Topological Model Categories Generated by Finite Complexes

 Our main result states that for each finite complex L the category TOP of topological spaces possesses a model category structure (in the sense of Quillen) whose weak equivalences are precisely maps which induce isomorphisms of all [L]-homotopy groups. The concept of [L]-homotopy has earlier been introduced by the first author and is based on Dranishnikov’s notion of extension dimension. As a corollary we obtain an algebraic characterization of [L]-homotopy equivalences between [L]-complexes. This result extends two classical theorems of J. H. C. Whitehead. One of them – describing homotopy equivalences between CW-complexes as maps inducing isomorphisms of all homotopy groups – is obtained by letting L = {point}. The other – describing n-homotopy equivalences between at most (n+1)-dimensional CW-complexes as maps inducing isomorphisms of k-dimensional homotopy groups with k ⩽ n – by letting L = S ⁿ⁺¹ , n ⩾ 0.     

Re-examined principles of thrust generation by a track on soft ground

Dr. Bekker’s first book Theory of land locomotion offers in fact two different concepts of thrust generation on soft ground with respect to the slip: (a) as the push of grousers causing horizontal soil “distortion” and (b) as the shear force in the failure plane linked with the shear deformation. Bekker preferred the second concept and backed it up by the unique shear-ring measuring technique. To clear up the matter, the author decided to re-examine the thrust generation by a track plate experimentally in field conditions. The tests have shown that the initial stage of thrust generation in compressible ground is always horizontal soil compression by grousers, which divides the soil under a track into separate blocks initially at rest. This compression increases at least to the transition point, when a block is sheared off simultaneously at the bottom and in both lateral planes and starts sliding along the channel formed by the preceding grouser. The analysis of these measurements enabled to define the compressive displacement of the face of the soil block (travel of the grouser) appurtenant to the mentioned transition point, useful to define the thrust–slip curve. The case may also be described by the conventional shear stress–shear displacement relationship, imagined to take place in the bottom failure plane, however, namely the “shear displacement” is rather an unusual quantity.     

High-throughput powder X-ray diffraction, IR-spectroscopy and ion chromatography analysis of urinary stones: A comparative study

The instrumental qualitative analysis of urinary stones is a critical step in clinical practice and urological research. A powder X-ray diffraction, IR-spectroscopy and ion chromatography have been applied for the qualitative analysis of 20 urinary stones. Suggestions for a sample preparation and an optimal measurement strategy were formulated. The main difficulties for the powder X-ray diffraction qualitative analysis are a limiting amount of the sample and a preferential orientation of crystals, both issues should be minimized by the special sample preparation. Urinary stones samples have been clustered into four groups using different sets of numerical input data (cation and anion content, phase composition). At the same time a high-throughput multivariate clustering has been applied for powder X-ray diffraction and IR-spectroscopy data. The multivariate whole-profile approach can be used as a tool for a high-throughput time reducing technique for clinical practice, when a quick and stable classification of samples is required. All three sets of the data can be automatically separated into three clusters: oxalate-reach, oxalate-pure and non-oxalate samples. Uricite-pure and uricite-rich samples can be easily clustered.      

X‐Ray Tomography Imaging of Porous Polyolefin Particles in an Electron Microscope

Advanced models of penetrant transport and reaction in spatially 3D porous polyolefin particles reconstructed from X‐ray µCT images require proper determination of particle morphology. Moreover, polyolefins exhibit a relatively low absorptivity for X‐rays, therefore their investigation using µCT can be difficult. In this paper, a low‐resolution µCT built into an SEM is used to examine how the µCT resolution and several user‐selected parameters associated with the scanning/reconstruction affect the resulting particle morphology. Using samples with known morphology and independent imaging techniques, the performance of the µCT device is critically assessed. Finally, a method suitable for the reliable reconstruction of polyolefin particles using low‐resolution µCT is proposed.

     

Kinetic model of olefin hydroalumination by HAlBui2 and AlBui3 in the presence of Cp2ZrCl2 catalyst

The mechanism of α‐olefin hydroalumination by HAlBuⁱ₂, ClAlBuⁱ₂, and AlBuⁱ₃ in the presence of Cp₂ZrCl₂ catalyst has been studied. It was established that the key intermediate of the reaction is a bimetallic complex [Cp₂ZrH₂ · ClAlBuⁱ₂]₂, which reacts with olefins and yields higher diisobutylalkylalanes. In parallel with this stage, the key complex can readily react with XAlBuⁱ₂ (X = H, Cl, Buⁱ) and form a stable trihydride complex Cp₂ZrH₂ · ClAlBuⁱ₂ · HAlBuⁱ₂, which does not exhibit reactivity in olefin hydroalumination. A kinetic model of α‐olefin hydroalumination with HAlBuⁱ₂ and AlBuⁱ₃ has been developed. The model explains the causes of the low stability of the key intermediate [Cp₂ZrH₂ · ClAlBuⁱ₂]₂ and of the different activities of organoaluminum compounds (OACs) in the olefin hydroalumination reaction. Moreover, the model gives information about the limit stages of the reaction and explains the influence of the length of the initial olefins on the rate of the whole catalytic process. © 2007 Wiley Periodicals, Inc. Int J Chem Kinet 39: 333–339, 2007     

Frank–Condon principle and adjustment of optical waveguides with nonhomogeneous refractive indices

The adjustment of two different selfocs is considered using both exact formulas for the mode-connection coefficients expressed in terms of Hermite polynomials of several variables and a qualitative approach based on the Frank–Condon principle. Several examples of the refractive-index dependence are studied and illustrative plots for these examples are presented. The connection with the tomographic approach to quantum states of a two-dimensional oscillator and the Frank–Condon factors is established.     

Decomposing Graphs into Long Paths

It is known that the edge set of a 2-edge-connected 3-regular graph can be decomposed into paths of length 3. W. Li asked whether the edge set of every 2-edge-connected graph can be decomposed into paths of length at least 3. The graphs C ₃, C ₄, C ₅, and K ₄−e have no such decompositions. We construct an infinite sequence {F _i } _i=0 ^∞ of nondecomposable graphs. On the other hand, we prove that every other 2-edge-connected graph has a desired decomposition. This revised version was published online in June 2006 with corrections to the Cover Date.