Analytic structure of solutions to multiconfiguration equations

We study the regularity at the positions of the (fixed) nuclei of solutions to (non-relativistic) multiconfiguration equations (including Hartree--Fock) of Coulomb systems. We prove the following: Let {phi_1,...,phi_M} be any solution to the rank--M multiconfiguration equations for a molecule with L fixed nuclei at R_1,...,R_L in R^3. Then, for any j in {1,...,M} and k in {1,...,L}, there exists a neighbourhood U_{j,k} in R^3 of R_k, and functions phi^{(1)}_{j,k}, phi^{(2)}_{j,k}, real analytic in U_{j,k}, such that phi_j(x) = phi^{(1)}_{j,k}(x) + |x - R_k| phi^{(2)}_{j,k}(x), x in U_{j,k} A similar result holds for the corresponding electron density. The proof uses the Kustaanheimo--Stiefel transformation, as applied earlier by the authors to the study of the eigenfunctions of the Schr"odinger operator of atoms and molecules near two-particle coalescence points.Comment: 15 page

Topological and geometrical restrictions, free-boundary problems and self-gravitating fluids

Let (P1) be certain elliptic free-boundary problem on a Riemannian manifold (M,g). In this paper we study the restrictions on the topology and geometry of the fibres (the level sets) of the solutions f to (P1). We give a technique based on certain remarkable property of the fibres (the analytic representation property) for going from the initial PDE to a global analytical characterization of the fibres (the equilibrium partition condition). We study this analytical characterization and obtain several topological and geometrical properties that the fibres of the solutions must possess, depending on the topology of M and the metric tensor g. We apply these results to the classical problem in physics of classifying the equilibrium shapes of both Newtonian and relativistic static self-gravitating fluids. We also suggest a relationship with the isometries of a Riemannian manifold.Comment: 36 pages. In this new version the analytic representation hypothesis is proved. Please address all correspondence to D. Peralta-Sala

Histopathological and immunohistochemical evaluation of cellular response to a woven and electrospun polydioxanone (PDO) and polycaprolactone (PCL) patch for tendon repair

We investigated endogenous tissue response to a woven and electrospun polydioxanone (PDO) and polycaprolactone (PCL) patch intended for tendon repair. A sheep tendon injury model characterised by a natural history of consistent failure of healing was chosen to assess the biological potential of woven and aligned electrospun fibres to induce a reparative response. Patches were implanted into 8 female adult English Mule sheep. Significant infiltration of tendon fibroblasts was observed within the electrospun component of the patch but not within the woven component. The cellular infiltrate into the electrospun fibres was accompanied by an extensive network of new blood vessel formation. Tendon fibroblasts were the most abundant scaffold-populating cell type. CD45+, CD4+ and CD14+ cells were also present, with few foreign body giant cells. There were no local or systemic signs of excessive inflammation with normal hematology and serology for inflammatory markers three months after scaffold implantation. In conclusion, we demonstrate that an endogenous healing response can be safely induced in tendon by means of biophysical cues using a woven and electrospun patch

The impact of the mixing properties within the Antarctic stratospheric vortex on ozone loss in spring

Calculations of equivalent length from an artificial advected tracer provide new insight into the isentropic transport processes occurring within the Antarctic stratospheric vortex. These calculations show two distinct regions of approximately equal area: a strongly mixed vortex core and a broad ring of weakly mixed air extending out to the vortex boundary. This broad ring of vortex air remains isolated from the core between late winter and midspring. Satellite measurements of stratospheric H2O confirm that the isolation lasts until at least mid-October. A three-dimensional chemical transport model simulation of the Antarctic ozone hole quantifies the ozone loss within this ring and demonstrates its isolation. In contrast to the vortex core, ozone loss in the weakly mixed broad ring is not complete. The reasons are twofold. First, warmer temperatures in the broad ring prevent continuous polar stratospheric cloud (PSC) formation and the associated chemical processing (i.e., the conversion of unreactive chlorine into reactive forms). Second, the isolation prevents ozone-rich air from the broad ring mixing with chemically processed air from the vortex core. If the stratosphere continues to cool, this will lead to increased PSC formation and more complete chemical processing in the broad ring. Despite the expected decline in halocarbons, sensitivity studies suggest that this mechanism will lead to enhanced ozone loss in the weakly mixed region, delaying the future recovery of the ozone hole

Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles

The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry. When the jet values are prescribed on a positive dimensional subvariety, it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive. We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded, if a square-integrable extension is known to be possible over a double point at the origin. It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory. The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections. We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi to a simple application of the standard method of constructing holomorphic functions by solving the d-bar equation with cut-off functions and additional blowup weight functions

Can osseous landmarks in the distal medial humerus be used to identify the attachment sites of ligaments and tendons: paleopathologic–anatomic imaging study in cadavers

Objective: To describe osseous landmarks that allow identification of the attachments of the ligaments and tendons in the distal medial aspect of the humerus. Materials and methods: Reliable osseous landmarks in the distal medial aspect of the humerus were identified in 34 well-preserved specimens from a paleopathologic collection. These osseous landmarks were then sought in magnetic resonance (MR) images of ten cadaveric elbow specimens so that the ease of their visualization and optimal imaging plane could be assessed. To assign these osseous landmarks to specific attachments of the tendons and ligaments in the distal medial humerus, we cut the specimens in slices and photographed and examined them. Subsequently, the prevalence of these osseous landmarks as well as the attachment sites of the tendons and ligaments in this location was determined. Results: We determined ten reliable osseous landmarks in the distal medial aspect of the humerus, their prevalence and ease of identification, and their relationship to the attachments of the tendons and ligaments at the medial distal humerus. Conclusion: It is possible to use osseous landmarks at the distal medial humerus to facilitate identification of the different attachments of tendons and ligaments when MR images of the elbow are assesse

Quasiconvexity at the boundary and the nucleation of austenite

Motivated by experimental observations of H. Seiner et al., we study the nucleation of austenite in a single crystal of a CuAlNi shape-memory alloy stabilized as a single variant of martensite. In the experiments the nucleation process was induced by localized heating and it was observed that, regardless of where the localized heating was applied, the nucleation points were always located at one of the corners of the sample - a rectangular parallelepiped in the austenite. Using a simplified nonlinear elasticity model, we propose an explanation for the location of the nucleation points by showing that the martensite is a local minimizer of the energy with respect to localized variations in the interior, on faces and edges of the sample, but not at some corners, where a localized microstructure, involving austenite and a simple laminate of martensite, can lower the energy. The result for the interior, faces and edges is established by showing that the free-energy function satisfies a set of quasiconvexity conditions at the stabilized variant in the interior, faces and edges, respectively, provided the specimen is suitably cut

Time-Independent Gravitational Fields

This article reviews, from a global point of view, rigorous results on time independent spacetimes. Throughout attention is confined to isolated bodies at rest or in uniform rotation in an otherwise empty universe. The discussion starts from first principles and is, as much as possible, self-contained.Comment: 47 pages, LaTeX, uses Springer cl2emult styl

Treatment of Late Stage Disease in a Model of Arenaviral Hemorrhagic Fever: T-705 Efficacy and Reduced Toxicity Suggests an Alternative to Ribavirin

A growing number of arenaviruses are known to cause viral hemorrhagic fever (HF), a severe and life-threatening syndrome characterized by fever, malaise, and increased vascular permeability. Ribavirin, the only licensed antiviral indicated for the treatment of certain arenaviral HFs, has had mixed success and significant toxicity. Since severe arenaviral infections initially do not present with distinguishing symptoms and are difficult to clinically diagnose at early stages, it is of utmost importance to identify antiviral therapies effective at later stages of infection. We have previously reported that T-705, a substituted pyrazine derivative currently under development as an anti-influenza drug, is highly active in hamsters infected with Pichinde virus when the drug is administered orally early during the course of infection. Here we demonstrate that T-705 offers significant protection against this lethal arenaviral infection in hamsters when treatment is begun after the animals are ill and the day before the animals begin to succumb to disease. Importantly, this coincides with the time when peak viral loads are present in most organs and considerable tissue damage is evident. We also show that T-705 is as effective as, and less toxic than, ribavirin, as infected T-705-treated hamsters on average maintain their weight better and recover more rapidly than animals treated with ribavirin. Further, there was no added benefit to combination therapy with T-705 and ribavirin. Finally, pharmacokinetic data indicate that plasma T-705 levels following oral administration are markedly reduced during the latter stages of disease, and may contribute to the reduced efficacy seen when treatment is withheld until day 7 of infection. Our findings support further pre-clinical development of T-705 for the treatment of severe arenaviral infections