Variable Modified Newtonian Mechanics I: Single Metric Universe

A few years ago Baker \cite{baker} proposed a Lema$\hat{i}$tre-Tolman metric which could vary smoothly between the Schwarzschild metric at small scales and the Friedmann-Robertson-Walker (FRW) metric at large scales. As it stands, by implementing the Bona-Stela construction \cite{bona} its predictions are incompatible with solar system data. We find a metric within the variants of the same construction, which avoids this problem while introducing a MOND-like gravitational acceleration which dominates Newtonian gravity for low central baryoinc densities at early time. This MOND-like acceleration can go some way to explain the growth rate of the baryonic matter density perturbation and the enhancement of the higher CMB acoustic peak anisotropies.Comment: 12 pages, 0 figure

On finite complete rewriting systems and large subsemigroups

Let $S$ be a semigroup and $T$ be a subsemigroup of finite index in $S$ (that is, the set $S\setminus T$ is finite). The subsemigroup $T$ is also called a large subsemigroup of $S$. It is well known that if $T$ has a finite complete rewriting system then so does $S$. In this paper, we will prove the converse, that is, if $S$ has a finite complete rewriting system then so does $T$. Our proof is purely combinatorial and also constructive.Comment: We have made major changes to the paper and simplified most of the proof

Vector potentials in gauge theories in flat spacetime

A recent suggestion that vector potentials in electrodynamics (ED) are nontensorial objects under 4D frame rotations is found to be both unnecessary and confusing. As traditionally used in ED, a vector potential $A$ always transforms homogeneously under 4D rotations in spacetime, but if the gauge is changed by the rotation, one can restore the gauge back to the original gauge by adding an inhomogeneous term. It is then "not a 4-vector", but two: one for rotation and one for translation. For such a gauge, it is much more important to preserve {\it explicit} homogeneous Lorentz covariance by simply skipping the troublesome gauge-restoration step. A gauge-independent separation of $A$ into a dynamical term and a non-dynamical term in Abelian gauge theories is re-defined more generally as the terms caused by the presence and absence respectively of the 4-current term in the inhomogeneous Maxwell equations for $A$. Such a separation {\it cannot} in general be extended to non-Abelian theories where $A$ satisfies nonlinear differential equations. However, in the linearized iterative solution that is perturbation theory, the usual Abelian quantizations in the usual gauges can be used. Some nonlinear complications are briefly reviewed.Comment: 7 page

Developing an Intelligent Table Tennis Umpiring System: Identifying the ball from the scene

This paper reports further development of an intelligent table tennis umpiring system, of which the idea and plan was previously published at this conference in 2007. Briefly, table tennis is a fast sport. A service usually takes a few seconds to complete but an umpire needs to make many observations and makes a judgment before or soon after the service is complete. This is a complex task and the author believes the employment of videography, image processing and artificial intelligence (AI) technologies could help evaluating the service. The aim of this research is to develop an intelligent system which is able to identify and track the location of the ball from live video images and evaluate the service according to the service rules. In this paper, the techniques of identifying a table tennis ball from the scene is described and discussed. A number of image processing techniques have been employed to identify and measure the characteristics of the ball. Artificial neural networks have been applied as a classifier. It classifies whether the detected object is not-a- ball, a ball on the palm or a ball in mid air. The system has been tested on 21 still images which contain pictures of ball-like objects, balls on the palm and in mid air. The preliminary results are very promising. Out of 83 objects, 82 have been correctly classified. The system will be further tested on video images once the video is captured and processed. This paper also discusses the idea of implementing the final system as a multi-agent system, which the author believes it is appropriate for this application because multiple cameras will have to be employed to obtain accurate results

Momentum Kick Model Description of the Ridge in (Delta-phi)-(Delta eta) Correlation in pp Collisions at 7 TeV

The near-side ridge structure in the (Delta phi)-(Delta eta) correlation observed by the CMS Collaboration for pp collisions at 7 TeV at LHC can be explained by the momentum kick model in which the ridge particles are medium partons that suffer a collision with the jet and acquire a momentum kick along the jet direction. Similar to the early medium parton momentum distribution obtained in previous analysis for nucleus-nucleus collisions at 0.2 TeV, the early medium parton momentum distribution in pp collisions at 7 TeV exhibits a rapidity plateau as arising from particle production in a flux tube.Comment: Talk presented at Workshop on High-pT Probes of High-Density QCD at the LHC, Palaiseau, May 30-June2, 201