Gabor Frames on Local Fields of Positive Characteristic

Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. Finding general and verifiable conditions which imply that the Gabor systems are Gabor frames is among the core problems in time-frequency analysis. In this paper, we give some simple and sufficient conditions that ensure a Gabor system ${M_{u(m)b}T_{u(n)a}g:m,n\in \mathbb N_{0}}$ to be a frame for L^2(K). The conditions proposed are stated in terms of the Fourier transforms of the Gabor system's generating functions.Comment: 11. arXiv admin note: text overlap with arXiv:1312.0443, arXiv:1103.0090 by other author

Limiting distributions of curves under geodesic flow on hyperbolic manifolds

We consider the evolution of a compact segment of an analytic curve on the unit tangent bundle of a finite volume hyperbolic $n$-manifold under the geodesic flow. Suppose that the curve is not contained in a stable leaf of the flow. It is shown that under the geodesic flow, the normalized parameter measure on the curve gets asymptotically equidistributed with respect to the normalized natural Riemannian measure on the unit tangent bundle of a closed totally geodesically immersed submanifold. Moreover, if this immersed submanifold is a proper subset, then a lift of the curve to the universal covering space $T^1(H^n)$ is mapped into a proper subsphere of the ideal boundary sphere $\partial H^n$ under the visual map. This proper subsphere can be realized as the ideal boundary of an isometrically embedded hyperbolic subspace in $H^n$ covering the closed immersed submanifold. In particular, if the visual map does not send a lift of the curve into a proper subsphere of $\partial H^n$, then under the geodesic flow the curve gets asymptotically equidistributed on the unit tangent bundle of the manifold with respect to the normalized natural Riemannian measure. The proof uses dynamical properties of unipotent flows on finite volume homogeneous spaces of SO(n,1).Comment: 27 pages, revised version, Proof of Theorem~3.1 simplified, remarks adde

Availability and use of electrotherapy devices: a survey

This item is published and the copyright holder of this article is the International Journal of Therapy and Rehabilitation © 2010 MA Healthcare Limited, http://www.ijtr.co.uk/. The article is available here with the permission of the copyright holder. Any use of the article from this site for personal use is permitted; however, if it is to be used for any other purpose, or reproduced in part or in full, the copyright holder must be contacted.Electrophysical agents such as radiofrequency electromagnetic fields (shortwave and microwave), ultrasound, laser and electrical stimulation are used for therapeutic purpose in physiotherapy departments. They are primarily used for treating a wide range of musculoskeletal injuries. This study investigated the availability and use of therapeutic diathermy, ultrasound, laser, transcutaneous electrical nerve stimulation (TENS) and interferential equipment in 46 physiotherapy departments in NHS hospitals in the south of England, using a self-administered questionnaire. Results indicated that therapeutic ultrasound was the most commonly available and most often used modality by surveyed departments. Pulsed shortwave diathermy, interferential, and laser were available to a lesser degree and also used less often. Continuous shortwave diathermy was used rarely and only in larger departments. Microwave diathermy was not available in any of the surveyed departments. The level of non-use of equipment despite availability was highest for continuous shortwave diathermy followed by pulsed shortwave diathermy and then laser. The rare use and total non-use of some of the modalities, despite availability of equipment, may have implications for purchasers of this expensive equipment. While the findings of this study show a regional trend in NHS physiotherapy departments, this may not be generalizable to a national level.This study was funded by the Health and Safety Executive, UK, (Grant No. 4371/R47.022

Duality mappings for the theory of risk aversion with vector outcomes

We consider a decision-making environment with an outcome space that is a convex and compact subset of a vector space belonging to a general class of such spaces. Given this outcome space, we de¯ne gen- eral classes of (a) risk averse von Neumann-Morgenstern utility func- tions de¯ned over the outcome space, (b) multi-valued mappings that yield the certainty equivalent outcomes corresponding to a lottery, (c) multi-valued mappings that yield the risk premia corresponding to a lottery, and (d) multi-valued mappings that yield the acceptance set of lotteries corresponding to an outcome. Our duality results establish that the usual mappings that generate (b), (c) and (d) from (a) are bi- jective. We apply these results to the problem of computing the value of ¯nancial assets to a risk averse decision-maker and show that this value will always be less than the arbitrage-free valuation.Risk aversion, vector outcomes, certainty equivalence, risk premia, acceptance set

Frustrated Metastable Behavior of Magnetic and Transport Properties in Charge Ordered La1-xCaxMnO3+d Manganites

We have studied the effect of metastable, irreversibility induced by repeated thermal cycles on the electric transport and magnetization of polycrystalline samples of La1-xCaxMnO3 (0.48\leq x \leq 0.55) close to charge ordering. With time and thermal cycling (T<300 K) there is an irreversible transformation of the low-temperature phase from a partially ferromagnetic and metallic to one that is less ferromagnetic and highly resistive for the composition close to charge ordering (x=050 and 0.52). Irrespective of the actual ground state of the compound, the effect of thermal cycling is towards an increase of the amount of the insulating phase. We have observed the magnetic relaxation in the metastable state and also the revival of the metastable state (in a relaxed sample) due to high temperature thermal treatment. We observed changes in the resistivity and magnetization as the revived metastable state is cycled. The time changes in the magnetization are logarithmic in general and activation energies are consistent with those expected for electron transfer between Mn ions. Changes induced by thermal cycling can be inhibited by applying magnetic field. These results suggest that oxygen non-stoichiometry results in mechanical strains in this two-phase system, leading to the development of frustrated metastable states which relax towards the more stable charge-ordered and antiferromagnetic microdomains. Our results also suggest that the growth and coexistence of phases gives rise to microstructural tracks and strain accommodation, producing the observed irreversibility.Comment: 13 Pages, 10 Figure

A NON-COOPERATIVE THEORY OF QUANTITY-RATIONING INTERNATIONAL TRANSFRONTIER POLLUTION

We study the problem caused by international transfrontier pollution. Our re-sults are derived from the analysis of an incomplete information, non-cooperative game model of the determination of emissions in a quantity-rationing setting. We model the emission capping negotiations using the best response dynamic pro-cess and provide natural conditions under which the process has a unique and globally asymptotically stable stationary point. We then analyze the link be-tween type profiles and the stationary points of the negotiation process to derive various comparative statics results and the type-contingent ordering of emission allocations. Finally, we study the investment strategies that nations can use prior to the negotiations in order to manipulate the equilibrium emission caps. The results have implications regarding the political economy of emission capping.Emission capping, non-cooperative game, negotiations, incomplete information, manipulation

Allocations and manipulation in Kyoto type protocols

We study an incomplete information, non-cooperative model of the determination of national emission endowments under a Kyoto type protocol with heterogeneous nations. The model generates a link between national types and equilibrium na-tional emission caps. We analyze this link to (a) derive the type-contingent ordering of emission allocations, (b) study the effects of growth on emission al-locations, and (c) study the strategies that nations can use to manipulate the emission allocation process. Synthesizing these results allows us to derive the implications of national heterogeneity and asymmetry of economic power in the capping process.correlated equilibrium, heterogeneity, incomplete information, Kyoto protocol, manipulation, non-cooperative game.