Classification of finite congruence-simple semirings with zero

Our main result states that a finite semiring of order >2 with zero which is not a ring is congruence-simple if and only if it is isomorphic to a `dense' subsemiring of the endomorphism semiring of a finite idempotent commutative monoid. We also investigate those subsemirings further, addressing e.g. the question of isomorphy.Comment: 16 page

Hardy Spaces on Weighted Homogeneous Trees

We consider an infinite homogeneous tree V endowed with the usual metric d defined on graphs and a weighted measure μ. The metric measure space (V, d, μ) is nondoubling and of exponential growth, hence the classical theory of Hardy spaces does not apply in this setting. We construct an atomic Hardy space H1(μ) on (V, d, μ) and investigate some of its properties, focusing in particular on real interpolation properties and on boundedness of singular integrals on H1(μ)

Simulations of Weighted Tree Automata

Simulations of weighted tree automata (wta) are considered. It is shown how such simulations can be decomposed into simpler functional and dual functional simulations also called forward and backward simulations. In addition, it is shown in several cases (fields, commutative rings, Noetherian semirings, semiring of natural numbers) that all equivalent wta M and N can be joined by a finite chain of simulations. More precisely, in all mentioned cases there exists a single wta that simulates both M and N. Those results immediately yield decidability of equivalence provided that the semiring is finitely (and effectively) presented.Comment: 17 pages, 2 figure

The Alexander-Orbach conjecture holds in high dimensions

We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established, namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We find that random walk on the IIC exhibits anomalous diffusion with the spectral dimension d_s=4/3, that is, p_t(x,x)= t^{-2/3+o(1)}. This establishes a conjecture of Alexander and Orbach. En route we calculate the one-arm exponent with respect to the intrinsic distance.Comment: 25 pages, 2 figures. To appear in Inventiones Mathematica

Interpolation Theorems for Self-adjoint Operators

We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a selfadjoint operator $L$, without assuming the gradient estimate for its spectral kernel. The result applies to the cases where $L$ is a uniformly elliptic operator or a Schr\"odinger operator with electro-magnetic potential.Comment: 8 pages. Submitte

Potential theory results for a class of PDOs admitting a global fundamental solution

We outline several results of Potential Theory for a class of linear par-tial differential operators L of the second order in divergence form. Under essentially the sole assumption of hypoellipticity, we present a non-invariant homogeneous Harnack inequality for L; under different geometrical assumptions on L (mainly, under global doubling/Poincar\ue9 assumptions), it is described how to obtainan invariant, non-homogeneous Harnack inequality. When L is equipped with a global fundamental solution \u393, further Potential Theory results are available (such as the Strong Maximum Principle). We present some assumptions on L ensuring that such a \u393 exists

Spectral multipliers for sublaplacians with drift on Lie groups

We study spectral multipliers of right invariant sub-Laplacians with drift LX on a connected Lie group G. The operators we consider are self-adjoint with respect to a positive measure \u3bbG,\u3c7 , whose density with respect to the left Haar measure \u3bbG is a nontrivial positive character \u3c7 of G. We show that if p \u338= 2 and G is amenable, then every Lp (\u3bbG,\u3c7 ) spectral multiplier of LX extends to a bounded holomorphic function on a parabolic region in the complex plane, which depends on p and on the drift. When G is of polynomial growth we show that this neces- sary condition is nearly sufficient, by proving that bounded holomorphic functions on the appropriate parabolic region which satisfy mild regularity conditions on its boundary are Lp (\u3bbG,\u3c7 ) spectral multipliers of LX

Psychobiologische Faktoren von Schwangerschaft und Geburt

Für die meisten Frauen sind Schwangerschaft und Geburt besondere Lebensereignisse. In einigen Fällen treten im Verlauf der Schwangerschaft jedoch Komplikationen wie vorzeitige Wehentätigkeit und Spätgestosen auf. Die ätiologischen Faktoren solcher Komplikationen sind bei bis zu 50% der Fälle ungeklärt. In der aktuellen Literatur gibt es zahlreiche Hinweise auf eine Mitbeteiligung von Stress an der Entstehung der genannten Pathologien. Psychosozialer Stress scheint insbesondere über das sympathikoadrenomedulläre System und die Hypothalamus-Hypophysen-Nebennierenrinden-Plazenta-Achse pathologiefördernd zu sein. Eine Reihe von Studien belegen die Interaktion zwischen Stresserleben, psychischem Befinden wie schwangerschaftsbezogener Angst und Dysregulationen der genannten endokrinen Systeme bei der Entstehung und Aufrechterhaltung von Schwangerschafts- und Geburtskomplikationen. Darüber hinaus scheint die Entstehung psychiatrischer Störungen post partum aufgrund von negativen Geburtserlebnissen (z. B. sekundäre Sectio) von Faktoren wie Angstsymptomen oder depressiver Gestimmtheit während der Schwangerschaft beeinflusst zu werden. Aus diesen Gründen ist es wichtig, das mögliche Vorliegen schwangerschaftsbezogener Ängste und ungünstiger Lebensbedingungen bereits zu Beginn der Schwangerschaftsbetreuung zu explorieren. Bei deutlich ausgeprägten Problemen ist eine psychotherapeutische Mitbehandlung indiziert. For most women pregnancy and delivery are important life events. In some cases pathologic processes arise during states such as early onset of spontaneous labor or gestational hypertension, preeclampsia, HELLP and eclampsia. The etiological factors of such complications remain unclear in up to 50% of all cases. Recent literature suggests that the course of pregnancy and birth outcome are influenced by the experience of stressful events. Psychosocial stress in particular seems to increase the risk of pregnancy complications via psychoneuroendocrinological pathways such as the sympathoadrenal medullary system or the hypothalamus-pituitary-adrenal-placenta axis. Various studies showed interactions between stressors experienced, psychological states (such as pregnancy-related anxiety or depression), endocrinological dysregulations of the above-mentioned hormonal systems and the onset and continuation of pregnancy complications. Additionally, the development of psychiatric disturbances following negative birth experiences such as secondary cesarean section seem to be triggered by preterm levels of anxiety. Taken together, it is important to explore emotional states and coping experiences during early pregnancy. In cases of serious anxiety and/or adverse living conditions, psychotherapeutic interventions should be initiated