A moment problem associated to rational Szegő functions

Leta ₁,...,a _p be distinct points in the finite complex plane ?, such that |a _j|>1,j=1,..., p and let \(b_j = 1/\bar \alpha _j ,\) j=1,..., p. Let μ₀, μ _π ^(j) , ν _π ^(j) j=1,..., p;n=1, 2,... be given complex numbers. We consider the following moment problem. Find a distribution ψ on [?π, π], with infinitely many points of increase, such that $$\begin{array}{l} \int_{ - \pi }^\pi {d\psi (\theta ) = \mu _0 ,} \\ \int_{ - \pi }^\pi {\frac{{d\psi (\theta )}}{{(e^{i\theta } - a_j )^n }} = \mu _n^{(j)} ,} \int_{ - \pi }^\pi {\frac{{d\psi (\theta )}}{{(e^{i\theta } - b_j )^n }} = v_n^{(j)} ,} j = 1,...,p;n = 1,2,.... \\ \end{array}$$ It will be shown that this problem has a unique solution if the moments generate a positive-definite Hermitian inner product on the linear space of rational functions with no poles in the extended complex plane ?^* outside {a ₁,...,a _p,b ₁,...,b _p}.     

Existence of generic homoclinic tangencies for henon mappings

It is an open question whether there is a strange attractor for the Henon mapping. We show that for certain maps close to the Henon map there are strange attractors.     

The conformation of rifamycin S in solution by 1H NMR spectroscopy

The ¹H NMR spectra of rifamycin S in different solvents and at different temperatures strongly suggest the existence of a dominant conformer. The nine dihedral angles of the ansa chain from C-28 to C-19, considered conformationally flexible, were obtained from the vicinal interproton coupling constants by the Karplus equation and the proper alternative for each of them compares well with the corresponding values given by X-ray analysis in solid state.All the possible conformations derivable from the intrinsic alternatives of the NMR method were calculated for the ansa chain between C-28 and C-19 and, by applying geometrical considerations, such as closure of the polygonal path of the ansa and the steric incompatibility between the various atoms of the ansa and of the chromophore, only two of them appeared real. Thus, NMR spectroscopy can be used for studying the conformation of the ansa chain of rifamycins in solution.     

Gear effect—10 : Conformational aspects of the positive or negative buttressing effects of methyl groups: polymethylpyridines

The effect of the shape of a methyl group on reactivity, which cannot be accounted for by considering a methyl group as a spherical substituent with the appropriate van der Waals radius, was considered in kinetics of alkylalion of substituted pyridines and barriers to rotation and ground state conformations of an isopropyl group attached to a planar framework. The perturbation of a methyl group by an o-methyl group is accounted for by a unique conformational explanation which involves the polyhedral shape of the methyl group.     

Anti-HIV Active Naphthyl Analogues of HEPT and DABO

Summary.  5-Isopropyl-6-naphthyl uracil and 5-isopropyl-6-naphthyl-2-thiouracil were alkylated to give N-1-(ethoxymethyl and methylthiomethyl) uracil and S²-cyclohexyl-thiouracil, respectively. 5-Ethyl-6-naphthyl uracil and 5-ethyl-6-naphthyl-2-thiouracil afforded N-1-(ethoxymethyl, methoxy-methyl, methylthiomethyl, acetoxyethoxy methyl and hydroxyethoxy methyl) uracil and S²-((2,2- diethoxyethyl), methoxycarbonylmethyl, ethoxycarbonylpropyl, methylthiomethyl, ethoxymethyl, methyl and cyclohexyl)-thiouracil upon alkylation. Received September 25, 2001. Accepted (revised) December 3, 2001     

Liquid chromatographic analysis of vitamin B6 in reconstituted infant formula: collaborative study

A liquid chromatographic (LC) method was validated for the determination of total vitamin B6 in infant formula. Total vitamin B6 was quantified by converting the phosphorylated and free vitamers into pyridoxine. Pyridoxine was determined by ion pair reversed-phase LC with fluorescence detection. The method was subjected to an AOAC collaborative study involving a factory-manufactured, milk- and soy-based infant formula. Each was spiked at 3 concentrations in the range of 0-1 microg/g and sent as blind duplicate to participant laboratories. Nine laboratories returned valid data which were statistically analyzed for outliers and precision parameters. The repeatability relative standard deviation (RSD(r)) ranges were 2.0-4.0 and 3.5-5.9% for fortified milk- and soy-based formulas, respectively. The reproducibility relative standard deviation (RSD(R)) ranges were 8.2-8.4 and 6.7-11.2% for fortified milk- and soy-based formulas, respectively. HORRAT values ranged from 0.42 to 0.53, indicating that the precision of the method is acceptable. The mean RSD(r):RSD(R) values were 0.60 and 0.55 for milk- and soy-based formulas, respectively. As expected, RSDs for the unfortified samples were higher, but their HORRAT values (0.81 and 2.06) helped define a realistic limit of quantitation as 0.05 microg/g. Recovery data were quantitative and varied between 81.4 and 98.0% (mean = 89.8%) for each of 6 spiked materials.     

Non-conventional Behavior of a 2,1-Benzazaphosphole: Heterodiene or Hidden Phosphinidene?

Invited for the cover of this issue are Zoltán Benkő, Libor Dostál and co-workers at the University of Pardubice and the Budapest University of Technology and Economics. The image depicts signs for the two different pathways representing the two differing reaction types which were clearly observed for 2,1-benzazaphosphole. Read the full text of the article at 10.1002/chem.202101686 .     

Prospects for p̄p → ȲY studies at PANDA

Strangeness and charm production provide an excellent probe of QCD in the confinement domain. With the PANDA detector at FAIR, this can be studied in e.g., hyperon production in the p?p → ?Y reactions. In PANDA, all ground state strange hyperons and single charmed Λ’s will be accessible. Simulations show that the differential cross sections and spin observables can be well reconstructed for these reaction channels.