Talk 1 (18.10.2017 – Gesina Schwalbe): Overview of some classical results. Recall the classical theorems of Freudenthal and Hurewicz and some elementary calculations of homotopy groups of spheres. Recall the definition of the stable homotopy groups of spheres and explain the ring structure. Show that the Hopf maps are stably essential, i.e. not stably null-homotopic, using Steenrod operations. ...

We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous semi-martingales, which is based on Fourier analysis. The co-volatility is reconstructed as a stochastic function of time by establishing a connection between the Fourier transform of the prices process and the Fourier transform of the co-volatility process. A nonparametric estimator is...

n-propylsalicylidene based on silica as ion exchanger (ie) was used for the separation by complexation of mn2+, co2+, ni2+, cu2+, hg2+, cr3+, fe3+, and uo22+ from their parent solutions. ie and its metal complexes are characterized by elemental analysis, electronic and infrared spectra, in addition to thermal analysis in atmospheric pressure. the mode of chelation and the proposed geometric str...

We propose a coupling interface method (CIM) under Cartesian grid for solving elliptic complex interface problems in arbitrary dimensions, where the coe cients, the source terms and the solutions may be discontinuous or singular across the interfaces. It is a dimension-by-dimension approach. It consisits of a rst-order version (CIM1) and a second-order version (CIM2). In one dimension, the CIM1...

Given a set of i (i = 1; 2; : : :; k) orientations (angles) in the plane, one can deene a distance function which induces a metric in the plane, called the orientation metric 3]. In the special case where all the angles are equal, we call the metric a uniform orientation metric 2]. Speciically, if there are orientations, forming angles ii ; 0 i ?1, with the x-axis, where 2 is an integer, we cal...

Objectives: Whether to perform mitral valve (MV) repair is often difficult during infective endocarditis (IE), especially in patients with extensive leaflet destruction. The aim of this study was to develop scoring system to predict feasibility of mitral valve (MV) repair and select appropriate surgical candidates for repair during active IE. Methods: Patients who underwent MV repair for active...

We derive the complete asymptotic expansion in terms of powers of N for the Riesz s-energy of N equally spaced points on the unit circle as N →∞. For s ≥ −2, such points form optimal energy N -point configurations with respect to the Riesz potential 1/r, s 6= 0, where r is the Euclidean distance between points. By analytic continuation we deduce the expansion for all complex values of s. The Ri...

Several recent papers have proposed the use of grids for solving unconstrained optimisation problems. Grid-based methods typically ge:nerate a sequence of grid local minimisers which converge to stationary points under mild conditions. The location and number of grid local minimisers is calculated for strictly convex quadratic functions in two dimensions with certain types of grids. These calcu...

This paper is concerned with a generalization of the Bernstein polynomials in which the approximated function is evaluated at points spaced in geometric progression instead of the equal spacing of the original polynomials.