Positive solutions of Schr\"odinger equations and fine regularity of boundary points

Given a Lipschitz domain $\Omega$ in ${\mathbb R} ^N$ and a nonnegative potential $V$ in $\Omega$ such that $V(x)\, d(x,\partial \Omega)^2$ is bounded in $\Omega$ we study the fine regularity of boundary points with respect to the Schr\"odinger operator $L_V:= \Delta -V$ in $\Omega$. Using potential theoretic methods, several conditions equivalent to the fine regularity of $z \in \partial \Omega$ are established. The main result is a simple (explicit if $\Omega$ is smooth) necessary and sufficient condition involving the size of $V$ for $z$ to be finely regular. An essential intermediate result consists in a majorization of $\int_A | {\frac {u} {d(.,\partial \Omega)}} | ^2\, dx$ for $u$ positive harmonic in $\Omega$ and $A \subset \Omega$. Conditions for almost everywhere regularity in a subset $A$ of $\partial \Omega$ are also given as well as an extension of the main results to a notion of fine ${\mathcal L}_1 | {\mathcal L}_0$-regularity, if ${\mathcal L}_j={\mathcal L}-V_j$, $V_0,\, V_1$ being two potentials, with $V_0 \leq V_1$ and ${\mathcal L}$ a second order elliptic operator.Comment: version 1. 23 pages version 3. 28 pages. Mainly a typo in Theorem 1.1 is correcte

Sedimentalological and Limnological Studies of Lake Champlain

Guidebook for field trips in Vermont: 64th annual meeting October 13, 14, 15, 1972 Burlington, Vermont: Trip LS-2; LS-

Alternative polyadenylation and salicylic acid modulate root responses to low nitrogen availability

Nitrogen (N) is probably the most important macronutrient and its scarcity limits plant growth, development and fitness. N starvation response has been largely studied by transcriptomic analyses, but little is known about the role of alternative polyadenylation (APA) in such response. In this work, we show that N starvation modifies poly(A) usage in a large number of transcripts, some of them mediated by FIP1, a component of the polyadenylation machinery. Interestingly, the number of mRNAs isoforms with poly(A) tags located in protein-coding regions or 5 '-UTRs significantly increases in response to N starvation. The set of genes affected by APA in response to N deficiency is enriched in N-metabolism, oxidation-reduction processes, response to stresses, and hormone responses, among others. A hormone profile analysis shows that the levels of salicylic acid (SA), a phytohormone that reduces nitrate accumulation and root growth, increase significantly upon N starvation. Meta-analyses of APA-affected and fip1-2-deregulated genes indicate a connection between the nitrogen starvation response and salicylic acid (SA) signaling. Genetic analyses show that SA may be important for preventing the overgrowth of the root system in low N environments. This work provides new insights on how plants interconnect different pathways, such as defense-related hormonal signaling and the regulation of genomic information by APA, to fine-tune the response to low N availability

Genetics and geography of leukocyte telomere length in sub-Saharan Africans

Leukocyte telomere length (LTL) might be causal in cardiovascular disease and major cancers. To elucidate the roles of genetics and geography in LTL variability across humans, we compared LTL measured in 1295 sub-Saharan Africans (SSAs) with 559 African-Americans (AAms) and 2464 European-Americans (EAms). LTL differed significantly across SSAs (P = 0.003), with the San from Botswana (with the oldest genomic ancestry) having the longest LTL and populations from Ethiopia having the shortest LTL. SSAs had significantly longer LTL than AAms [P = 6.5(e-16)] whose LTL was significantly longer than EAms [P = 2.5(e-7)]. Genetic variation in SSAs explained 52% of LTL variance versus 27% in AAms and 34% in EAms. Adjustment for genetic variation removed the LTL differences among SSAs. LTL genetic variation among SSAs, with the longest LTL in the San, supports the hypothesis that longer LTL was ancestral in humans. Identifying factors driving LTL variation in Africa may have important ramifications for LTL-associated diseases

Time-orthogonal unitary dilations and noncommutative Feynman-Kac formulae

An analysis of Feynman-Kac formulae reveals that, typically, the unperturbed semigroup is expressed as the expectation of a random unitary evolution and the perturbed semigroup is the expectation of a perturbation of this evolution in which the latter perturbation is effected by a cocycle with certain covariance properties with respect to the group of translations and reflections of the line. We consider generalisations of the classical commutative formalism in which the probabilistic properties are described in terms of non-commutative probability theory based on von Neumann algebras. Examples of this type are generated, by means of second quantisation, from a unitary dilation of a given self-adjoint contraction semigroup, called the time orthogonal unitary dilation, whose key feature is that the dilation operators corresponding to disjoint time intervals act nontrivially only in mutually orthogonal supplementary Hilbert spaces.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46525/1/220_2005_Article_BF01976044.pd

Employment After Liver Transplantation: A Review

BackgroundReturn to productive employment is often an important milestone in the recovery and rehabilitation process after liver transplantation (OLT). This literature review identifies factors associated with employment in patients who underwent OLT.MethodsWe searched PubMed for articles that addressed the various factors affecting employment after OLT.ResultsThe studies demonstrated improvement in the quality of life and examined factors that predicted whether patients would return to work after OLT. Demographic variable associated with posttransplant employment included young age, male sex, college degree, Caucasian race, and pretransplant employment. Patients with alcohol-related liver disease had a significantly lower rate of employment than did those with other etiologies of liver disease. Recipients who were employed after transplantation had a significantly better posttransplant functional status than did those who were not employed.ConclusionEconomic pressures are increasing the expectation that patients who undergo successful OLT will return to work. Thus, transplant teams need to have a better understanding of posttransplant work outcomes for this vulnerable population, and greater attention must be paid to the full social rehabilitation of transplant recipients. Specific interventions for OLT recipients should be designed to evaluate and change their health perceptions and encourage their return to work

Search for the standard model Higgs boson decaying into two photons in pp collisions at sqrt(s)=7 TeV

A search for a Higgs boson decaying into two photons is described. The analysis is performed using a dataset recorded by the CMS experiment at the LHC from pp collisions at a centre-of-mass energy of 7 TeV, which corresponds to an integrated luminosity of 4.8 inverse femtobarns. Limits are set on the cross section of the standard model Higgs boson decaying to two photons. The expected exclusion limit at 95% confidence level is between 1.4 and 2.4 times the standard model cross section in the mass range between 110 and 150 GeV. The analysis of the data excludes, at 95% confidence level, the standard model Higgs boson decaying into two photons in the mass range 128 to 132 GeV. The largest excess of events above the expected standard model background is observed for a Higgs boson mass hypothesis of 124 GeV with a local significance of 3.1 sigma. The global significance of observing an excess with a local significance greater than 3.1 sigma anywhere in the search range 110-150 GeV is estimated to be 1.8 sigma. More data are required to ascertain the origin of this excess.Comment: Submitted to Physics Letters

Measurement of isolated photon production in pp and PbPb collisions at sqrt(sNN) = 2.76 TeV

Isolated photon production is measured in proton-proton and lead-lead collisions at nucleon-nucleon centre-of-mass energies of 2.76 TeV in the pseudorapidity range |eta|<1.44 and transverse energies ET between 20 and 80 GeV with the CMS detector at the LHC. The measured ET spectra are found to be in good agreement with next-to-leading-order perturbative QCD predictions. The ratio of PbPb to pp isolated photon ET-differential yields, scaled by the number of incoherent nucleon-nucleon collisions, is consistent with unity for all PbPb reaction centralities.Comment: Submitted to Physics Letters