137,273 research outputs found
Parity Reversing Involutions on Plane Trees and 2-Motzkin Paths
The problem of counting plane trees with 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
New Approach on the General Shape Equation of Axisymmetric Vesicles
The general Helfrich shape equation determined by minimizing the curvature
free energy describes the equilibrium shapes of the axisymmetric lipid bilayer
vesicles in different conditions. It is a non-linear differential equation with
variable coefficients. In this letter, by analyzing the unique property of the
solution, we change this shape equation into a system of the two differential
equations. One of them is a linear differential equation. This equation system
contains all of the known rigorous solutions of the general shape equation. And
the more general constraint conditions are found for the solution of the
general shape equation.Comment: 8 pages, LaTex, submit to Mod. Phys. Lett.
Spin relaxation in diluted magnetic semiconductor quantum dots
Electron spin relaxation induced by phonon-mediated s-d exchange interaction
in a II-VI diluted magnetic semiconductor quantum dot is investigated
theoretically. The electron-acoustic phonon interaction due to piezoelectric
coupling and deformation potential is included. The resulting spin lifetime is
typically on the order of microseconds. The effectiveness of the
phonon-mediated spin-flip mechanism increases with increasing Mn concentration,
electron spin splitting, vertical confining strength and lateral diameter,
while it shows non-monotonic dependence on the magnetic field and temperature.
An interesting finding is that the spin relaxation in a small quantum dot is
suppressed for strong magnetic field and low Mn concentration at low
temperature.Comment: 11 pages, 11 figures, to be published in Phys. Rev.
Preparation of (Pb,Ba)TiO3 powders and highly oriented thin films by a sol-gel process
Solid solution Pb1-xBaxTiO3, with particular emphasis on Pb0.5Ba0.5TiO3, was prepared using a sol-gel process incorporating lead acetate trihydrate, barium acetate, and titanium isopropoxide as precursors, acetylacetone (2,4 pentanedione) as a chelating agent, and ethylene glycol as a solvent. The synthesis procedure was optimized by systematically varying acetylacetone: Ti and H2O:Ti molar ratios and calcination temperature. The resulting effects on sol and powder properties were studied using thermogravimetric analysis/differential scanning calorimetry, Fourier transform infrared spectroscopy, Brunauer-Emmett-Teller analysis, and x-ray diffraction (XRD). Crystallization of the perovskite structure occurred at a temperature as low as 450 °C. Thin films were prepared by spin coating on (100) MgO. Pyrolysis temperature and heating rate were varied, and the resultant film properties investigated using field-emission scanning electron microscopy, atomic force microscopy, and XRD. Under optimized conditions, highly oriented films were obtained at a crystallization temperature of 600 °C
Differential Phase-contrast Interior Tomography
Differential phase contrast interior tomography allows for reconstruction of
a refractive index distribution over a region of interest (ROI) for
visualization and analysis of internal structures inside a large biological
specimen. In this imaging mode, x-ray beams target the ROI with a narrow beam
aperture, offering more imaging flexibility at less ionizing radiation.
Inspired by recently developed compressive sensing theory, in numerical
analysis framework, we prove that exact interior reconstruction can be achieved
on an ROI via the total variation minimization from truncated differential
projection data through the ROI, assuming a piecewise constant distribution of
the refractive index in the ROI. Then, we develop an iterative algorithm for
the interior reconstruction and perform numerical simulation experiments to
demonstrate the feasibility of our proposed approach
Perturbative calculation of the scaled factorial moments in second-order quark-hadron phase transition within the Ginzburg-Landau description
The scaled factorial moments are studied for a second-order
quark-hadron phase transition within the Ginzburg-Landau description. The role
played by the ground state of the system under low temperature is emphasized.
After a local shift of the order parameter the fluctuations are around the
ground state, and a perturbative calculation for can be carried out.
Power scaling between 's is shown, and a universal scaling exponent
is given for the case with weak correlations and weak
self-interactions.Comment: 12 pages in RevTeX, 12 eps figure
- …