Conformal fields,restriction properties,degenerate representations and SLEChamps conformes,propriété de restriction,représentations dégénérées et SLE

We relate the Schramm–Loewner Evolution processes (SLE) to highest-weight representations of the Virasoro Algebra. The restriction properties of SLE that have been recently derived in [19] play a crucial role. In this setup, various considerations from conformal field theory can be interpreted and reformulated via SLE. This enables one to make a concrete link between the two-dimensional discrete critical systems from statistical physics and conformal field theory. To cite this article: R. Friedrich, W. Werner, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 947–952.     

Über die Identifizierung von Alkoholen mit 1-Chlormethyl-isatin

Monatshefte für Chemie - Chemical Monthly - Primary, secondary and tertiary aliphatic alcohols quickly react with 1-chloromethyl-isatin (1) to give good yields of alkoxymethylisatines4-novel...     

Synthesis and Structure Investigations of Potential Sedative and Anticonvulsant Hydroxy- and Acetoxy-N-(3-oxobutyl)-pyrido[2,3-d]pyridazinonesa

Summary.  Novel N-(3-oxobutyl)-hydroxy- and acetoxypyrido[2,3-d]pyridazinones were synthesized and tested in vivo for their sedative and anticonvulsant activity. The Michael-type reaction of quinolinic acid hydrazide and methyl vinyl ketone afforded a mixture of two isomers, 5-hydroxy-N ⁷-(3-oxobutyl)-pyrido[2,3-d]pyridazin-8(7H)-one and 8-hydroxy-N ⁶-(3-oxobutyl)-pyrido[2,3,-d]pyridazin-5-(6H)-one, in a ratio of 2:1 which were separated by crystallization. Subsequent acetylation of both isomers yielded the corresponding 5- and 8-acetoxy compounds. The structures of the compounds were proven and completely assigned on the basis of ¹H, ¹³C, ¹⁵N NMR, and 1D NOE difference spectra as well as 2D C,H-correlation experiments. Preliminary pharmacological tests showed low acute toxicity with a LD ₅₀ > 1000 mg/kg in the mouse and sedative activity for the title compounds. 5-Acetoxy-N ⁷- (3-oxobutyl)-pyrido[2,3-d]pyridazin-8(7H)-one displayed a borderline anticonvulsant activity in the metrazole test model. Corresponding author. E-mail: edith.goessnitzer@uni-graz.at Received March 20, 2002; accepted April 3, 2002     

Über die Reaktionen von Guanidin bzw. Thioharnstoff mit α,β,γ,δ-ungesättigten Ketonen

Guanidine and phenylguanidine react with phenylhexadienone1b and 1,5-diaryl-2,4-pentadien-1-ones1c–k respectively (via unstable dihydropyrimidines of type2 as intermediates) to 4-methyl- and 4-aryl-6-styryl-2-pyrimidinamines3b–j and N²-phenyl-2-pyrimidinamines7c, k. Efforts to stabilize the intermediates2 by introduction of electron-withdrawing substituents (compare^2,3) were not successful. Similarly, thiourea reacts with diphenylpentadienone1c to afford (via8c) 4-phenyl-6-phenethylpyrimidinethione9c. Action of guanidine on 1,3,5-triphenylpentadienone101 and on the 5-(3-chlorophenyl) analogue10m under decomposition of the ketones yields 4,6-diphenyl-and 4-(3-chlorophenyl)-6-phenyl-2-pyrimidineamine (121 andm), respectively. The formation of12m proves that acetophenone splits off from101,m during the reactions. However, heating of thiourea with10m in sodium butylate/butanol gives the expected 4,6-diphenyl-4-styryldihydropyrimidinethione13m. The reaction of thiourea with triphenylpentadienone101 is taking an atypical course: Addition of thiourea to the δ- and β-carbon atom of101 affords 2-(4,6-diphenyl-2-thioxohexahydro-4-pyrimidinyl)acetophenone (141); the conformation of the latter was deduced from¹H-NMR data.     

Über 4-Ureidooctahydropyrano[4,3-d]pyrimidinone

Zusammenfassung 5,6-Dihydro-2H-pyran-3-aldehyde reagieren mit Harnstoff zu 4-ureidooctahydropyrano[4,3-d]pyrimidin-2-ones. Einwirkung von Säure führt das 4-Ureidooctahydropyrano[4,3-d]pyrimidin-2-on in das 4-(2-Hydroxyäthyl)-hexahydropyrimido[4,5-d]pyrimidin-2,7-dion über.

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Heterocycles, XVIII: 4-Ureido-octahydropyrano[4,3-d]-pyrimidinones

5,6-Dihydro-2H-pyran-3-aldehydes react with urea to give 4-ureidooctahydropyrano[4,3-d]pyrimidin-2-ones. 4-Ureidooctahydropyrano[4,3-d]pyrimidin-2-one is cleaved by HCl to 4-(2-hydroxyethyl)-hexahydropyrimido[4,5-d]pyrimidin-2,7-dione.

