On the Turan number of forests

The Turan number of a graph H, ex(n,H), is the maximum number of edges in a graph on n vertices which does not have H as a subgraph. We determine the Turan number and find the unique extremal graph for forests consisting of paths when n is sufficiently large. This generalizes a result of Bushaw and Kettle [ Combinatorics, Probability and Computing 20:837--853, 2011]. We also determine the Turan number and extremal graphs for forests consisting of stars of arbitrary order

Renormalization of Bilinear Quark Operators for Overlap Fermions

We present non-perturbative renormalization constants of fermionic bilinears on the lattice in the quenched approximation at beta=6.1 using an overlap fermion action with hypercubic(HYP)-blocked links. We consider the effects of the exact zero modes of the Dirac operator and find they are important in calculating the renormalization constants of the scalar and pseudoscalar density. The results are given in the RI' and MS bar schemes and compared to the perturbative calculations.Comment: 14 pages, 13 figure

Mechanical compression to characterize the robustness of liquid marbles

In this work, we have devised a new approach to measure the critical pressure that a liquid marble can withstand. A liquid marble is gradually squeezed under a mechanical compression applied by two parallel plates. It ruptures at a sufficiently large applied pressure. Combining the force measurement and the high-speed imaging, we can determine the critical pressure that ruptures the liquid marble. This critical pressure, which reflects the mechanical robustness of liquid marbles, depends on the type and size of the stabilizing particles as well as the chemical nature of the liquid droplet. By investigating the surface of the liquid marble, we attribute its rupture under the critical pressure to the low surface coverage of particles when highly stretched. Moreover, the applied pressure can be reflected by the inner Laplace pressure of the liquid marble considering the squeezing test is a quasi-static process. By analyzing the Laplace pressure upon rupture of the liquid marble, we predict the dependence of the critical pressure on the size of the liquid marble, which agrees well with experimental results

Lattice study on kaon pion scattering length in the I=3/2I=3/2 channel

Using the tadpole improved Wilson quark action on small, coarse and anisotropic lattices, $K\pi$ scattering length in the $I=3/2$ 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. Our result is compared with the results obtained using Roy equations, Chiral Perturbation Theory, dispersion relations and the experimental data.Comment: Latex file typeset with elsart.cls, 9 pages, 3 figure

Coalescence of electrically charged liquid marbles

© The Royal Society of Chemistry. In this work, we investigated the coalescence of liquid water marbles driven by a DC electric field. We have found that two contacting liquid marbles can be forced to coalesce when they are charged by a sufficiently high voltage. The threshold voltage leading to the electro-coalescence sensitively depends on the stabilizing particles as well as the surface tension of the aqueous phase. By evaluating the electric stress and surface tension effect, we attribute such coalescence to the formation of a connecting bridge driven by the electric stress. This liquid bridge subsequently grows and leads to the merging of the marbles. Our interpretation is confirmed by the scaling relation between the electric stress and the restoring capillary pressure. In addition, multiple marbles in a chain can be driven to coalesce by a sufficiently high threshold voltage that increases linearly with the number of the marbles. We have further proposed a simple model to predict the relationship between the threshold voltage and the number of liquid marbles, which agrees well with the experimental results. The concept of electro-coalescence of liquid marbles can be potentially useful in their use as containers for chemical and biomedical reactions involving multiple reagents

I=2 pion scattering length with the parametrized fixed point action

We report on the pion-pion scattering length in the I=2 channel using the parametrized fixed point action. Pion masses of 320 MeV were reached in this quenched calculation of the scattering length.Comment: 3 pages, 5 figures, Lattice2003 (Spectrum

Calculating the I=2 Pion Scattering Length Using Tadpole Improved Clover Wilson Action on Coarse Anisotropic Lattices

In an exploratory study, using the tadpole improved clover Wilson quark action on small, coarse and anisotropic lattices, the $\pi\pi$ scattering length in the I=2 channel is calculated within quenched approximation. A new method is proposed which enables us to make chiral extrapolation of our lattice results without calculating the decay constant on the lattice. Finite volume and finite lattice spacing errors are analyzed and the results are extrapolated towards the infinite volume and continuum limit. Comparisons of our lattice results with the new experiment and the results from Chiral Perturbation Theory are made. Good agreements are found.Comment: 21 pages, 8 figures, latex file typeset with elsart.cls, minor change

Self-Improving Algorithms

We investigate ways in which an algorithm can improve its expected performance by fine-tuning itself automatically with respect to an unknown input distribution D. We assume here that D is of product type. More precisely, suppose that we need to process a sequence I_1, I_2, ... of inputs I = (x_1, x_2, ..., x_n) of some fixed length n, where each x_i is drawn independently from some arbitrary, unknown distribution D_i. The goal is to design an algorithm for these inputs so that eventually the expected running time will be optimal for the input distribution D = D_1 * D_2 * ... * D_n. We give such self-improving algorithms for two problems: (i) sorting a sequence of numbers and (ii) computing the Delaunay triangulation of a planar point set. Both algorithms achieve optimal expected limiting complexity. The algorithms begin with a training phase during which they collect information about the input distribution, followed by a stationary regime in which the algorithms settle to their optimized incarnations.Comment: 26 pages, 8 figures, preliminary versions appeared at SODA 2006 and SoCG 2008. Thorough revision to improve the presentation of the pape