The su(1,1) dynamical algebra from the Schr\"odinger ladder operators for N-dimensional systems: hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator

We apply the Schr\"odinger factorization to construct the ladder operators for hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator in arbitrary dimensions. By generalizing these operators we show that the dynamical algebra for these problems is the $su(1,1)$ Lie algebra.Comment: 10 page

Hadley circulation and precipitation changes control black shale deposition in the Late Jurassic Boreal Seaway

New climate simulations using the HadCM3L model with a paleogeography of the Late Jurassic [155.5 Ma], and proxy-data corroborate that warm and wet tropical-like conditions reached as far north as the UK sector of the Jurassic Boreal Seaway [~35oN]. This is associated with a northern hemisphere Jurassic Hadley cell and an intensified subtropical jet which both extend significantly polewards than in the modern (July-September). Deposition of the Kimmeridge Clay Formation [KCF] occurred in the shallow, storm-dominated, epeiric Boreal Seaway. High resolution paleo-environmental proxy data from the Kimmeridge Clay Formation [KCF; ~155–150 Ma], UK are used to test for the role of tropical atmospheric circulation on meter-scale heterogeneities in black shale deposition. Proxy and model data show that the most organic-rich section [eudoxus to mid-hudlestoni zones] is characterised by a positive δ13Corg excursion and up to 37 wt% total organic carbon [%TOC]. Orbital-modulation of organic carbon burial primarily in the long eccentricity power band combined with a clear positive correlation between %TOC carbonate-free and the kaolinite/illite ratio supports peak organic carbon burial under the influence of very humid climate conditions, similar to the modern tropics. This re-interpretation of large-scale climate relationships, supported by independent modelling and geological data, has profound implications for atmospheric circulation patterns and processes affecting marine productivity and organic carbon burial further north along the Boreal Seaway, including the Arctic

The Effects of Rewards on Tax Compliance Decisions

We analyze how the redistribution of tax revenues influences tax compliance behavior by applying different reward mechanisms. In our experiment, subjects have to make two decisions. In the first stage, subjects decide on the contribution to a public good. In the second stage, subjects declare their income from the first stage for taxation. Our main results are threefold: First, from an aggregated perspective, rewards have a negative overall effect on tax compliance. Second, we observe that rewards affect the decision of taxpayers asymmetrically. In particular, rewards have either no effect (for those who are rewarded) or a negative effect (for those who are not rewarded) on tax compliance. Thus, if a high compliance rate of taxpayers is preferred, rewards should not be used by the tax authority. Third, we find an inverse u-shaped relationship between public good contribution and tax compliance. In particular, up to a certain level, tax compliance increases with subjects' own contributions to the public good. Above this level, however, tax compliance decreases with the public good contribution

Triangleland. II. Quantum Mechanics of Pure Shape

Relational particle models are of value in the absolute versus relative motion debate. They are also analogous to the dynamical formulation of general relativity, and as such are useful for investigating conceptual strategies proposed for resolving the problem of time in quantum general relativity. Moreover, to date there are few explicit examples of these at the quantum level. In this paper I exploit recent geometrical and classical dynamics work to provide such a study based on reduced quantization in the case of pure shape (no scale) in 2-d for 3 particles (triangleland) with multiple harmonic oscillator type potentials. I explore solutions for these making use of exact, asymptotic, perturbative and numerical methods. An analogy to the mathematics of the linear rigid rotor in a background electric field is useful throughout. I argue that further relational models are accessible by the methods used in this paper, and for specific uses of the models covered by this paper in the investigation of the problem of time (and other conceptual and technical issues) in quantum general relativity.Comment: Journal Reference added, minor updates to References and Figure

Why are the δ 13 C org values in Phanerozoic black shales more negative than in modern marine organic matter?

The δ 13 C org values of Phanerozoic black shales average −27‰, whereas those of modern marine organic matter average −20‰. The black shale isotopic values mimic those of continental organic matter, yet their organic geochemical properties mandate that they contain predominantly marine organic matter. Hypotheses that proposed to explain the low δ 13 C values of black shales include diagenetic losses of isotopically heavier organic matter components, releases of isotopically light carbon from methane clathrates or extensive magmatic events, greater photosynthetic discrimination against 13 C during times of higher atmospheric p CO 2 , and greenhouse climate stratification of the surface ocean that magnified photic zone recycling of isotopically light organic matter. Although the last possibility seems contrary to the vertical mixing that leads to the high productivity of modern oceanic upwelling systems, it is consistent with the strongly stratified conditions that accompanied deposition of the organic carbon‐rich Pliocene‐Pleistocene sapropels of the Mediterranean Sea. Because most Phanerozoic black shales contain evidence of photic zone anoxia similar to the sapropels, well‐developed surface stratification of the oceans was likely involved in their formation. Existence of isotopically light land plant organic matter during several episodes of extensive magmatism that accompanied black shale deposition implies massive release of mantle CO 2 that added to the greenhouse conditions that favored oceanic stratification. The 13 C depletion common to most Phanerozoic black shales apparently resulted from a greenhouse climate associated with elevated atmospheric p CO 2 that led to a strongly stratified ocean and photic zone recycling of organic matter in, augmented by magmatic CO 2 releases. Key Points Photic zone recycling of organic carbon is responsible for their low δ 13 C values Black shales deposited during periods of strong surface ocean stratification Periods of greenhouse climate established conditions for black shale depositionPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/108327/1/ggge20506.pd

A risk management approach for assessing adaptation to changing flood and drought risks in Europe

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