The spectrum of the Hilbert space valued second derivative with general self-adjoint boundary conditions

We consider a large class of self-adjoint elliptic problem associated with the second derivative acting on a space of vector-valued functions. We present two different approaches to the study of the associated eigenvalues problems. The first, more general one allows to replace a secular equation (which is well-known in some special cases) by an abstract rank condition. The latter seems to apply particularly well to a specific boundary condition, sometimes dubbed "anti-Kirchhoff" in the literature, that arise in the theory of differential operators on graphs; it also permits to discuss interesting and more direct connections between the spectrum of the differential operator and some graph theoretical quantities. In either case our results yield, among other, some results on the symmetry of the spectrum

Paris'te Yahya Kemal

Taha Toros Arşivi, Dosya No: 182-Yahya Kemal Beyatlı. Not: Ekteki belgede Eric von Post'un "Bir Mayıs gecesinde" başlıklı yazısı bulunmaktadır.İstanbul Kalkınma Ajansı (TR10/14/YEN/0033) İstanbul Development Agency (TR10/14/YEN/0033

Large-time asymptotic equivalence for a class of non-autonomous semilinear parabolic equations

AbstractIn this article we prove new results concerning the long-time behavior of solutions to a class of non-autonomous semilinear parabolic Neumann boundary-value problems defined on open bounded connected subsets Ω of RN. The nature of the equations that we investigate leads us to consider two complementary situations, according to whether the time-dependent lower order terms in the equations possess recurrence properties. If the lower order terms are recurrent, we prove that every solution stabilizes around a spatially homogeneous and recurrent solution of the same Neumann problem in the C1 (Ω)-topology. In contrast, if the lower order terms are not recurrent, the asymptotic states need not be solutions to the original problem and we prove that every solution stabilizes around such an asymptotic state again in the C1 (Ω)-topology. In all cases the dynamics of the asymptotic solutions are governed by a compact and connected set of scalar ordinary differential equations, which are thereby asymptotically equivalent to the original Neumann problem for large times. A major difficulty to be bypassed in the proofs of our theorems stems from the fact that we allow the nonlinearitics to depend explicitly on the gradient of the unknown function. Our method of proof rests upon the use of comparison principles and upon the existence of exponential dichotomies for the family of evolution operators associated with the principal part of the equations. It is also based on ideas that stem for the classic reduction methods for non-autonomous finite-dimentional dynamical systems originally devised by Miller, Strauss-Yorke and Sell

Assessing habitat quality of farm-dwelling house sparrows in different agricultural landscapes.

Having historically been abundant throughout Europe, the house sparrow (Passer domesticus) has in recent decades suffered severe population declines in many urban and rural areas. The decline in rural environments is believed to be caused by agricultural intensification, which has resulted in landscape simplification. We used giving-up densities (GUDs) of house sparrows feeding in artificial food patches placed in farmlands of southern Sweden to determine habitat quality during the breeding season at two different spatial scales: the landscape and the patch scale. At the landscape scale, GUDs were lower on farms in homogeneous landscapes dominated by crop production compared to more heterogeneous landscapes with mixed farming or animal husbandry. At the patch level, feeding patches with a higher predation risk (caused by fitting a wall to the patch to obstruct vigilance) had higher GUDs. In addition, GUDs were positively related to population size, which strongly implies that GUDs reflect habitat quality. However, the increase followed different patterns in homogeneous and heterogeneous landscapes, indicating differing population limiting mechanisms in these two environments. We found no effect of the interaction between patch type and landscape type, suggesting that predation risk was similar in both landscape types. Thus, our study suggests that simplified landscapes constitute a poorer feeding environment for house sparrows during breeding, that the population-regulating mechanisms in the landscapes differ, but that predation risk is the same across the landscape types

Effective Theories for Circuits and Automata

Abstracting an effective theory from a complicated process is central to the study of complexity. Even when the underlying mechanisms are understood, or at least measurable, the presence of dissipation and irreversibility in biological, computational and social systems makes the problem harder. Here we demonstrate the construction of effective theories in the presence of both irreversibility and noise, in a dynamical model with underlying feedback. We use the Krohn-Rhodes theorem to show how the composition of underlying mechanisms can lead to innovations in the emergent effective theory. We show how dissipation and irreversibility fundamentally limit the lifetimes of these emergent structures, even though, on short timescales, the group properties may be enriched compared to their noiseless counterparts.Comment: 11 pages, 9 figure

Oönskade effekter

Den här studien syftar till att ta reda på hur Arbetsmiljöverkets implementering av nya direktiv gällande riskbedömning av praoplatser kunde medföra att många skolor i landet har valt att ta bort prao som ett moment ur utbildningen, då rektorer eller skolförvaltning bedömt att arbetet inför praon blir för omfattande. Studien är upplagd som en teoribaserad processutvärderingsanalys där implementeringsteori använts för att analysera implementeringsproblemet. En idealtyp har konstruerats av hur projektet var tänkt att påverka arbetet i skolorna, och detta har sedan jämförts med det verkliga händelseförloppet. Resultatet visar att anledningen till att prao uteslutits på vissa skolor är att arbetsbördan blev så stor att det i många fall var omöjligt att leva upp till kraven, och att Arbetsmiljöverket inte tog detta i beaktning när de planerade sitt projekt eftersom att de inte har insikt i hur det dagliga arbetet sker på skolorna, och vilka prioriteringar anställda på skolorna tvingas göra varje dag. Slutligen kunde det konstateras att det fanns yttre faktorer som påverkade projektets resultat mycket mer än som först antagits

Healthy aims: developing new medical implants and diagnostic equipment

Healthy Aims is a €23-million, four-year project, funded under the EU’s Information Society Technology Sixth Framework program to develop intelligent medical implants and diagnostic systems (www.healthyaims.org). The project has 25 partners from 10 countries, including commercial, clinical, and research groups. This consortium represents a combination of disciplines to design and fabricate new medical devices and components as well as to test them in laboratories and subsequent clinical trials. The project focuses on medical implants for nerve stimulation and diagnostic equipment based on straingauge technology