Chaotic resonance: A simulation

Stochastic resonance is a statistical phenomenon that has been observed in periodically modulated, noise-driven, bistable systems. The characteristic signatures of the effect include an increase in the signal-to-noise of the output as noise is added to the system, and exponentially decreasing peaks in the probability density as a function of residence times in one state. Presented are the results of a numerical simulation where these same signatures were observed by adding achaotic driving term instead of a white noise term. Although the probability distributions of the noise and chaos inputs were significantly different, the stochastic and chaotic resonances were equal within the experimental error.     

G-invariante Morse-funktionen

If f is a Morse function on a smooth manifold M there exists a homotopy equivalence from M to a CW complex X such that the critical points of f with index are in a one-one correspondence to the -cells of X. In the equivariant case, a similar result holds for a special type of invariant Morse functions. In this paper we prove the existence of such special invariant Morse functions on compact smooth G-manifolds. As a consequence, any compact smooth G-manifold is homotopy equivalent to a G-CW complex. Other applications deal with the Euler number of the fixed point set and Morse inequalities in equivariant homology theory.     

Image guide couplers with dielectric coupling elements and radiation reduction

Directional couplers in image guide technique for millimeter-wave circuits are discussed, and steps to improve their properties are demonstrated. The simple two-line-9 dB coupler with periodical coupling is compared to a design with an intermediate dielectric coupling element to reduce the frequency dependence. Radiation from the waveguide bends can be reduced significantly by inserting absorber materials at critical points. Experimental results for a-3 dB coupler are also given.     

Otpically illuminated dielectric interfaces as high-speed far-infrared modulators

A new device for the gigahertz modulation of far-infrared radiation is analytically and numerically analyzed. It consists of a thin layer of a high-mobility, direct-bandgap semiconductor, such as GaAs, in which a high-density electron-hole plasma is rapidly created and destroyed, thereby rapidly changing the free-carrier reflectivity of the active layer. Illumination by a high-power, near-infrared laser diode array generates the plasma through intrinsic photoconduction. It is shown that this device acis primarily as an amplitude modulator, and that its efficiency increases sharply with increasing far-IR frequency, in contrast to a Schottky diode, which acts primarily as a phase modulator, and whose efficiency falls off sharply with far-IR frequency. The breakeven frequency lies at about 1.5 THz, depending slightly on the assumed device parameters. The relative advantage of the new device increases rapidly with increasing far-infrared frequency. At an operating frequency of 2.5 THz (119 m), for example, a 1 GHz modulation bandwidth may be achieved with a single-sideband conversion loss of only-21 db, versus a Schottky's loss of-39 db, assuming a laser diode power of 1 W, which is readily available from recently developed laser diode arrays.     

4-Amino-imidazole durchThorpe-Cyclisierung

The alkylation of arylaminomethylenecyanamides1 or cyano-imidothiocarbamates2 with -halogen carbonyl compounds followed by base catalysed cyclization yields substituted 4-amino-imidazoles4. Imidazo[4,5-d]pyrimidones5, 6 and imidazo[4,5-b]pyridines7 can be obtained from4.     

Formulas for \bar \beta parameters and their limitations

The operator relationship p=[r, h] between linear momentum, position vector and Hamiltonian is the basis for an investigation of formulas for ¦ atomic orbitals is discussed. Formulas for parameters useful in extended Hückel methods are presented.

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Zusammenfassung Die Operatorengleichung p=[r, h] zwischen Impuls, Ortsvektor und Hamiltonoperator ist die Grundlage für eine Untersuchung von Formeln für -Parameter in der erweiterten Hückel[1]- und CNDO [2]-Methode. Das Eichproblem dieser Gleichung in Verbindung mit abgebrochenen Entwicklungen für Matrixelemente ¦P¦ über Atomfunktionen wird diskutiert. Nützliche Formeln für die erweiterte Hückel-Methode werden abgeleitet.

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Résumé La relation entre opérateurs moment linéaire, position et hamiltonien: p=[r, h] sert de base à une étude de formules pour les paramètres dans les méthodes de type Hückel étendu [1] et CNDO [2]. Le problème de jauge de cette équation est discuté par rapport au développement limité des éléments de matrice ¦P¦ dans une base d'orbitales atomiques. Présentation de formules pour les paramètres utiles dans les méthodes Hückel étendu.

     

Stereochemie von Metallocenen, 40. Mitt.

Starting from optically active methylferrocene-- and--carboxylic acids (1 a and1 b) of known absolute configuration and enantiomeric purity about 15 chiral ferrocenes (of each isomeric series— and ) were obtained by suitable ligand transformations. Thereby (almost) all possible chiral combinations of the ligands CH₃, COOH (COO^–), COOCH₃, CN and NH₂ (NH₃ ⁺) were accessible which are necessary for a potential test of approximations of chirality functions for compounds with basic symmetry C_5v. The chiroptical properties of these disubstituted ferrocenes are recorded.Preliminary tests using a shortened Ansatz revealed large discrepancies between calculated () and found [M]_D-values. Possible reasons for this failure are discussed.

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61. Mitt. über Ferrocenderivate

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39. Mitt.:A. Meyer, H. Neudeck undK. Schlögl, Chem. Ber.110, 1403 (1977).

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60. Mitt.:V. Rapi, K. Schlögl undB. Steinitz, J. Organometal. Chem.94, 87 (1975).