New inequalities from classical Sturm theorems

Inequalities satisfied by the zeros of the solutions of second-order hypergeometric equations are derived through a systematic use of Liouville transformations together with the application of classical Sturm theorems. This systematic study allows us to improve previously known inequalities and to extend their range of validity as well as to discover inequalities which appear to be new. Among other properties obtained, Szegő's bounds on the zeros of Jacobi polynomials for , are completed with results for the rest of parameter values, Grosjean's inequality (J. Approx. Theory 50 (1987) 84) on the zeros of Legendre polynomials is shown to be valid for Jacobi polynomials with |β|1, bounds on ratios of consecutive zeros of Gauss and confluent hypergeometric functions are derived as well as an inequality involving the geometric mean of zeros of Bessel functions.     

A simple Markov chain structure for the evolution of credit ratings

We focus on continuous Markov chains as a model to describe the evolution of credit ratings. In this work it is checked whether a simple, tridiagonal type of generator provides a good approximation to a general one. Three different tridiagonal approximations are proposed and their performance is checked against two generators, corresponding to a volatile and a stable period, respectively. Copyright © 2007 John Wiley & Sons, Ltd.     

Studies on the metal-nuclotide (Co-5′IMP,Co-5′GMP) interaction via mössbauer emission spectroscopy and magnetic susceptibility measurements

By means of⁵⁷Co Mössbauer emission spectroscopy and magnetic susceptibility measurements, the local symmetries and electronic structure of the Co(II) ions in the Co-5IMO and Co-5GMP complexes in the hydrated and dehydrated forms have been determined.     

Mössbauer studies on one-dimensional iron phthalocyanines

Summary Magnetic moments and⁵⁷Fe Mössbauer spectra at room temperature and at liquid nitrogen temperature of polynuclear ligand-bridged iron phthalocyanines, FePcL (L = pyrazine and 4,4-bipyridyl), are reported. The experimental data are in agreement with a pseudo-octahedral environment around the iron(II) cation. Partially oxidized derivatives, FePc(pz)I_0.26 and FePc(bipy)I_1.06 have been synthesized and their⁵⁷Fe Mössbauer spectra and magnetic moments within the same temperature range obtained. Oxidation is shown to be metal centred and the iodine is found to be in I^– form for FePc(pz)_0.26 and as both I^– and I ₃ ^– species for FePc(bipy)I_1.06. While the magnetic moment of FePc(pz) increases upon oxidation, the opposite occurs for FePc(bipy).     

Microwave-assisted synthesis of bipyrazolyls and pyrazolyl-substituted pyrimidines

We describe the preparation of 1,4′-bipyrazolyls and 4-pyrazolylpyrimidines by the reaction of 2-pyrazolyl-3-dimethylamino acrylate and acrylonitrile with double nucleophilic reagents such as hydrazines, urea and guanidine. Reactions were performed under microwave irradiation in 5-60 min. This is a useful procedure for the preparation of valuable compounds with applications in medicinal and coordination chemistry.     

An Efficient and Simple Entry to N-Substituted beta-Enamino Acid Derivatives from 2-Alkyl-2-oxazolines and 2-Alkyl-2-thiazolines

Reaction of azaenolates of 2-alkyl-oxa(thia)zolines 6 with imidoyl chlorides 7 as electrophiles to furnish masked N-substituted beta-enamino acid derivatives 1-2 in 70-90% yield is described. Alternative routes are discussed. Compounds 1-2 generally appear in one tautomeric form, imino or enamino, depending on the nature of the imidoyl chloride. The configuration of the enamino moiety (Z) and the conformation (s-cis) of compounds 1-2 obtained were established by an NMR study and unequivocally set by nuclear Overhauser effect difference experiments. An X-ray structure of compound 1e is also reported, showing a strong intramolecular NH.N hydrogen bond. Ab initio calculations (HF/3-21G and HF/3-21+G) have been carried out on several representative examples (1e, 1p, and 1l) in an attempt to support and provide the correct geometry of these derivatives. Structural considerations among the possible isomers of compounds 1 are discussed. From these studies it was concluded that the theoretical calculations agree with the experimental results. In addition, a very simple one-pot procedure for the preparation of masked N-substituted alpha-alkylated beta-enamino acid derivatives 2 from 6, 7, and different alkyl halides (R(3)Y) is described.     

Design of ordered bimetallic complexes,Part 2:Trans-1,2-cyclohexanediaminetetraacetate bimetallates

Summary Knowledge of the kinetic and thermodynamic behaviour of aqueous solutions containing two divalent cations andtrans-1,2-cyclohexanediaminetetraacetate has been used to design synthetic pathways to ordered bimetallic complexesPart 1: E. Escriva, A. Fuertes and D. Beltran,Transition Met. Chem.,9, 184 (1984).     

Biocatalytic approaches toward the synthesis of both enantiomers of trans-cyclopentane-1,2-diamine

[reaction: see text] A lipase-catalyzed double monoaminolysis of dimethyl malonate by (+/-)-trans-cyclopentane-1,2-diamine allows the sequential resolution of the latter compound, affording an enantiopure bis(amidoester), which is subsequently transformed into an optically active polyamine. As an alternative, both enantiomers of the diamine can be obtained from enantiopure (+)- or (-)-2-aminocyclopentanol, prepared by enzymatic resolution.     

On-line preconcentration and determination of mercury in biological samples by flow injection vapour generation inductively coupled plasma atomic emission spectrometry

An FI-ICP-AES method for the determination of trace levels of mercury in biological samples has been described, which is based on the extraction of the mercury complex with 1,5-bis (di-2-pyridyl)methylene thiocarbonohydrazide (DPTH) on-line into isobuthyl-methyl ketone (IBMK). The organic phase (containing the complex) has been mixed on-line with SnCl₂ in N,N-dimethylformamide. Thus, mercury vapour can be generated directly from the organic phase and separated in a gas-liquid separation device. The detection limit for mercury is 4 ng/ml and the calibration curve is linear at least from 10 to 2500 ng/ml. The relative standard deviation for 10 replicate measurements is ±1% for 100 ng/ml of Hg(II). Results from the analysis of some certified biological reference materials are given.