Uranium assay and trace element analysis of the fourth collaborative material exercise samples by the modified Davies-Gray method and the ICP-MS/OES techniques

Journal of Radioanalytical and Nuclear Chemistry - An international group of laboratories participating in CMX-4 subjected three samples to comparative nuclear forensic analysis using uranium assay...     

Synthesis and application of monoterpene-based chiral aminodiols

Primary, secondary and tertiary aminodiols were synthetized regio- and stereoselectively from (−)-α-pinene 1 via α-pinene oxide 2, (−)-trans-pinocarveol 3 and key intermediate epoxy alcohol 4. N-Benzyl derivative 5 was transformed to spiro-fused oxazolidine 13 in a highly regioselective ring closure. Aminodiols and their derivatives 5-13 were applied as chiral catalysts in the enantioselective addition of diethylzinc to benzaldehyde, resulting in chiral 1-phenyl-1-propanol. The substituent effect on the nitrogen was studied in detail and the best enantioselectivity was observed in the case of N-methyl-N-benzyl-substituted derivative 8. The phenomenon was interpreted by using molecular modelling at an ab initio level.     

Uniform Mixed Hypergraphs: The Possible Numbers of Colors

For a mixed hypergraph , where and are set systems over the vertex set X, a coloring is a partition of X into ‘color classes’ such that every meets some class in more than one vertex, and every has a nonempty intersection with at least two classes. The feasible set of , denoted , is the set of integers k such that admits a coloring with precisely k nonempty color classes. It was proved by Jiang et al. [Graphs and Combinatorics 18 (2002), 309–318] that a set S of natural numbers is the feasible set of some mixed hypergraph if and only if either or S is an ‘interval’ for some integer k ≥ 1. In this note we consider r-uniform mixed hypergraphs, i.e. those with |C| = |D| = r for all and all , r ≥ 3. We prove that S is the feasible set of some r-uniform mixed hypergraph with at least one edge if and only if either for some natural number k ≥ r − 1, or S is of the form where S′′ is any (possibly empty) subset of and S′ is either the empty set or {r − 1} or an ‘interval’ {k, k + 1, ..., r − 1} for some k, 2 ≤ k ≤ r − 2. We also prove that all these feasible sets can be obtained under the restriction , i.e. within the class of ‘bi-hypergraphs’. Research supported in part by the Hungarian Scientific Research Fund, OTKA grant T-049613.     

Upper chromatic number of finite projective planes

For a finite projective plane , let denote the maximum number of classes in a partition of the point set, such that each line has at least two points in the same partition class. We prove that the best possible general estimate in terms of the order of projective planes is , which is tight apart from a multiplicative constant in the third term :

• (1) As holds for every projective plane of order q.
• (2) If q is a square, then the Galois plane of order q satisfies .

Our results asymptotically solve a ten‐year‐old open problem in the coloring theory of mixed hypergraphs, where is termed the upper chromatic number of . Further improvements on the upper bound (1) are presented for Galois planes and their subclasses. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 221–230, 2008     

Synthesis and Characterization of GaIII,YIII, and LuIII Complexes with Etifenin and Analogues

Complexes of etifenin ( 1a ), disofenin ( 1b ), and mebrofenin ( 1c ) with Ga^III, Y^III, and Lu^III were synthesized and characterized by NMR spectroscopy and UV/Vis spectroscopy. Stability and protonation constants of the complexes of 1a were determined by potentiometry and distribution diagrams were calculated. It was shown that the Y^III and Lu^III species are most stable as bis chelates at higher pH, whereas the Ga^III complex degrades at pH < 4.5.     

On a normed version of a Rogers–Shephard type problem

A translation body of a convex body is the convex hull of two of its translates intersecting each other. In the 1950s, Rogers and Shephard found the extremal values, over the family of n-dimensional convex bodies, of the maximal volume of the translation bodies of a given convex body. In our paper, we introduce a normed version of this problem, and for the planar case, determine the corresponding quantities for the four types of volumes regularly used in the literature: Busemann, Holmes–Thompson, and Gromov’s mass and mass*. We examine the problem also for higher dimensions, and for centrally symmetric convex bodies.     

An improved colorimetric method for chlorine dioxide and chlorite ion in drinking water using lissamine green B and horseradish peroxidase

Lissamine Green B (LGB) was carefully selected as a potential candidate for the development of a new U.S. Environmental Protection Agency (EPA) method that is intended for use at water utilities to determine chlorine dioxide (ClO₂) in drinking water. Chlorine dioxide reacts with LGB in aqueous solution to decrease the absorbance of LGB in direct proportion to the ClO₂ concentration. LGB was confirmed to have adequate sensitivity, and to suffer less interference than other dyes reported in the literature. The stoichiometry for the reaction between LGB and ClO₂ was found not to be 1:1 and is dependent on the LGB concentration. This required calibration of each LGB stock solution and prompted the investigation of alternate means of calibration, which utilized a horseradish peroxidase (HRP)-catalyzed conversion of chlorite ion (ClO₂⁻) to ClO₂. This approach allowed the simultaneous determination of ClO₂⁻ concentration, which is also required each day at water plants that use ClO₂. Studies were conducted to characterize and carefully optimize the HRP-conversion of ClO₂⁻ to ClO₂ in order to yield reaction conditions that could be accomplished in less than 30 min at modest cost, yet meet EPA's sensitivity and robustness requirements for routine monitoring. An assessment of method detection limit, linearity and slope (or sensitivity), precision, and accuracy in finished drinking water matrices indicated that this approach was suitable for publication as EPA Method 327.0.     

Smart nanocomposite polymer gels

The combination of polymers with nanomaterials displays novel and often enhanced properties compared to the traditional materials. They can open up possibilities for new technological applications. The magnetic polymer gel represents a new type of composites consisting of small magnetic particles, usually from the nanometer range to the micron range, dispersed in a highly elastic polymeric gel matrix. Combination of magnetic and elastic properties leads to a number of striking phenomena that are exhibited in response to impressed magnetic fields. Giant deformational effects, high elasticity, anisotropic properties, temporary reinforcement and quick response to magnetic field open new opportunities for using such materials for various applications.     

Adoption of the Numerical Method of Chebyshev Polynomials to the Stability Analysis of Delayed DEs

We propose a new way of the application of the numerical method based on Chebyshev approximation concerning the stability analysis of (periodic) delay‐differential equations. The technique is tested on the delayed Mathieu equation.