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}.     

The charge delocalised beta,beta-carotene dication--preparation, structure elucidation by NMR and reactions with nucleophiles

The reaction between beta,beta-carotene and BF3-etherates has been investigated, leading to structural elucidation of the blue product, formed in appropriate organic solvents, as a symmetrical charge delocalised dication (lambda(max) 985 nm at room temperature in CHCl3) with considerable stability. The reaction, monitored by EPR studies at -25 degrees C, occurred via free radical intermediates. A C40H56BF3 intermediate was captured by EIMS. The detailed structure of the dication was established by COSY, HSQC, HMBC and 1D and 2D ROESY NMR techniques (600 MHz, CDCl3, -20 degrees C) leading to complete assignments of 1H and 13C chemical shifts and 3J(H,H) coupling constants. The effects of the two delocalised charges on chemical shift (charge distribution) and bond distance (3J(H,H)) were considered. The results are consistent with charge delocalisation mainly in the C-5-C-9 and C-5'-C-9' regions and with bond inversion to retro shifted double bonds in the central C-13-C-13' region. A convention for denoting the charge delocalisation and bond types is presented. The experimental results are discussed relative to previous theoretical calculations of the beta,beta-carotene dication structure. (All-E) and (15-Z)-beta,beta-carotene provided the same dication. The NIR spectra and stability of dications prepared in the same manner from the related carotenes 20,20'-dinor-beta,beta-carotene, heptapreno-beta,beta-carotene and nonapreno-beta,beta-carotene were examined for comparison. Reactions of the beta,beta-carotene dication with selected nucleophiles provided products including isocryptoxanthin, isocarotene and mutatochrome with H2O as nucleophile, and isocryptoxanthin methyl ether, 8-methoxy-7,8-dihydro-beta,beta-carotene and isocarotene with CH3ONa as nucleophile. The formation of these products is rationalised from the structure assigned to the dication.     

Electron capture dissociation Fourier transform ion cyclotron resonance mass spectrometry in the electron energy range 0-50 eV

Electron capture dissociation (ECD) of polypeptide cations was obtained with pencil and hollow electron beams for both sidekick and gas-assisted dynamic ion trapping (GADT) using Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) with an electrostatic ion transfer line. Increasing the number of trapped ions by multiple ICR trap loads using GADT improved the ECD sensitivity in comparison with sidekick ion trapping and ECD efficiency in comparison with single ion trap load by GADT. Furthermore, enhanced sensitivity made it possible to observe ECD in a wide range of electron energies (0-50 eV). The degree, rate and fragmentation characteristics of ECD FTICR-MS were investigated as functions of electron energy, electron irradiation time, electron flux and ion trapping parameters for this broad energy range. The results obtained show that the rate of ECD is higher for more energetic (>1 eV) electrons. Long electron irradiation time with energetic electrons reduces average fragment ion mass and decreases efficiency of formation of c- and z-type ions. The obtained dependencies suggest that the average fragment ion mass and the ECD efficiency are functions of the total fluence of the electron beam (electron energy multiplied by irradiation time). The measured electron energy distributions in low-energy ECD and hot ECD regimes are about 1 eV at full width half maximum in employed experimental configurations.     

A neutron powder diffraction study of the κ phase in the FeWC system

The crystal structure of the κ-carbide in the FeWC system has been refined from neutron powder diffraction data using the Rietveld profile analysis method. κ-(FeWC) is isostructural with κ-(CoWC); space group $\text{P6}{}_3\text{mmc}$; unit cell dimensions a = 7.7982(2)Å, c = 7.8298(4) Å. The structure refinement indicates $\text{Fe}\text{W}$ substitution at two of the tungsten sites, and 46% vacancies at one of the carbon sites. The composition corresponds to the formula Fe_3+xW_10?xC_4?y, with x = 0.57(3) and y = 0.46(1).     

The use of polymeric amines to enhance the mechanical properties of lignocellulosic fibrous networks

Cationic polyelectrolytes (polyallylamine and polyvinylamine with different molecular masses) were adsorbed onto lignocellulosic fibres from unbleached and unbeaten spruce chemical fibres with different kappa numbers to investigate the effects on the mechanical properties of the final paper materials. Adsorption isotherms were first established to determine the maximum quantity of polymer that could be adsorbed onto each type of fibre. Paper sheets were then made with different amounts of added polyelectrolyte, and the structural and mechanical properties of the sheets were investigated, as well as the effect of an extra heating. The use of fibres with different kappa numbers led to different responses in terms of adsorption, and thus to differences in the mechanical properties of the resulting sheets. The tensile strength index was significantly increased (almost 50 % improvement in the best case) as a consequence of this polyelectrolyte adsorption onto the fibres, even at as low an adsorption level as 2 mg/g. The heating of paper sheets for 10 min at 160 °C was also shown to improve the tensile strength index by about 10 % for pulps with high kappa number.     

Enumerating Perfect Matchings in n-Cubes

The perfect matchings in the n-cube have earlier been enumerated for n?≤?6. A dynamic programming approach is here used to obtain the total number of perfect matchings in the 7-cube, which is 391 689 748 492 473 664 721 077 609 089. The number of equivalence classes of perfect matchings is further shown to be 336 in the 5-cube, 356 788 059 in the 6-cube and 607 158 046 495 120 886 820 621 in the 7-cube. The techniques used can be generalized to arbitrary bipartite and general graphs.     

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.     

An Aldehyde Responsive,Cleavable Linker for Glucose Responsive Insulins

A glucose responsive insulin (GRI) that responds to changes in blood glucose concentrations has remained an elusive goal. Here we describe the development of glucose cleavable linkers based on hydrazone and thiazolidine structures. We developed linkers with low levels of spontaneous hydrolysis but increased level of hydrolysis with rising concentrations of glucose, which demonstrated their glucose responsiveness in vitro. Lipidated hydrazones and thiazolidines were conjugated to the LysB29 side-chain of HI by pH-controlled acylations providing GRIs with glucose responsiveness confirmed in vitro for thiazolidines. Clamp studies showed increased glucose infusion at hyperglycemic conditions for one GRI indicative of a true glucose response. The glucose responsive cleavable linker in these GRIs allow changes in glucose levels to drive the release of active insulin from a circulating depot. We have demonstrated an unprecedented, chemically responsive linker concept for biopharmaceuticals.