Magnetooptical studies on thin iron films

Magnetooptical measurements on Fe-films in the layer system ZnS-Fe-MgF₂-Ag showed a decrease of the Kerr-intensity values with Fe-film thicknesses below 15nm, not predicted by theoretical calculations. Magnetization curves obtained magnetooptically indicate a significant influence of the layer system on the magnetic properties of Fe-films.     

Local well-posedness for the Maxwell-Schrödinger equation

Time local well-posedness for the Maxwell-Schrödinger equation in the Coulomb gauge is studied in Sobolev spaces by the contraction mapping principle. The Lorentz gauge and the temporal gauge cases are also treated by the gauge transform.     

Enlarging the domain of convergence for multiple shooting by the homotopy method

Summary The homotopy method is a frequently used technique in overcoming the local convergence nature of multiple shooting. In this paper sufficient conditions are given that guarantee the homotopy process to be feasible. The results are applicable to a class of two-point boundary value problems. Finally, the numerical solution of two practical problems arising in physiology is described.     

Numerische Behandlung von Verzweigungsproblemen bei gewöhnlichen Differentialgleichungen

Summary We present a new method for the numerical solution of bifurcation problems for ordinary differential equations. It is based on a modification of the classical Ljapunov-Schmidt-theory. We transform the problem of determining the nontrivial branch bifurcating from the trivial solution into the problem of solving regular nonlinear boundary value problems, which can be treated numerically by standard methods (multiple shooting, difference methods).

     

On theA-stability of implicit Runge-Kutta processes

A new technique to calculate the characteristic functions and to examine theA-stability of implicit Runge-Kutta processes is presented. This technique is based on a direct algebraic approach and an application of theC-polynomial theory of Nørsett. New processes are suggested. These processes can be exponentially fitted in anA-stable manner.     

Characterization and quantification of anthocyanins in selected artichoke (Cynara scolymus L.) cultivars by HPLC–DAD–ESI–MS n

The anthocyanin pattern of artichoke heads (Cynara scolymus L.) has been investigated by high-performance liquid chromatography–electrospray ionization mass spectrometry. For this purpose a suitable extraction and liquid chromatographic method was developed. Besides the main anthocyanins—cyanidin 3,5-diglucoside, cyanidin 3-glucoside, cyanidin 3,5-malonyldiglucoside, cyanidin 3-(3′′-malonyl)glucoside, and cyanidin 3-(6′′-malonyl)glucoside—several minor compounds were identified. Among these, two peonidin derivatives and one delphinidin derivative were characterized on the basis of their fragmentation patterns. To the best of our knowledge this is the first report on anthocyanins in artichoke heads consisting of aglycones other than those of cyanidin. Quantification of individual compounds was performed by external calibration. Cyanidin 3-(6′′-malonyl)glucoside was found to be the major anthocyanin in all the samples analyzed. Total anthocyanin content ranged from 8.4 to 1,705.4 mg kg⁻¹ dry mass.      

Existence of infinitely many stationary solutions of the L2-subcritical and critical NLSE on compact metric graphs

We investigate the existence of stationary solutions for the nonlinear Schrödinger equation on compact metric graphs. In the $L^2$-subcritical setting, we prove the existence of an infinite number of such solutions, for every value of the mass. In the critical regime, the existence of infinitely many solutions is established if the mass is lower than a threshold value, while global minimizers of the NLS energy exist if and only if the mass is lower or equal to the threshold. Moreover, the relation between this threshold and the topology of the graph is characterized. The investigation is based on variational techniques and some new versions of Gagliardo–Nirenberg inequalities.     

On stochastic calculus with respect to q-Brownian motion

Following the approach and the terminology introduced in Deya and Schott (2013) [6], we construct a product Lévy area above the q-Brownian motion (for $q\in [0,1)$) and use this object to study differential equations driven by the process.We also provide a detailed comparison between the resulting “rough” integral and the stochastic “Itô” integral exhibited by Donati-Martin (2003) [7].