Hopf Map and Quantization on Sphere

Quantization of a system constrained to move on a sphere is considered by taking a square root of the ``on sphere condition''. We arrive at the fibre bundle structure of the Hopf map in the cases of $S^{2}$and $S^{4}$. This leads to more geometrical understanding of monopole and instanton gauge structures that emerge in the course of quantization.Comment: 9 pages, LaTeX2e, uses amsmath.st

Inequivalent Quantization in the Skyrme Model

Quantum mechanics on manifolds is not unique and in general infinite number of inequivalent quantizations can be considered. They are specified by the induced spin and the induced gauge structures on the manifold. The configuration space of collective mode in the Skyrme model can be identified with $S^{3}$ and thus the quantization is not unique. This leads to the different predictions for the physical observables.Comment: 16 pages, LaTeX2

Further progress on application of ADAPT-VPA to Antarctic minke whales

The ADAPT-VPA assessment methodology originally developed by Butterworth et al. (1999) has been appreciably advanced by taking into account various comments made during a series of IWC-SC meetings and is applied here to abundance estimates (from both IDCR/SOWER and JARPA surveys) as well as catch at age data (both commercial and scientific) for the I and P-stocks of Antarctic minke whales. The improvements to the methodology allow account to be taken of various further aspects, primarily: 1) inter-annual differences in the distribution of the population between different management Areas, 2) a stock-recruitment relationship, 3) the effects of possible ageing-error, and 4) the effects of possible change in age-at-sexual maturity over time as indicated by analyses of readings of transition phases in ear plugs. Furthermore sensitivities to various functional forms for selectivity and natural mortality with age are explored. The general pattern shown by analysis for both stocks is of a minke whale abundance trend that increased over the middle decades of the 20th Century to peak at about 1970, and then stabilized or declined somewhat for the next three decades. The recruitment trend is similar, though with its peak slightly earlier. The annual natural mortality rate, M, is estimated to be 0.056 with a CV of 0.16 for the I-stock, and 0.069 with a CV of 0.15 for the P-stock for the “Reference case” assessments. When only the JARPA abundance estimates are used for tuning, M is estimated as 0.037 and 0.060 for the I- and P-stocks, respectively. The estimation of M is fairly robust to the various assumptions of the model. This analysis is considered preliminary, as conclusions relating to estimates of M and trends in abundance and recruitment obtained using this approach await further revisions of 1) abundance estimates obtained from IDCR and JARPA surveys, and 2) error-models for the catch-at-age data, particularly those obtained from the commercial harvests

Berry Connections and Induced Gauge Fields in Quantum Mechanics on Sphere

Quantum mechanics on sphere $S^{n}$ is studied from the viewpoint that the Berry's connection has to appear as a topological term in the effective action. Furthermore we show that this term is the Chern-Simons term of gauge variables that correspond to the extra degrees of freedom of the enlarged space.Comment: 12 pages, LaTeX2

Lost equivalence of nonlinear sigma and CP1CP^{1} models on noncommutative space

We show that the equivalence of nonlinear sigma and $CP^{1}$ models which is valid on the commutative space is broken on the noncommutative space. This conclusion is arrived at through investigation of new BPS solitons that do not exist in the commutative limit.Comment: 17 pages, LaTeX2

Application of ADAPT-VPA to Antarctic minke whales in the JARPA research area

The ADAPT-VPA assessment methodology originally developed by Butterworth et al. (1999) has been greatly improved by taking into account various comments made during a series of IWC-SC meetings and is applied here to abundance estimates (from both IDCR/SOWER and JARPA surveys) as well as catch at age data (both commercial and scientific) for the I and P-stocks of Antarctic minke whales. The improvements to the methodology allow account to be taken of various further aspects, primarily: 1) inter-annual differences in the distribution of the population between different management Areas, 2) a stock-recruitment relationship, and 3) the effects of possible ageing-error. Furthermore sensitivities to various functional forms for selectivity and natural mortality with age are explored. The general pattern shown by the results for both stocks is of a minke whale abundance trend that increased over the middle decades of the 20th Century to peak at about 1970, and then stabilized or declined somewhat for the next three decades. The recruitment trend is similar, though with its peak slightly earlier. The annual natural mortality rate, M, is estimated to be 0.056 with a CV of 0.16 for the I-stock, and 0.069 with a CV of 0.15 for the P-stock for the “Reference case” assessments. When only the JARPA abundance estimates are used for tuning, M is estimated as 0.038 and 0.060 for the I- and P-stocks, respectively. The estimation of M is fairly robust to the various assumptions of the model. The CVs of these M estimates for the “Reference case” assessments, when compared with those of typically 0.35 for the Areaspecific assessments of Butterworth et al. (1999) which were based on fewer data, indicate an improvement in the precision of these estimates due to the accumulation of data over the long-term of the JARPA surveys. The fits of the stock-recruitment model generally require a carrying capacity for minke whales that first increased and then stabilized or declined somewhat during the last century, and suggest MSYR(1+) values in the 4-6% range. The improved precision in the estimation of M may contribute in the improvement of management and assessment of this species on a stock-specific basis, since it can reduce the uncertainty concerning the value of M and can provide an improved prior distribution for MSYR. The latter in particular, in the context of providing a measure of the productivity of which the species is capable, is essential information for effective RMP implementation through reduction of the range of plausible scenarios which need to be considered in Implementation Simulation Trials.http://www.mth.uct.ac.za/maram/pub/2006/SC_D06_J14.pd

An integrated approach for the estimation of abundance through a random-effects model

Let Nay be the true abundance in the a-th survey block in the year y, and let Nˆ ay (P) and Nˆ ay (C) denote estimates of Nay obtained from passing-mode and closing-mode surveys respectively. If abundance estimates in different blocks or years include common parameters such as effective search half-width, then any two of them are correlated, and the method following takes this into account