We present a method of producing normal subgroups of the free group on r generators not containing a given word. Special attention is given to the normal subgroups of the free group on two generators. In considering the exponent sum of the generators in a given word, we produce such subgroups and clearly state for what class of words these subgroups are not easily obtainable. We also provide a ...

The determination of the mean survival time t ~i.e., inverse reaction rate! associated with diffusion-controlled reactions among static traps is a problem of long-standing interest, dating back to the classical work of Smoluchkowski. For the broad class of model particulateand digitized-based models considered here, we find a universal curve for the mean survival time t for a wide range of poro...

For at least partially ordered three-way tables, it is well known how to arithmetically decompose Pearson’s X2 P statistic into informative components that enable a close scrutiny of the data. Similarly well-known are smooth models for two-way tables from which score tests for homogeneity and independence can be derived. From these models, both the components of Pearson’s X2 P and information a...

We analyze the general structure of soft scalar masses emerging in superstring models involving anomalous U(1) symmetries, with the aim of characterizing more systematically the circumstances under which they can happen to be flavor universal. We consider both heterotic orbifold and intersecting brane models, possibly with several anomalous and non-anomalous spontaneously broken U(1) symmetries...

Previously, the weight parameter of the finite mixture of regression models has been assumed to be invariant of the characteristics of the observations under study. Recently, it has been shown that the weight parameter of the finite mixture of negative binomial (NB) models can be dependent upon the attributes of the sites. Since the selection of the functional form for weight parameter has a si...

The evolution with energy scale of the partonic logarithmic scaled energy spectra is investigated in the framework of the modified leading logarithmic approximation (MLLA). The behaviour of the higher order moments is compared to a number of analytic predictions and e + e − data.

The purpose of this article is to present the theory of higher order connections on vector bundles from a viewpoint inspired by projective differential geometry.

We have designed agents to participate in one of the internet auctions|Michigan AuctionBot. The agents communicate with the AuctionBot through API. For the inference mechanism underlying the agent, we use regression methods for online derivation of functional relations between other agents' actions and their internal states. The functional form of a regression model is based on an agent's assum...

We studied the mathematical relations between species abundance distributions (SADs) and species-area relationships (SARs) and found that a power-law SAR can be generally derived from a power-law SAD without a special assumption such as the “canonical hypothesis”. In the present analysis, an SAR-exponent is obtained as a function of an SAD-exponent for a finite number of species. We also studie...