Symbolic-numeric integration of rational functions

Numerical Algorithms - We consider the problem of symbolic-numeric integration of symbolic functions, focusing on rational functions. Using a hybrid method allows the reliable yet efficient...     

Cyclicity of a simple focus via the vanishing multiplicity of inverse integrating factors

First we provide new properties about the vanishing multiplicity of the inverse integrating factor of a planar analytic differential system at a focus. After we use this vanishing multiplicity for studying the cyclicity of foci with pure imaginary eigenvalues and with homogeneous nonlinearities of arbitrary degree having either its radial or angular speed independent of the angle variable in polar coordinates. After we study the cyclicity of a class of nilpotent foci in their analytic normal form.     

Chondroitin Sulfate Tetrasaccharides: Synthesis,Three‐Dimensional Structure and Interaction with Midkine

The biological activity of midkine, a cytokine implicated in neuro‐ and tumourigenesis, is regulated by its binding to glycosaminoglycans (GAGs), such as heparin and chondroitin sulfate (CS). To better understand the molecular recognition of GAG sequences by this growth factor, the interactions between synthetic chondroitin sulfate‐like tetrasaccharides and midkine were studied by using different techniques. Firstly, a synthetic approach for the preparation of CS‐like oligosaccharides in the sequence GalNAc–GlcA was developed. A fluorescence polarisation competition assay was then employed to analyse the relative binding affinities of the synthetic compounds and revealed that midkine interacted with CS‐like tetrasaccharides in the micromolar range. The 3D structure of these tetramers was studied in detail by a combination of NMR spectroscopy experiments and molecular dynamics simulations. Saturation transfer difference (STD) NMR spectroscopy experiments indicate that the CS tetrasaccharides bind to midkine in an extended conformation, with similar saturation effects along the entire sugar chain. These results are compatible with docking studies that suggest an interaction of the tetrasaccharide with midkine in a folded structure. Overall, this study provides valuable information on the interaction between midkine and well‐defined, chemically synthesised CS oligosaccharides and these data can be useful for the design of more active compounds that modulate the biological function of this protein.     

Characterisation of a prehistorical ceramic object

Archaeological ceramics findings are usually characterised by a combination of methods to provide as many as possible information about their origin, use and deposition. Unique moon-shaped idol approximately 0.5 m long from the Final Bronze Age was studied by XRD, XRF, Raman spectroscopy and thermal analyses (TG, DTA, DSC). Special attention was given to processes occurring during its thermal treatment, which were specified by thermal analysis. It was proved that the process of kaolinite dehydroxylation proceeded less intensively in the central part of the object and the maximum of peak was shifted to lower temperature compared to the border parts. It is supposed that the moon-shaped idol was thermally treated not until its use, and the border parts of the object were exposed to lower temperatures compared to the central part.     

Silo clogging reduction by the presence of an obstacle

We present experimental results on the effect that inserting an obstacle just above the outlet of a silo has on the clogging process. We find that, if the obstacle position is properly selected, the probability that the granular flow is arrested can be reduced by a factor of 100. This dramatic effect occurs without any remarkable modification of the flow rate or the packing fraction above the outlet, which are discarded as the cause of the change in the clogging probability. Hence, inspired by previous results of pedestrian crowd dynamics, we propose that the physical mechanism behind the clogging reduction is a pressure decrease in the region of arch formation.     

Quantum topology phase diagrams for the cis‐ and trans‐isomers of the cyclic contryphan‐Sm peptide

Within the quantum theory of atoms in molecules (QTAIM) framework we present a quantum topology phase diagram (QTPD) using the Poincaré–Hopf relation of a total of 17 all new QTAIM topologies of the cis‐ and trans‐isomers of the cyclic contryphan‐Sm peptide. The resultant QTPD consists of separate regions for the cis‐ and trans‐isomers that only overlap for topologies associated with the lowest energy minima of the cis‐ and trans‐isomers. We determine the QTAIM topologies of 29 “missing” isomers. A new, contracted formulation of the QTPD is presented, this contracted formulation includes the interamino acid bond critical points (BCPs) that link together the amino acid units, the disulphide bridge “pivot” BCP and side chain bonding interactions. The seven interamino acid BCPs linking the amino acid units coincide with the so‐called peptide backbone, the conventional qualitative approach to reduce the complexity of the peptide. We expand the interpretation of ellipticity to include the associated eigenvectors and find that higher values of the ellipticity ? are associated with a greater preference to conserve folding states. We quantify previous qualitative findings that suggested the disulfide bond is central to the folding behavior of the cyclic contryphan‐Sm peptide and why the cis‐isomer is the major form of the cyclic contryphan‐Sm peptide. © 2014 Wiley Periodicals, Inc.     

Solubilizing interactions of octylphenol surfactants with liposomes modeling the stratum corneum lipid composition

 The interaction of a series of polyethoxylated octylphenols (ethylene oxide units average 8.5–20.0) with liposomes modeling the stratum corneum (SC) lipid composition (40% ceramides, 25% cholesterol, 25% palmitic acid and 10% of cholesteryl sulfate) was investigated. The surfactant/lipid molar ratios (Re) and the bilayer/aqueous-phase partition coefficients (K) were determined by monitoring the changes in the static light scattering of the system during solubilization. The fact that free concentration for each surfactant tested was always similar to its critical micelle concentration (CMC) indi-cates that the liposome solubilization was mainly ruled by the formation of mixed micelles. The Re and K para-meters for liposome saturation fell as the surfactant HLB increased. Thus, at this interaction step the higher the surfactant HLB, the higher the ability of these surfactants to saturate SC liposomes and the lower their degree of partitioning into liposomes. However, the maximum solubilizing ability was achieved at intermediate HLB values. Thus, the octylphenols with 20 and 12.5 ethylene oxide units showed, respectively, the highest power of saturation and solubilization of SC structures in terms of the total surfactant amounts needed to produce these effects. Different trends in the interaction of these surfactants with SC liposomes were observed when comparing the Re and K parameters with those reported for PC ones. Thus, whereas the SC liposomes were more resistant to the surfactant action, the affinity of these surfactants with these bilayer structures was higher in all cases. Received: 3 March 1997 Accepted: 22 May 1997     

Finite Aomoto-Ito-Macdonald sums

We present finite truncations of the Aomoto-Ito-Macdonald sums associated with root systems through a two-step reduction procedure. The first reduction restricts the sum from the root lattice to a Weyl chamber; the second reduction arises after imposing a truncation condition on the parameters, and gives rise to a finite sum over a Weyl alcove.

     

Coherent production ofρ − mesons in charged current antineutrino-neon interactions in BEBC

Coherent production ofρ ^? mesons in charged current antineutrino interactions on neon nuclei is studied in the BEBC bubble chamber exposed to the CERN SPS wide band beam. The cross section is measured to be (95±25)·10^?40 cm² per neon nucleus, averaged over the beam energy spectrum. The distributions of kinematical variables and the absolute value of the cross section are in agreement with theoretical predictions based on the CVC hypothesis and the vector meson dominance model.