TT-adic exponential sums of polynomials in one variable

The $T$-adic exponential sum of a polynomial in one variable is studied. An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the $C$-function of the T-adic exponential sum. This bound gives lower bounds for the Newton polygon of the $L$-function of exponential sums of $p$-power order

Lattice study on kaon nucleon scattering length in the I=1 channel

Using the tadpole improved clover Wilson quark action on small, coarse and anisotropic lattices, $KN$ scattering length in the I=1 channel is calculated within quenched approximation. The results are extrapolated towards the chiral and physical kaon mass region. Finite volume and finite lattice spacing errors are also analyzed and a result in the infinite volume and continuum limit is obtained which is compatible with the experiment and the results from Chiral Perturbation Theory.Comment: 15 pages, 4 figures, typeset by latex using elsart.cls,minor change

Geometry dependence of the clogging transition in tilted hoppers

We report the effect of system geometry on the clogging of granular material flowing out of flat-bottomed hoppers with variable aperture size D. For such systems, there exists a critical aperture size Dc at which there is a divergence in the time for a flow to clog. To better understand the origins of Dc, we perturb the system by tilting the hopper an angle Q and mapping out a clogging phase diagram as a function of Q and D. The clogging transition demarcates the boundary between the freely-flowing (large D, small Q) and clogging (small D, large Q) regimes. We investigate how the system geometry affects Dc by mapping out this phase diagram for hoppers with either a circular hole or a rectangular narrow slit. Additionally, we vary the grain shape, investigating smooth spheres (glass beads), compact angular grains (beach sand), disk-like grains (lentils), and rod-like grains (rice). We find that the value of Dc grows with increasing Q, diverging at pi-Qr where Qr is the angle of repose. For circular apertures, the shape of the clogging transition is the same for all grain types. However, this is not the case for the narrow slit apertures, where the rate of growth of the critical hole size with tilt angle depends on the material

The classification of traveling wave solutions and superposition of multi-solutions to Camassa-Holm equation with dispersion

Under the traveling wave transformation, Camassa-Holm equation with dispersion is reduced to an integrable ODE whose general solution can be obtained using the trick of one-parameter group. Furthermore combining complete discrimination system for polynomial, the classifications of all single traveling wave solutions to the Camassa-Holm equation with dispersion is obtained. In particular, an affine subspace structure in the set of the solutions of the reduced ODE is obtained. More general, an implicit linear structure in Camassa-Holm equation with dispersion is found. According to the linear structure, we obtain the superposition of multi-solutions to Camassa-Holm equation with dispersion

On the QCD corrections to the charged Higgs decay of a heavy quark

Using dimensional regularization for both infrared and ultraviolet divergences, we confirm that the QCD corrections to the decay width $\Gamma(t\to H^+b)$ are equal to those to $\Gamma(t\to W^+b)$ in the limit of a large $t$ quark mass.Comment: 6 pages, report Alberta Thy-25-9

Driven activation versus thermal activation

Activated dynamics in a glassy system undergoing steady shear deformation is studied by numerical simulations. Our results show that the external driving force has a strong influence on the barrier crossing rate, even though the reaction coordinate is only weakly coupled to the nonequilibrium system. This "driven activation" can be quantified by introducing in the Arrhenius expression an effective temperature, which is close to the one determined from the fluctuation-dissipation relation. This conclusion is supported by analytical results for a simplified model system.Comment: 5 pages, 3 figure

On landmark selection and sampling in high-dimensional data analysis

In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the low-dimensional structure often prevalent in high-dimensional data. Here we provide an introduction to spectral methods for linear and nonlinear dimension reduction, emphasizing ways to overcome the computational limitations currently faced by practitioners with massive datasets. In particular, a data subsampling or landmark selection process is often employed to construct a kernel based on partial information, followed by an approximate spectral analysis termed the Nystrom extension. We provide a quantitative framework to analyse this procedure, and use it to demonstrate algorithmic performance bounds on a range of practical approaches designed to optimize the landmark selection process. We compare the practical implications of these bounds by way of real-world examples drawn from the field of computer vision, whereby low-dimensional manifold structure is shown to emerge from high-dimensional video data streams.Comment: 18 pages, 6 figures, submitted for publicatio

Ellipsometric and optical study of some uncommon insulator films on 3-5 semiconductors

Optical properties of three types of insulating films that show promise in potential applications in the 3-4 semiconductor technology were evaluated, namely a-C:H, BN and CaF2. The plasma deposited a-C:H shows an amorphous behavior with optical energy gaps of approximately 2 to 2.4 eV. These a-C:H films have higher density and/or hardness, higher refractive index and lower optical energy gaps with increasing energy of the particles in the plasma, while the density of states remains unchanged. These results are in agreement, and give a fine-tuned positive confirmation to an existing conjecture on the nature of a-C:H films (1). Ion beam deposited BN films show amorphous behavior with energy gap of 5 eV. These films are nonstoichiometric (B/N approximately 2) and have refractive index, density and/or hardness which are dependent on the deposition conditions. The epitaxially grown CaF2 on GaAs films have optical parameters equal to bulk, but evidence of damage was found in the GaAs at the interface

Representations and classification of traveling wave solutions to Sinh-G{\"o}rdon equation

Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to Sinh-G{\"o}rdon equation is obtained, and qualitative properties of solutions are discussed. In particular, we point out that some qualitative properties derived intuitively from dynamic system method aren't true. In final, we prove that our solutions to Sinh-G{\"o}rdon equation include all solutions obtained in the paper[Fu Z T et al, Commu. in Theor. Phys.(Beijing) 2006 45 55]. Through an example, we show how to give some new identities on Jacobian elliptic functions.Comment: 12 pages. accepted by Communications in theoretical physics (Beijing

Corrections to Scaling in the Phase-Ordering Dynamics of a Vector Order Parameter

Corrections to scaling, associated with deviations of the order parameter from the scaling morphology in the initial state, are studied for systems with O(n) symmetry at zero temperature in phase-ordering kinetics. Including corrections to scaling, the equal-time pair correlation function has the form C(r,t) = f_0(r/L) + L^{-omega} f_1(r/L) + ..., where L is the coarsening length scale. The correction-to-scaling exponent, omega, and the correction-to-scaling function, f_1(x), are calculated for both nonconserved and conserved order parameter systems using the approximate Gaussian closure theory of Mazenko. In general, omega is a non-trivial exponent which depends on both the dimensionality, d, of the system and the number of components, n, of the order parameter. Corrections to scaling are also calculated for the nonconserved 1-d XY model, where an exact solution is possible.Comment: REVTeX, 20 pages, 2 figure