Spreading Code Design Using a Global Optimization Method

The performance of a code division multiple access system depends on the correlation properties of the employed spreading code. Low cross-correlation values between spreading sequences are desired to suppress multiple access interference and to improve bit error performance. An auto-correlation function with a distinct peak enables proper synchronization and suppresses intersymbol interference. However, these requirements contradict each other and a trade-off needs to be established. In this paper, a global two dimensional optimization method is proposed to minimize the out-of-phase average mean-square aperiodic auto-correlation with average mean-square aperiodic cross-correlation being allowed to lie within a fixed region. This approach is applied to design sets of complex spreading sequences. A design example is presented to illustrate the relation between various correlation characteristics. The correlations of the obtained sets are compared with correlations of other known sequences.     

On Matter and Metric in Affine Theory of Gravity

The affine theory was conceived as a geometric model, wherein the connection field is the primary structure of the space-time. According to the program lying on the basis of this theory, metric and some sort of matter are somehow to be deduced from the connection field. In the present paper, we point out classical ways to a realization of this program. It is shown that, even in that case where the introduction of the metric seems to exclude the coupling of gravity to matter, the situation is not so hopeless as one may assume. In particular, for a symmetric Einstein tensor, it is answered the old question as to a self-consistent introduction of a metric and a metrical energy-momentum tensor controversially debated by Einstein, Eddington, and Weyl.     

Diagrams,orientations, and varieties

One of the central problems in the theory of ordered sets is to describe the orientations of the covering graph of an ordered set. We show that the particular operation called inversion, together with the classical constructions of retraction and product, provide a context for the classification of all such orientations. AMS subject classifications (1980). 06A10, 05C75, 05C20.     

Eine direkt formulierte lineare Theorie für viskoelastische Platten und Schalen

Übersicht Eine Möglichkeit der Entwicklung einer allgemeinen Theorie für Platten und Schalen besteht in der Modellierung des Flächentragwerks durch ein zweidimensionales deformierbares Kontimmm und der direkten Ableitung der kinematischen Beziehungen, der Bewegungsgleichungen und der konstitutiveu Gleichungen. Eine so erhaltene Theorie ist mathematisch und physikalisch widerspruchsfrei, jedoch ist es für ihre Anwendung notwendig, die sogenannten Ersatzeigenschaften zu ermitteln. Im Beitrag wird eine geometrisch und physikalisch lineare Theorie behandelt. Jeder Punkt des Kontinuums ist ein infinitesimal kleiner Starrkörper mit nur 5 Freiheitsgraden (3 Translationen, 2 Rotationen). Bei Annahme dieser Einschränkungen gelingt es, eine Theorie direkt abzuleiten, wobei alle Ersatzeigenschaften des Flächentragwerks bestimmt werden können. Im Beitrag werden die Möglichkeiten der allgemeinen Theorie am Beispiel isotropen viskoelastischen Materials mit über die Dicke veränderlichen Eigenschaften gezeigt. Die Theorie schließt die Betrachtung mehrschichtiger Flächentragwerke ein.

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A directly formulated linear theory of viscoelastic plates and shells

Summary One kind to develop a general theory for plates and shells is the modelling of the structure as a two-dimensional deformable continuum and the direct approach to the kinematical relations, equations of motion and constitutive equations. Such a theory is physically and mathematically correct. For the application of such directly formulated theories it is nessecery to identify the so-called effective properties. In the paper the theory is formulated for geometrical and physical linearity. Each point of the continuum is an infinitesimal small rigid body with only 5 degrees of freedom (3 translations, 2 rotations). For such a kinematical assumption it is possible to develop a direct theory and to determinate all effective properties of the structure. The paper demonstrates the possibilities of the general theory for an isotropic viscoelastic plate with material properties varying over the thickness. The theory includes also the analysis of multilayered plates and shells.

     

Force field and 13C-NMR investigations of substituted cyclopentanes. A concept for the adaption of 13C NMR shifts to varying torsional arrangements in flexible conformers

MM2 Exploration of the conformational space for methylcyclopentane, in contrast to cyclopentanone yields more and flatter minima than known previously. Calculations of cyclopentanes with substituents X = F, Cl, CHMe₂, and CMe₃ with two stable conformations indicate <2° torsional angle changes with the different substituents. Cyclopentanes bearing not more than 2 substituents can accommodate all groups in pseudoequatorial positions without changing the basic envelope and twist chair geometries significantly. A model for ¹³C-shift calculation is proposed in which shift increments for the different torsional arrangements are obtained by linear interpolation between corresponding cyclohexane values. After correction for the nonequivalent carbon shifts in the hydrocarbon itself, again using the linear interpolation, a significant improvement of the shift correlations is observed. For disubstituted cyclopentanes these predict the shifts within ± 1.7 ppm with Me, CHMe₂, CMe₃, Cl, Br and OH as substituents. Configurational assignments are difficult with 1,3-di-substituted cyclopentanes, but straightforward with 1,2-di- and trisubstituted compounds. Thus, due to the presence of smaller torsional angles between, e.g. diequatorial vicinal substituents in the 1,2- cis series as compared to the trans compounds, the latter show deshielding, particularly at C2, by 1–4 ppm. Several epimers are stereo-selectively prepared by suitable ketone reduction and displacement methods.     

Silver(I) Complexes with Nitrogen-Containing Noncyclic, Macrocyclic, and Macrobicyclic Ligands in Propylene Carbonate

Stability constants and thermodynamic data for complex formation of silver(I) with noncyclic, macrocyclic, and macrobicyclic ligands have been measured in propylene carbonate using potentiometric and calorimetric methods. All ligands containing two nitrogen donor atoms form extremely stable complexes. Only if substituents reduce the basicity of the nitrogen donor atoms, the stability of the complexes decreases drastically. However, the cryptand (221) forms the most stable complex of all ligands examined. In this case, the dimensions of the ligand cavity and of the cation are nearly identical.