On multipliers on compact Lie groups

In this note we announce Lp multiplier theorems for invariant and non-invariant operators on compact Lie groups in the spirit of the well-known Hormander-Mikhlin theorem on Rn and its variants on tori Tn. Applications are given to the mapping properties of pseudo-differential operators on Lp-spaces and to a-priori estimates for non-hypoelliptic operators.Comment: 8 page

Global functional calculus for operators on compact Lie groups

In this paper we develop the functional calculus for elliptic operators on compact Lie groups without the assumption that the operator is a classical pseudo-differential operator. Consequently, we provide a symbolic descriptions of complex powers of such operators. As an application, we give a constructive symbolic proof of the G\r{a}rding inequality for operators in $(\rho,\delta)$-classes in the setting of compact Lie groups.Comment: 23 pages; minor correction

Physical and mathematical justification of the numerical Brillouin zone integration of the Boltzmann rate equation by Gaussian smearing

Scatterings of electrons at quasiparticles or photons are very important for many topics in solid state physics, e.g., spintronics, magnonics or photonics, and therefore a correct numerical treatment of these scatterings is very important. For a quantum-mechanical description of these scatterings Fermi's golden rule is used in order to calculate the transition rate from an initial state to a final state in a first-order time-dependent perturbation theory. One can calculate the total transition rate from all initial states to all final states with Boltzmann rate equations involving Brillouin zone integrations. The numerical treatment of these integrations on a finite grid is often done via a replacement of the Dirac delta distribution by a Gaussian. The Dirac delta distribution appears in Fermi's golden rule where it describes the energy conservation among the interacting particles. Since the Dirac delta distribution is a not a function it is not clear from a mathematical point of view that this procedure is justified. We show with physical and mathematical arguments that this numerical procedure is in general correct, and we comment on critical points

Latent Heat Flux Profiles from Collocated Airborne Water Vapor and Wind Lidars during IHOP_2002

Latent heat flux profiles in the convective boundary layer (CBL) are obtained for the first time with the combination of the DLR water vapor differential absorption lidar (DIAL) and the NOAA high resolution Doppler wind lidar (HRDL). Both instruments were integrated nadir viewing on board the DLR “Falcon” research aircraft during the International H2O Project (IHOP_2002) over the U.S. Southern Great Plains. Flux profiles from 300 – 2500 m AGL are computed from high spatial resolution (150 m horizontal and vertical) two-dimensional water vapor and vertical velocity lidar cross sections using the eddy covariance technique. All cospectra show significant contributions to the flux between 1 and 10 km wavelength, with peaks between 2 and 6 km, originating from large eddies. The main flux uncertainty is due to low sampling (55 % rmse at mid-CBL), while instrument noise (15 %) and systematic errors (7 %) play a minor role. The combination of a water vapor and a wind lidar on an aircraft appears as an attractive new tool that allows measuring latent heat flux profiles from a single over-flight of the investigated area

Differences in the performance tests of the fast and slow stretch and shortening cycle among professional, amateur and elite youth soccer players

The purpose of this study was to establish whether physical attributes can differentiate between professional, amateur and elite youth soccer players; such a distinction could aid in the selection process for youth soccer. Therefore, this investigation evaluated a suspected difference in the performance tests of the slow and fast stretch and the shortening cycle (squat jump [SJ], countermovement jump [CMJ], and drop jump from varying heights [DJ]) among professional, amateur and elite youth soccer players. Cross-sectional data were collected. The results indicate that higher performance in the SJ and CMJ seem to depend on the level of player because the mean performance of the PRO was 38.7 ± 4.0 cm in the SJ and 41.2 ± 3.8 in the CMJ, which were significantly (p<0.05) different compared with all other groups. In the DJ, there were significant (p<0.05) differences between the professional players (PRO) and lower-level players as well as between the PRO and youth soccer players. The results suggest that jump performance can differentiate between elite, sub-elite, and youth soccer players and highlights the importance of appropriate conditioning for developing strength and power in youth soccer players

Structural investigations of CeIrIn5{_5} and CeCoIn5{_5} on macroscopic and atomic length scales

For any thorough investigation of complex physical properties, as encountered in strongly correlated electron systems, not only single crystals of highest quality but also a detailed knowledge of the structural properties of the material are pivotal prerequisites. Here, we combine physical and chemical investigations on the prototypical heavy fermion superconductors CeIrIn${_5}$ and CeCoIn${_5}$ on atomic and macroscopic length scale to gain insight into their precise structural properties. Our approach spans from enhanced resolution X-ray diffraction experiments to atomic resolution by means of Scanning Tunneling Microscopy (STM) and reveal a certain type of local features (coexistence of minority and majority structural patterns) in the tetragonal HoCoGa$_5$-type structure of both compounds.Comment: 8 pages, 5 figures, submitted to JPSJ (SCES 2013

Performance Evaluation in Image Processing

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