Stochastic homogenization of a class of monotone eigenvalue problems

Stochastic homogenization (with multiple fine scales) is studied for a class of nonlinear monotone eigenvalue problems. More specifically, we are interested in the asymptotic behaviour of a sequence of realizations of the form

Strichartz estimates for Schrödinger equations on irrational tori in two and three dimensions

In this paper, we prove new multilinear Strichartz estimates, which are obtained by using techniques of Bourgain. These estimates lead to new critical well-posedness results for the nonlinear Schrödinger equation on irrational tori in two and three dimensions with small initial data. In three dimensions, this includes the energy critical case. This extends recent work of Guo–Oh–Wang.     

A nonlinear superposition principle and multibump solutions of periodic Schrödinger equations

In an abstract setting we prove a nonlinear superposition principle for zeros of equivariant vector fields that are asymptotically additive in a well-defined sense. This result is used to obtain multibump solutions for two basic types of periodic stationary Schrödinger equations with superlinear nonlinearity. The nonlinear term may be of convolution type. If the superquadratic term in the energy functional is convex, our results also apply in certain cases if 0 is in a gap of the spectrum of the Schrödinger operator.     

A Paley-Wiener theorem for the spherical Laplace transform on causal symmetric spaces of rank 1

We formulate and prove a topological Paley-Wiener theorem for the normalized spherical Laplace transform defined on the rank 1 causal symmetric spaces , for .

     

Vertex Algebras, Lie Algebras, and Superstrings

We construct Lie algebras from vertex superalgebras and study their structure. They are sometimes generalized Kac–Moody algebras. In some special cases we can calculate the multiplicities of the roots.     

Evidence for N2N3N45 super coster kronig processes in metallic Nb,Mo, Ru and Rh

The 4p photoelectron spectra of metallic Nb, Mo, Ru and Rh have been recorded. By use of a deconvolution procedure it is shown that the 4p_{$\text{1}\text{2}$} spin-orbit component has a linewidth which significantly exceeds that of the 4p_{$\text{3}\text{2}$} component. This suggests that N₂N₃N₄₅ super Coster Kronig processes give a considerable contribution to the decay rata of the 4p_{$\text{1}\text{2}$} hole state.     

Spectral density estimates with partial symmetries and an application to Bahri–Lions-type results

We are concerned with the existence of infinitely many solutions for the problem \(-\Delta u=|u|^{p-2}u+f\) in \(\Omega \), \(u=u_0\) on \(\partial \Omega \), where \(\Omega \) is a bounded domain in \(\mathbb {R}^N\), \(N\ge 3\). This can be seen as a perturbation of the problem with \(f=0\) and \(u_0=0\), which is odd in u. If \(\Omega \) is invariant with respect to a closed strict subgroup of O(N), then we prove infinite existence for all functions f and \(u_0\) in certain spaces of invariant functions for a larger range of exponents p than known before. In order to achieve this, we prove Lieb–Cwikel–Rosenbljum-type bounds for invariant potentials on \(\Omega \), employing improved Sobolev embeddings for spaces of invariant functions.     

Bifurcation of critical points for continuous families of C 2 functionals of Fredholm type

Given a continuous family of C ² functionals of Fredholm type, we show that the nonvanishing of the spectral flow for the family of Hessians along a known (trivial) branch of critical points not only entails bifurcation of nontrivial critical points but also allows to estimate the number of bifurcation points along the branch. We use this result for several parameter bifurcation, estimating the number of connected components of the complement of the set of bifurcation points in the parameter space and apply our results to bifurcation of periodic orbits of Hamiltonian systems. By means of a comparison principle for the spectral flow, we obtain lower bounds for the number of bifurcation points of periodic orbits on a given interval in terms of the coefficients of the linearization.     

Driving student-centred calculus: results of a comprehensive case study for Kaizen learning in the Sultanate of Oman

The art of teaching freshmen students is undergoing a rapid paradigm change. Classical forms of teaching are not applicable any more and an unmanageable offer of new multimedia tools and concepts is glutting the market. Moreover, compared to previous courses, the class size triples. In view of these challenges, we implemented a new teaching concept best described as Kaizen learning. By Kaizen learning, we define a teaching philosophy that is based on a concise mix of short learning units (with feedback loops and tests) and of carefully chosen repetitions (also with feedback loops and tests) to calibrate a course for the students. Here, this intensive blended, student-centred learning paradigm is analysed together with its direct impact on the students’ performance. This case study leads to easy-to-implement key drivers for successfully teaching science in Oman, such as (1) human–human interaction, (2) clearly communicated expectations, (3) avoidance of a short-term learning attitude, (4) a no-calculator policy, (5) continuous Kaizen learning, and (6) balanced combination of traditional teaching and e-learning.