Crystal structures of the novel hydrated borates Ba2B5O9(OH), Sr2B5O9(OH) and Li2Sr8B22O41(OH)2

Three novel hydrated borates Ba₂B₅O₉(OH) (1), Sr₂B₅O₉(OH) (2) and Li₂Sr₈B₂₂O₄₁(OH)₂ (3) have been synthesized hydrothermally and their structures determined. Compounds (1) and (2) are isostructural, crystallizing in space group P2₁/c and having lattice parameters of a=6.6330(13) Å, b=8.6250(17) Å, c=14.680(3) Å, β=93.46(3)° and a=6.4970(13) Å, b=8.4180(17) Å, c=14.177(3) Å, β=94.35(3)°, respectively. Compound (3) crystallizes in P-1 with lattice parameters of a=6.4684(13) Å, b=8.4513(17) Å, c=14.881(3) Å, α=101.21(3)°, β=93.96(3)°, γ=90.67(3)°. While similar in their axis lengths, (3) differs greatly in structure and formulation from (1) and (2). The structure of (1) and (2) is contrasted to that of the well-known mineral hilgardite (Ca₂B₅O₉Cl·H₂O).     

A tension approach to controlling the shape of cubic spline surfaces on FVS triangulations

We propose a parametric tensioned version of the FVS macro-element to control the shape of the composite surface and remove artificial oscillations, bumps and other undesired behaviour. In particular, this approach is applied to C¹ cubic spline surfaces over a four-directional mesh produced by two-stage scattered data fitting methods.     

Euler's partition theorem and the combinatorics of ℓ-sequences

Euler's partition theorem states that the number of partitions of an integer N into odd parts is equal to the number of partitions of N in which the ratio of successive parts is greater than 1. It was shown by Bousquet-Mélou and Eriksson in [M. Bousquet-Mélou, K. Eriksson, Lecture hall partitions II, Ramanujan J. 1 (2) (1997) 165–185] that a similar result holds when “odd parts” is replaced by “parts that are sums of successive terms of an ℓ-sequence” and the ratio “1” is replaced by a root of the characteristic polynomial of the ℓ-sequence. This generalization of Euler's theorem is intrinsically different from the many others that have appeared, as it involves a family of partitions constrained by the ratio of successive parts.In this paper, we provide a surprisingly simple bijection for this result, a question suggested by Richard Stanley. In fact, we give a parametrized family of bijections, that include, as special cases, Sylvester's bijection and a bijection for the lecture hall theorem. We introduce Sylvester diagrams as a way to visualize these bijections and deduce their properties.In proving the bijections, we uncover the intrinsic role played by the combinatorics of ℓ-sequences and use this structure to give a combinatorial characterization of the partitions defined by the ratio constraint. Several open questions suggested by this work are described.     

Strong convergence rates for the estimation of a covariance operator for associated samples

Let X _n , n ≥ 1, be a strictly stationary associated sequence of random variables, with common continuous distribution function F. Using histogram type estimators we consider the estimation of the two-dimensional distribution function of (X ₁,X _k+1) as well as the estimation of the covariance function of the limit empirical process induced by the sequence X _n , n ≥ 1. Assuming a convenient decrease rate of the covariances Cov(X ₁,X _n+1), n ≥ 1, we derive uniform strong convergence rates for these estimators. The condition on the covariance structure of the variables is satisfied either if Cov(X ₁,X _n+1) decreases polynomially or if it decreases geometrically, but as we could expect, under the latter condition we are able to establish faster convergence rates. For the two-dimensional distribution function the rate of convergence derived under a geometrical decrease of the covariances is close to the optimal rate for independent samples.      

