Reflection groups on Riemannian manifolds

We investigate discrete groups G of isometries of a complete connected Riemannian manifold M which are generated by reflections, in particular those generated by disecting reflections. We show that these are Coxeter groups, and that the orbit space M/G is isometric to a Weyl chamber C which is a Riemannian manifold with corners and certain angle conditions along intersections of faces. We can also reconstruct the manifold and its action from the Riemannian chamber and its equipment of isotropy group data along the faces. We also discuss these results from the point of view of Riemannian orbifolds. Mathematics Subject Classification Primary 51F15, 53C20, 20F55, 22E40     

One-step assembly of carbamoyl substituted annulated 1,4-oxazepines

We present a convenient synthesis of heterocyclic scaffolds using a novel modification of four-component Ugi condensation. Two complementary variants of this useful synthetic strategy provide an efficient one-step assembly of four novel pharmaceutically relevant (hetero)aryl-fused 1,4-oxazepines with different substituents’ profile.     

Influence of exposure to vitrification solutions on 2-cell mouse embryos: I. Intracellular potassium and sodium content

Intracellular concentrations of potassium and sodium in two-cell mouse embryos in G1/S phase after exposure to vitrification solutions containing vitrificant agents (VFAs) ethane-1,2-diol (ethylene glycol, EG), propane-1,2-diol (propylene glycol, PG), or dimethyl sulfoxide (DMSO), and sucrose (S) after incubation in Dulbecco solution were measured by electron probe microanalysis (EPMA) as described earlier (CryoLetters, 2006, 27: 87-98). The 4-step protocol was as followed: 10% VFA for 10 min => 30% VFA + 0.7 M S for 1.5 min ==> 0.5 M S for 10 min ==> 10 min pure Dulbecco's. The cytoplasmic concentration of potassium and sodium in immediately flashed out from the oviduct embryos was in range of 120 +/- 2 mM, with good concordance with the previous data (CryoLetters, 2006, 27:87-98). Exposure in Dulbecco's for 30 min did not alter elemental composition, neither did exposure in PG or DMSO for 1.5 min. In contrast, exposure for 1.5 min in EG dropped the level of potassium to 96 +/- 2 mM while elevating level of cytoplasmic sodium to 136 +/- 3 mM. Further exposure to 30%-EG for 3 min led to a two-fold decrease of both elements (60 +/- 3 mM and 66 +/- 2 mM for K and Na, respectively).     

Composite and filament models for the mechanical behaviour of elastomeric materials

In this work we present a composite model, which combines the approach of Poisson's function with the filament theory and requires three material parameters. We also suggest the form for a strain-energy function that approximates the constitutive equations of the composite model. Furthermore, a simple asymptotic analysis allows us to reduce the number of material constants to only two, thus, forming a new filament model. The predictive capability of the two models to reproduce the mechanical behaviour of elastomeric materials in deformation experiments is evaluated against the extensive data of Kawabata et al. (Macromolecules 14 (1981) 154). The models give excellent agreement in not only uniaxial and equibiaxial but also non-equibiaxial extension. Although being rather more simplistic in comparison with some successful network models involving non-Gaussian chain statistics, the two models conform much more closely to the classical experimental data of Treloar (Trans. Faraday Soc. 40 (1944) 59).     

Experimental investigation of various turbulator inserts in gas-heated channels

This experimental research was focused on the investigation of the heat transfer augmentation by various turbulator inserts in gas-heated channels. The work was conducted directly in a convective part of a two fire-tube boiler. The flue ducts were positioned vertically and horizontally for various design applications. Twisted-tape insert (with the twist ratio y=4.12), the straight-tape insert, and the combined turbulator insert (the internal twisted tape with the twist ratio of 180° y=2.16 and an external tape, which spirally winded on an internal tape, with longitudinal pitch H_360°=110 mm and the relative height of a tape (rib) e/D₀=0.098;0.2) were investigated. The working fluids were the combustion products of light oil fuel and wood pellets. In addition, the experiments were conducted in the two fire-tube boiler without any inserts. Despite of relatively large data scattering obtained in these experiments some qualitative and quantitative conclusions were drawn.     

Synthesis and Evaluation of GdIII‐Based Magnetic Resonance Contrast Agents for Molecular Imaging of Prostate‐Specific Membrane Antigen

Magnetic resonance (MR) imaging is advantageous because it concurrently provides anatomic, functional, and molecular information. MR molecular imaging can combine the high spatial resolution of this established clinical modality with molecular profiling in vivo. However, as a result of the intrinsically low sensitivity of MR imaging, high local concentrations of biological targets are required to generate discernable MR contrast. We hypothesize that the prostate‐specific membrane antigen (PSMA), an attractive target for imaging and therapy of prostate cancer, could serve as a suitable biomarker for MR‐based molecular imaging. We have synthesized three new high‐affinity, low‐molecular‐weight Gd^III‐based PSMA‐targeted contrast agents containing one to three Gd^III chelates per molecule. We evaluated the relaxometric properties of these agents in solution, in prostate cancer cells, and in an in vivo experimental model to demonstrate the feasibility of PSMA‐based MR molecular imaging.     

Extraction products from <Emphasis Type="Italic">Miscanthus</Emphasis> var. ‘Soranovskii’

The chemical structures of Miscanthus var. ‘Soranovskii’ lignin fractions released via extraction of lignin from the lignocellulosic feedstock using moderately heated acetone under atmospheric pressure, without acidic and alkaline catalysts, were studied. A blend of Miscanthus stems and leaves was pretreated with water under thermobaric conditions. The acetone organosolv process subsequently afforded a substance related to a lignin-like matter-acetone organosolv Miscanthus lignin (AOML). Non-destructive analytical techniques such as FTIR spectroscopy, gas chromatography-mass spectrometry, size-exclusion chromatography, and 2D NMR were used. The IR and NMR spectroscopies revealed the AOML structure to comprise all the three major types of phenylpropane units: guaiacyl (G), syringyl (S), and p-hydroxyphenyl (H). The resultant acetone-organosolv lignin exhibits good solubility in polar solvents, moderate solubility in aromatic chemicals, and is insoluble in non-polar solvents, exhibiting the physicochemical properties of a thermoplastic polymer with a softening point of 67.0°C (onset 33.0°C, endset 81.5°C).     

Slow Effects of Fast Harmonic Excitation for Elastic Structures

High-frequency excitation may affect the slow behavior of a dynamical system. For example, equilibria may move, disappear, or gain or loose stability. We consider such slow effects of fast excitation for a simple mechanical system that incorporates features of many engineering structures. The study is intended to contribute to the general understanding of periodically excited linear and nonlinear systems, as well as to the current attempts to utilize high-frequency excitation for altering the low-frequency properties of structures.