Complete Intersection Problems for Finite Permutations

We find the maximal number of permutations on a set of n elements such that any pair of permutations has at least t common cycles.     

Shift operators contained in contractions, pseudocontinuable Schur functions and orthogonal systems on the unit circle

The main aim of this paper is to establish the connection between well-known criteria for the pseudocontinuability of a non-inner Schur function ?? in the unit disk (see Theorems 3.9, 4.2). In a canonical way we associate a probability measure ?? on the unit circle with ??. One of the two criteria will be reformulated in the face of ??, whereas the other one is drafted in view of a completely nonunitary contraction T having ?? as corresponding characteristic function. Our main result clarifies an immediate connection between the above-mentioned two criteria. In this way, we rewrite these criteria in terms of orthogonal systems with respect to the measure ?? (see Theorem 7.2).     

Probability representation and state-extended uncertainty relations

The new inequality recently found by Trifonov and called the state-extended inequality is considered in the tomographic-probability representation of quantum mechanics. The Trifonov uncertainty relations are expressed in terms of optical tomograms and can be checked in experiments on homodyne detection of the photon states.     

A convenient approach towards boron cluster modifications with adenosine and 2′-deoxyadenosine

New 2′-deoxyadenosine and adenosoine modifications: 8-[(2-dimethylaminoethyl)amino]-2′-deoxyadenosine and 8-[(2-dimethylaminoethyl)amino]adenosine were prepared and their reactivity towards cyclic oxonium adducts of closo-dodecaborate and cobalt-bis-dicarbollide was studied. The cleavage reactions of clusters oxonium rings by N,N-dimethylanio group of modified nucleosides led to the first [B₁₂H₁₂]²⁻ and new [Co(C₂B₉H₁₁)₂]⁻ conjugates with adenosine and 2′-deoxyadenosine respectively. The proposed methodology provides a convenient route for the synthesis of libraries of boron cluster modified adenosine and 2′-deoxyadenosine derivatives for biological screening.     

Monitoring of tropospheric ozone in the ambient air with passive samplers

Two sampling campaigns in suburban places in the north zone of Santa Clara city, Cuba, have been carried out on a weekly base with the use of Radiello passive diffusion tubes in order to monitor the tropospheric ozone (O₃) levels in 2010. The first campaign was scheduled from February to April (cold season) and the second one in August and October (warm season), both of them at two sampling sites, i.e., Farm and School of Art Instructors. After aqueous extraction, the samples were analyzed by UV–VIS spectrophotometry.A seasonal trend was observed with the maximum O₃ concentrations in the cold season and the minimum levels in the warm season. Samples collected during the cold season showed the highest O₃ levels. Higher levels were reached at the Farm site with average values of about 58 ± 12 μg/m³, which exceeded the limit of the Cuban Standard 99:1999. In the warm season, the O₃ concentrations were similar for both sites, but lower than those observed in the cold season. The overall, seasonal average value was found to be 24 μg/m³. Despite the higher weekly average temperatures in August, the O₃ concentrations during this month showed the lowest values of the whole sampling period, which finding is in agreement with that reported by the Meteorological Institute of Cuba.Mathematical models, based on the Cochrane-Orcutt algorithm, were fitted to the acquired data set to explain the change in the tropospheric ozone concentrations under various meteorological conditions during the two campaigns. The correlation coefficients for both the cold and the warm seasons demonstrated a strong correlation, i.e., 0.779 and 0.951, respectively. The high correlation of wind speed in the model from the first sampling campaign explains the sharp decrease in O₃ concentrations at the SAI sampling site from the sixth week of sampling.     

Highly diastereoselective synthesis of new heterolignan-like 6,7-methylendioxy-tetrahydroquinolines using the clove bud essential oil as raw material

The diastereoselective synthesis toward novel heterolignan-like 2-aryl-4-(4-hydroxy-3-methoxyphenyl)-6,7-methylendioxy-1,2,3,4-tetrahydroquinolines using for the first time clove bud essential oil as a renewable material was carried out. The synthetic protocol consisted of the hydrodistillation of dried flower buds, the solid base-catalyzed isomerization of the obtained essential oil enriched with eugenol in order to give isoeugenol and its participation, as a chemical reagent (dienophile) in the BF₃·OEt₂-catalyzed three component Povarov reaction, without previous purification. Final products were obtained as racemic mixtures of new trans-2,4-diaryl-r-3-Me-1,2,3,4-tetrahydroquinolines in moderate to good yields.     

Enumeration of substitutional isomers with restrictive mutual positions of ligands: I. Overall counts

We address systematics for the enumeration of substitutional isomers when there is constrained positioning of ligands on a molecular skeleton. One constraint involves ‘restrictive ligands’ where two of the same kind are forbidden to occupy adjacent sites in a molecular skeleton. This may arise because of steric hindrance, or because of groups which in neighbor proximity react to eliminate one. For instance, no pair of –OH groups attach to the same C atom in a molecular skeleton. In another case, malonic acid residues decarboxylate leaving no more than one decarboxylation in each residue. The enumeration with such restrictive ligands may be addressed via a Polya-theoretic cycle index hybridized with the graph-theoretic independence polynomial (when there is just a single such neighbor-excluding ligand and another which is not), while more generally a hybridization with the chromatic polynomial is needed. Another substitional-isomer constraint involves bidentate ligands, with each ligand-part occupying adjacent sites, and possibly also with additional separate unidentate ligands. Here, the set of all pure & mixed such ligand placements is analytically represented by a ‘symmetry-reduced’ matching polynomial (which is a hybrid now of the matching polynomial and Polya’s cycle index). This result gives the generating function for isomer enumeration, taking into account every possible so-restricted assortment of the employed ligands. Here we make such novel hybridizations (for these and other graphtheoretic polynomials) to deal with such oft-encountered chemical problems, which nevertheless transcend typical earlier unconstrained formulizations. Further subsymmetry classification & enumerations, along with examples are considered in a further article.     

Synthesis and Spatial Structure of the Derivatives of 2,5-Dioxo-3,3-Bis(Trifluoromethyl)-6,7-Benzo-1,4,2-and 2,5-Dioxo-4,4-Bis(Trifluoromethyl)-6,7-Benzo-1,3,2-Oxazaphosphepines

Abstract

Hexafluoroacetone imine easily interacts with compounds (I, R = OMe, OCH₂CF₂CHF₂, NEt₂, Ph) in two directions unlike hexafluoroacttone and gives 1,4,2-oxazaphosphepines (II) (pathway I) or 1,3,2-oxszaphosphepines (III) (pathway 2). The compound (II) (R = NEt₂) lightly hydrolyzes to yield the salt (IV). The structure of heterocycles II-IV) has been confirmed by X-ray analysis (see fig. I, II, R = OMe; fig. 2, IV). The detail structural peculiarities of the compounds am discussed.