Embedding Theorems for the Dunkl Harmonic Oscillator on the Line

Embedding results of Sobolev type are proved for the Dunkl harmonic oscillator on the line

Near-infrared light increases ATP, extends lifespan and improves mobility in aged Drosophila melanogaster.

Ageing is an irreversible cellular decline partly driven by failing mitochondrial integrity. Mitochondria accumulate DNA mutations and reduce ATP production necessary for cellular metabolism. This is associated with inflammation. Near-infrared exposure increases retinal ATP in old mice via cytochrome c oxidase absorption and reduces inflammation. Here, we expose fruitflies daily to 670 nm radiation, revealing elevated ATP and reduced inflammation with age. Critically, there was a significant increase in average lifespan: 100-175% more flies survived into old age following 670 nm exposure and these had significantly improved mobility. This may be a simple route to extending lifespan and improving function in old age

El modelo de Passinetti: prsentación analítica

De formal general, los modelos de crecimiento que incorporan el progreso técnico postulan un crecimiento uniforme y proporcional de la demanda. El rasgo fundamental del análisis de Pasinetti es la relación entre el progreso técnico y la desestructuración del sistema productivo en el largo plazo. En concreto, como los coeficientes de demanda aumentan de forma discontínua, el modelo muestra la tendencia persistente de las economías industriales hacia el paro tecnológico. Este esquema (que corresponde a un sistema económico "natural") es independiente de la organización institucional (economía de mercado o planificada).Passinetti's Model: an Analytical View. All the models of economic growth with technical progress have postulated either uniform and homothetic expansion of demand. The essential feature of Pasinetti's analysis is the link between technical progress and the change of whole production structure over time. In particular, since production coefficients are decreasing over time while demand coefficients increase in a discontinous way the model give rise to the result of a persistent tendency towards technological unemployment. This scheme (the theoretical scheme of a "natural" economic system) is the most relevant to explain the long-term evolution of industrial systems, independent of the institutional organisation

Witten's perturbation on strata with general adapted metrics

Let $M$ be a stratum of a compact stratified space $A$. It is equipped with a general adapted metric $g$, which is slightly more general than the adapted metrics of Nagase and Brasselet-Hector-Saralegi. In particular, $g$ has a general type, which is an extension of the type of an adapted metric. A restriction on this general type is assumed, and then $g$ is called good. We consider the maximum/minimun ideal boundary condition, $d_{\text{\rm max/min}}$, of the compactly supported de~Rham complex on $M$, in the sense of Br\"uning-Lesch. Let $H^*_{\text{\rm max/min}}(M)$ and $\Delta_{\text{\rm max/min}}$ denote the cohomology and Laplacian of $d_{\text{\rm max/min}}$. The first main theorem states that $\Delta_{\text{\rm max/min}}$ has a discrete spectrum satisfying a weak form of the Weyl's asymptotic formula. The second main theorem is a version of Morse inequalities using $H_{\text{\rm max/min}}^*(M)$ and what we call rel-Morse functions. An ingredient of the proofs of both theorems is a version for $d_{\text{\rm max/min}}$ of the Witten's perturbation of the de~Rham complex. Another ingredient is certain perturbation of the Dunkl harmonic oscillator previously studied by the authors using classical perturbation theory. Assume that $A$ is a stratified pseudomanifold, and consider its intersection homology $I^{\bar p}H_*(A)$ with perversity $\bar p$; in particular, the lower and upper middle perversities are denoted by $\bar m$ and $\bar n$, respectively. Then, for any perversity $\bar p\le\bar m$, there is an associated good adapted metric on $M$ satisfying the Nagase isomorphism $H^r_{\text{\rm max}}(M)\cong I^{\bar p}H_r(A)^*$ ($r\in\N$). If $M$ is oriented and $\bar p\ge\bar n$, we also get $H^r_{\text{\rm min}}(M)\cong I^{\bar p}H_r(A)$. Thus our version of the Morse inequalities can be described in terms of $I^{\bar p}H_*(A)$.Comment: 46 pages. A few minor corrections were mad

Improved thermal isolation of silicon suspended platforms for an all-silicon thermoelectric microgenerator based on large scale integration of Si nanowires as thermoelectric material

Special suspended micro-platforms have been designed as a part of silicon compatible planar thermoelectric microgenerators. Bottom-up grown silicon nanowires are going to bridge in the future such platforms to the surrounding silicon bulk rim. They will act as thermoelectric material thus configuring an all-silicon thermoelectric device. In the new platform design other additional bridging elements (usually auxiliary support silicon beams) are substituted by low conductance thin film dielectric membranes in order to maximize the temperature difference developed between both areas. These membranes follow a sieve-like design that allows fabricating them with a short additional wet anisotropic etch step. © Published under licence by IOP Publishing Ltd.Peer ReviewedPostprint (published version

A type of perturbation of the harmonic oscillator

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