The Hyperplane is the Only Stable, Smooth Solution to the Isoperimetric Problem in Gaussian Space

We study stable smooth solutions to the isoperimetric type problem for a Gaussian weight on Euclidean Space. That is, we study hypersurfaces $\Sigma^n \subset \mathbb R^{n+1}$ that are second order stable critical points of compact variations that minimize Gaussian weighted area and preserve Gaussian weighted volume. We show that such $\Sigma$ satisfy a curvature condition, and derive the Jacobi operator $L$ for the second variation of such $\Sigma$. Our first main result is that for non-planar $\Sigma$, bounds on the index of $L$, acting on volume preserving variations, gives us that $\Sigma$ splits off a linear space. A corollary of this result is that hyperplanes are the only stable smooth complete solutions to this Gaussian isoperimetric type problem, and that there are no hypersurfaces of index one. Finally, we show that for the case of $\Sigma^2 \subset \mathbb R^3$, there is a gradient decay estimate depending on bounds for the curvature condition and an appropriate area growth bound. This shows that, in the limit as $R \to \infty$, stable $(\Sigma, \partial\Sigma) \subset (B_{2R}(0), \partial B_{2R}(0))$ with good area growth bounds approach hyperplanes.Comment: 20 page

POPULATION AGEING AND INTERTEMPORAL CONSUMPTION: REPRESENTATIVE AGENT VERSUS SOCIAL PLANNER

This paper examines the optimal path of consumption over time in the context of population ageing. Older age groups are considered to have relatively greater ‘needs’, resulting for example from additional health costs. These differences give rise to the concept of the ‘equivalent number of persons’, as distinct from the population size. Emphasis is given to the difference between a framework involving a representative agent and one in which plans are made by a social planner. The precise conditions under which consumption growth paths are the same under the representative agent and the social planner are established. This equivalence is found to hold only in the case where the social planner’s value judgements are such that individuals are considered to be the appropriate unit of analysis. An alternative assumption, in which equivalent persons are regarded as the appropriate units, is found to give rise to a different optimal consumption path. Numerical examples demonstrate the relative orders of magnitude for a range of parameter values. The differences are found to be potentially important. The choice of appropriate consumption units – individuals or equivalent persons – is far from arbitrary since it involves possibly conflicting value judgements. This choice has implications for policies designed to influence the optimal saving rate, such as superannuation policy and the fiscal balance.Ageing;Intertemporal Consumption

Changes in the Taxation of Superannuation:Macroeconomic and Welfare Effects

This paper provides an applied general equilibrium analysis of several alternative taxation regimes applying to superannuation. It is motivated by the decision, announced by the Australian Government in its 2006 Budget, to exempt from tax all superannuation benefits received by recipients over 60 years of age. The analysis focuses on the implications of this and other superannuation tax regimes for intergenerational equity, national living standards, labour supply, saving and social welfare. The method of analysis is simulation of an open economy overlapping generations CGE model, calibrated to Australia. Acknowledgements The authors wish to thank the Australian Research Council for financial support for this work; and the Productivity Commission for providing data on age-specific government spending.

Sustainable Preferences and Damage Abatement:Value Judgments and Implications for Consumption Streams

This paper examines the implications of adopting alternative value judgements when evaluating future consumption streams in the context of damage abatement. The paper focusses on a form of ‘sustainable preferences’ designed to avoid either a dictatorship by present or by future generations which can arise when using a ‘standard’ social welfare function. Numerical examples are reported, based on a simple growth model, under alternative damage abatement parameters and welfare functions. The results illustrate how sustainable preferences effectively reduce the damages on future consumption by shifting consumption from the present to the future. This implies an intergenerational trade-off. An explicit policy of damage abatement under a standard social welfare function implies a similar intergenerational trade-off. However, the results suggest that damage abatement does not penalise current generations as much under sustainable preferences as it does under standard value judgements

Teen-age participation in neighborhood centers

Thesis (M.S.)--Boston Universit

Discounting and the Time Preference Rate: An Introduction

This paper provides an introduction to the evaluation of alternative time streams of consumption and the closely related concept of time preference. The potential sensitivity of comparisons, especially to the choice of time preference rate and elasticity of marginal valuation, is demonstrated. The nature of time preference, based on an axiomatic approach, is then discussed. The analysis of optimisation over time leads to the concept of the social time preference rate, and a difficulty with using this rate is highlighted. Finally, complications introduced by non-income differences between individuals are examined. Emphasis is placed on the central role of value judgements.

The Labour Supply and Savings Effects of Superannuation Tax Changes

This paper investigates the effects on labour supply, consumption and savings of a change in the superannuation tax structure, involving the taxation of contributions to a fund, pre-retirement earnings of the fund, and the benefits received from the fund during retirement. The effects on lifetime plans of tax changes are investigated using a simple three-period model in which the final period is retirement. The effects of unanticipated changes, requiring revisions to plans, are examined. Although the partial effects of particular tax changes are unambiguous, the effects of allowing for a government budget constraint mean that it is difficult to predict a priori how labour supply is likely to be affected. However, private savings unambiguously fall.

Gluon Contributions to Parity-Violating Asymmetries in Polarized Proton-Proton Scattering

We report on a calculation of one-loop weak corrections to polarized quark-gluon scattering and the corresponding crossed channels. Such contributions are suppressed formally by one power of alpha_s relative to W- or Z-mediated quark-quark scattering, but would enable the spin asymmetry of the gluon distribution to contribute to parity-violating asymmetries that will soon be investigated in polarized proton-proton scattering experiments at RHIC. In certain kinematic regions, gluon contributions to parity-violating asymmetries can be as large as 10% of the tree-level W- and Z-exchanges in quark-quark scattering, but usually only where the parity-violating asymmetries are already small.Comment: LATEX 12 pages, 6 figure

Effects of in-season uphill sprinting on physical characteristics in semi-professional soccer players

AIM: Soccer performance is determined by a number of physiological adaptations that can be altered by high intensity training. However, the effectiveness of using an uphill sprint based protocol has not been demonstrated for soccer players. We sought to determine the effectiveness of an in-season uphill sprint training (UST) programme on soccer related physiological outcomes. METHODS: 14 male soccer players (age: 22 ± 8 years, height: 1.81 ± 8 m, body mass: 76 ± 12 kg) underwent testing (5-10-5 agility drill, Yo-Yo Intermittent Recovery Test Level 1, leg and back dynamometry & 3km time trial) at baseline and after 6 weeks of UST or normal activity. Participants were allocated to a control (n=7) or UST (n=7) group. The UST group took part in twice weekly training consisting of 10 x 10 sec sprints with 60s recovery on a 7% gradient for 6 weeks. The control group maintained normal activity patterns. RESULTS: 3km time trial, strength, agility and Yo-Yo performance were all significantly improved pre to post following 6 weeks of UST (Agility 3%, d=1.3; Strength 10%, d=-3.2; VO2 max 3%, d=-1.4; 3-km TT 4%, d=1.3). In the control group 3km time trial, strength, agility and Yo-Yo performance remained unchanged after 6 weeks (Agility 0.1%, d=-0.2; Strength 2%, d=0.0; VO2 max -0.1%, d=0.0; 3-km TT 1.3%, d=0.3). CONCLUSION: Therefore in-season short duration UST is an effective way to improve soccer fitness in a time efficient manner