Covariants, Invariant Subsets, and First Integrals

Let $k$ be an algebraically closed field of characteristic 0, and let $V$ be a finite-dimensional vector space. Let $End(V)$ be the semigroup of all polynomial endomorphisms of $V$. Let $E$ be a subset of $End(V)$ which is a linear subspace and also a semi-subgroup. Both $End(V)$ and $E$ are ind-varieties which act on $V$ in the obvious way. In this paper, we study important aspects of such actions. We assign to $E$ a linear subspace $D_{E}$ of the vector fields on $V$. A subvariety $X$ of $V$ is said to $D_{E}$ -invariant if $h(x)$ is in the tangent space of $x$ for all $h$ in $D_{E}$ and $x$ in $X$. We show that $X$ is $D_{E}$ -invariant if and only if it is the union of $E$-orbits. For such $X$, we define first integrals and construct a quotient space for the $E$-action. An important case occurs when $G$ is an algebraic subgroup of $GL(V$) and $E$ consists of the $G$-equivariant polynomial endomorphisms. In this case, the associated $D_{E}$ is the space the $G$-invariant vector fields. A significant question here is whether there are non-constant $G$-invariant first integrals on $X$. As examples, we study the adjoint representation, orbit closures of highest weight vectors, and representations of the additive group. We also look at finite-dimensional irreducible representations of SL2 and its nullcone

Foundations of continuous-time recursive utility : differentiability and normalization of certainty equivalents

This paper relates recursive utility in continuous time to its discrete-time origins and provides a rigorous and intuitive alternative to a heuristic approach presented in [Duffie, Epstein 1992], who formally define recursive utility in continuous time via backward stochastic differential equations (stochastic differential utility). Furthermore, we show that the notion of Gâteaux differentiability of certainty equivalents used in their paper has to be replaced by a different concept. Our approach allows us to address the important issue of normalization of aggregators in non-Brownian settings. We show that normalization is always feasible if the certainty equivalent of the aggregator is of expected utility type. Conversely, we prove that in general L´evy frameworks this is essentially also necessary, i.e. aggregators that are not of expected utility type cannot be normalized in general. Besides, for these settings we clarify the relationship of our approach to stochastic differential utility and, finally, establish dynamic programming results. JEL Classifications: D81, D91, C6

Stochastic differential utility as the continuous-time limit of recursive utility

We establish a convergence theorem that shows that discrete-time recursive utility, as developed by Kreps and Porteus (1978), converges to stochastic differential utility, as introduced by Dufffie and Epstein (1992), in the continuous-time limit of vanishing grid size

