The Tits alternative for generalized triangle groups of type (3, 4, 2)

A generalized triangle group is a group that can be presented in the form G = h x, y | xp = yq = w(x, y)r = 1 i where p, q, r ? 2 and w(x, y) is a cyclically reduced word of length at least 2 in the free product Zp ? Zq = h x, y | xp = yq = 1i. Rosenberger has conjectured that every generalized triangle group G satisfies the Tits alternative. It is known that the conjecture holds except possibly when the triple (p, q, r) is one of (2, 3, 2), (2, 4, 2), (2, 5, 2), (3, 3, 2), (3, 4, 2), or (3, 5, 2). Building on a result of Benyash-Krivets and Barkovich from this journal, we show that the Tits alternative holds in the case (p, q, r) = (3, 4, 2)

Seifert fibred knot manifolds

We consider the question of when is the closed manifold obtained by elementary surgery on an $n$-knot Seifert fibred over a 2-orbifold. After some observations on the classical case, we concentrate on the cases n=2 and 3. We have found a new family of 2-knots with torsion-free, solvable group, overlooked in earlier work. We know of no higher dimensional examples.Comment: New co-author, stronger restrictions on possible Seifert bases. Final section on 3-knots reduced to a paragraph, as a lemma was misused in the original version. Version 3; minor improvements to first paragraph and notatio

New Developments in Panel Data Estimation: Full-Factorial Panel Data Model

Panel data has been widely used in many social science studies. Pooling data across cross-sections and time-series improves quality of data analysis; however, the model is limited in its ability to actually accurately predict variables of interest due to severe practical data limitations and the ability of properly capturing varying market structures. In this article, a simple and innovative model of product share is introduced. The Full-Factorial Panel Data Model is based on the simple premises of re-conceptualization of any zero-sum group as a series of two-entity markets. This model solves the challenges associated with pooling data across disparate cross-sections and time-periods as well as the changing competitive market structure issues and therefore results in reliable variable of interest estimates.Research Methods/ Statistical Methods,

Mapping the potential within a nanoscale undoped GaAs region using a scanning electron microscope

Semiconductor dopant profiling using secondary electron imaging in a scanning electron microscope (SEM) has been developed in recent years. In this paper, we show that the mechanism behind it also allows mapping of the electric potential of undoped regions. By using an unbiased GaAs/AlGaAs heterostructure, this article demonstrates the direct observation of the electrostatic potential variation inside a 90nm wide undoped GaAs channel surrounded by ionized dopants. The secondary electron emission intensities are compared with two-dimensional numerical solutions of the electric potential.Comment: 7 pages, 3 figure

