Chiral phosphinoferrocene carboxamides with amino acid substituents as ligands for Pd-catalysed asymmetric allylic substitutions. Synthesis and structural characterisation of catalytically relevant Pd complexes

An extensive series of chiral amino acid amides prepared from 1'-(diphenylphosphino)ferrocene-1-carboxylic acid (Hdpf) or its planar-chiral isomer, 2-(diphenylphosphino)ferrocene-1-carboxylic acid, have been tested as ligands for Pd-catalysed asymmetric allylic substitution reactions. In alkylation of 1,3-diphenylallyl acetate as a model substrate with dimethyl malonate the ligands performed well in terms of both reaction rate and enantioselectivity, achieving up to 98% ee. In contrast, the reactions of the same substrate with other nucleophiles proceeded either slowly and with poor ee's (amination with benzylamine) or not at all (etherification with benzyl alcohol). In order to rationalise the influence of the ligand structure on the reaction course, three model complexes, viz. [(η(3)-methallyl)PdCl(L-κP)], [(η(3)-methallyl)Pd(L-κ(2)O,P)]ClO(4) and [(η(3)-methallyl)Pd(L-κP)(2)]ClO(4) have been prepared from the achiral amide Ph(2)PfcCONHCH(2)CO(2)Me (L; fc = ferrocene-1,1'-diyl) and structurally characterised. The coordination study showed that the amido-phosphines readily form 1?:?1 complexes as O,P-chelates where the amino acid chirality is brought close to the Pd atom. At higher ligand-to-metal ratios, however, simple P-monodentate coordination prevails, minimising the influence of the chiral amino acid pendant.     

Native polyacrylamide electrophoresis in the presence of Ponceau Red to study oligomeric states of protein complexes

Native polyacrylamide electrophoresis in the presence of two reversible protein anionic stains (Ponceau S and Ponceau 2R) was used to study the oligomeric states of soluble proteins. A mild binding of the used protein stains to nondissociated protein oligomers imposed a charge shift on the proteins resulting into separation of protein species according to their size under physiological conditions. Adsorbed stains could be easily removed after electrophoresis by washing of polyacrylamide gel with buffer and protein complexes could be visualized either by the detection of their enzyme activity or by using a nonspecific protein stain. The specific detection of enzyme activity of glycosidases, lactate dehydrogenase, or phosphatases was shown as an example.     

Conjugation reactions in the preparations of quantum dot-based immunoluminescent probes for analysis of proteins by capillary electrophoresis

A number of biologically important molecules, such as DNA, proteins, and antibodies, are routinely conjugated with fluorescent tags for high-sensitivity analyses. Here, the application of quantum dots in the place of bright and size-tunable luminophores is studied. Several selected bioconjugation reactions via zero-length cross-linkers, long-chain linkers, and oriented methods for linking of quantum dots with proteins were tested. Anti-ovalbumin, anti-proliferating cell nuclear antigen, anti-hemagglutinin, and anti-CD3 membrane protein as model antibodies and annexin V were used as high-specificity selectors. The reaction yield and efficiency of the prepared immunoluminescent probes were tested by capillary zone electrophoresis with laser-induced fluorescence detection.     

Analysis of space–time discontinuous Galerkin method for nonlinear convection–diffusion problems

The paper presents the theory of the discontinuous Galerkin finite element method for the space–time discretization of a nonstationary convection–diffusion initial-boundary value problem with nonlinear convection and linear diffusion. The problem is not singularly perturbed with dominating convection. The discontinuous Galerkin method is applied separately in space and time using, in general, different space grids on different time levels and different polynomial degrees p and q in space and time dicretization. In the space discretization the nonsymmetric, symmetric and incomplete interior and boundary penalty (NIPG, SIPG, IIPG) approximation of diffusion terms is used. The paper is concerned with the proof of error estimates in “L ²(L ²)”- and “DG”-norm formed by the “L ²(H ¹)”-seminorm and penalty terms. A special technique based on the use of the Gauss–Radau interpolation and numerical integration has been used for the derivation of an abstract error estimate. In the “DG”-norm the error estimates are optimal with respect to the size of the space grid. They are optimal with respect to the time step, if the Dirichlet boundary condition has behaviour in time as a polynomial of degree ≤ q.     

Weak Solutions for the Motion of a Self-propelled Deformable Structure in a Viscous Incompressible Fluid

We consider the three-dimensional motion of a self-propelled deformable structure into a viscous incompressible fluid. The deformation of the solid is given whereas its position is unknown. Such a system could model the propulsion of fish-like swimmers. The equations of motion of the fluid are the Navier-Stokes equations and the equations for the structure are deduced from Newton’s laws. The corresponding system is a free boundary problem and the main result of the paper is the existence of weak solutions for this problem.     

Crack behavior in a welded polyolefin pipe

A three-dimensional model of a pressured polymer pipe with a weld is created in order to estimate the stress intensity factor for a crack located inside the weld. A comparison with values obtained for an edge-cracked tension specimen, usually employed for an experimental determination of weld properties, is performed. The difference between the stress intensity factor in a homogeneous pipe and the results taking into account the changes in material properties inside the weld is presented. A conservative and easily applicable relationship for calculating the stress intensity factor in a pipe weld is proposed.     

On the Fourier coefficients of linear fractional stable motion

Inspired by a theorem of Marcinkiewicz [J. Marcinkiewicz, On a class of functions and their Fourier series, C. R. Soc. Sci. Varsovie, 26:71–77, 1934. Reprinted in: J. Marcinkiewicz, Collected Papers (A. Zygmund (Ed.)), PaństwoweWydawnictwo Naukowe,Warsaw, 1964] stating that the maximum of the absolute values of real Fourier coefficients a _n and b _n of a function of bounded p-variation ( p \geqslant 1 ) \left( {p \geqslant 1} \right) on an interval [0, 1] is of order O(n ^−1/p ) as n → ∞, we compute the Fourier coefficients of the linear fractional stable motion (LFSM) and of the closely related Riemann–Liouville (RL) process and investigate the rate of their decay.     

Error rates in classification of multivariate Gaussian random field observation

We consider the problem of supervised classifying the multivariate Gaussian random field (GRF) single observation into one of two populations in case of given training sample. The populations are specified by different regression mean models and by common factorized covariance function. For completely specified populations, we derive a formula for Bayes error rate. In the case of unknown regression parameters and feature covariance matrix, the plug-in Bayes discriminant function based on ML estimators of parameters is used for classification. We derive the actual error rate and the asymptotic expansion of the expected error rate associated with plug-in Bayes discriminant function. These results are multivariate generalizations of previous ones. Numerical analysis of the derived formulas is implemented for the bivariate GRF observations at locations belonging to the two-dimensional lattice with unit spacing.     

Line graphs of multigraphs and Hamilton‐connectedness of claw‐free graphs

We introduce a closure concept that turns a claw‐free graph into the line graph of a multigraph while preserving its (non‐)Hamilton‐connectedness. As an application, we show that every 7‐connected claw‐free graph is Hamilton‐connected, and we show that the well‐known conjecture by Matthews and Sumner (every 4‐connected claw‐free graph is hamiltonian) is equivalent with the statement that every 4‐connected claw‐free graph is Hamilton‐connected. Finally, we show a natural way to avoid the non‐uniqueness of a preimage of a line graph of a multigraph, and we prove that the closure operation is, in a sense, best possible. © 2010 Wiley Periodicals, Inc. J Graph Theory 66:152‐173, 2011