Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms

We present an introduction to the framework of strongly local Dirichlet forms and discuss connections between the existence of certain generalized eigenfunctions and spectral properties within this framework. The range of applications is illustrated by a list of examples

Constant sign and nodal solutions for a class of nonlinear Dirichlet problems

We consider a nonlinear Dirichlet problem with a Carathéodory reaction which has arbitrary growth from below. We show that the problem has at least three nontrivial smooth solutions, two of constant sign and the third nodal. In the semilinear case (i.e., p =2), with the reaction f(z, .)being C1and with subcritical growth, we show that there is a second nodal solution, for a total of four nontrivial smooth solutions. Finally,when the reaction has concave terms and is subcritical and for the nonlinear problem (i.e., 1 <p <∞) we show that again we can have the existence of three nontrivial smooth solutions, two of constant sign and a third nodal

Computing the first eigenpair of the p-Laplacian via inverse iteration of sublinear supersolutions

We introduce an iterative method for computing the first eigenpair $(\lambda_{p},e_{p})$ for the $p$-Laplacian operator with homogeneous Dirichlet data as the limit of $(\mu_{q,}u_{q})$ as $q\rightarrow p^{-}$, where $u_{q}$ is the positive solution of the sublinear Lane-Emden equation $-\Delta_{p}u_{q}=\mu_{q}u_{q}^{q-1}$ with same boundary data. The method is shown to work for any smooth, bounded domain. Solutions to the Lane-Emden problem are obtained through inverse iteration of a super-solution which is derived from the solution to the torsional creep problem. Convergence of $u_{q}$ to $e_{p}$ is in the $C^{1}$-norm and the rate of convergence of $\mu_{q}$ to $\lambda_{p}$ is at least $O(p-q)$. Numerical evidence is presented.Comment: Section 5 was rewritten. Jed Brown was added as autho

The Effect of Minimum Wages on Labour Market Flows Evidence from Germany

Using a linked employer-employee data set on the German construction industry, we analyse the effects of the introduction of minimum wages in this sector on labour market dynamics at the establishment level, i.e. turnover and churning flows, as well as accessions and separations and their underlying worker flows. The fact that minimum wages in Germany are sector-specific enables us to apply a between approach using other industries as control groups in a difference-in-differences framework. Furthermore, we use a within approach with high-wage workers as control group. While the within approach shows that the minimum wage reduced worker flows in East Germany, the between approach yields positive effect on labour market dynamics in West Germany. Our results can be explained by differences between East and West Germany with respect to the bite of the minimum wage, as well as the much higher prevalence of posted workers in West Germany. Furthermore, spillover effects to highwage workers are likely to have played a role in East Germany.In dem Papier werden die Auswirkungen der Mindestlohneinführung im deutschen Bauhauptgewerbe auf Arbeitsmarktdynamiken untersucht, wobei die Analyse von Einstellungen und Trennungen sowie der damit zusammenhängenden Arbeitsmarktübergänge auf Betriebsebene erfolgt. Dabei kommt ein einzigartiger Linked Employer-Employee Datensatz zum Einsatz. Da der Mindestlohn zunächst nur im Bauhauptgewerbe eingeführt wurde, können Betriebe einer anderen Branche als Kontrollgruppe in einem Differenz-von-Differenzen-Ansatz genutzt werden (between-Ansatz). Zusätzlich wird ein within-Ansatz verwendet, bei dem Arbeitnehmer mit relativ hohem Lohn innerhalb des Bauhauptgewerbes als Kontrollgruppe dienen. Während der within-Ansatz zeigt, dass der Mindestlohn Arbeiterflüsse in Ostdeutschland reduzierte, bringt der between-Ansatz positive Effekte auf Arbeitsmarktdynamiken in Westdeutschland zutage. Diese Ergebnisse können auf Ost-West-Unterschiede hinsichtlich der Eingriffsintensität des Mindestlohns sowie die deutlich höhere Anzahl entsendeter Arbeitnehmer in Westdeutschland zurückgeführt werden. Zudem sind spillover-Effekte auf Arbeitnehmer mit relativ hohen Löhnen in Ostdeutschland wahrscheinlich

Retinoids cause apoptosis in pancreatic cancer cells via activation of RAR-γ and altered expression of Bcl-2/Bax

All-trans-retinoic acid and 9-cis-retinoic acid have been reported to have inhibitory effects on pancreatic adenocarcinoma cells and we have shown that this is partly due to induction of apoptosis. In this study, the mechanisms whereby 9-cis-retinoic acid induces apoptosis in these cells were investigated. An involvement of the Bcl-2 family of proteins was shown, such that 9-cis-retinoic acid causes a decrease in the Bcl-2/Bax ratio. Overexpression of Bcl-2 also resulted in inhibition of apoptosis induced by 9-cis-retinoic acid. Furthermore, two broad-range caspase inhibitors blocked DNA fragmentation induced by 9-cis-retinoic acid, but had no effect on viability defined by mitochondrial activity. Using synthetic retinoids, which bind selectively to specific retinoic acid receptor subtypes, we further established that activation of retinoic acid receptor-γ is essential for induction of apoptosis. Only pan-retinoic acid receptor and retinoic acid receptor-γ selective agonists reduced viability and a cell line expressing very low levels of retinoic acid receptor-γ is resistant to the effects of 9-cis-retinoic acid. A retinoic acid receptor-β/γ selective antagonist also suppressed the cytotoxic effects of 9-cis-retinoic acid in a dose-dependent manner. This study provides important insight into the mechanisms involved in suppression of pancreatic tumour cell growth by retinoids. Our results encourage further work evaluating the clinical use of receptor subtype selective retinoids in pancreatic carcinoma

Sexual Orientation and Household Decision Making: Same-Sex Couples' Balance of Power and Labor Supply Choices

I estimate how intra-household bargaining affects gay and lesbian couples' labor supplies, investigating their similarity to heterosexual decision-making, in a collective household framework. Data from the 2000 US Census show that couples of all types exhibit a significant response to bargaining power shifts, as measured by differences between partners in age or non-labor income. In gay, lesbian, and heterosexual cohabiting couples, a relatively young or rich partner has more bargaining power and hence supplies less labor, the opposite holding for his/her mate. Married couples value the older spouse instead, or the richer. No effects are found for same-sex roommates