A theory based stochastic investment model for actuarial use

Includes bibliographical references (leaves 73-79).This thesis reviews the origins, development and uses of asset-liability modelling, as well as existing largely stochastic investment models, notably those of the Maturity Guarantees Working Party (1980), Wilkie (1986,1995) and Thomson (1996). A stochastic investment model is developed which describes returns from equities, bonds and cash, as well as inflation and economic growth. The model is consistent with economic theory, adequately fits past data, and is relatively parsimonious compared with other models. A series of assumptions about the causal relationships between inflation, economic growth and interest rates are made based on standard economic theory. It is noted that consensus does not exist on some of the economic theory. Similarly a series of assumptions on the pricing of assets are made based on financial economic theory on market efficiency, expectations and asset pricing. Notably, it is assumed that financial markets are efficient. An economic model is described for inflation, economic growth and interest rates based on the set of assumptions. Each variable is modelled such that its value in one period is a function of its value in the previous period, the value of the other economic variables in the current and previous period, and a normally distributed residual. The model is a mixture of a random walk and autoregressive process that has two special cases of a (non-mean-reverting) pure random walk, and a (mean-reverting) pure autoregressive process. A financial market model is described for bond and equity returns based on the set of assumptions. Expected returns are derived from the expected real interest rate plus a risk premium, where the risk premium is linearly related to the standard deviation of real return. Bond yields are modelled as the sum of expected future short term real interest rates, expected future inflation, and a risk premium. Share prices are modelled as the present value of expected future distributable earnings, discounted at a rate equal to the sum of expected future short term real interest rates, expected future inflation, and a risk premium. The growth in earnings per share is modelled as the sum of inflation, real economic growth and a normal residual, and is also linked to real interest rates. Dividends are modelled as a smoothed function of earnings, with unit-gain from earnings to dividends. Annual data for a 15 year period is used to parameterise the model for the United States, Britain and South Africa respectively. The modelled volatilities of financial market returns, together with the economic data, are used to fit the economic model. The procedure is similar to the method of moments for statistical estimation. Parameters in the economic model that are not statistically significant or are not consistent with the assumptions are excluded. It was found that neither the random walk nor the autoregressive special case models could adequately explain observed volatility in financial markets, so the general case (mixture model) was adopted for economic variables. The parameterised models for the three countries studied exhibited a ""cascade structure"" where all variables are a function of one or two ""driving variables"", without any circularity/""feedback"". The models for the United States and Britain all have inflation as the driving variable, whereas the South African model has both inflation and economic growth as driving variables. The model achieves the objectives of consistency with economic theory as well as parsimony (when compared to Wilkie (1995)). With regards to the criterion of producing reasonable output, the model has advantages over existing models. These include that financial market returns simulated by the model are non-normal and exhibit significant leptokursis (fat-tails) with higher probabilities of severe down-market returns than are predicted by normal or log-normal distributions. Simulated returns also exhibit the weak and slow mean reversion that is observed in markets, and the simulated yield curve exhibits non-parallel shifts and inversions. However, simulated interest rates (particularly nominal interest rates), and even bond yields can become negative, although the probability of negative nominal interest rates is small in the model, and that of negative bond yields is negligible. Two areas where a good fit was not achieved were in the models of risk premiums and dividends. It is recommended that alternative approaches for estimating risk premiums be used. The poor fit to dividend data is not regarded as a significant weakness because modelled equity returns are not dependent on dividends

One Relator Quotients of Graph Products

In this paper, we generalise Magnus' Freiheitssatz and solution to the word problem for one-relator groups by considering one relator quotients of certain classes of right-angled Artin groups and graph products of locally indicable polycyclic groups

L^2-Betti numbers of one-relator groups

We determine the L^2-Betti numbers of all one-relator groups and all surface-plus-one-relation groups (surface-plus-one-relation groups were introduced by Hempel who called them one-relator surface groups). In particular we show that for all such groups G, the L^2-Betti numbers b_n^{(2)}(G) are 0 for all n>1. We also obtain some information about the L^2-cohomology of left-orderable groups, and deduce the non-L^2 result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free.Comment: 18 pages, version 3, minor changes. To appear in Math. An

Young's experiment and the finiteness of information

Young's experiment is the quintessential quantum experiment. It is argued here that quantum interference is a consequence of the finiteness of information. The observer has the choice whether that information manifests itself as path information or in the interference pattern or in both partially to the extent defined by the finiteness of information.Comment: 5 pages, 3 figures, typos remove

Possible detection of singly-ionized oxygen in the Type Ia SN 2010kg

We present direct spectroscopic modeling of 11 high-S/N observed spectra of the Type Ia SN 2010kg, taken between -10 and +5 days with respect to B-maximum. The synthetic spectra, calculated with the SYN++ code, span the range between 4100 and 8500 \r{A}. Our results are in good agreement with previous findings for other Type Ia SNe. Most of the spectral features are formed at or close to the photosphere, but some ions, like Fe II and Mg II, also form features at ~2000 - 5000 km s$^{-1}$ above the photosphere. The well-known high-velocity features of the Ca II IR-triplet as well as Si II $\lambda$6355 are also detected. The single absorption feature at ~4400 \r{A}, which usually has been identified as due to Si III, is poorly fit with Si III in SN 2010kg. We find that the fit can be improved by assuming that this feature is due to either C III or O II, located in the outermost part of the ejecta, ~4000 - 5000 km s$^{-1}$ above the photosphere. Since the presence of C III is unlikely, because of the lack of the necessary excitation/ionization conditions in the outer ejecta, we identify this feature as due to O II. The simultaneous presence of O I and O II is in good agreement with the optical depth calculations and the temperature distribution in the ejecta of SN 2010kg. This could be the first identification of singly ionized oxygen in a Type Ia SN atmosphere.Comment: Submitted to MNRA