Parity Reversing Involutions on Plane Trees and 2-Motzkin Paths

The problem of counting plane trees with $n$ edges and an even or an odd number of leaves was studied by Eu, Liu and Yeh, in connection with an identity on coloring nets due to Stanley. This identity was also obtained by Bonin, Shapiro and Simion in their study of Schr\"oder paths, and it was recently derived by Coker using the Lagrange inversion formula. An equivalent problem for partitions was independently studied by Klazar. We present three parity reversing involutions, one for unlabelled plane trees, the other for labelled plane trees and one for 2-Motzkin paths which are in one-to-one correspondence with Dyck paths.Comment: 8 pages, 4 figure

An Investigation of the Large-scale Variability of the Apparently Single Wolf-Rayet Star WR 1

In recent years, much studies have focused on determining the origin of the large-scale line-profile and/or photometric patterns of variability displayed by some apparently single Wolf-Rayet stars, with the existence of an unseen (collapsed?) companion or of spatially extended wind structures as potential candidates. We present observations of WR 1 which highlight the unusual character of the variations in this object. Our narrowband photometric observations reveal a gradual increase of the stellar continuum flux amounting to Delta v = 0.09 mag followed by a decline on about the same timescale (3-4 days). Only marginal evidence for variability is found during the 11 following nights. Strong, daily line-profile variations are also observed but they cannot be easily linked to the photometric variations. Similarly to the continuum flux variations, coherent time-dependent changes are observed in 1996 in the centroid, equivalent width, and skewness of He II 4686. Despite the generally coherent nature of the variations, we do not find evidence in our data for the periods claimed in previous studies. While the issue of a cyclical pattern of variability in WR 1 is still controversial, it is clear that this object might constitute in the future a cornerstone for our understanding of the mechanisms leading to the formation of largely anisotropic outflows in Wolf-Rayet stars.Comment: 11 pages, 9 figures, accepted for publication in Astronomy & Astrophysic

Fracture driven by a Thermal Gradient

Motivated by recent experiments by Yuse and Sano (Nature, 362, 329 (1993)), we propose a discrete model of linear springs for studying fracture in thin and elastically isotropic brittle films. The method enables us to draw a map of the stresses in the material. Cracks generated by the model, imposing a moving thermal gradient in the material, can branch or wiggle depending on the driving parameters. The results may be used to compare with other recent theoretical work, or to design future experiments.Comment: RevTeX file (9 pages) and 5 postscript figure

On relativistic elements of reality

Several arguments have been proposed some years ago, attempting to prove the impossibility of defining Lorentz-invariant elements of reality. I find that a sufficient condition for the existence of elements of reality, introduced in these proofs, seems to be used also as a necessary condition. I argue that Lorentz-invariant elements of reality can be defined but, as Vaidman pointed out, they won't satisfy the so-called product rule. In so doing I obtain algebraic constraints on elements of reality associated with a maximal set of commuting Hermitian operators.Comment: Clarifications, reference added; published versio

Reactions of biologically inspired hydride sources with B(C6F5)3

The combination of 1-benzyl-1,4-dihydropyridines with the strong Lewis acid, B(C6F5)3, generates a stable pyridinium borohydride species in high yields (94%) in as little as 10 min. This use of biologically inspired hydride sources further builds on the recent work of new hydride donors in the formation of borohydrides. When functionalizing the dihydropyridine with an amide or carboxylic acid moiety, a disproportionation reaction composed of a series of protonation/reduction steps is observed upon the addition of B(C6F5)3. As a result, one equivalent of dihydropyridine undergoes net hydrogenation, whereas the other is dehydrogenated yielding the pyridinium counterpart in a transfer hydrogenation-type mechanism

Level Statistics and Localization for Two Interacting Particles in a Random Potential

We consider two particles with a local interaction $U$ in a random potential at a scale $L_1$ (the one particle localization length). A simplified description is provided by a Gaussian matrix ensemble with a preferential basis. We define the symmetry breaking parameter $\mu \propto U^{-2}$ associated to the statistical invariance under change of basis. We show that the Wigner-Dyson rigidity of the energy levels is maintained up to an energy $E_{\mu}$. We find that $E_{\mu} \propto 1/\sqrt{\mu}$ when $\Gamma$ (the inverse lifetime of the states of the preferential basis) is smaller than $\Delta_2$ (the level spacing), and $E_{\mu} \propto 1/\mu$ when $\Gamma > \Delta_2$. This implies that the two-particle localization length $L_2$ first increases as $|U|$ before eventually behaving as $U^2$.Comment: 4 pages REVTEX, 4 Figures EPS, UUENCODE

Generalized symmetries and invariant matter couplings in two-dimensional dilaton gravity

New features of the generalized symmetries of generic two-dimensional dilaton models of gravity are presented and invariant gravity-matter couplings are introduced. We show that there is a continuum set of Noether symmetries, which contains half a de Witt algebra. Two of these symmetries are area-preserving transformations. We show that gravity-matter couplings which are invariant under area preserving transformations only contribute to the dynamics of the dilaton-gravity sector with a reshaping of the dilaton potential. The interaction with matter by means of invariant metrics is also considered. We show in a constructive way that there are metrics which are invariant under two of the symmetries. The most general metrics and minimal couplings that fulfil this condition are found.Comment: LateX file, no macros, 14pp: minor changes have been made and some misprints have been correcte

X-ray absorption and optical spectroscopy studies of (Mg1−x_{1-x}Alx_x)B2_2

X-ray absorption spectroscopy and optical reflectance measurements have been carried out to elucidate the evolution of the electronic structure in (Mg$_{1-x}$Al$_{x}$)B$_{2}$ for \emph{x} = 0.0,0.1, 0.2, 0.3, and 0.4. The important role of B 2\emph{p} $\sigma$ hole states to superconductivity has been identified, and the decrease in the hole carrier number is \emph{quantitatively} determined. The rate of the decrease in the hole concentration agree well with the theoretical calculations. On the other hand,while the evolution of the electronic structure is gradual through the doping range, $T_c$ suppression is most significant at \emph{x} = 0.4. These results suggest that the superstructure in (Mg$_{1-x}$Al$_{x}$)B$_{2}$, in addition to the $\sigma$ holes, can affect the lattice dynamics and contributes to the $T_c$ suppression effect. Other possible explanations like the topological change of the $\sigma$ band Fermi surface are also discussed.Comment: 17 pages, 5 figures. Phys. Rev. B, in pres