Szegö-Kolmogorov-Krein theorems on weighted trigonometrical approximation and Cárleman-type relations

We consider the well-known Szegö — Kolmogorov — Krein theorems on weighted approximations by functions with semibounded spectra defined on a circle or on a line and suggest an efficient construction that realizes these approximations. This construction is based on relations similar to the Cárleman formula for reconstructing analytic functions in terms of their traces on the boundary of their domains of definition.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, Nos. 1–2, pp. 100–127, January–February. 1994.     

Optically Anomalous Crystals

The optical symmetry of many crystals is lower than would be expected from their external form and X-ray diffraction data. Recently such optical anomalies have been attributed to nonequilibrium structures resulting from kinetically controlled crystal growth. Impurities are incorporated to different extents at various surface sites that would otherwise have become symmetry-related within the bulk crystal. After their discovery by Brewster in 1815, optically anomalous crystals were the subject of lively debate throughout the 19th century among some of the most distinguished contributors to the development of crystallography including Biot, Berzelius, Herschel, Mitscherlich, Frankenheim, Pasteur, Mallard, Klein, Groth, Wyrouboff, Barlow, Brauns, Rinne, Pockels, and Friedel. From a sea of wild speculation two conflicting postulates emerged: that the symmetric form resulted from accidental twinning of segments with lower symmetry, or that the optical peculiarities resulted from stress due to impurities or external perturbations. Neither postulate expresses the present view. Interest in this research waned at the turn of the century, and after 1917 no one pursued Tammann's alternative correct insight. The problem of anomalous double refraction attracted no attention for more than half a century until its recent solution. This review discusses both mineral and organic systems with particular emphasis on the phyllosilicate apophyllite and on 1,5-dichloro-2,3-dinitrobenzene. These nonequilibrium structures relate to questions of crystal order, crystal growth, molecular recognition, and the design of new materials. The review provides a reminder of the enduring value of the polarizing microscope as a research tool in chemistry.     

On Weaknesses of Non–surjective Round Functions

We propose a new attack on Feistel ciphers with a non-surjective round function such as the CAST cipher family and LOKI91. We extend the attack towards block ciphers that use a non-uniformly distributed round function and apply the extended attack to the CAST family. This attack demonstrates that the round function of a Feistel cipher with six to eight rounds needs to be surjective and sufficiently uniform.     

Spectral Gap for Stable Process on Convex Planar Double Symmetric Domains

We study the semigroup of the symmetric α-stable process in bounded domains in R ². We obtain a variational formula for the spectral gap, i.e. the difference between two first eigenvalues of the generator of this semigroup. This variational formula allows us to obtain lower bound estimates of the spectral gap for convex planar domains which are symmetric with respect to both coordinate axes. For rectangles, using “midconcavity” of the first eigenfunction (Bañuelos et al., Potential Anal. 24(3): 205–221, 2006), we obtain sharp upper and lower bound estimates of the spectral gap.     

Impact of Turbulent Flow and Mean Mixture Fraction Results on Mixing Model Behavior in Transported Scalar PDF Simulations of Turbulent Non-premixed Bluff Body Flames

Numerical simulation results are presented for three turbulent jet diffusion flames, stabilized behind a bluff body (Sydney Flames HM1-3). Interaction between turbulence and combustion is modeled with the transported joint-scalar PDF approach. The focus of the study is on the impact of the quality of simulation results in physical space on the behavior of two micro-mixing models in composition space: the Euclidean Minimum Spanning Tree (‘EMST’) model and the modified Curl coalescence dispersion (‘CD’) model. Profiles of conditional means and variances of thermo-chemical quantities, conditioned on the mixture fraction, are discussed in the recirculation region and in the neck zone behind. The impact of the flow and mixing fields in physical space on the mixing model behavior in composition space is strong for the CD model and increases as the turbulence – chemistry interaction becomes stronger. The EMST conditional profiles, on the contrary, are hardly affected.     

Study of the distribution of actinides in human tissues using synchrotron radiation micro X-ray fluorescence spectrometry

This study aims at evaluating the capabilities of synchrotron radiation micro X-ray fluorescence spectrometry (SR micro-XRF) for qualitative and semi-quantitative elemental mapping of the distribution of actinides in human tissues originating from individuals with documented occupational exposure. The investigated lymph node tissues were provided by the United States Transuranium and Uranium Registries (USTUR) and were analyzed following appropriate sample pre-treatment. Semi-quantitative results were obtained via calibration by external standards and demonstrated that the uranium concentration level in the detected actinide hot spots reaches more than 100 μg/g. For the plutonium hot spots, concentration levels up to 31 μg/g were found. As illustrated by this case study on these unique samples, SR micro-XRF has a high potential for this type of elemental bio-imaging owing to its high sensitivity, high spatial resolution, and non-destructive character.

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Graphical Abstract SR micro-XRF study of the distribution of actinitides in human tissues. Left Location of the U-contaminated tissue sample in the human body. Middle U distribution derived from the high resolution SR micro-XRF scan on the tissue sample, indication of five U hot spots. Right Detail of the point measurement spectrum of U hot spot 3, intense U-L_α fluorescence peak located at 13.6 keV.

     

Characterizations of the Suzuki tower near polygons

In recent work, we constructed a new near octagon \(\mathcal {G}\) from certain involutions of the finite simple group \(G_2(4)\) and showed a correspondence between the Suzuki tower of finite simple groups, \(L_3(2)< U_3(3)< J_2< G_2(4) < Suz\), and the tower of near polygons, \(\mathrm {H}(2,1) \subset \mathrm {H}(2)^D \subset \mathsf {HJ} \subset \mathcal {G}\). Here we characterize each of these near polygons (except for the first one) as the unique near polygon of the given order and diameter containing an isometrically embedded copy of the previous near polygon of the tower. In particular, our characterization of the Hall–Janko near octagon \(\mathsf {HJ}\) is similar to an earlier characterization due to Cohen and Tits who proved that it is the unique regular near octagon with parameters (2, 4; 0, 3), but instead of regularity we assume existence of an isometrically embedded dual split Cayley hexagon, \(\mathrm {H}(2)^D\). We also give a complete classification of near hexagons of order (2, 2) and use it to prove the uniqueness result for \(\mathrm {H}(2)^D\).     

Sequences of harmonic maps in the 3‐sphere

We define two transforms of non‐conformal harmonic maps from a surface into the 3‐sphere. With these transforms one can construct, from one such harmonic map, a sequence of harmonic maps. We show that there is a correspondence between harmonic maps into the 3‐sphere, H‐surfaces in Euclidean 3‐space and almost complex surfaces in the nearly Kähler manifold . As a consequence we can construct sequences of H‐surfaces and almost complex surfaces.     

Stimuli-responsive electrospun fibers and their applications

Stimuli-responsive electrospun nanofibers are gaining considerable attention as highly versatile tools which offer great potential in the biomedical field. In this critical review, an overview is given on recent advances made in the development and application of stimuli-responsive fibers. The specific features of these electrospun fibers are highlighted and discussed in view of the properties required for the diverse applications. Furthermore, several novel biomedical applications are discussed and the respective advantages and shortcomings inherent to stimuli-responsive electrospun fibers are addressed (136 references).