid for all values of the coupling constant and include an HVZ theorem, non-degeneracy of ground states, existence of isolated groundstates in dimensions 1 and 2, non-existence of ground states embedded in the bottom of the essential spectrum in dimensions 3 and 4, (i.e., at total momenta where no isolated groundstate eigenvalue exists), and we study regularity and monotonicity properties of the bottom of the essential spectrum, as a function of total momentum. Communicated by Joel Feldman submitted 04/11/04, accepted 17/02/05     

On Rado's Boundedness Conjecture

We prove that Rado's Boundedness Conjecture from Richard Rado's 1933 famous dissertation Studien zur Kombinatorik is true if it is true for homogeneous equations. We then prove the first nontrivial case of Rado's Boundedness Conjecture: if a₁,a₂, and a₃ are integers, and if for every 24-coloring of the positive integers (or even the nonzero rational numbers) there is a monochromatic solution to the equation a₁x₁+a₂x₂+a₃x₃=0, then for every finite coloring of the positive integers there is a monochromatic solution to a₁x₁+a₂x₂+a₃x₃=0.     

Rhythmic pattern formations in gels and Matalon—Packter law: A fresh perspective

The periodic precipitation pattern formation in gelatinous media is interpreted as a moving boundary problem. The time law, spacing law and width law are revisited on the basis of the new scenario. The explicit dependence of the geometric structure on the initial concentrations of the reactants is derived. Matalon—Packter law, which relates the spacing coefficient with the initial concentrations is reformulated removing many ambiguities and impractical parameters. Experimental results are discussed to establish the significance of moving boundary concept in the diffusion controlled pattern forming systems     

Graded parafermions: standard and quasiparticle bases

Two bases of states are presented for modules of the graded parafermionic conformal field theory associated to the coset . The first one is formulated in terms of the two fundamental (i.e., lowest-dimensional) parafermionic modes. In that basis, one can identify the completely reducible representations, i.e., those whose modules contain an infinite number of singular vectors; the explicit form of these vectors is also given. The second basis is a quasiparticle basis, determined in terms of a modified version of the exclusion principle. A novel feature of this model is that none of its bases are fully ordered and this reflects a hidden structural exclusion principle.     

On the Log-Laplace Equation for Nonlocal Operators Generating Sub-Markovian Semigroups

We consider the semilinear Cauchy problem for a class of pseudo-differential operators generating sub-Markovian semigroups. Solutions of such problems with negative definite nonlinearity play an important role in constructing branching measure-valued processes. We establish local existence and uniqueness of solutions in the context of the Dirichlet space associated to the problem. Comparison and global properties of solutions are also studied. Accepted 29 August 2001. Online publication 17 December 2001.