Spectral simplicity and asymptotic separation of variables

We describe a method for comparing the real analytic eigenbranches of two families of quadratic forms that degenerate as t tends to zero. One of the families is assumed to be amenable to `separation of variables' and the other one not. With certain additional assumptions, we show that if the families are asymptotic at first order as t tends to 0, then the generic spectral simplicity of the separable family implies that the eigenbranches of the second family are also generically one-dimensional. As an application, we prove that for the generic triangle (simplex) in Euclidean space (constant curvature space form) each eigenspace of the Laplacian is one-dimensional. We also show that for all but countably many t, the geodesic triangle in the hyperbolic plane with interior angles 0, t, and t, has simple spectrum.Comment: 53 pages, 2 figure

Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone

In this article we consider the zeta regularized determinant of Laplace-type operators on the generalized cone. For {\it arbitrary} self-adjoint extensions of a matrix of singular ordinary differential operators modelled on the generalized cone, a closed expression for the determinant is given. The result involves a determinant of an endomorphism of a finite-dimensional vector space, the endomorphism encoding the self-adjoint extension chosen. For particular examples, like the Friedrich's extension, the answer is easily extracted from the general result. In combination with \cite{BKD}, a closed expression for the determinant of an arbitrary self-adjoint extension of the full Laplace-type operator on the generalized cone can be obtained.Comment: 27 pages, 2 figures; to appear in Manuscripta Mathematic

Surface atomic defect structures and growth of gold nanorods

We present atomic and defect structural studies of technologically important gold nanorods synthesized by a wet chemical process. Our surface atomic structural studies and electron nanodiffraction from single nanorods have provided the first direct evidence of the stabilization of the highly unstable (110) surface by surfactant molecules. The insights into surface defect structures have important implications in the applications of nanorods in the molecular device technology. The origin and the development of the growth process of nanorods have been inferred from the results

Novel mesoporous silica–perfluorosulfonic acid hybrids as strong heterogeneous Brønsted catalysts

Perfluorinated sulfonic acids have been immobilised into mesoporous silica frameworks by a one-step process, representing the first example of the successful incorporation of charged silanes using this route, and have been shown to be excellent catalysts for Brønsted acid catalysed transformations

A single administration of microbial D-alanine to healthy volunteers augments reaction to negative emotions: a comparison with D-serine

Health and self-regulatio

Molecular characterization of the variable domains of an alphaIIbbeta3-specific immunoglobulin M kappa platelet cold agglutinin in a follicular lymphoma patient with treatment refractory autoimmune thrombocytopenia: idiotypic overlap between alphaIIbbeta3 integrin antibodies.

BACKGROUND - Cold hemagglutinins are generally immunoglobulin M (IgM) kappa antibodies reactive at temperatures below 37 degrees C and if of high titer may cause hemolysis. Platelet (PLT) cold agglutinins (CAs) are rare and poorly characterized. A detailed molecular characterization of the variable domains of a pathologic, PLT-reactive, CA is presented. CASE REPORT - A 70-year-old woman was admitted with rectal bleeding accompanied by widespread petechiae, bruising, tongue and buccal mucosa bleeding, and epistaxes and proved refractory to HLA- and HPA-matched PLTs. Detailed investigation showed monoclonal heavy-chain gene rearrangement with an IgM paraprotein of 3.3 g per L and a trace of kappa Bence Jones protein in the urine, compatible with a diagnosis of secretory B-cell non-Hodgkin's lymphoma (B-NHL). PLT antibody (PAIg) investigations revealed a potent IgM kappa PLT CA. Sequencing of the rearranged variable domain genes of the malignant clone together with idiotype-specific antibodies obtained by DNA-based immunization of rabbits and matrix-assisted laser desorption/ionization-time-of-flight analysis of the PAIgM provided a irrefutable link between the thrombocytopenia, the IgM paraprotein, and the PAIgM against alphaIIbbeta3. The thrombocytopenia and bleeding were refractory to standard treatment and PLT transfusion, but treatment with rituximab resulted in a recovery of the PLT count and a complete remission of B-NHL. CONCLUSION - The IgM kappa paraprotein derived from the malignant B-cell clone was a potent and clinically significant CA against alphaIIbbeta3. The testing for PLT CAs in patients with a paraprotein and refractory to matched PLTs may aid the selection of appropriate treatment.</p

Muscle metabolism during sprint exercise in man: Influence of sprint training

In order to examine the influence of sprint training on metabolism and exercise performance during sprint exercise, 16 recreationally-active, untrained, men (TO2peak= 3.8+/-0.1 1.min(-1)) were randomly assigned to either a training (n=8) or control group (n=8). Each subject performed a 30-sec cycle sprint and a test to measure VO2peak before and after eight weeks of sprint training. The training group completed a series of sprints three times per week which progressed from three 30-sec cycle sprints in weeks 1 and 2, to six 30-sec sprints in weeks 7 and 8. Three mins of passive recovery separated each sprint throughout the training period. Muscle samples were obtained at rest and immediately following the pre- and post-training sprints and analysed for high energy phosphagens, glycogen and lactate; the activities of both phosphofructokinase (PFK) and citrate synthase (CS) were also measured and muscle fibre types were quantified, Training resulted in a 7.1% increase in mean power output (