Novel Bisphosphonates Derived from 1H‐Indazole, 1H‐Pyrazolo[3,4‐b]Pyridine,and 1H‐Pyrazolo[3,4‐b]Quinoline

Novel tetraethyl ethylene‐1,1‐bisphosphonate esters derived from 1H‐indazole, 1H‐pyrazolo[3,4‐b]pyridine, and 1H‐pyrazolo[3,4‐b]quinoline were synthesized by a Michael addition reaction of tetraethyl ethylidene‐1,1‐bisphosphonate with the corresponding heterocycle, using conventional heating and microwave‐assisted methods. The microwave‐assisted method provides shorter reaction times and better yields. The hydrolysis of bisphosphonates afforded the corresponding bisphosphonic acids or salt, using concentrated hydrochloric acid or TMSBr/collidine, respectively. All new compounds were fully characterized, and their structures were assigned using ¹H, ³¹P, and ¹³C NMR and IR spectroscopies and mass spectrometry. The molecular structure of compound 6 was confirmed by X‐ray diffraction studies.     

Characterization of Gasoline by 1H Nuclear Magnetic Resonance and Chemometrics

Automotive fuel adulteration is an old and significant problem. One common type of fuel adulteration is the addition of diesel to gasoline. Unsupervised models were developed through hierarchical cluster and principal component analysis models. Supervised models through partial least square discriminant analysis using ¹H nuclear magnetic resonance spectra as the input were used to classify samples as adulterated or unadulterated. Quantitative models were developed using partial least squares to determine the gasoline and diesel concentrations in the samples. This set contained samples composed of pure gasoline and anhydrous ethanol reproducing commercial gasoline and other samples treated with diesel. Hierarchical cluster and principal component analysis did not distinguish between adulterated and unadulterated samples except for the most adulterated materials. However, partial least square discriminant analysis classified 100% of the samples correctly. The partial least square algorithm provided excellent regression models for the gasoline and diesel content. The determination coefficient was 0.9920 for both models, whereas the root mean square error of cross-validation and root mean square error of prediction for the diesel model were 2.32 and 1.42%, respectively, and 2.40 and 1.38% for the gasoline model.     

Effects of potassium on the supramolecular structure and electronic properties of eumelanin thin films

The role of potassium in the formation of synthetic eumelanin aggregates is investigated by atomic force microscopy and soft-X-ray spectroscopy. Control over the thin film granularity is achieved by using K salts, in both drop casting and electrodeposition of eumelanin thin films. Further control over orientation is made possible by a suitable choice of the substrate: evidence of self-assembly is found for thin films deposited on gold. Finally, it is shown that the potassium content affects not only the samples morphology, but also the low-lying states in the valence band, where a transfer of spectral weight across the HOMO-LUMO gap is observed, disclosing possible applications of this multifunctional biomacromolecule.     

FTIR microspectroscopy of melanocytic skin lesions: a preliminary study

Fourier transform infrared (FTIR) microspectroscopy has been employed to investigate benign (ordinary dermal and Reed nevi), dysplastic and malignant (invasive melanoma) skin lesions through the analysis of spectral changes of melanocytes as well as in the evaluation of the presence of melanin. Hierarchical cluster analysis and principal component analysis led to a satisfactory separation of malignant from dysplastic and normal melanocytes. Also, on enlarging the clustering with spectra from Reed and dermal nevi, the multivariate analysis segregated well the spectral data into discrete clusters, allowing the obtaining of reliable average spectra for analysis at the molecular level of the main groups or components responsible for the biological and biochemical changes. The most significant spectral characteristics appear to be related to differences in secondary protein structures, in nucleic acid conformation, in intra- and intermolecular bonding. In all cases, supervised and unsupervised spectral analyses resulted in satisfactory agreement with histopathological findings.     

Separation of cis/trans geometrical fatty acid isomers by silver-exchanged zeolite Y

The separation of cis and trans isomers is relevant for biological and nutritional applications, silver-exchanged zeolite Y was prepared and applied for the treatment of mixtures of cis and trans geometrical isomers of mono- and polyunsaturated fatty acid methyl esters (FAMEs). cis FAMEs were adsorbed into zeolite with a high degree of selectivity (cis/trans ratio in the range of 1.9-3.2). The effectiveness was due to the synergism of the π-complexation between the silver ion and the double bonds and the different FAME structures trapped into the zeolite cages. Some indication of the complex stabilities came from theoretical studies using unsaturated lipids. A prototype cartridge was also designed for application in the fractionation of cis/trans FAME mixtures.