Application of very weak formulation on homogenization of boundary value problems in porous media

Czechoslovak Mathematical Journal - The goal of this paper is to present a different approach to the homogenization of the Dirichlet boundary value problem in porous medium. Unlike the standard...     

A theoretical description of elastic pillar substrates in biophysical experiments.

Arrays of elastic pillars are used in biophysical experiments as sensors for traction forces. The evaluation of the forces can be complicated if they are coupled to the pillar displacements over large distances. This is the case if many of the pillars are interconnected by elastic linkages as, for example, in fiber networks that are grown on top of pillars. To calculate the traction forces in such a network, we developed a set of nonlinear inhomogeneous equations relating the forces in the linking elements to the resulting pillar deflections. We chose a homogeneous, activated two-dimensional network of cytoskeletal actin filaments to illustrate that a pillar substrate is generally not a force sensor but a force-gradient sensor. In homogeneous networks the forces acting along the filaments can be approximated by analyzing only pillar deflections in the edge zones of the substrate and by integration over the corresponding force gradients.     

Asymptotic behavior of Markov semigroups on preduals of von Neumann algebras

We develop a new approach for investigation of asymptotic behavior of Markov semigroup on preduals of von Neumann algebras. With using of our technique we establish several results about mean ergodicity, statistical stability, and constrictiviness of Markov semigroups.     

Impurity optical absorption in parabolic quantum well

Optical absorption in GaAs parabolic quantum well in the presence of hydrogenic impurity is considered. The absorption coefficient associated with the transitions between the upper valence subband and donor ground state is calculated. The impurity ground state wave function and energy are obtained using the variational method. Dependence of the absorption spectra on impurity position in quantum well was investigated. It is shown, that along with quantum well width decrease the absorption threshold shifts to higher frequencies. Results obtained within frames of parabolic approximation are compared with results for rectangular infinite-barrier quantum well case. The acceptor state → conduction band transitions considered as well.     

Fluorolactonization of norbornenecarboxylic acids and their methyl esters with F-TEDA-BF4 and XeF2

The selective fluorolactonization was achieved by treatment of cis-5-norbornene-2,3-endo-dicarboxylic acid or its monomethyl and dimethyl esters with F-TEDA-BF₄ or XeF₂. The reactions of 5-norbornene-endo-2-carboxylic acid and its monomethyl ester with F-TEDA-BF₄ or XeF₂ proceed in a non-selective manner to give fluorolactonization, addition and rearrangement products. The basic factor responsible for selectivity of the fluorolactonization is the presence of two endo-oriented carboxyl groups in the substrate molecule. The electrophilicity and type of the fluorinating agent is of secondary importance in this regard. It is postulated that the fluorolactonization of norbornenecarboxylic acids and their methyl esters with F-TEDA-BF₄ or XeF₂ is realized mainly via “open” fluoronorbornyl carbocation intermediates which in the reaction with XeF₂ are postulated as the tight ion pairs.     

On locality in quantum general relativity and quantum gravity

The physical concept of locality is first analyzed in the special relativistic quantum regime, and compared with that of microcausality and the local commutativity of quantum fields. Its extrapolation to quantum general relativity on quantum bundles over curved spacetime is then described. It is shown that the resulting formulation of quantum-geometric locality based on the concept of local quantum frame incorporating a fundamental length embodies the key geometric and topological aspects of this concept. Taken in conjunction with the strong equivalence principle and the path-integral formulation of quantum propagation, quantum-geometric locality leads in a natural manner to the formulation of quantum-geometric propagation in curved spacetime. Its extrapolation to geometric quantum gravity formulated over quantum spacetime is described and analyzed.     

Die Unterscheidung von Harz?l und Mineral?l

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Verbiegungen höherer Ordnung und ebene Flächenrinnen

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