(2,2′‐Bipyridine)bis(tri‐tert‐butoxysilanethiolato‐κS)lead(II) and (4,7‐diphenyl‐1,10‐phenanthroline‐κ2N,N′)bis(tri‐tert‐butoxysilanethiolato‐κS)lead(II) benzene hemisolvate

In the title mononuclear lead silanethiolates, [Pb(C₁₂H₂₇O₃SSi)₂(C₁₀H₈N₂)], (I), and [Pb(C₁₂H₂₇O₃SSi)₂(C₂₄H₁₆N₂)]·0.5C₆H₆, (II), the Pb atom shows a distorted square‐pyramidal coordination with a PbON₂S₂ core in which one S atom lies in an axial position. Intermolecular π–π and C—H...π interactions stabilize the structures. The benzene solvent molecule in (II) lies on an inversion centre.     

Natural (+)-carotol as a donor of chirality in the synthesis of enantiomerically pure hydroindene building blocks

3-Isopropyl-7a-methyl-1,2,3,6,7,7a-hexahydro-inden-5-one is a building block used in the reconstruction of the cyathane skeleton. In this article, a new and efficient method of the synthesis for (3R,7aR)-3-isopropyl-7a-methyl-1,2,3,6,7,7a-hexahydro-inden-5-one has been described.     

On MIMO model reduction by the weighted equation–error approach

The paper deals with the problem of approximating a stable continuous-time multivariable system by minimizing the L ₂-norm of a weighted equation error. Necessary and sufficient conditions of optimality are derived, and the main properties of the optimal reduced-order models are presented. Based on these conditions and properties, two efficient procedures for generating approximants that retain different numbers of Markov parameters and time moments are suggested and applied to benchmark examples. The results show that both the transient and the steady-state behaviour of the original systems are reproduced satisfactorily.     

Frequency domain imaging of absorbers obscured by scattering.

Multiple pixel, frequency domain measurements of phase shift, theta, and modulation, m, in a phantom containing an absorber obscured by a relatively non-absorbing scattering solution are presented in combination with a theory of photon migration imaging. Results employing a single point source show that two dimensional theta measurements made in the presence (theta presence) and in the absence (theta absence) of an absorber can be used to create delta theta images. delta theta (theta absence-theta presence) images can be used to detect as well as locate the three dimensional position of the absorber. Images of mpresence measured in the presence of the absorber normalized by mabsence also provided detection and two dimensional location of its position. Images of % mpresence/mabsence at higher modulation frequencies provided greater resolution as predicted by photon migration theory. Neither theta nor m images alone could be used to detect or locate the presence of the absorber.     

An investigation of squaraines as a new class of fluorophores with long-wavelength excitation and emission

We present an overview of our investigation of the spectral properties and photostabilities of squaraine derivatives. The objective was to identify long-wavelength probes with reasonable quantum yields, reasonably long lifetimes, and good photostabilities for use in fluorescence-based assays and/or imaging. Both symmetrical and unsymmetrical squaraines were studied. Based on this investigation the most suitable probes for use in a biological application were found to be the symmetrical indolenine derivatives of the squaraines, which display the highest photostability. Importantly, their quantum yields and lifetimes increase significantly upon covalent and noncovalent binding to proteins (bovine serum albumin, antibodies), demonstrating the usefulness of the squaraines as long wavelength probes. The squaraine absorbance maxima between 630 and 650 nm allows the use of the new commercially available 635- and 650-nm diode lasers.     

A non-archimedean Dugundji extension theorem

We prove a non-archimedean Dugundji extension theorem for the spaces C*(X, C* (X, K) of continuous bounded functions on an ultranormal space X with values in a non-archimedean non-trivially valued complete field K. Assuming that K is discretely valued and Y is a closed subspace of X we show that there exists an isometric linear extender T: C* (Y, K) → K* (X, K) if X is collectionwise normal or Y is Lindelöf or K is separable. We provide also a self contained proof of the known fact that any metrizable compact subspace Y of an ultraregular space X is a retract of X.     

Damage identification for beams in noisy conditions based on Teager energy operator-wavelet transform modal curvature

Modal curvatures have been widely used in the detection of structural damage. Attractive features of modal curvature include great sensitivity to damage and instant determination of damage location. However, an intrinsic deficiency in a modal curvature is its susceptibility to the measurement noise present in the displacement mode shape that produces the modal curvature, likely obscuring the features of damage. To address this deficiency, the Teager energy operator together with wavelet transform is tactically utilized to treat modal curvature, producing a new modal curvature, termed the Teager energy operator-wavelet transform modal curvature. This new modal curvature features distinct capabilities of suppressing noise, canceling global trends, and intensifying the singular feature caused by damage for a measured mode shape involving noise. These features maximize the sensitivity to damage and accuracy of damage localization. The proposed modal curvature is demonstrated in several analytical cases of cracked pinned–pinned, clamped–free and clamped–clamped beams, with emphasis on characterizing damage in noisy conditions, and it is further validated by an experimental program using a scanning laser vibrometer to acquire mode shapes of a cracked aluminum beam. The Teager energy operator-wavelet transform modal curvature essentially overcomes the deficiency of conventional modal curvature, providing a new dynamic feature well suited for damage characterization in noisy environments. (The Matlab code for implementing Teager energy operator-wavelet transform modal curvature can be provided by the corresponding author on request.)     

Precursor and Solvent Effects in the Nonhydrolytic Synthesis of Complex Oxide Nanoparticles for Bioimaging Applications by the Ether Elimination (Bradley) Reaction

Investigation of the solvent and alkoxide precursor effect on the nonhydrolytic sol–gel synthesis of oxide nanoparticles by means of an ether elimination (Bradley) reaction indicates that the best crystallinity of the resulting oxide particles is achieved on application of aprotic ketone solvents, such as acetophenone, and of smallest possible alkoxide groups. The size of the produced primary particles is always about 5 nm caused by intrinsic mechanisms of their formation. The produced particles, possessing the composition of natural highly insoluble minerals, are biocompatible. Optical characteristics of the perovskite complex oxide nanoparticles can easily be controlled through doping with rare earth cations; for example, by Eu³⁺. They can be targeted through surface modification by anchoring the directing biomolecules through a phosphate or phosphonate moiety. Testing of the distribution of Eu‐doped BaTiO₃ particles, modified with ethylphosphonic acid, demonstrates their facile uptake by the plants with active fluid transport, resulting finally in their enhanced concentration within the cell membranes.     

Structure of Malicious Singularities

In this paper, we investigate relativistic spacetimes, together with their singular boundaries (including the strongest singularities of the Big Bang type, called malicious singularities), as noncommutative spaces. Such a space is defined by a noncommutative algebra on the transformation groupoid = × G, where is the total space of the frame bundle over spacetime with its singular boundary, and G is its structural group. We show that there exists the bijective correspondence between unitary representations of the groupoid and the systems of imprimitivity of the group G. This allows us to apply the Mackey theorem to this case, and deduce from it some information concerning singular fibers of the groupoid . At regular points the group representation, which is a part of the corresponding system of imprimitivity, does not have discrete components, whereas at the malicious singularity such a group representation can be a single representation (in particular, an irreducible one) or a direct sum of such representations. A subgroup K G, from which—according to the Mackey theorem—the representation is induced to the whole of G, can be regarded as measuring the richness of the singularity structure. In this sense, the structure of malicious singularities is richer than those of milder ones.