Spectral Order Automorphisms of the Spaces of Hilbert Space Effects and Observables

We describe the general form of bijective maps on the space of all Hilbert space effects or all observables on a finite dimensional space which preserve the spectral order in both directions. The first author was supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. T043080, T046203, and the second author was partially supported by a grant from the Ministry of Science of Slovenia. Both authors were supported by a joint Hungarian-Slovene grant, Reg. No. SLO-5/05.     

On an identity of Ramanujan over finitely generated domains

Summary We show that a well-known identity of Ramanujan admits only a bounded number of solutions over general finitely generated domains. The bound is explicit and uniform in the sense that it depends only on the dimensions of the domains involved. Our method is constructive, and opens up a possibility to determine the solutions in concrete instances. In some special cases all solutions are determined. Our results can also be considered as a continuation of some theorems of Z. Daróczy and G. Hajdu, obtained over Z. We note that in case of Hosszú's equation, similar results were obtained by several authors.     

Sticks and clubs

We study combinatorial principles known as stick and club. Several variants of these principles and cardinal invariants connected to them are also considered. We introduce a new kind of side by-side product of partial orderings which we call pseudo-product. Using such products, we give several generic extensions where some of these principles hold together with ¬CH and Martin's axiom for countable p.o.-sets. An iterative version of the pseudo-product is used under an inaccessible cardinal to show the consistency of the club principle for every stationary subset of limits of ω₁ together with ¬CH and Martin's axiom for countable p.o.-sets.     

Asymptotics for Lp-norms of Fourier series density estimators

LetX ₁, X₂, , be a sequence of independent, identically distributed bounded random variables with a smooth density functionf. We prove that is asymptotically normal, wheref _{m, n} is the Fourier series density estimator offandw is a nonnegative weight function.Communicated by Edward B. Saff.AMS classification: Primary 60F05, 60F25; Secondary 62G05.     

Solubility characteristics ofβ-cyclodextrin inclusion complexes

Some inclusion complexes of-cyclodextrin (cyclomaltoheptaose) have been investigated, particularly with respect to their solubility. The mathematical characterization of the equilibrated host-guest system containing both solid and solution phases is discussed (first of all those, which contain 1:1 or 1:1 + 2:1 species) and demonstrated by different examples.     

Some anomalous reactions of 4-quinolone-5-diazonium salts

Diazotisation of the 5-amino function in 6,7-alkoxy-l-ethyl-l,4-dihydro-4-oxoquinoline-3-carboxylic acids led to various products. Dediazoniation was always accompanied by fission of the 6-alkoxy substituent; 6,7-methylenedioxy groups gave formaldehyde which could form a m-dioxino ring. Hydrolysis of the diazonium chlorides resulted in halo-dediazoniation.     

Synthèses dans la série des bis-indéno-fluorènes,VI [1] Dihydro-12, 15–6H-bis-indéno[1. 2-b; 2′.1′-h]fluorène et dihydro-14, 15–8H-bis-indéno[2. 1-a; 2′. 1′-h]fluoréne

Starting from cyclohexene and 2, 2′, 5, 5′-tetramethylbiphenyl the linear bisindenofluorene 12, 15-dihydro-6H-diindeno [1.2-b; 2′.1′-h] fluorene (XX) has been synthesized in 5 steps (overall yield 27%). As an intermediate product the 6, 12, 15-trioxo-derivative XIX (greyish green crystals, blue alcaline vat) was obtained. By a side way, the 6-oxo-derivative of XX and the already known monoangular bis-indenofluorene 14, 15-dihydro-8H-diindeno [2.1-a; 2′.1′ -h] fluorene (XXVII) were also obtained. XX can also be prepared in several steps starting from 3-methyl-fluorene or fluorene.     

Synthesis of vinca alakaloids and realated compounds 98. Oxidation with dimethyldioxirane of compounds containing the aspidospermane and quebrachamine ring system. A simple synthesis of (7S,20S)‐(+)‐rhazidigenine and (2R,7S,20S)‐(+)‐rhazidine

The oxidation of (‐)‐tabersonine ( 1 ) with dimethyldioxirane (DMD) in neutral and acidic medium gave 16‐hydroxytabersonine‐N‐oxide ( 3 ) and the didehydrovincamine isomers 4 and 5 , respectively. (+)‐14,15‐Didehydro‐quebrachamine ( 7 ) furnished the hydroxyindolenine 9 , and the pentacyclic derivative 11 . (+)‐Quebrachamine ( 8 ) and DMD in neutral medium gave (7S,20S)‐(+)‐rhazidigenine ( 12 ) which was converted to (2R,7S,20S)‐(+)‐rhazidine ( 13b ) with hydrochloric acid.     

Stabilization and Solubilization of Lipophilic Natural Colorants with Cyclodextrins

The paper provides data on the practical utilization of the benefits of the molecular encapsulation of natural colorants by cyclodextrins. Experimental results on the stability of cyclodextrin complexed curcumin, curcuma oleoresin, -carotene and carotenoid oleoresins against light-, heat- and oxygen prove the benefits of molecular encapsulation of colorants. The parent -cyclodextrin stabilized most effectively the curcumines, while the stability of carotenoids was most effectively achieved by -cyclodextrin complexation. Methylated -cyclodextrin was found to be the most potent solubilizing agent for both carotenoids and curcuminoids.     

Uncommon Interactions of Aliphatic Dicarboxylic Acids with Cyclodextrins

A relatively high and unexpected increase of inclusion complex stabilities could be detected in some half dissociated dicarboxylic acids (HA⁻ ions) with intramolecular H-bonding. The intermolecular hydrogen bonds between the protruding functional groups of the guest and the hydroxy groups of the host are known to enhance the stability of the cyclodextrin (CD) inclusion complexes. The enhanced inclusion of HA⁻ species is promoted, not by the intermolecular but by the intramolecular H-bond indirectly, resulting in a compact shape of the guest with more favourable space filling.