Singularities of Affine Schubert Varieties

This paper studies the singularities of affine Schubert varieties in the affine Grassmannian (of type $\mathrm{A}^{(1)}_\ell$). For two classes of affine Schubert varieties, we determine the singular loci; and for one class, we also determine explicitly the tangent spaces at singular points. For a general affine Schubert variety, we give partial results on the singular locus.Comment: 13 figure

Singularities of Affine Schubert Varieties

This paper studies the singularities of affine Schubert varieties in the affine Grassmannian (of type Al⁽¹⁾). For two classes of affine Schubert varieties, we determine the singular loci; and for one class, we also determine explicitly the tangent spaces at singular points. For a general affine Schubert variety, we give partial results on the singular locus

Analyticity and criticality results for the eigenvalues of the biharmonic operator

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.Comment: To appear on the proceedings of the conference "Geometric Properties for Parabolic and Elliptic PDE's - 4th Italian-Japanese Workshop" held in Palinuro (Italy), May 25-29, 201

Annihilation of positrons trapped at the (100) and (111) surfaces of Si

We present results of theoretical studies of positron surface states and positron annihilation characteristics at the clean non reconstructed (100) and (111) surfaces of Si performed within the modified atomistic, superposition method. It is found that in the case of non reconstructed semiconductor surfaces, the positron surface state is localized mainly on the vacuum side of the topmost layer. The computed positron surface state energies Eb at the (100) and (111) surfaces of Si are -2.81 and -2.69 eV. In addition, calculations of the positron work functions with respect to the vacuum for bulk Si(100) and Si(111) yielded 2.34 and 2.23 eV, respectively demonstrating the stability of positron surface state on these surfaces. The positron surface state lifetime as well as probabilities for a positron trapped in a surface state to annihilate with relevant core-level electrons are computed for both surfaces, and compared with available experimental data

Theoretical study of the positron surface state at an alkali-metal surface

We present a quantum mechanical analysis of positrons trapped in a bound state at the (100) surface of bulk Cs, based on the treatment of a positron as a single charged particle trapped in an image potential-correlation well in the proximity of the surface atoms. The image-potential-induced positron surface state is calculated using the corrugated-mirror model in full three-dimensional geometry. Calculations show that the positron bound state is delocalized in the surface plane, but is strongly localized perpendicular to the surface mainly in the region between the top and the second layers of Cs atoms. The positron binding energy Eb in the surface state is computed to be 4.92 eV. Calculations on the positron annihilation rates for different Cs core levels are performed using the independent particle model. The positron surface state lifetime is calculated using the local density approximation method. The annihilation probabilities of a positron trapped at the Cs(100) surface with Cs 4p and 4d core electron levels are computed to be 0.065% and 0.22%, respectively. © 1995

Study of positron surface states on the alkali-metal-covered transition-metal surface

We present a first-principles study of annihilation probabilities of surface trapped positrons with core electrons at the Cu(100) surface with sub-monolayers of Cs adsorbed. Image-potential-induced positron surface states are calculated using a corrugated-mirror model in a full three-dimensional geometry. These states are studied for various arrangements of Cs atoms below and above the critical alkali-metal coverage of approximately 0.7 physical monolayer. Computer simulations of the deposition of Cs atoms are used to show that hexagonal close-packed Cs islands are formed at about 0.7 physical monolayer coverage of Cs. It is found that the abrupt decrease in the positron annihilation rate with Cu 3p electrons observed experimentally results from a metallization of the Cs islands. This causes a shift in the localization of the positron bound state from the Cs Cu interface to the vacuum side of the Cs overlayer, with the corresponding abrupt decrease in the positron annihilation probability with Cu electrons. Annihilation probabilities for positrons with Cs electrons are also computed and compared with experiment. © 1995

Biochemical Reaction Rules with Constraints

International audienceWe propose React(C), an expressive programming language for stochastic modeling and simulation in systems biology, that is based on biochemical reactions with constraints. We prove that React(C) can express the stochastic pi-calculus, in contrast to previous rule-based programming languages, and further illustrate the high expressiveness of React(C). We present a stochastic simulator for React(C) independently of the choice of the constraint language C. Our simulator must decide for a given reaction rule whether it can be applied to the current biochemical solution. We show that this decision problem is NP-complete for arbitrary constraint systems C, and that it can be solved in polynomial time for rules of bounded arity. In practice, we propose to solve this problem by constraint programming

Repositioning approved drugs for the treatment of problematic cancers using a screening approach

Advances in treatment strategies together with an earlier diagnosis have considerably increased the average survival of cancer patients over the last four decades. Nevertheless, despite the growing number of new antineoplastic agents introduced each year, there is still no adequate therapy for problematic malignancies such as pancreatic, lung and stomach cancers. Consequently, it is important to ensure that existing drugs used to treat other types of cancers, and potentially other diseases, are not overlooked when searching for new chemotherapy regimens for these problematic cancer types. We describe a screening approach that identifies chemotherapeutics for the treatment of lung and pancreatic cancers, based on drugs already approved for other applications. Initially, the 1280 chemically and pharmacologically diverse compounds from the Prestwick Chemical Library (R) (PCL) were screened against A549 (lung cancer) and PANC-1 (pancreatic carcinoma) cells using the PrestoBlue fluorescent-based cell viability assay. More than 100 compounds from the PCL were identified as hits in one or both cell lines (80 of them, being drugs used to treat diseases other than cancer). Selected PCL hits were further evaluated in a dose-response manner. Promising candidates for repositioning emanating from this study include antiparasitics, cardiac glycosides, as well as the anticancer drugs vorinostat and topotecan

Finite Element Convergence for the Joule Heating Problem with Mixed Boundary Conditions

We prove strong convergence of conforming finite element approximations to the stationary Joule heating problem with mixed boundary conditions on Lipschitz domains in three spatial dimensions. We show optimal global regularity estimates on creased domains and prove a priori and a posteriori bounds for shape regular meshes.Comment: Keywords: Joule heating problem, thermistors, a posteriori error analysis, a priori error analysis, finite element metho