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.     

Raman spectroscopy of carbon fibres

Investigations of coated carbon fibres are reported using Raman spectroscopy. Relationships between different process parameters (for example precursor concentration, reactor temperature and various precursors) and the resulting types of carbon fibres are discussed.     

Structural changes in discotic samples during transition from crystal to discotic mesophase as revealed by electron microscopy and diffraction

Classical methods of structural analysis cannot be applied to liquid crystals because higher order reflections disappear during the transition from crystal to liquid crystal due to the reduction in long range orientational and translational correlations. However, in order to relate physical properties to the molecular architecture, it is essential to have information about molecular positions and orientations in the crystalline state as well as in the liquid crystalline state. In this work, the transition from crystalline to liquid crystalline phase is carefully monitored and the relationship between the original lattice and the new molecular positions found using electron diffraction. In addition to this, a new high resolution electron-microscopic technique is described in which the positions of molecules in the crystalline and the quenched discotic phase are directly imaged and the defects observed in the crystalline and LC phase compared and quantitatively analysed.     

The case of missing incommensurate smectic A phases

Two binary mixtures of polar liquid crystal materials were previously reported to exhibit three incommensurate smectic A phases predicted for such materials on the basis of phenomenological theory. Results of our recent high-resolution X-ray scattering experiments show that no incommensurate phases exist in the two systems. Wide coexistence regions are found at first order transitions between various frustrated smectic phases of these mixtures. These regions were previously identified as the incommensurate smectic A phases. The phase diagrams of the two systems determined with high-resolution X-ray technique are shown to be in excellent agreement with Baroisa-Prost-Lubensky theory.     

Trace determination of Tl, Cu, Pb, Cd, and Zn in specimens of the limnic environment using isotope dilution mass spectrometry with thermal ionization

Within the framework of the German Environmental Specimen Bank program, Tl, Cu, Pb, Cd and Zn were determined in homogenized materials from the limnic environment using Isotope Dilution Mass Spectrometry (IDMS) with thermal ionization. The analytical procedures which were developed for the trace metal analysis of bioindicator and sediment samples are described in detail. Results obtained in bream, mussels (Dreissena polymorpha) and sediments of Lake Constance/Estuary of Constance in the sampling years 1981, 1985, 1988, 1990, 1992 and 1993 are discussed and compared with those of bream from the lakeland district of Born-hoeved/Lake Belau and from the River Saar as well as from reference materials.     

Liquid crystalline hexa-amides and side chain polysiloxanes of azacrown [18]-N6

The hexa-4-dodecyloxybenzoyl derivative 1 of azacrown [18]-N₆ was originally reported to have a 'tubular' mesophase on the basis of its large central ring and 6-fold symmetry. Starting in the mesophase, annealing of 1 under a cover slip results in formation of a new crystalline phase that melts directly to an isotropic liquid at the temperature previously observed for the mesophase to isotropic transition. Thus the phase behaviour of 1 is kinetically controlled. The analogous hexa-3,4-bisdodecyloxybenzoyl derivative 2 of azacrown [18]-N₆ has no kinetic limitations to its phase changes and has an enantiotropic columnar liquid crystalline phase. We have synthesized side chain copolysiloxanes with a (CH₂)₁₁ spacer and 75-84 per cent by weight of the same 4-dodecyloxybenzoyl-[18]-N₆ mesogen. The polysiloxanes also display a liquid crystalline phase.