On the continuation for variational inequalities depending on an eigenvalue parameter

In this paper we generalize recent theoretical results on the local continuation of parameter-dependent non-linear variational inequalities. The variational inequalities are rather general and describe, for example, the buckling of beams, plates or shells subject to obstacles. Under a technical hypothesis that is satisfied by the simply supported beam, we obtain the existence of a continuation of both the solution and the eigenvalue with respect to a local parameter. A numerical continuation method is presented that easily overcomes turning points. Numerical results are presented for the non-linear beam.     

Standardization of Methods for Characterizing the Surface Geometry of Solids

Since a comprehensive survey published in 1999 [1] much work was done in standardizing measuring methods to characterize the surface geometry of dispersed and/or porous solids and to certify reference materials. The present paper is an extension of a short communication [2]. It gives a survey on existing standards and reports on new drafts and proposals.     

The use of an atomizer for chemical pleurodesis

Summary An atomizer had been designed that could create an aerosol of a liquid with high viscosity. The amount of additional driving gas that had to be used was very low. In a cooperation with the University Hospital in Zurich the atomizer was miniaturized and used for treating six patients.     

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.     

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.     

The average a posteriori error of numerical methods

Summary The definition of the average error of numerical methods (by example of a quadrature formula to approximateS(f)= f d on a function classF) is difficult, because on many important setsF there is no natural probability measure in the sense of an equidistribution. We define the average a posteriori error of an approximation by an averaging process over the set of possible information, which is used by (in the example of a quadrature formula,N(F)={(f(a ₁), ...,f/fF} is the set of posible information). This approach has the practical advantage that the averaging process is related only to finite dimensional sets and uses only the usual Lebesgue measure. As an application of the theory I consider the numerical integration of functions of the classF={f:[0,1]/f(x)–f(y)||x–y|}. For arbitrary (fixed) knotsa _i we determine the optimal coefficientsc _i for the approximation and compute the resulting average error. The latter is minimal for the knots . (It is well known that the maximal error is minimal for the knotsa _i .) Then the adaptive methods for the same problem and methods for seeking the maximum of a Lipschitz function are considered. While adaptive methods are not better when considering the maximal error (this is valid for our examples as well as for many others) this is in general not the case with the average error.     

Reaktionen mit phosphororganischen Verbindungen, 48. Mitt.

Reaction of the vicinal diols of steroids1, 5, 7, 10, 13, and16 with TPP/DEAD yields both regio-and stereospecifically the oxosteroids2, 6, 8, 11, 14, and15 by displacement of an axial hydrogen and extrusion ofTPPO besides the cholest-4-en-6-ols9 and12 and the cyclic carbonate3. 16, 17-androstandiol16 gives only the cyclic carbonate17. The different structures of the carbohydrates withcis-diol arrangement19 and21 lead exclusively to cyclic carbonates20 and22 in moderate yields. Treatment of1 with TPP/DEAD/HN₃ affords 3-azido-2-hydroxycholestane4 in addition to the above mentioned2.

     

Substituenteneffekte auf azido-tetrazolo-gleichgewichte elektronische und sterische effekte bei s-triazolo[4,3-c]tetrazolo[1,5-a]pyrimidinen1

The azido tetrazolo valence isomerism of twenty 9-methyl-s-triazolo[4,3-c]tetrazolo[1,5-a]pyrimidines with different substituents at position 5 has been studied by means of ¹H NMR spectroscopy. All the compounds have been found to be tetrazoles in the solid state and in (CD₃)₂SO solution; in CF₃COOH azido and tetrazolo isomers are in equilibrium. From equilibrium constants K and thermodynamic data determined it is concluded that in this series K depends on both electronic effects and steric requirements of the 5-substituents. A linear relation between K and σ was found for 5-arylderivatives because ΔS° keeps approximately constant and the substituent mainly operates on ΔH°.     

Zur Aktivierung partiell silylierter Kohlenhydrate mittels Triphenylphosphan/Azodicarbonsäureester

On the Activation of Partially Silylated Carbohydrates Using Triphenylphosphane/Diethylazodicarboxylate Reaction of methyl α-D-glucopyranoside ( 1 ) with two equivalents of t-butyldimethylchlorosilane yields methyl 2,6-bis[O-(t-butyldimethylsilyl)]-α-D-glucopyranoside ( 1a ) and methyl 3,6-bis[O(t-butyldimethylsilyl)]-α-D-glucopyranoside ( 1b ) in a ratio of 4:1. The anomeric β-pyranoside 2 affords methyl 2,6-bis[O(t-butyldimethylsilyl)]-β-D-glucopyranoside ( 2a ) and methyl 3,6-bis[O(t-butyldimethylsilyl)]-β-D-glucopyranoside ( 2b ) in nearly equal amounts. 2b is isomerized to methyl 4,6-bis[O(t-butyldimethylsilyl)]-β;-D-glucopyranoside ( 2c ) (83%) and 2a (10%) with triphenylphosphane/diethylazodicarboxylate. Structures were assigned by NMR.-analysis and CD.-analysis of the corresponding benzoates 1c , 1d and 2d and of the acetates 2e and 2f . 1a is transformed into methyl 4-azido-2, 6-bis[O(t-butyldimethylsilyl)]-4-deoxy-α-D-galactopyranoside ( 3 ) with triphenylphosphane/diethylazodicarboxylate/HN₃. 2a and 2c yield the 3-azido-allosides 5 and 7 respectively under similar conditions. The activation by triphenylphosphane/diethylazodicarboxylate is high enough to introduce also p-nitrobenzoate groups with inversion of configuration at the reaction center. By this way 1a and 2a give methyl 2, 6-bis[O(t-butyldimethylsilyl)]-4-O-p-nitrobenzoyl-α-D-galactopyranoside ( 4 ) and methyl 2, 6-bis[O-(t-butyldimethylsilyl)]-3-O?ptrobenzoyl-β-D-allopyranoside ( 6 ) respectively. For elucidation of structures the acetate derivatives 3a-7a were prepared.