Teil III: Makromolekulare Verbindungen mit Einschlußbezirken,Gaseinschlußsysteme und sterische Spezifität

Zusammenfassung zu Teil III Auf Grund der beobachteten Polarisationswirkungen (Verschiebung derpKWerte, der Keto-Enol- und der Nitro-Azinitro-Gleichgewichte) an Hochmolekularen mit definierten Einschlu?bezirken vom Cyclodextrin-, Harnstoff- und Peptid-Typus, wird die sterische Spezifit?t von Fermentmodellen und Adsorbentien mit der F?higkeit zur Bildung von Ketten-, Ring-, Netz- und Schichtsowie Assoziat-Einschlu?systembildnern geprüft an der Racematspaltung von DL-Aminos?uren und ihren Derivaten mit einschlu?begünstigenden Atomgruppen (z. B. TCA-Aminos?uren). Die aromatischen und heterozyklischen Seitenketten von Aminos?uren stellen einschlu?begünstigende Atomgruppen dar. Aus der Tatsache, da? in der Regel die unnatürliche D-Form st?rker gebunden wird als der natürliche Antipode, ergibt sich die Notwendigkeit, die sterische Spezifit?t der Enzyme durch eine Kooperation von Substrat und Enzymhelix über ihre Seitenketten gema? Abb. 22 zu kl?ren. Für die zur Funktion von Redoxasen anzunehmende Elektronenleitung über die Peptidkette war der Nachweis von O₂-Einsehlu?systemen erforderlich. Das Problem wurde durch Verwendung von¹⁴CO und¹⁴C-Acetylen in Angriff genommen, von den genannten physiologisch aktiven Gasen liefert das Acetylen Gaseinschlu?systeme, CO wirkt als Komplexbildner mit Schwermetallen. Der Nachweis von Gaseinschlu?systemen führte zur Aufstellung eines Funktionsschemas für Redoxasen, Welches ein Zusammenspiel von Redox- und Einschlu?gleichgewichten vorsieht.     

The natural atomic orbital point charge model for PM3: Multipole moments and molecular electrostatic potentials

The natural atomic orbital/point (NAO-PC) model originally developed to calculate molecular electrostatic potentials (MEPs) and multiple moments based on the AM1 wave function has been extended to PM3. As for AM1, NAO-PC/PM3 reproduces dipole moments calculated by the standard PM3 method very well. There is also a surprisingly good correlation between experimental and calculated quadrupole moments. The MEPs calculated using PM3/NAO-PC are found to be in better agreement with those given by RHF/6-31G* than those obtained from the PM3 wave function using Coulson charges. On the other hand, the NAO-PC model is often slightly worse then the method implemented in MOPAC-ESP. The MEPs calculated using our model based on the PM3 wave function are often in better agreement with those given by RHF/6-31G* than those obtain with AM1. © 1994 by John Wiley & Sons, Inc.     

Vibronic-spin-orbit coupling in 1,3,6,8-tetrachlorodibenzo-p-dioxin

The squared dipole moments (P _0R )² of vibronic transitions caused by vibronic-spin-orbit coupling along the coordinates of out-of-plane vibration modes R were calculated for the triplet ππ* electronic states (with u and g types of orbital symmetry) in a 1,3,6,8-tetrachlorodibenzo-p-dioxin (αβTCDD) molecule. Special features of distribution (P _0R )² over R related to transitions from various sublevels of triplet states are ascertained. The obtained data made it possible to infer that the observed fine-structure phosphorescence spectrum of an αβTCDD solid solution corresponded to the ³ A _g →S ₀ and to eliminate a certain ambiguity in interpreting the vibronic structure of this spectrum.     

Bemerkungen zu einem Rundungsproblem bei der Lagerhaltung

Zusammenfassung Bei der Auffüllung eines Lagers treten in der Praxis häufig Rundungen auf, die etwa durch Abweichungen des errechneten Bedarfs von der lieferbaren Menge entstehen können und die nicht immer von vornherein vernachlässigt werden dürfen. Es werden innerhalb eines speziellen Modells u. a. die entstehenden mittleren Abweichungen ermittelt und für drei Beispiele einige der interessierenden Größen angegeben.

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Summary Frequently in practice it is not possible to order just the quantities, which are needed to meet the demand; for instance the calculated requirements are not identical to the quantities actually available for consignment. Sometimes these deviations cannot be neglected. This paper investigates some aspects of this problem. The mean deviation and some other interesting quantities are determined for a special model and they are given explicitly for three examples.

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Vorgel. v.:J. Nitsche.     

$\Phi $-functions for complex 2D-objects

Within two-dimensional cutting and packing problems with irregular shaped objects, the concept of -functions has been proven to be very helpful for several solution approaches. In order to construct such -functions a previous work, in which so-called primary objects are considered, is continued. Now -functions are constructed for pairs of objects which can be represented as a finite combination (union, intersection, complement) of primary objects which allows the handling of arbitrary shaped objects by appropriate approximations of sufficient accuracy.Received: October 2002, Revised: October 2003, AMS classification: 65K05, 90C26, 90B06All correspondence to: Guntram Scheithauer     

Toward an understanding of the furoxan-dinitrosoethylene equilibrium

The tautomerism of furoxan (1,2,5-oxadiazole-2-oxide) has been investigated by different computational methods comprising modern density functionals as well as single-reference and multi-reference ab initio methods. The ring-opening process to 1,2-dinitrosoethylene is the most critical step of the reaction and cannot be treated reliably by low-level computations. The existence of cis-cis-trans-1,2-dinitrosoethylene as a stable intermediate is advocated by perturbational methods, but high-level coupled-cluster calculations identify this as an artifact. In contrast to the analogous reaction in benzofuroxans, cis-cis-cis-1,2-dinitrosoethylene was found to be a transition state rather than a local minimum. Model potentials were used to explain the occurrence and the disappearing of transition states and local minima relative to the reaction of benzofuroxan. Low-lying triplet states that can be accessed due to spin-orbit coupling were investigated as taking part in alternative routes to a proposed singlet pathway. Barriers for rotations of the nitroso groups on the S(0) and T(1) surfaces are reported.     

Does ignorance promote norm compliance?

A large extent of undetected norm violations may have positive effects for society. If many norm violations are hidden, society seems to be in good order so that actors are more willing to comply with the norms themselves. In this sense, ignorance promotes norm compliance. We challenge this view by arguing that in scenarios, in which norms are controlled and enforced by third parties who receive rewards for their success, the opposite is true: Ignorance promotes norm violations. The reason is that unsuspicious inspectors who believe that little hidden norm violations are committed will spend less effort for detection, some formerly detected norm violations will go undetected, norm targets will be less deterred from the lower detection probability and will commit more norm violations over time. This article develops a respective mathematical model and confirms the above described intuition.     

Continuous Frames, Function Spaces, and the Discretization Problem

A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certain Banach spaces. Many classical function spaces can be identified as such spaces. We provide a general method to derive Banach frames and atomic decompositions for these Banach spaces by sampling the continuous frame. This is done by generalizing the coorbit space theory developed by Feichtinger and Gröchenig. As an important tool the concept of localization of frames is extended to continuous frames. As a byproduct we give a partial answer to the question raised by Ali, Antoine, and Gazeau whether any continuous frame admits a corresponding discrete realization generated by sampling.