Past changes in riverine input and ocean circulation in the Gulf of Guinea

Large river systems draining the West African Monsoon area deliver sediments and dissolved trace elements into the Gulf of Guinea (GoG) in the easternmost equatorial Atlantic. The different catchment areas of these river systems are characterized by different geological ages and rock types releasing distinct radiogenic neodymium isotope compositions during weathering which are supplied to the GoG. The main rivers discharging into the GoG are the Niger, the Sanaga, the Nyong and the Ntem with present day εNd signatures of -10.5 [1], -12.3, -12.5 and -28.1 [2], respectively. These riverine inputs mix with the tropical Atlantic surface waters. At intermediate water depths Antarctic Intermediate Water (AAIW) prevails whereas the deep basin at this location is mainly filled with NADW. We focus on a marine sediment core that was recovered off the Sanaga and Ntem Rivers and we reconstruct changes in riverine inputs and in mixing of surface and deep water masses over the past 140,000 years. Changes in riverine inputs most likely reflecting latitudinal shifts of the rainfall zones across the different catchment areas were obtained from the Nd isotope signatures of the residual detrital fraction of the sediment. Sediment leachates of several GoG core top samples reflect the riverine input from nearby rivers indicating transport of particles coated in the rivers. Both the sediment leachates and the residual detrital fraction show similar patterns, with shifts towards radiogenic values during the interglacials and least radiogenic values during glacial periods. This shift in εNd values may be attributed to the migration of the rainfall zones towards the north during interglacial times and thus implies the increased influence of the northern rivers, the Sanaga and Nyong. The oxidatively-reductively cleaned planktonic foraminiferal calcite of the core top samples in the GoG reflects surface seawater signatures. Non-reductively cleaned planktonic foraminiferal tests and cleaned shallow endo-benthic and epi-benthic foraminiferal tests were used to acquire information about past bottom waters. Difficulties in cleaning down core foraminiferal samples were experienced and these samples appear to be contaminated by secondary manganese and iron bearing phases, even after cleaning. Those phases may have overprinted the original surface water Nd isotope composition in the planktonic foraminiferal tests. As the planktonic and benthic foraminiferal values are overall similar to the sediment leachates, the foraminiferal isotope signatures are most likely overprinted by isotopic signals originating from the rivers due to remobilization processes in the sediments and formation of secondary phases such as Mn-carbonates, which are attached to the foraminiferal calcites. References: [1] Goldstein et al. (1984) Earth and Planetary Science Letter 70, 221-236. [2] Weldeab et al. (2011) Geophysical Research Letter 38, pp. 5

Consumption habits and humps : [Version 23 June 2013]

We show that the optimal consumption of an individual over the life cycle can have the hump shape (inverted U-shape) observed empirically if the preferences of the individual exhibit internal habit formation. In the absence of habit formation, an impatient individual would prefer a decreasing consumption path over life. However, because of habit formation, a high initial consumption would lead to high required consumption in the future. To cover the future required consumption, wealth is set aside, but the necessary amount decreases with age which allows consumption to increase in the early part of life. At some age, the impatience outweighs the habit concerns so that consumption starts to decrease. We derive the optimal consumption strategy in closed form, deduce sufficient conditions for the presence of a consumption hump, and characterize the age at which the hump occurs. Numerical examples illustrate our findings. We show that our model calibrates well to U.S. consumption data from the Consumer Expenditure Survey

New Copper-based Heat Exchangers for Alternative Refrigerants

The ongoing global effort to replace current refrigerants with zero Ozone Depletion Potential (ODP) and virtually zero Global Warming Potential (GWP) refrigerants has important implications for heat exchangers, air conditioning system design, and the materials choices in these designs. Natural refrigerants with higher flammability, CO2, new HFC blends, and new HFO’s each place different requirements on the heat exchanger design, whether it be for higher equipment efficiency, to reduce refrigerant charge, to operate to much higher operating pressures or temperatures, to prevent corrosion or to avoid leakage. This paper presents critical information that engineers need to know about how heat exchangers based on round inner-grooved small-diameter copper Microgroove™ tube and newly-developed flat copper microchannel tube can be applied in air conditioning equipment using new alternative refrigerants. Heat exchangers based on Microgroove™ tubes with 5mm or 4mm diameter provide solutions for new refrigerants. For example, Microgroove™ tube systems have been found to provide a proven and safe solution for air conditioners using new refrigerant R290 (propane). They permit significantly smaller refrigerant charge, equivalent to those used in microchannel extrusions, while providing reduced manufacturing complexity and maintaining energy efficiency similar to traditional units. These tubes have antimicrobial properties that eliminate mold growth. They have a high level of solution flexibility to provide special circuiting or enlarged coils and eliminate over-sizing for standard products. Thin wall Copper microchannel extruded tubes exhibit high burst pressure at post-brazed conditions. These tubes are especially attractive for use at the high operating temperature and pressure associated with R744 systems. Heat exchangers constructed with such tubes maintain their post braze strength and burst pressure resistance at 180°C operating temperature, have high thermal conductivity, and thus maintain a small heat exchanger size. In addition, microchannel tube produced with a copper alloy such as brass provides the additional benefits of lower cost, corrosion resistance and higher material strength that can lead to even thinner walls and reduced heat exchanger size. Examples of heat exchangers made using copper microchannel extruded tubes fabricated using Cuprobraze technology are provided in this paper. In the quest to improve the environmental performance of air conditioning systems, it is critical to examine the total Life Cycle Climate Performance (LCCP) including the effects of the refrigerant choice and the effect of energy use across the system life cycle. All-copper heat exchangers using either copper Microgroove™ or microchannel tubes suppress the growth of bacteria and mold that reduce system energy efficiency, cause product deterioration and foul odors. Mold growth studies show aluminum fin heat exchanger performance decreases up to 20% after four years of operation, where mold growth covered 60% of the fin surface. These new copper-based solutions provide an added protection against longer term potential efficiency losses in systems using new refrigerants. They are appropriate for use in air conditioning systems that achieve the highest level of Life Cycle Climate Performance

