The Conley index over a base

We construct a generalization of the Conley index for flows. The new index preserves information which in the classical case is lost in the process of collapsing the exit set to a point. The new index has most of the properties of the classical index. As examples, we study a flow with a knotted orbit in , and the problem of continuing two periodic orbits which are not homotopic as loops.

     

Effects of electron-beam irradiation on surface oxidation of polymer composites

The aim of this article was to show the effects of an electron radiation dose and presence of a compatibilizer on the oxidation of composites made of blends of low-density polyethylene (LDPE), high-density polyethylene (HDPE), polypropylene (PP), polystyrene (PS), and poly(ethylene terephthalate) (PET) as well as of blends of LDPE, HDPE, and PP. As the compatibilizers, the styrene-ethylene/butylene-styrene elastomer grafted with maleic anhydride (SEBS-g-MA) and trimethylol propane trimethylacrylate (TMPTA) were used; they were added in the amounts of 5, 10, and 15 wt% and 1, 2, and 3 wt%, respectively. The oxidation of the surface layer (SL) was investigated by the X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared spectroscopy (FTIR). It was found that the extent of the composite oxidation increased with the increasing dose of the electron radiation. The addition of the compatibilizers enhanced the oxidation of the SL but hindered the oxidation of the bulk of the material.     

Atmospheric plasma treatment of pre‐electrospinning polymer solution: A feasible method to improve electrospinnability

The electrospinnability of polyethylene oxide (PEO) was manipulated by atmospheric plasma treatment of pre‐electrospinning solutions. Conductivity, viscosity, and surface tension of PEO solutions increased after plasma treatment, and the plasma effect remained longer when the solution concentrate increased. Both untreated and treated solutions were then electrospun, and the morphology of the resultant nanofibers was observed by SEM. Atmospheric plasma treatment improved the electrospinnability of PEO solutions and led to less beads and finer diameter distribution in the resultant nanofibers. Additionally, plasma treatment of the pre‐electrospinning solutions affected the crystal structure of resultant nanofibers. These results suggest that atmospheric plasma treatment is a feasible approach to improve the electrospinnability of polymer solutions and can used to control the structure of electrospun nanofibers. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Pressure‐induced polymerization of tetraethylene glycol dimethacrylate

The polymerization and crosslinking of tetraethylene glycol dimethacrylate were induced by high pressure. The product was analyzed by both swelling experiments and broadband dielectric spectroscopy to determine the structure, with IR measurements used to follow the extent of reaction and its temperature dependence. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3795–3801, 2008     

ERROR ESTIMATES FOR THE TIME DISCRETIZATION FOR NONLINEAR MAXWELL＇S EQUATIONS

This paper is devoted to the study of a nonlinear evolution eddy current model of the type δtB（H） ＋ △↓× （ △↓ × H） =0 subject to homogeneous Dirichlet boundary conditions H × v = 0 and a given initial datum. Here, the magnetic properties of a soft ferromagnet are linked by a nonlinear material law described by B（H）. We apply the backward Euler method for the time discretization and we derive the error estimates in suitable function spaces. The results depend on the nonlinearity of B（H）.     

Synthesis of organofunctional silanes with sterically hindered substituents at silicon atoms

Organofunctional silanes with more sterically hindered substituents at the silicon atom than the typical methoxy (ethoxy) group have lately been frequently used as silane coupling agents, in polymer coupling systems, sol‐gel processes and also as interpenetrating polymer network substrates. New and very efficient synthetic ways leading to organofunctional silanes of the above type with methacryl, amine, chloro and isocyanato functional groups are proposed here. Catalytic transesterification and/or alcoholysis of chloropropyltrialkoxysilanes followed by­nucleophilic substitution has been employed. Copyright © 2001 John Wiley & Sons, Ltd.     

Entropy criterion of random states for granular material in a mixing process

Mathematical assessment of homogenisation progress of the granular material mixing process is presented. The mixing process was realised using a vessel in the form of two partly penetrating horizontal cylinders equipped with two multi-ribbon agitators. The experimental system consisted of three sets of particles of different colour. Random states of the mixed granular material were characterised by the sampling procedure at different moments of the mixing process. Informational entropy as well as the flow of quantum of information were applied to describe the progress of the homogenisation process. Analysis of this process was based on experimental investigations in the form of informational entropy patterns and described by means of the average informational entropy or the quantum of information. Presented at the 34th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 21–25 May 2007.     

Convergence of algebraic multigrid based on smoothed aggregation

Summary. We prove an abstract convergence estimate for the Algebraic Multigrid Method with prolongator defined by a disaggregation followed by a smoothing. The method input is the problem matrix and a matrix of the zero energy modes of the same problem but with natural boundary conditions. The construction is described in the case of a general elliptic system. The condition number bound increases only as a polynomial of the number of levels, and requires only a uniform weak approximation property for the aggregation operators. This property can be a-priori verified computationally once the aggregates are known. For illustration, it is also verified here for a uniformly elliptic diffusion equations discretized by linear conforming quasiuniform finite elements. Only very weak and natural assumptions on the hierarchy of aggregates are needed. Received March 1, 1998 / Revised version received January 28, 2000 / Published online: December 19, 2000     

Ueber die Analogie des Verhaltens von Emulsionen und des Verhaltens von Fett im Protoplasma

Ohne Zusammenfassung Uebersetzt von J. Matula (Wien). Eine vorl?ufige Mitteilung der in dieser und einer vorhergehenden in dieser Zeitschrift erschienenen Abhandlung niedergelegten Ergebnisse erschien in Science43 (1916).