Mineral?le

Ohne Zusammenfassung     

Dynamics of learning for the binary perceptron problem

A polynomial learning algorithm for a perceptron with binary bonds and random patterns is investigated within dynamic mean field theory. A discontinuous freezing transition is found at a temperature where the entropy is still positive. Critical slowing down is observed approaching this temperature from above. The fraction of errors resulting from this learning procedure is finite in the thermodynamic limit for all temperatures and all finite values of the number of patterns per bond. Monte-Carlo simulations on larger samples (N127) are in quantitative agreement. Simulations on smaller samples indicate a finite bound for the existence of perfect solutions in agreement with the replica theory and the zero entropy criterion. This suggests that perfect solutions exist also in larger samples but cannot be found with a polynomial procedure as expected for a combinatorial hard problem.     

Effect of geometrical and material imperfections on damping flexural vibrations in plates with attached wedges of power law profile

In the present paper, an efficient method of damping structural vibrations using the acoustic black hole effect is further investigated experimentally. This method is based on some specific properties of flexural wave propagation in tapered plates (wedges) of power-law profile that have to be partially covered by narrow thin strips of absorbing layers. Ideally, if the power-law exponent of the profile is equal or larger than two, the flexural wave never reaches the sharp edge and therefore never reflects back, which constitutes the acoustic black hole effect. It has been previously established theoretically and confirmed experimentally that this method of damping structural vibrations is very efficient even in the presence of edge truncations. The present work describes the results of the experimental studies of the effects of manufacturing intolerances on damping flexural vibrations in wedge-like structures of power-law profile. In particular, the effect of mechanical damage resulting from the use of cutting tools to wedge tips is investigated, including tip curling and early truncation, as well as the placement of absorbing layers on different wedge surfaces. Also, the effects of welded and glued bonding of wedge attachments to basic rectangular plates (strips) are investigated. The results show that, although the above-mentioned geometrical and material imperfections reduce the damping efficiency by varying degrees, the method of damping structural vibrations using the acoustic black hole effect is robust enough and can be used widely without the need of high precision manufacturing.     

PHOSPHORORGANISCHE VERBINDUNGEN 901

Abstract

Aus Allylamido-phosphoniumsalzen wird durch trockenes Tetrabutylammoniumcyanid in Methylenchlorid die Allylgruppe unter Erhaltung der Konfiguration und Bildung von Phosphinigsäureamiden abgespalten (P-C-Cyanolyse). Allyl-O-alkyl-phosphoniumsalze reagieren unter den oben genannten Bedingungen nach Arbusov, Allyl-S-alkyl-phosphoniumsalze aber unter Spaltung der P-S-Bindung ab. (P-S-Cyanolyse).

Das System: Tetrabutyl-ammoniumcyanid in Methylenchlorid kann ohne Nachteil für die Ausbeute durch KCN und katalytische Mengen 18-Krone-6 in Methylenchlorid ersetzt werden. Optisch aktives Benzyl-methyl-phenyl-phosphinsulfid kann auf diese Weise unter Erhaltung der Konfiguration desulfuriert werden.

Auch Dithiophosphinsäureester und Thiophosphinsäureamide werden nach vorausgehender S-Alkylierung (Überführung in die entsprechenden Quasiphosphoniumsalze) mit Tetrabutylammoniumcyanid unter Bildung von Thiophosphinigsäureestern bzw. Phosphinigsäureamiden desulfuriert. Thiophosphinsäure-O-alkylester R₂P(S)OR' liefern über diese Reaktionsfolge nach Arbusov Thiophosphinsäure-S-alkylester R₂P(O)SR′.

Die P-C-Cyanolyse von Allyltriphenyl-phosphoniumbromid mit KCN/18-Krone-6 oder Tetrabutyl-ammoniumcyanid bleibt im aprotischen Medium auf der rotgefärbten Ylidstufe stehen. Erst nach Zugabe eines Protonendonators läuft die Isomerisierung zum Propenyl-phosphoniumsalz ab.

Treatment of allylamido-phosphorlum salts with dry tetrabutylammonium cyanide in methylenechloride delivers after removal of the allyl group phosphinous acid amides with retention of configuration (P-C-cyanolysis).

Allyl-O-alkylphosphonium salts undergo the Arbusov reaction under the above conditions, while allyl-S-alkyl phosphonium salts undergo fission of the P[sbnd]S bond (P-S cyanolysis).

Equally good results were obtained using KCN in methylene chloride accompanied by catalytic amounts of 18-crown-6 ether; thus optically active benzyl-methyl-phenyl-phosphine-sulfid gave the corresponding phosphine with retention of configuration.

Dithiophosphinic acid esters and thiophosphinic acid amides, after conversion to the corresponding quasiphosphonium salts via S-alkylation and subsequent treatment with tetrabutylammonium cyanide in methylenechloride, also give the corresponding thiophosphinous acid ester and phosphinous acid amide respectively. Thiophosphinic acid O-alkyl esters (R₂P(S)OR′) give however the thiophosphinic S-alkyl ester (R₂P(O)SR′) via an Arbusov reaction.

The P-C cyanolysis of allyl-triphenylphosphoniumbromide using KCN/18-crown-6 or tetrabutylammonium cyanide in aprotic medium stops at the stage of the intermediary red-coloured ylide; addition of a proton-donor then results in the subsequent rearrangement to the corresponding propenyl-phosphonium salt.     

PHOSPHORORGANISCHE VERBINDUNGEN 88.1 OPTISCH AKTIVE PHOSPHINIGSÄUREAMIDE DARSTELLUNG,EIGENSCHAFTEN UND ABSOLUTE KONFIGURATION

Abstract

Optisch aktive Amidophosphoniumsalze, z.B. (7a) und (7b), werden elektroreduktiv unter Retention in die bisher unbekannten Phosphinigsäureamide (4a) und (4b) überführt. Die absolute Konfiguration von (4a) und (4b) wird durch chemische Korrelation mit Verbindungen bekannter absoluter Konfiguration ermittelt. Durch Umsetzung von optisch aktivem (4b) mit Trifluoressigsäure-p-kresylester erhält man unter Retention Ethyl-phenyl-phosphinigsäure p-kresylester (13).

Optically active amidophosphonium salts (e.g. 7a, 7b) may be electrochemically reduced with retention of configuration at phosphorus to the corresponding phosphinous acid amides (4a, 4b), previously unreported compounds. The absolute configuration were deduced through further chemical reaction under known stereochemical control to products of defined absolute configuration. Reaction of optically active (4b) with para-cresyl trifluoroacetate gives the ethyl–phenyl phosphinous acid para-cresyl ester (13) under retention of configuration.