We studied the pressure effect of polycrystal BiMnO3 (type-I multiferroic) and single crystal Co3TeO6 (type-II multiferroic) with different magnetic fields and pressures. With the primary objective of understanding the pressure effect on BiMnO3, complex multiple magnetic transitions (kink I, II and III) are observed under the maximum applied pressure of 15.94 kbar (~1.6 GPa). Kink I, a long-range soft ferromagnetic transition at TcI ~ 100 K under ambient pressure, is suppressed completely at 11.74 kbar. Kink II emerges at 8.66 kbar along with TcII ~ 93 K. Kink II is a long-range soft ferromagnetic the same as kink I but canted in nature. Kink III, a canted antiferromagnetic transition at TcIII ~ 72.5 K appears along with kink II also at 8.66 kbar. These results indicate the complicated correlation between the lattice distortion and the spin configuration under pressures and magnetic fields in multiferroic system. Whereas, two distinct anomalies (T1 ~ 26 K and T2 ~ 18 K) are observed on single crystal Co3TeO6 in magnetic susceptibility, specific heat, and neutron diffraction measurements. Interestingly, the strong anisotropic magnetic variations are also noticed in high-magnetic-field hysteresis measurements with applied magnetic field parallel to a- and c- axes. Dielectric studies were also carried out in different magnetic fields at the temperature range 5 ¡V 300 K. Concomitantly, frequency-independent step-like dielectric anomaly is observed around 18 K, coinciding with the transition of magnetic susceptibility, specific heat, and neutron diffraction. The dielectric constant is also modified by external magnetic fields. These experimental results strongly suggest the multiferroicity of Co3TeO6. From temperature-dependent X-ray diffraction studies, it is evident that a structural distortion appears around 18 K, responsible of dielectric and/or magnetic ordering. The transition at 18 K is disappeared under pressure above 9.82 kbar, indicative of suppressing structural distortion. Similarly, the lattice distortion and the spin configuration under pressures are important factors for multiferroic property. Through the specific heat and pressure-dependent susceptibility, the structural distortion probably results from the magnetic ordering, indication the dielectric anomaly at 18 K.

We study the approximation of functions defined on different domains by trigonometric and transformed trigonometric functions. We investigate which of the many results known from the approximation theory on the d-dimensional torus can be transfered to other domains. We define invertible parameterized transformations and prove conditions under which functions from a weighted Sobolev space can be transformed into functions defined on the torus, that still have a certain degree of Sobolev smoothness and for which we know worst-case upper error bounds. By reverting the initial change of variables we transfer the fast algorithms based on rank-1 lattices used to approximate functions on the torus efficiently over to other domains and obtain adapted FFT algorithms.:1 Introduction 2 Preliminaries and notations 3 Fourier approximation on the torus 4 Torus-to-R d transformation mappings 5 Torus-to-cube transformation mappings 6 Conclusion Alphabetical Index / Wir betrachten die Approximation von Funktionen, die auf verschiedenen Gebieten definiert sind, mittels trigonometrischer und transformierter trigonometrischer Funktionen. Wir untersuchen, welche bisherigen Ergebnisse für die Approximation von Funktionen, die auf einem d-dimensionalen Torus definiert wurden, auf andere Definitionsgebiete übertragen werden können. Dazu definieren wir parametrisierte Transformationsabbildungen und beweisen Bedingungen, bei denen Funktionen aus einem gewichteten Sobolevraum in Funktionen, die auf dem Torus definiert sind, transformiert werden können, die dabei einen gewissen Grad an Sobolevglattheit behalten und für die obere Schranken der Approximationsfehler bewiesen wurden. Durch Umkehrung der ursprünglichen Koordinatentransformation übertragen wir die schnellen Algorithmen, die Rang-1 Gitter Methoden verwenden um Funktionen auf dem Torus effizient zu approximieren, auf andere Definitionsgebiete und erhalten adaptierte FFT Algorithmen.:1 Introduction 2 Preliminaries and notations 3 Fourier approximation on the torus 4 Torus-to-R d transformation mappings 5 Torus-to-cube transformation mappings 6 Conclusion Alphabetical Index