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

Last in, first out? Estimating the effect of seniority rules in Sweden

In this paper we investigate whether a relaxation in seniority rules (the ‘last-in-first-out’ principle) had any effect on firms’ employment behaviour. Seniority rules exist in several countries and, like Sweden, most European countries have a more lenient employment protection for firms below a certain size. Despite the fact that small firms represent a large share of all firms and stand for a substantial share of total employment, there is limited knowledge of how such exemption rules affect firms’ employment behaviour — the consequences of seniority rules on firms’ employment behaviour have not been examined at all. Using data including the population of firms matched with the population of workers for the period 1999–2002, we do not find any general effects on worker flows or on hires and separations. The only exception is a tendency of an increase in the share of separations for older workers and workers with longer seniority. The result points to the importance of considering in detail how legislation is formulated and how it works in practice.Employment protection; employment change; hires; separations; regression discontinuity

Uncertainty, Climate Change and the Global Economy

The paper illustrates how one may assess our comprehensive uncertainty about the various relations in the entire chain from human activity to climate change. Using a modified version of the RICE model of the global economy and climate, we perform Monte Carlo simulations, where full sets of parameters in the model’s most important equations are drawn randomly from pre-specified distributions, and present results in the forms of fan charts and histograms. Our results suggest that under a Business-As-Usual scenario, the median increase of global mean temperature in 2105 relative to 1900 will be around 4.5 C. The 99 percent confidence interval ranges from 3.0 C to 6.9 C. Uncertainty about socio-economic drivers of climate change lie behind a non-trivial part of this uncertainty about global warming.Climate-economy models; Global warming; Monte Carlo study

Harmonic functions on metric graphs under the anti-Kirchhoff law

When does an infinite metric graph allow nonconstant bounded harmonic functions under the anti-Kirchhoff transition law? We give a complete answer to this question in the cases where Liouville’s theorem holds, for trees, for graphs with finitely many essential ramification nodes and for generalized lattices. It turns out that the occurrence of nonconstant bounded harmonic functions under the anti-Kirchhoff law differs strongly from the one under the classical continuity condition combined with the Kirchhoff incident flow law.Peer ReviewedPostprint (author's final draft

A characterization of even doubly-stochastic matrices

AbstractEven doubly-stochastic matrices are characterized with the aid of the minima of functionals defined by the even diagonals contained in the matrix

Evolutionary -Laplacian with convection and reaction under dynamic boundary condition

Möten med palliativa cancerpatienter utgör en del av allmänsjuksköterskans yrkesområde. Osäkerhet som leder till svårigheter att bemöta dessa patienter finns hos sjuksköterskor och sjuksköterskestudenter. Syftet var att undersöka vilka tankar, känslor och prioriteringar som var viktiga för den palliativa cancerpatienten samt vad som utmärkte en god relation till sjuksköterskan. En systematisk litteraturstudie enligt Goodmans sju steg genomfördes modifierat. I resultatet framkommer att patienter känner rädsla för att bli en börda och upplever osäkerhet samt ett kroppsligt förfall. Patienternas prioriteringar handlade om symtomkontroll, bevarandet av värdighet, det dagliga livet samt relationen till anhöriga. Att sjuksköterskan såg och tillgodosåg patientens behov samt hjälpte och skyddade patienten ingav tillit och hopp vilket stärkte relationen och kommunikationen.Encounters with palliative cancer patients are a part of the nursing profession. Uncertainty that leads to difficulties to respond to these patients exists in both nurses and nursing students. The aim was to explore which thoughts, feelings and priorities were important for the palliative cancer patient and features important for a good relationship with the nurse. A systematic literature review after Goodman´s seven steps was carried out with modifications. Emerging in the result was patient´s thoughts about fear of becoming a burden, feelings of insecurity and a bodily decay. Patient´s priorities concerned symptom control, preservation of dignity, daily life and the relationship with relatives. Nurses who saw and met patient´s needs and also helped and protected them gave trust and hope which strengthened the relationship and communication

Uncertainty, Climate Change and the Global Economy

The paper illustrates how one may assess our comprehensive uncertainty about the various relations in the entire chain from human activity to climate change. Using a modified version of the RICE model of the global economy and climate, we perform Monte Carlo simulations, where full sets of parameters in the model's most important equations are drawn randomly from pre-specified distributions, and present results in the forms of fan charts and histograms. Our results suggest that under a Business-As-Usual scenario, the median increase of global mean temperature in 2105 relative to 1900 will be around 4.5 °C. The 99 percent confidence interval ranges from 3.0 °C to 6.9 °C. Uncertainty about socio-economic drivers of climate change lie behind a non-trivial part of this uncertainty about global warming.

