Unavoidable Traces Of Set Systems

Sauer, Shelah, Vapnik and Chervonenkis proved that if a set system on n vertices contains many sets, then the set system has full trace on a large set. Although the restriction on the size of the groundset cannot be lifted, Frankl and Pach found a trace structure that is guaranteed to occur in uniform set systems even if we do not bound the size of the groundset. In this note we shall give three sequences of structures such that every set system consisting of sufficiently many sets contains at least one of these structures with many sets.     

Moments of an exponential functional of random walks and permutations with given descent sets

The exponential functional of simple, symmetric random walks with negative drift is an infinite polynomial Y = 1 + ξ₁ + ξ₁ξ₂ + ξ₁ξ₂ξ₃ + ⋯ of independent and identically distributed non-negative random variables. It has moments that are rational functions of the variables μ _k = E(ξ ^k ) < 1 with universal coefficients. It turns out that such a coefficient is equal to the number of permutations with descent set defined by the multiindex of the coefficient. A recursion enumerates all numbers of permutations with given descent sets in the form of a Pascal-type triangle. This revised version was published online in August 2006 with corrections to the Cover Date.     

Synthesis of paramagnetic BODIPY dyes as new double (spin and fluorescence) sensors

Paramagnetic pyrroline and 1,2,3,6-tetrahydropyridine derivatives of BODIPY and their diamagnetic analogs have been synthesized and characterized as novel redox double sensor and cation sensitive reagents.     

Synthesis,properties, and crystal structure of a novel 3-hydroxy-(4<Emphasis Type="Italic">H</Emphasis>)-benzopyran-4-one containing copper(II) complex,and its oxygenation and relevance to quercetinase

The preparation, spectroscopic properties, and crystal structure of [Cu(ind)(mco)] [ind is the anion of 1,3-bis(2-pyridylimino)isoindoline and mco is the anion of 3-hydroxy-(4H)-benzopyran-4-one] are reported. The complex exhibits a distorted square pyramidal geometry. The oxygenation of the title compound results in oxidative cleavage of the heterocyclic ring to give the (acetylsalicylato)copper(II) complex [Cu(asp)(ind)] (asp is the anion of acetylsalicylic acid) and CO as primary products, which reaction resembles the enzymatic reaction of quercetinase.     

Weighted approximation of functions on the real line by Bernstein polynomials

The authors give error estimates, a Voronovskaya-type relation, strong converse results and saturation for the weighted approximation of functions on the real line with Freud weights by Bernstein-type operators.     

Evaluation of cyclodextrin polymer as a disintegrating agent

Cyclodextrin polymer was compared to other well known disintegrants concerning the swelling properties /water uptake, moisture uptake, hydration capacity, sedimentation volume in water/. Its high disintegrating effect was proved in directly compressed tablets as well as in tablets made by wet granulation. A remarkable improvement in tablet properties was observed. Not only the disintegration of tablets and the dissolution of the drug was accelerated but also the hardness increased when CDP was used as disintegrant.     

In situ enzymatic digestion of oligopeptides on a direct insertion probe tip combined with fast atom bombardment and tandem mass spectrometry

The applicability of an approach to establish the sequence of oligopeptides involving on-probe-tip enzymatic fragmentation and subsequent direct fast atom bombardment (FAB) mass spectrometry (MS) and FAB-MS/MS of the subpeptide mixture was tested using two model peptides consisting of 19 and 25 amino acid residues. The method was found to be both time and sample sparing and flexible enough to use even subsequent digests, if necessary, with enzymes of different specificity. It provided in both cases complete information, not only for the sequence of enzymic fragments but also for their order in the original oligopeptide. Consequently, this approach to the sequence analysis of oligopeptides can be a method of choice when the FAB-MS/MS technique itself is unsuitable for obtaining detailed structural information. The method seems to be applicable to enzymically digestible peptides with an upper mass limit of about 3500.     

Mass spectrometric studies on azidomorphine derivatives

The mass spectrometric behaviour of nine azidomorphine derivatives have been studied. These compounds proved to have surprisingly specific and selective fragmentation under electron-impact. For 6-deoxy-6-azido-dihydro-isomorphine derivatives (I to V) the main decomposition pathway involves the loss of an N₂ molecule followed by a very rapid and selective fragmentation process. On the other hand, the molecular ions of 6-deoxy-8-azido-pseudomorphine derivatives (VI to VIII) and 6-deoxy-6-azido-14-hydroxy-isocodein (IX) primarily decompose by loss of the N₃ radical. This is due to the allylic effect of the double bond in ring C, corresponding to the chemical behaviour of these compounds.     

On triazoles. VII Synthesis of novel tri- and tetracyclic ring systems

The ring-closure of the 5-amino-1-(2-aminophenyl)-3-methylthio-1H-1,2,4-triazole derivatives 3 and 4 with different simple and cyclic C₁ components lead to the formation of 1,2,4-triazolo[1,5-α]-1,3,5-benzotriazepines 5–6 , their 4,5-dihydro- 7 , different 5-spiro-homocyclic- 8–13 , and 5-spiro-heterocyclic- 14-15 analogues. The structure of the compounds obtained was proved with the use of their ir, uv, ¹H-nmr and ¹³C-nmr spectra.