Complete nonorientable minimal surfaces in R3

We consider complete nonorientable minimal immersionsx(M)⊇R ³. Assuming the double coverN ofM has finite total curvature, we generalize an argument of Lopez/Ros to give a sufficient condition for the instability ofx(M) in terms of the total curvature ofM and the genus γ of . We apply this condition to prove that if the immersion is regular thenx(M) is unstable. We also consider the case where the immersion is finitely branched, and we classify the possibilities under the assumption the is hyperelliptic.     

On the fundamental solutions of the operators of S. Timoshenko and R. D. Mindlin

Our recent paper about some new fundamental solutions is complemented by a representation of the fundamental solution of certain evolution operators of fourth order in terms of a family of fundamental solutions of operators of second order. By applying this to the operators of vibrating beams and plates we deduce representations of their fundamental solutions as simple definite integrals over tabulated functions.     

The Influence of Window Parameters on the Transmission Characteristics of Millimeter Waves

This work reports about the influence of some window parameters, such as the mechanical tolerance of disk thickness, the variation of distance between two disks, and the frequency drift during gyrotron operation on the transmission characteristics of millimeter waves. Detailed calculations of the transmission characteristics for a single-disk gyrotron window and frequency tunable double-disk plasma fusion torus windows have been performed. The geometry of the window units has been optimized in order to obtain a suitable transmission characteristic, i.e. power reflection less than –20 dB within a frequency bandwidth of about 1 GHz around the chosen frequencies.     

Correspondence between spin-dynamic phases and pulse program phases of NMR spectrometers

Spin state selective experiments have become very useful tools in solution NMR spectroscopy, particularly in the context of TROSY line narrowing. However, the practical implementation of such pulse sequences is frequently complicated by unexpected instrument behavior. Furthermore, a literal theoretical analysis of sequences published with specific phase settings can fail to rationalize such experiments and can seemingly contradict experimental findings. In this communication, we develop a practical approach to this ostensible paradox. Spin-dynamic design, rationalization, and simulation of NMR pulse sequences, as well as their confident and reliable implementation across current spectrometer hardware platforms, require precise understanding of the underlying nutation axis conventions. While currently often approached empirically, we demonstrate with a simple but general pulse program how to uncover these correspondences a priori in the general case. From this, we deduce a correspondence table between the spin-dynamic phases used in NMR theory and simulation on the one hand and pulse program phases of current commercial spectrometers on the other. As a practical application of these results, we analyze implementations of the original (1)H-(15)N TROSY experiment and illustrate how steady-state magnetization can be predictably, rather than empirically, added to a desired component. We show why and under which circumstances a literal adoption of phases from published sequences can lead to incorrect results. We suggest that pulse sequences should be consistently given with spin-dynamically correct (physical) phases, rather than in spectrometer-specific (software) syntax.