Bipyridinophane‐containing conjugated polymers modulated with an intramolecular aromatic C?H/π interaction

Bipyridinophane–fluorene conjugated copolymers have been synthesized via Suzuki and Heck coupling reactions from 5,8‐dibromo‐2,11‐dithia[3]paracyclo[3](4,4′)‐2,2′‐bipyridinophane and suitable fluorene precursors. Poly[2,7‐(9,9‐dihexylfluorene)‐co‐alt‐5,8‐(2,11‐dithia[3]paracyclo[3](4,4′)‐2,2′‐bipyridinophane)] ( P7 ) exhibits large absorption and emission redshifts of 20 and 34 nm, respectively, with respect to its planar reference polymer Poly[2,7‐(9,9‐dihexylfluorene)‐co‐alt‐1,4‐(2,5‐dimethylbenzene)] ( P11 ), which bears the same polymer backbone as P7 . These spectral shifts originate from intramolecular aromatic C? H/π interactions, which are evidenced by ultraviolet–visible and ¹H NMR spectra as well as X‐ray single‐crystal structural analysis. However, the effect of the intramolecular aromatic C? H/π interactions on the spectral shift in poly[9,9‐dihexylfluorene‐2,7‐yleneethynylene‐co‐alt‐5,8‐(2,11‐dithia[3]paracyclo[3](4,4′)‐2,2′‐bipyridinophane)] ( P10 ) is much weaker. Most interestingly, the quenching behaviors of these two conjugated polymers are largely dependent on the polymer backbone. For example, the fluorescence of P7 is efficiently quenched by Cu²⁺, Co²⁺, Ni²⁺, Zn²⁺, Mn²⁺, and Ag⁺ ions. In contrast, only Cu²⁺, Co²⁺, and Ni²⁺ ions can partially quench the fluorescence of P10 , but much less efficiently than the fluorescence of P7 . The static Stern–Volmer quenching constants of Cu²⁺, Co²⁺, and Ni²⁺ ions toward P7 are of the order of 10⁶ M^?1, being 1300, 2500, and 37,300 times larger than those of P10 , respectively. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4154–4164, 2006     

Codiameters of 3‐connected 3‐domination critical graphs

A graph G is 3‐domination critical if its domination number γ is 3 and the addition of any edge decreases γ by 1. Let G be a 3‐connected 3‐domination critical graph of order n. In this paper, we show that there is a path of length at least n?2 between any two distinct vertices in G and the lower bound is sharp. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 76–85, 2002     

Spectroscopic imaging display and analysis.

A system for display of magnetic resonance (MR) spectroscopic imaging (SI) data is described which provides for efficient review and analysis of the multidimensional spectroscopic and spatial data format of this technique. Features include the rapid display of spectra from selected image voxels, formation of spectroscopic images, spectral and image data processing operations, methods for correlating spectroscopic image data with high resolution 1H MR images, and hardcopy facilities. Examples are shown for 31P and 1H spectroscopic imaging studies obtained in human and rat brain.     

Inertia-preserving secant updates

Corrections to the last two equations of Ref. 1 are given.     

Short-range order in miscible polymer blends: A monte carlo study

Local ordering in miscible binary polymer blends with strong attractive interactions between the two types of chains was investigated by computer simulation of allowable conformations on an incompressible cubic lattice. A tendency toward maximum ordering (in which chains pack in alternate parallel rows) is shown by the calculation of pair correlations and in “snapshots” of the mixtures. A specific directional interaction is not necessarily required for ordering. A comparison of these results with those recently obtained using mean-field theory is presented. The heat capacity of mixing was also calculated and found to be positive, with a value close to that reported experimentally.     

Models of linear logic

We engage a study of nonmodal linear logic which takes times ⊗ and the linear conditional ⊸ to be the basic connectives instead of times and linear negation ()^⊥ as in Girard's approach. This difference enables us to obtain a very large subsystem of linear logic (called positive linear logic) without an involutionary negation (if the law of double negation is removed from linear logic in Girard's formulation, the resulting subsystem is extremely limited). Our approach enables us to obtain several natural models for various subsystems of linear logic, including a generic model for the so-called minimal linear logic. In particular, it is seen that these models arise spontaneously in the transition from set theory to multiset theory. We also construct a model of full (nonmodal) linear logic that is generic relative to any model of positive linear logic. However, the problem of constructing a generic model for positive linear logic remains open. Bibliography: 2 titles. Published inZapiski Nauchnykh Seminarov POMI, Vol. 220, 1995, pp. 23–35. Original     

A projective criterion to the coordinate partitioning method for multibody dynamics

Summary The paper discusses some developments in the coordinate partitioning method for the dynamic analysis of constrained/closed-loop multibody systems. First, the method is reformulated to a more compact form. Then, a simple and reliable projective criterion for choosing the best coordinates from the redundant ones is proposed, and some advantages are pointed out that may arise in the method by applying inverse kinematics algorithms. Finally, the problem of determination ofphysical reactions of constraints and closing conditions is discussed. A four-bar linkage mechanism serves for an illustration of some aspects of the paper.

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Ein Projektionskriterium zur Koordinatenwahl bei Mehrkörpersystemen mit kinematischen Schleifen

Übersicht Bei der Simulation der Bewegunsgleichungen von Mehrkörpersystemen mit kinematischen Schleifen in Minimalform stellt sich die Frage nach der Wahl günstiger verallgemeinerter Koordinaten. Hierfür wird ein Projektionskriterium vorgeschlagen, welches die Trennung der systembeschreibenden redundanten Koordinaten in die verallgemeinerten und davon abhängige Koordinaten gestattet. Durch Anwendung eines Verfahrens zur Rückwärtstransformation der kinematischen Beschreibung lassen sich in diesen explizite Schließbedingungen formulieren, was sich bei der Simulation vorteilhaft auswirkt; diese kann ohne Verletzung der Schließbedingungen erfolgen. Es wird auch gezeigt, wie auch bei Verwendung verallgemeinerter Koordinatenphysikalisch interpretierbare Reaktionen ermittelt werden können. Als Anwendungsbeispiel dient ein ebenes Viergelenk.

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On leave from the Department of Mechanics, Technical University of Radom, ul. Malczewskiego 29, 26-600 Radom, Poland     

Intercalated smectic-A structures in a new class of laterally branched substances

X-ray, DSC and optical studies of a new class of substances with aromatic rings in the lateral branches are reported. The thermal behaviour of the substances is discussed. The X-ray measurements lead to a structural model of the SA phases consisting of layer structures with intercalating molecules.