The Analogue of Bohm-Bell Processes on a Graph

Bohm-Bell processes, of interest in the foundations of quantum field theory, form a class of Markov processes $Q_t$ generalizing in a natural way both Bohm's dynamical system in configuration space for nonrelativistic quantum mechanics and Bell's jump process for lattice quantum field theories. They are such that at any time $t$ the distribution of $Q_t$ is $|\psi_t|^2$ with $\psi$ the wave function of quantum theory. We extend this class here by introducing the analogous Markov process for quantum mechanics on a graph (also called a network, i.e., a space consisting of line segments glued together at their ends). It is a piecewise deterministic process whose innovations occur only when it passes through a vertex.Comment: 15 pages LaTeX, 1 figure; v2 minor correction

Bildungschancen von Jugendlichen in Ost- und Westdeutschland

"Im Rahmen dieser Untersuchung wird der Fragestellung nachgegangen, inwieweit die in den 60er Jahren festgestellten Merkmale für ungleiche Chancen im Bildungssystem (Vaterberuf, Geschlecht, Region) noch heute Gültigkeit haben. Besonderes Augenmerk wird dabei auf die Unterschiede zwischen den einzelnen Bundesländern gelegt, da diese die seit den 60er Jahren (bzw. in den neuen Bundesländern seit der Vereinigung) erfolgten Bildungsreformen in unterschiedlicher Weise umgesetzt haben. Indikator für die Bildungschancen ist die Bildungsdichte der 16- bis 19jährigen, also der Anteil von Schülern und Studierenden an dieser Altersgruppe. Folgende Ergebnisse werden festgestellt: Insgesamt hat die Bildungsdichte stark zugenommen; Mädchen haben die Jungen überholt und weisen eine durchgehend höhere Bildungsdichte auf, insbesondere in den neuen Bundesländern. Kinder von Arbeitern und gering Qualifizierten sowie wenig Gebildeten sind auch heute noch deutlich unterrepräsentiert. Diese Benachteiligung betrifft insbesondere Jungen und diese besonders stark in Bundesländern mit konservativer Bildungspolitik. Für Nicht-Arbeiterkinder und Jugendliche mit höher gebildeten Haushaltsbezugspersonen spielt die Bildungspolitik des jeweiligen Bundeslandes eine geringere Rolle. Seit den 60er Jahren haben sich also viele Veränderungen ergeben; dennoch bestehen deutliche Unterschiede zwischen Jugendlichen verschiedener sozialer und regionaler Herkunft." (Autorenreferat)"Analyses in this paper concentrate on how strongly aspects that were found to be influential for participation in the educational system in the sixties (parents' occupational status, gender, region) are still effective today. Special attention is given to the differences between the Laender as these have a certain sovereignty over their educational system and have implemented educational reforms very differently since the sixties (or rather since unification in the New Laender). Chances of youths within the educational system are measured by the 'educational density' in a certain region, i.e. the percentage of 16-19 year-olds who attend schools or universities among all 16-19 year-olds. The findings are the following: All in all, educational density has risen strongly; girls have overtaken boys and have a higher participation in the educational System, which is especially the case in the New Laender. Children of blue-collar workers and of lower qualified and less educated persons are still greatly underrepresented today. This disadvantage is especially true for boys, and for them especially in Laender with conservative educational policies. For children of persons with other occupational s atus than blue-collar-worker and for youths with better educated heads of households, the educational policies of the respective Land do not have such a strong influence. Thus, since the sixties, many changes have taken place; yet there still are considerable differences between youths of different social and regional backgrounds." (author's abstract

Stability implies constancy for fully autonomous reaction-diffusion-equations on finite metric graphs

We show that there are no stable stationary nonconstant solutions of the evolution problem (1) for fully autonomous reaction-diffusion-equations on the edges of a finite metric graph G under continuity and Kirchhoff flow transition conditions at the verticesPeer ReviewedPostprint (author's final draft