On Cesàro Limit Distribution of a Class of Permutative Cellular Automata

We study Cesàro means (time averages) of the evolution measures of the class of permutative cellular automata over {0, 1} defined by % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiabew% 9aQnaaBaaaleaacaWGcbaabeaakiaadIhacaGGPaWaaSbaaSqaaiaa% d6gaaeqaaOGaeyypa0JaamiEamaaBaaaleaacaWGUbGaaGjcVlaayI% W7cqGHRaWkcaaMi8UaaGjcVlaadkfaaeqaaOGaey4kaSIaeuiOda1a% a0baaSqaaiaadQgacaaMi8UaaGjcVlabg2da9iaayIW7caaMi8UaaG% imaaqaaiaadkfacaaMi8UaaGjcVlabgkHiTiaayIW7caaMi8UaaGym% aaaakiaayIW7caaMi8UaaGjcVlaayIW7caaMi8UaaGjcVlaacIcaca% aIXaGaey4kaSIaamOyamaaBaaaleaacaWGQbaabeaakiabgUcaRiaa% dIhadaWgaaWcbaGaamOBaiaayIW7caaMi8Uaey4kaSIaaGjcVlaayI% W7caWGQbaabeaakiaacMcaaaa!7530! $$(\varphi _B x)_n = x_{n{\kern 1pt} {\kern 1pt} + {\kern 1pt} {\kern 1pt} R} + \Pi _{j{\kern 1pt} {\kern 1pt} = {\kern 1pt} {\kern 1pt} 0}^{R{\kern 1pt} {\kern 1pt} - {\kern 1pt} {\kern 1pt} 1} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} (1 + b_j + x_{n{\kern 1pt} {\kern 1pt} + {\kern 1pt} {\kern 1pt} j} )$$ where B=b ₀ b _R-1is an aperiodic block in {0, 1} ^R and operations are taken mod 2. If the initial measure is Bernoulli, we prove that the limit of the Cesàro mean of the first column distribution exists. When R = 1 and B = 1, _B is the mod 2 sum automaton. For this automaton we show that the limit is the (1/2, 1/2(-Bernoulli measure, and if the initial measure is Markov, we show that the limit of Cesàro mean of the one-site distribution is equidistributed.     

Specific Lipid Studies in Complex Membranes by Solid-State NMR Spectroscopy

Specific interactions with phospholipids are often critical for the function of proteins or drugs, but studying these interactions at high resolution remains difficult, especially in complex membranes that mimic biological conditions. In principle, molecular interactions with phospholipids could be directly probed by solid-state NMR (ssNMR). However, due to the challenge to detect specific lipids in mixed liposomes and limited spectral sensitivity, ssNMR studies of specific lipids in complex membranes are scarce. Here, by using purified biological ¹³C,¹⁵N-labeled phospholipids, we show that we can selectively detect traces of specific lipids in complex membranes. In combination with ¹H-detected ssNMR, we show that our approach provides unprecedented high-resolution insights into the mechanisms of drugs that target specific lipids. This broadly applicable approach opens new opportunities for the molecular characterization of specific lipid interactions with proteins or drugs in complex fluid membranes.     

Design and performance of a microchip electrophoresis instrument with sensitive variable-wavelength fluorescence detection

A modular instrument for high-speed microchip electrophoresis (MCE) equipped with a sensitive variable-wavelength fluorescence detection system was developed and evaluated. The experimental setup consists mainly of a lamp-based epifluorescence microscope for variable-wavelength fluorescence detection and imaging and a programmable four-channel bipolar high-voltage source capable of delivering up to +/- 10 kV per channel. The optical unit was equipped with a high-sensitivity photomultiplier tube and an adjustable aperture. The system was applied to MCE separations of flurescein isothiocyanate (FITC)-labelled amines utilizing blue light (450-480 nm) for excitation as well as for the separation of rhodamines utilizing excitation light in the green spectral region (531-560 nm). At optimized conditions baseline separation of four FITC-labelled amines could be obtained in less than 50 s at a detection limit of 460 ppt (1 nM) with a signal-to-noise ratio of 3:1. Three rhodamines could be baseline-separated in less than 6 s at a detection limit of 240 ppt (500 pM). The relative standard deviations of absolute migration times determined in repetitive MCE separations of FITC-labelled amines were below 2.5% (n= 25). By the application of cyclodextrin-modified electrolytes, chiral separation of FITC-labelled amines could be performed in seconds demonstrating the potential of microchip electrophoresis for chiral high-throughput screening.     

Splitting properties and jump classes

We show that the promptly simple sets of Maass form a filter in the lattice ℰ of recursively enumerable sets. The degrees of the promptly simple sets form a filter in the upper semilattice of r.e. degrees. This filter nontrivially splits the high degrees (a is high ifa′=0″). The property of prompt simplicity is neither definable in ℰ nor invariant under automorphisms of ℰ. However, prompt simplicity is easily shown to imply a property of r.e. sets which is definable in ℰ and which we have called the splitting property. The splitting property is used to answer many questions about automorphisms of ℰ. In particular, we construct lowd-simple sets which are not automorphic, answering a question of Lerman and Soare. We produce classes invariant under automorphisms of ℰ which nontrivially split the high degrees as well as all of the other classes of r.e. degrees defined in terms of the jump operator. This refutes a conjecture of Soare and answers a question of H. Friedman. During preparation of this paper, the first author was supported by the Heisenberg Programm der Deutschen Forschungsgemeinschaft, West Germany. The second author was partially supported by NSF Grant MSC 77-04013. The third author was partially supported by NSF Grant MSC 80-02937.     

ONSAGER-CASIMIR Relations and Dynamical Optimization Principle

The ONSAGER -CASIMIR reciprocal relations for finite dimensional thermodynamic systems are shown to be closely related to an optimization principle (in the sense of PONTRYAGIN ) for a time integral of entropy. A simple numerical example is given.     

Über die Verteilung der zweidimensionalen Untergitter in einem euklidischen Gitter

Ohne Zusammenfassung     

Stability Properties of a Damped Nonlinear Oscillator Including Persistent Perturbations

The equation of motion of a damped nonlinear multidimensional oscillator disturbed by some (stochastic) persistent force is investigated for Lyapunov stability. With the aid of stability statements on the stationary solutions of the undisturbed equation, estimations for the trajectories are found. Applications of this oscillator as useful model in physics are mentioned.