Bootstrapping Relational Affordances of Object Pairs using Transfer

This work was supported in part by the U.K. EPSRC DTG EP/J5000343/1 at Aberdeen, and in part by the EU Cognitive Systems Project XPERIENCE at SDU under Grant FP7-ICT-270273.Peer reviewedPostprin

Consumption and wage humps in a life-cycle model with education

The observed hump-shaped life-cycle pattern in individuals' consumption cannot be explained by the classical consumption-savings model. We explicitly solve a model with utility of both consumption and leisure and with educational decisions affecting future wages. We show optimal consumption is hump shaped and determine the peak age. The hump results from consumption and leisure being substitutes and from the implicit price of leisure being decreasing over time; more leisure means less education, which lowers future wages, and the present value of foregone wages decreases with age. Consumption is hump shaped whether the wage is hump shaped or increasing over life

Nonacademic student selection criteria for medical school admissions in Germany and Austria

Deutsche medizinische Fachbereiche und Fakultäten sollen ihre Studienanfänger nach eigenen Kriterien aussuchen. Da bis zu 40 000 Bewerbungen pro Jahr erwartet werden können, ist eine Vorauswahl erforderlich, bevor arbeitsintensivere Auswahlmechanismen eingesetzt werden können. Wir haben einen Fragebogen konzipiert für den Versuch, zusätzlich zu schulischen Leistungen weitere Bewerbercharakteristika zu erfassen wie vorbestehendes medizinisch relevantes Wissen, musische, soziale, sportliche und berufliche Aktivitäten. Alle Studienanfänger des Wintersemesters 2005/2006 (860 Studierende) der Medizinischen Fachbereiche/Fakultäten an der Johann Wolfgang Goethe-Universität Frankfurt (FFM) und der Medizinischen Universität Innsbruck (MUI) wurden gebeten, diesen Fragebogen auszufüllen. Zum Wintersemester 2005/2006 wurde in FFM ausschließlich nach Abiturnote zugelassen, während die Zulassung an der MUI nach dem Posteingang der Bewerbung erfolgte, ohne Berücksichtigung von Schulnoten. Beide Gruppen (FFM 431 Studierende, MUI 429 Studierende) gaben vergleichbare nichtschulische Aktivitäten mit fast identischer Häufigkeit an, mit der Ausnahme der Ableistung eines Krankenhauspraktikums. Ein Pflegepraktikum wird von der deutschen Approbationsordnung verlangt, kann aber vor Studienbeginn absolviert werden, so dass deutsche Studienbeginner (sowohl Zulassung in FFM - 53%; deutsche Studienanfänger an der MUI - 67%) überwiegend ein Praktikum absolviert hatten, während österreichische Studienanfänger ein Praktikum wesentlich seltener abgeleistet hatten (14%). Derzeit sollten die erfassten nichtschulischen Leistungen als Zulassungskriterium für das Medizinstudium nur nach vorheriger Überprüfung der Eignung verwendet werden