Landau Migdal Theory of Interacting Fermi Systems: A Framework for Effective Theories in Nuclear Structure Physics

We review Migdal's Theory of Finite Fermi Systems and its application to the structure of nuclei. The theory is an extension of Landau's Theory of Interacting Fermi Systems. In the first part the basic formulas are derived within the many body Green functions approach. The theory is applied to isovector electric giant resonances in medium and heavy mass nuclei. The parameterizations of the enormalized effective ph-interaction and the effective operators are discussed. It is shown that the number of free parameters are restricted due to conservation laws. We also present an extension of Migdal's theory, where the low-lying phonons are considered in a consistent manner. The extended theory is again applied to the same isovector electric giant resonances and to the analysis of $(\alpha,\alpha^\prime)$ reaction data. We point out that the extended theory is the appropriate frame for self consistent nuclear structure calculations starting from effective Lagrangians and Hamiltonians.Comment: 6 figure

CBBN in the CMSSM

Catalyzed big bang nucleosynthesis (CBBN) can lead to an overproduction of ^6Li in gravitino dark matter scenarios in which the lighter stau is the lightest Standard Model superpartner. Based on a treatment using the state-of-the-art result for the catalyzed ^6Li production cross section, we update the resulting constraint within the framework of the constrained minimal supersymmetric Standard Model (CMSSM). We confront our numerical findings with recently derived conservative limits on the gaugino mass parameter and the reheating temperature.Comment: 4 pages, 4 figures; Submitted for the SUSY07 proceeding

Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case

In John Nash’s proofs for the existence of (Nash) equilibria based on Brouwer’s theorem, an iteration mapping is used. A continuous— time analogue of the same mapping has been studied even earlier by Brown and von Neumann. This differential equation has recently been suggested as a plausible boundedly rational learning process in games. In the current paper we study this Brown—von Neumann—Nash dynamics for the case of continuous strategy spaces. We show that for continuous payoff functions, the set of rest points of the dynamics coincides with the set of Nash equilibria of the underlying game. We also study the asymptotic stability properties of rest points. While strict Nash equilibria may be unstable, we identify sufficient conditions for local and global asymptotic stability which use concepts developed in evolutionary game theory.Learning in games; evolutionary stability; BNN

Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case

In John Nash’s proofs for the existence of (Nash) equilibria based on Brouwer’s theorem, an iteration mapping is used. A continuous— time analogue of the same mapping has been studied even earlier by Brown and von Neumann. This differential equation has recently been suggested as a plausible boundedly rational learning process in games. In the current paper we study this Brown—von Neumann—Nash dynamics for the case of continuous strategy spaces. We show that for continuous payoff functions, the set of rest points of the dynamics coincides with the set of Nash equilibria of the underlying game. We also study the asymptotic stability properties of rest points. While strict Nash equilibria may be unstable, we identify sufficient conditions for local and global asymptotic stability which use concepts developed in evolutionary game theory.

Stability of the Replicator Equation for a Single-Species with a Multi-Dimensional Continuous Trait Space

The replicator equation model for the evolution of individual behaviors in a single-species with a multi-dimensional continuous trait space is developed as a dynamics on the set of probability measures. Stability of monomorphisms in this model using the weak topology is compared to more traditional methods of adaptive dynamics. For quadratic fitness functions and initial normal trait distributions, it is shown that the multi-dimensional CSS (Continuously Stable Strategy) of adaptive dynamics is often relevant for predicting stability of the measure-theoretic model but may be too strong in general. For general fitness functions and trait distributions, the CSS is related to dominance solvability which can be used to characterize local stability for a large class of trait distributions that have no gaps in their supports whereas the stronger NIS (Neighborhood Invader Strategy) concept is needed if the supports are arbitrary.Adaptive dynamics, CSS, NIS, replicator equation, local superiority, strategy dominance, measure dynamics, weak topology

Estimating optimal conservation in agricultural landscapes when costs and benefits of conservation measures are heterogeneous in space and over time

Designing agri-environmental schemes targeted at conservation poses the key question of how many financial resources should be allocated to address a particular aim such as the conservation of an endangered species. Economists can contribute to an answer by estimating the 'optimal level of species conservation'. This requires an assessment of the supply and the demand curve for conservation and a comparison of the two curves to identify the optimal conservation level. In a case study we estimate the optimal conservation level of Large Blue butterflies (protected by the EU Habitats Directive) in the region of Landau, Germany. The difference to other studies estimating optimal conservation is that a problem is addressed where costs and benefits of conservation measures are heterogeneous in space and over time. In our case study we find a corner solution where the highest proposed level of butterfly conservation is optimal. Although our results are specific to the area and species studied, the methodology is generally applicable to estimate how many financial resources should be allocated to conserve an endangered species in the context of agri-environmental schemes. --agri-environmental policy,biodiversity,optimal conservation,spatial heterogeneity,willingness-to-pay

Correlation of crystal growth rates in supersaturated solutions

This investigation has shown that crystals of copper sulfate and magnesium sulfate when grown in supersaturated solutions exhibit a growth rate according to the following equation: RL = 5.0 (ΔCDm)1/ρU Vs.292 where, RL, is the growth rate in Microns/min, is the change in concentration, Dm, the diffusivity coefficient, , density of solution, U, viscosity and Vs, solution velocity past the crystal. The equation shown demonstrates that a mass transfer process is taking place from the solution to the crystal surface, and that within the velocity range studied, there was no effect shown by the interface orientation rate. In a crystallizer where there is a mixture of crystals, the larger crystals will grow faster than those of a smaller size due to its higher relative solution velocity. Crystal growth is dependent upon the other factors described in conjunction with the formulae, and the analogy between these factors is described in the main paper

Re: Sodium Valproate-Induced Myopathy in a Child

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Scenarios and Capability Planning: Creation of Scenarios as a Tool for Predicting the Future Operating Environment

The goal of the present paper is to introduce the audience to selected methods (especially future scenario-based method) and their usability in predicting future developments of a security and operating environment. Furthermore, this paper highlights the place of these methods in the process of capability planning and creation of a security and defence policy of the state. This paper explores the possibilities, practical applications, risks and limitations of using the selected methods in predicting the future development of a security and operating environment