A Jordan Curve Spanned by a Complete Minimal Surface

In this paper we construct complete (conformal) minimal immersions which admit continuous extensions to the closed disk, . Moreover, is a homeomorphism and is a (non-rectifiable) Jordan curve with Hausdorff dimension 1. It turns out that the set of Jordan curves constructed by the above procedure is dense in the space of Jordan curves of with the Hausdorff metric.     

π‐Expanded α,β‐Unsaturated Ketones: Synthesis,Optical Properties,and Two‐Photon‐Induced Polymerization

A library of π‐expanded α,β‐unsaturated ketones was designed and synthesized. They were prepared by a combination of Wittig reaction, Sonogashira reaction, and aldol condensation. It was further demonstrated that the double aldol condensation can be performed effectively for highly polarized styrene‐ and diphenylacetylene‐derived aldehydes. The strategic placement of two dialkylamino groups at the periphery of D ‐π‐A‐π‐D molecules resulted in dyes with excellent solubility. These ketones absorb light in the region 400–550 nm. Many of them display strong solvatochromism so that the emission ranges from 530–580 nm in toluene to the near‐IR region in benzonitrile. Ketones based on cyclobutanone as central moieties display very high fluorescence quantum yields in nonpolar solvents, which decrease drastically in polar media. Photophysical studies of these new functional dyes revealed that they possess an enhanced two‐photon absorption cross section when compared with simpler ketone derivatives. Due to strong polarization of the resulting dyes, values of two‐photon absorption cross sections on the level of 200–300 GM at 800 nm were achieved, and thanks to that as well as the presence of the keto group, these new two‐photon initiators display excellent performance so that the operating region is 5–75 mW in some cases.     

The Synthesis of New Organoselenium Heterocyclic Compounds: 2‐aryl‐4‐phenyl‐5,6,7,8‐tetrahydro‐4H‐selenochromenes

We have explored the reactions of 2‐(3‐oxo‐1‐aryl‐3‐phenylpropyl)cyclohexanone ( 1–3 ) with hydrogen selenide in situ in conditions of acid catalysis, and synthesized new 2‐aryl‐4‐phenyl‐5,6,7,8‐tetrahydro‐4H‐selenochromenes ( 4–6 ).     

Sharp Hardy Inequalities in Star-shaped Domains with Double Singular Kernels

Improved Hardy inequality with double singular kernel in bounded, star-shaped domains \(\Omega \subset R^n\) is proved. The case of singularity at an interior point and on the boundary of the domain is considered. The Hardy constant is optimal and the inequality is sharp due to the additional term.     

Singular Solutions to Conformal Hessian Equations

The authors show that for any e ∈]0,1[,there exists an analytic outside zero solution to a uniformly elliptic conformal Hessian equation in a ball B C R5 which belongs to C1'ε(B) \ C1'ε+(B).     

Structural design sensitivity analysis in context of non-linear buckling

Structural stability is an important issue to ensure the safety of thin walled structures. Shell structures are considered in context of linear and non-linear buckling. The design sensitivity analysis with respect to modifications in shape is motivated. Analytically derived gradient information is employed for shape optimisation purposes using solid shells. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Biodistribution and toxicity of engineered gold nanoparticles: a review of in vitro and in vivo studies

Recent advances in wet chemical synthesis and biomolecular functionalization of gold nanoparticles have led to a dramatic expansion of their potential biomedical applications, including biosensorics, bioimaging, photothermal therapy, and targeted drug delivery. As the range of gold nanoparticle types and their applications continues to increase, human safety concerns are gaining attention, which makes it necessary to better understand the potential toxicity hazards of these novel materials. Whereas about 80 reports on the in vivo biodistribution and in vitro cell toxicity of gold nanoparticles are available in the literature, there is lack of correlation between both fields and there is no clear understanding of intrinsic nanoparticle effects. At present, the major obstacle is the significant discrepancy in experimental conditions under which biodistribution and toxicity effects have been evaluated. This critical review presents a detailed analysis of data on the in vitro and in vivo biodistribution and toxicity of most popular gold nanoparticles, including atomic clusters and colloidal particles of diameters from 1 to 200 nm, gold nanoshells, nanorods, and nanowires. Emphasis is placed on the systematization of data over particle types and parameters, particle surface functionalization, animal and cell models, organs examined, doses applied, the type of particle administration and the time of examination, assays for evaluating gold particle toxicity, and methods for determining the gold concentration in organs and distribution of particles over cells. On the basis of a critical analysis of data, we arrive at some general conclusions on key nanoparticle parameters, methods of particle surface modification, and doses administered that determine the type and kinetics of biodistribution and toxicity at cellular and organismal levels (197 references).     

Cluster resolution: a metric for automated, objective and optimized feature selection in chemometric modeling

A novel metric termed cluster resolution is presented. This metric compares the separation of clusters of data points while simultaneously considering the shapes of the clusters and their relative orientations. Using cluster resolution in conjunction with an objective variable ranking metric allows for fully automated feature selection for the construction of chemometric models. The metric is based upon considering the maximum size of confidence ellipses around clusters of points representing different classes of objects that can be constructed without any overlap of the ellipses. For demonstration purposes we utilized PCA to classify samples of gasoline based upon their octane rating. The entire GC-MS chromatogram of each sample comprising over 2 × 10⁶ variables was considered. As an example, automated ranking by ANOVA was applied followed by a forward selection approach to choose variables for inclusion. This approach can be generally applied to feature selection for a variety of applications and represents a significant step towards the development of fully automated, objective construction of chemometric models.