On length spectrum metrics and weak metrics on Teichmüller spaces of surfaces with boundary

We define and study metrics and weak metrics on the Teichmüller space of a surface of topologically finite type with boundary. These metrics and weak metrics are associated to the hyperbolic length spectrum of simple closed curves and of properly embedded arcs in the surface. We give a comparison between the defined metrics on regions of Teichmüller space which we call $\varepsilon_0$-relative $\epsilon$-thick parts} for $\epsilon >0$ and $\varepsilon_0\geq \epsilon>0$

Length spectra and the Teichmüller metric for surfaces with boundary

International audienceWe consider some metrics and weak metrics defined on the Teichmmüller space of a surface of finite type with nonempty boundary, that are defined using the hyperbolic length spectrum of simple closed curves and of properly embedded arcs, and we compare these metrics and weak metrics with the Teichmüller metric. The comparison is on subsets of Teichmüller space which we call ''$\varepsilon_0$-relative $\epsilon$-thick parts", and whose definition depends on the choice of some positive constants $\varepsilon_0$ and $\epsilon$. Meanwhile, we give a formula for the Teichmüller metric of a surface with boundary in terms of extremal lengths of families of arcs

Local Density of States and Angle-Resolved Photoemission Spectral Function of an Inhomogeneous D-wave Superconductor

Nanoscale inhomogeneity seems to be a central feature of the d-wave superconductivity in the cuprates. Such a feature can strongly affect the local density of states (LDOS) and the spectral weight functions. Within the Bogoliubov-de Gennes formalism we examine various inhomogeneous configurations of the superconducting order parameter to see which ones better agree with the experimental data. Nanoscale large amplitude oscillations in the order parameter seem to fit the LDOS data for the underdoped cuprates. The one-particle spectral function for a general inhomogeneous configuration exhibits a coherent peak in the nodal direction. In contrast, the spectral function in the antinodal region is easily rendered incoherent by the inhomogeneity. This throws new light on the dichotomy between the nodal and antinodal quasiparticles in the underdoped cuprates.Comment: 5 pages, 9 pictures. Phys. Rev. B (in press

Monte Carlo simulations of bosonic reaction-diffusion systems

An efficient Monte Carlo simulation method for bosonic reaction-diffusion systems which are mainly used in the renormalization group (RG) study is proposed. Using this method, one dimensional bosonic single species annihilation model is studied and, in turn, the results are compared with RG calculations. The numerical data are consistent with RG predictions. As a second application, a bosonic variant of the pair contact process with diffusion (PCPD) is simulated and shown to share the critical behavior with the PCPD. The invariance under the Galilean transformation of this boson model is also checked and discussion about the invariance in conjunction with other models are in order.Comment: Publishe

Hamiltonian type Lie bialgebras

We first prove that, for any generalized Hamiltonian type Lie algebra $L$, the first cohomology group $H^1(L,L \otimes L)$ is trivial. We then show that all Lie bialgebra structures on $L$ are triangular.Comment: LaTeX, 16 page

Characterizing Ranked Chinese Syllable-to-Character Mapping Spectrum: A Bridge Between the Spoken and Written Chinese Language

One important aspect of the relationship between spoken and written Chinese is the ranked syllable-to-character mapping spectrum, which is the ranked list of syllables by the number of characters that map to the syllable. Previously, this spectrum is analyzed for more than 400 syllables without distinguishing the four intonations. In the current study, the spectrum with 1280 toned syllables is analyzed by logarithmic function, Beta rank function, and piecewise logarithmic function. Out of the three fitting functions, the two-piece logarithmic function fits the data the best, both by the smallest sum of squared errors (SSE) and by the lowest Akaike information criterion (AIC) value. The Beta rank function is the close second. By sampling from a Poisson distribution whose parameter value is chosen from the observed data, we empirically estimate the $p$-value for testing the two-piece-logarithmic-function being better than the Beta rank function hypothesis, to be 0.16. For practical purposes, the piecewise logarithmic function and the Beta rank function can be considered a tie.Comment: 15 pages, 4 figure

Lie bialgebras of generalized Witt type

In a paper by Michaelis a class of infinite-dimensional Lie bialgebras containing the Virasoro algebra was presented. This type of Lie bialgebras was classified by Ng and Taft. In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are classified. It is proved that, for any Lie algebra $W$ of generalized Witt type, all Lie bialgebras on $W$ are coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group $H^1(W,W \otimes W)$ is trivial.Comment: 14 page

Common Warm Dust Temperatures Around Main-sequence Stars

We compare the properties of warm dust emission from a sample of main-sequence A-type stars (B8-A7) to those of dust around solar-type stars (F5-K0) with similar Spitzer Space Telescope Infrared Spectrograph/MIPS data and similar ages. Both samples include stars with sources with infrared spectral energy distributions that show evidence of multiple components. Over the range of stellar types considered, we obtain nearly the same characteristic dust temperatures (~190 K and ~60 K for the inner and outer dust components, respectively)—slightly above the ice evaporation temperature for the inner belts. The warm inner dust temperature is readily explained if populations of small grains are being released by sublimation of ice from icy planetesimals. Evaporation of low-eccentricity icy bodies at ~150 K can deposit particles into an inner/warm belt, where the small grains are heated to T_(dust)~ 190 K. Alternatively, enhanced collisional processing of an asteroid belt-like system of parent planetesimals just interior to the snow line may account for the observed uniformity in dust temperature. The similarity in temperature of the warmer dust across our B8-K0 stellar sample strongly suggests that dust-producing planetesimals are not found at similar radial locations around all stars, but that dust production is favored at a characteristic temperature horizon