     

Über Heterocyclen, 16. Mitt.: Über das 1,4-Dimethyl-3-acetoxy-7-acetamido-2-oxabicyclo [2,2,1]heptan

Zusammenfassung 3,4-Dihydro-2H-pyran-2-aldehyd bzw. 2,5-Dimethyl-3,4-dihydro-2H-pyran-2-aldehyd reagieren mit Acetamid bzw. Harnstoffen zu Pyranylmethylenbisamiden bzw.-bisureiden. Die Dimethylpyranaldehydaminale werden durch Essigsäureanhydrid zum 1,4-Dimethyl-3-acetoxy-7-acetamido-2-oxabicyclo[2,2,1]-heptan umgewandelt. Die Struktur dieser Verbindung wird bewiesen.

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3,4-Dihydro-2H-pyran-2-aldehyde and 2,5-dimethyl-3,4-dihydro-2H-pyran-2-aldehyde, resp. react with acetamide or ureas to give pyranylmethylenebisamides and-bisureides. The dimethylpyranaldehydeaminals are converted by acetic anhydride to 1,4-dimethyl-3-acetoxy-7-acetamido-2-oxabicyclo[2.2.1]-heptane. The structure of this compound has been proved by chemical and physical methods.

     

On the occupation times of cones by Brownian motion

Summary We study some features concerning the occupation timeA _t of a d-dimensional coneC by Brownian motion. In particular, in the case whereC is convex, we investigate the asymptotic behaviour ofP(A₁u0, when the Brownian motion starts at the vertex ofC. We also give the precise integral test, which decides whether a.s., lim inf _t A _t/(tf(t))=0 or for a decreasing functionf.     

Über die Reaktionen von Guanidin bzw. Harnstoff mit Cyanhydrinen

Action of guanidine or urea on cyclohexanone-, cyclopentanone-, cycloheptanone-and acetonecyanohydrine3 a?3 d generates very different products: 3 a reacts with guanidine inDMF to yield 1,3-diazaspiro[4.5]decane-2,4-diimine (5 a). Heating the components without solvent affords 7,14-diazadispiro[5.1.5.2]pentadecan-15-one(7)^15–17, the guanidine not participating in the reaction; similarly3 b is transformed by guanidine to a pentacyclic dispirocompound (possible formulae19 and20), whereas3 d reacts to give 3,3,5,5-tetramethylpiperazine-2,6-dione(21)¹⁹. In 3-pentanone guanidine-cyanide condensates itself to give 2,4-diamino-triazine (22)^{21, 22}. Action of urea on3 a?3 d yields the 4-imino-1,3-diazaspiroalkan-2-ones6 a?6 c and the 4-imino-5,5-dimethylimidazolidin-2-one6 d ^6–8 resp. If the reaction of urea and3 d is carried out inDMF, however, 5,5-dimethyl-4-ureido-3-imidazolin-2-one (28) (or the tautomeric carbamoyliminoimidazolidinone27) is produced. The structures of the compounds prepared are proved by NMR-, IR- and mass spectra.     

Über substituierte 1,6-Dihydro-1,3,5-triazin-2,4-diamine, 1′,5′,6′,7′-Tetrahydrospiro[cyclopentan-1,4′-cyclopentapyrimidin]-2′(3′ H)-imine und das 6-Phenyl-2,4-pyrimidindiamin

Guanidine reacts with cyclohexanone, cycloheptanone, acetone and 3-pentanone, resp., in a molar ratio 2∶1 to give the 1,3,5-triazaspiro[5.5]undeca-and [5.6]dodeca-1,3-dien-2,4-diamines3 a and3 b resp. and the 6,6-dimethylresp. diethyl-1,6-dihydro-1,3,5-triazin-2,4-diamines3 d and3 e resp. On the contrary, action of guanidine on cyclopentanone yields not3 c, but the 1′,5′,7′-tetrahydrospiro[cyclopentane-1,4′-cyclopentapyrimidine]-2′(3′H)-imines2 c, 5 c and6 c resp., which are 1∶2- and 1∶3-condensates. Phenylacetone is transformed by guanidine (1∶2) to give 6-phenyl-2,4-pyrimidindiamine (8 f). The structure of the compounds cited is proved by NMR-, IR-, and (partially) mass spectra. The different courses of the formation of3 a, b, d, e, 2 c, 5 c and6 c resp. and8 f are also discussed. The structural formulae of some additional bases, which were synthesized from guanidine and cyclopentanone, 3-pentanone and phenylacetone resp. could not be established.