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.     

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.     

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.     

Determination of N9/N7-isomer ratio of alkyl (guaninyl)acetates by electrospray ionization tandem mass spectrometry

N9- and N7-substituted (guaninyl)acetic esters were studied by electrospray ionization tandem mass spectrometry (ESI-MS/MS) in order to determine their ratio in alkylation reactions. The loss of ammonia is significantly different for the N9- and N7-alkylated guanine regioisomer pairs. More importantly, the abundance of the [MH-17]+ ion is in linear correlation with the N9-isomer content. Therefore, the ratio of regioisomers can be determined in a mixture containing these compounds.     

Emissions-spektralanalytische Methode zur Bestimmung des Spurenelementgehaltes in geringen Pulvermengen und Lösungen

Zusammenfassung Für die spektrographische und spektrometrische Bestimmung nicht leitender Stoffe wurde ein Elektrodensystem mit Kunststoffbindung entwickelt. In einem Konzentrationsbereich von 0,01–1,0% ließ sich damit der relative Fehler von 4–15% auf 0,5–4,0% herabsetzen. Die Selbstabsorption wird in erheblichem Ausmaß zurückgedrängt; demzufolge werden die Eichkurven in einem größeren Konzentrationsbereich linear.

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A method of emission spectrum analysis for determining the trace element content in small amounts of powder and solutions

Summary An electrode system with plastic binding was developed for spectrographic and spectrometric determination of non-conducting substances. In a concentration range of 0.01–1.0%, the relative error of 4–15% could thereby be reduced to 0.5–4.0%. The autoabsorption is suppressed to an appreciable extent; in consequence, the calibration curves become linear in a larger concentration range.

     

From Peptide Nucleic Acids to Supramolecular Structures of Nucleic Acid Derivatives

Nucleic acids play a pivotal role in life processes. The endeavours to shed light on the essential properties of these intriguing building blocks led us to the synthesis of different analogues and the investigation of their properties. First various peptide nucleic acid monomers and oligomers have been synthesized, using an Fmoc/acyl protecting group strategy, and their properties studied. The serendipitous discovery of a side reaction of coupling agents led us to the elaboration of a peptide sequencing method. The capricious behaviour of guanine derivatives spurred the determination of their substitution pattern using ¹³C, ¹⁵N NMR, and mass spectrometric methods. The properties of guanines initiated the logical transition to the study of supramolecular systems composed of purine analogues. Thus, xanthine and uracil derivatives have been obtained and their supramolecular self-assembly properties scrutinized in gas, solid, and liquid states and at solid-liquid interfaces.