Synthesis and Characterization of the (5′ → 5″)-Ester of Adenosine 5′-diphosphate with α-D-ribofuranose cyclic 1″,2″-phosphate: A NAD derivative produced during tRNA splicing

The synthesis and spectroscopic properties of the (5′ → 5″)-ester of adenosine 5′-diphosphate with ribofuranose cyclic 1″, 2″-phosphate 3 , a recently discovered metabolite produced during tRNA splicing, are reported.     

Finding the contour of a union of iso-oriented rectangies

Let R₁,…,R_m be rectangles on the plane with sides parallel to the coordinate axes. An algorithm is described for finding the contour of F = R₁ ∪ … ∪ R_m in $\text{O(m}\text{log}\text{m + p}\text{log}\text{(}\text{2m}{}^2\text{p}\text{))}$ time, where p is the number of edges in the contour. This is O(m²) in the general case, and O(m log m) when F is without holes (then p ≤ 8m ? 4); both of these performances are optimal.     

Über Verdazyliumsalze

Zusammenfassung Verdazyle reagieren mit FeCl₃ und anderen Metallhalogeniden in HCOOH unter Bildung von Doppelsalzen. Mit Tetranitromethan erhält man Verdazylium; C(NO₂)₃ ; und Verdazylium^;NO₃ ;. Verdazyliumsalze und Tetramethyl-p-phenylendiamin ergeben unter Elektronenübergang Verdazyle undWursters Blau. Dabei werden aus 2 diamagnetischen Verbindungen 2 paramagnetische Radikale gebildet. Die Absorptionsspektren verschiedenartig substituierter Verdazyliumsalze werden im Zusammenhang mit den Spektren der entsprechenden Verdazyle diskutiert.

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Verdazyls react with FeCl₃ and other metal halides in formic acid to give double-salts. Verdazylium;·C(NO₂)₃ ; and Verdazylium;NO₃ ; were obtained with tetranitromethane. Verdazyliumsalts and tetramethyl-p-phenylenediamine yield, in an electron transfer reaction, the corresponding verdazyls andWurster's-blue; i. e. two diamagnetic compounds react to give two stable paramagnetic species. The absorption spectra of different substituted verdazylium salts are discussed in relation to the spectra of the corresponding verdazyls.

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10. Mitt.:F. A. Neugebauer, Mh. Chem.97, 853 (1966).     

Ergodic Properties of the Quantum Geodesic Flow on Tori

We study ergodic averages for a class of pseudodifferential operators on the flatN-dimensional torus with respect to the Schrödinger evolution. The later can be consider a quantization of the geodesic flow on . We prove that, up to semi-classically negligible corrections, such ergodic averages are translationally invariant operators.Mathematics Subject Classifications (2000) 58J50, 58J40, 81S10.     

Predicting thermal displacements in modular tool systems

In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated first from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite element spindle model. We find that our approach is a powerful tool to describe the relation between temperatures and displacements for simulated data. Next, we analyze the temperature-displacement relationship in a silent real experimental setup, where the tool system is thermally forced. Again, the ACE algorithm is powerful to estimate the deformation with high precision. The corresponding errors obtained by using the nonlinear regression approach are 10-fold lower in comparison to multiple linear regression analysis. Finally, we investigate the thermal behavior of a modular tool system in a working milling machine and again get promising results. The thermally induced errors can be estimated with 1-2 microm accuracy using this nonlinear regression analysis. Therefore, this approach seems to be very useful for the development of new modular tool systems.     

Möbius function of coordinate hyperplanes in complex ellipsoids

For 0$">, let be a complex ellipsoid. We present effective formulas for the generalized Möbius and Green functions , in the case where ( ).

     

Self-organized critical drainage networks

We introduce time-dependent boundary conditions in a model of drainage network evolution based on local erosion rules. The changing boundary conditions prevent the model from becoming stationary; it approaches a state where fluctuations of all sizes occur. The fluctuations in the sizes of the drainage areas show power law behavior with an exponent that differs significantly from that of the static distribution of the drainage areas. Thus, the model exhibits self-organized criticality and proposes a novel concept for predicting fractal properties of drainage networks.