Winding Clusters in Percolation on the Torus and the Möbius Strip

Using a simulation technique introduced recently, we study winding clusters in percolation on the torus and the Möbius strip for different aspect ratios. The asynchronous parallelization of the simulation makes very large system and sample sizes possible. Our high accuracy results are fully consistent with predictions from conformal field theory. The numerical results for the Möbius strip and the number distribution of winding clusters on the torus await theoretical explanation. To our knowledge, this study is the first of its kind.     

Lebesgue constants for periodic Hermite spline interpolation operators on uniform lattices

We derive a complex line integral representation for the ebyshev norm of periodic spline interpolation operators of odd degree on uniform lattices. Several generalizations are indicated.     

Measurement of the transverse Doppler shift using a stored relativistic7Li+ ion beam

We have performed for the first time precision spectroscopy on a coasting fast⁷Li⁺ ion beam in a storage ring. The ion beam moving with 6.4% speed of light was first electron cooled and then merged with two counterpropagating laser beams acting on two different hyperfine transitions sharing a common upper level (λ-system). One laser was frequency locked to thea ₃ ¹²⁷J₂ hfs frequency component established as a secondary frequency standard at 514 nm. The second laser was tuned over theλ-resonance, which was recorded relative to¹²⁷J₂ hfs components. This experiment is sensitive to the time dilation in fast moving frames and will lead to new limits for the verification of special relatively. The present status of the experiment and perspectives in accuracy are discussed.     

Quantum correlations in dual quantum measurements

 We analyze the quantum measurement properties of dual non-degenerate parametric amplifers in the twin-beam configuration, in the cascaded back-action-evasion configuration, and in Kerr-type photon-number quantum non-demolition measurements. It is found that Einstein-Podolsky-Rosen correlations can be obtained between the quadrature components of an idler mode and the sum of the readout of two signal modes. Furthermore, we discuss dual-mode quantum non-demolition measurements on the combination of two light modes, and the generation of number-state entanglement. Received: 12 April 1996/Revised version: 2 July 1996     

On certainp-harmonic functions in the plane

A representation theorem is given for certainp-harmonic functions (1<p<) in the plane, near a corner of the domain of definition. The proof uses stream functions and the hodograph transformation. The stream function of ap-harmonic function isp-harmonic, where 1/p+1/p=1. Solutions of the formr ^k f(ø) (polar coord.) are crucial for the representation.     

The investigation of critical parameters in the glycolytic response of single living cells by rapid microspectrofluorometric analysis

Summary NAD(P)H fluorescence emission spectra are recorded from single living cells, by a recently developed multichannel microspectrofluorometric technique, in correlation with the intracellular microelectrophoretic addition of substrate (i. e., glucose-6-P). These spectra may be used as a reference basis in establishing the critical parameters to be followed when the same studies are extended to a variety of cells, submitted to various drug effects or physical treatments. The sum-spectra corresponding to channel by channel (wavelength by wavelength) summation of spectra obtained from various cells within a series, before and after addition of substrate, and their difference spectrum may be normalized and evaluated comparatively. The NAD(P)H emission maximum prior to addition of substrate seems to present a mixture of dehydrogenase-bound and free coenzyme. There is a suggestion that immediately after substrate, i. e., at 5 sec, an increase in free NADH is first observed. While the overall changes in fluorescence intensity associated with substrate are quite large (50–150% increase), the counts (i. e., an expression of photons) associated with shifts in the emission maximum (free vs. bound NAD(P)H changes) are at times barely above noise. Rapid microspectrofluorometry provides in principle the most direct approach for the identification of coenzyme bound to various dehydrogenases in single living cells, but further improvements in spectral resolution and signal-to-noise ratio are required, for a better definition of the spectral shifts which may be observed.

---

Zusammenfassung Mit Hilfe einer kürzlich entwickelten Mehrkanal-Mikrospektrofluorometer-Methode wurden von einzelnen lebenden Zellen nach intrazellulär mikroelektrophoretischer Substratzugabe (z. B. Glucose-6-P) NAD(P)H Fluoreszenz-Emissionsspektren aufgenommen. Diese Spektren können als Vergleichsbasis bei der Festsetzung der entscheidenden Parameter verwendet werden, wenn die gleichen Untersuchungen auf eine Reihe von Zellen ausgedehnt werden sollen, die verschiedenen Medikamenteffekten oder physikalischer Behandlung ausgesetzt werden. Die Summenspektren, die der kanalmäßigen (wellenlängenmäßigen) Summierung der Spektren von verschiedenen Zellen innerhalb einer Serie, vor und nach Substratzugabe entsprechen, sowie ihre Differenzspektren können normalisiert und vergleichsweise ausgewertet werden. Das NAD(P)H-Emissionsmaximum vor der Substratzugabe scheint ein Gemisch von freiem und dehydrogenasegebundenem Coenzym darzustellen. Unmittelbar nach Substratzugabe (d. h. nach 5 sec) ist ein Anstieg an freiem NADH das erste Mal zu beobachten. Während die mit dem Substrat einhergehenden Gesamtveränderungen der Fluoreszenzintensität recht groß sind (50–150% Anstieg), sind die Impulse (als Effekt der Photonen), die mit einer Verschiebung im Emissionsmaximum verbunden sind (Veränderungen von freiem und gebundenem NAD(P)H) zu manchen Zeiten kaum höher als das Rauschen. Die rasche Mikrospektrofluorometrie stellt im Prinzip die direkteste Methode zur Identifizierung von Coenzymen dar, die an verschiedenen Dehydrogenasen in einzelnen lebenden Zellen gebunden sind. Weitere Verbesserungen der Spektralauflösung und der Empfindlichkeit (signal-to-noise ratio) sind notwendig, um die Spektralverschiebungen, die beobachtet werden, besser auswerten zu können.