Boron trifluoride–etherate mediated synthesis of 3-desoxyanthocyanidins including a total synthesis of tricetanidin from black tea

The synthesis of a series of 3-desoxyanthocyanidins via a BF₃·Et₂O-mediated aldol condensation between a substituted acetophenone and salicylaldehyde derivatives is described. Using this new synthetic methodology the synthesis of tricetanidin, a natural pigment isolated from black tea, was accomplished.     

Fusion of 2-D SIMS Images Using the Wavelet Transform

 Secondary ion mass spectroscopy (SIMS) is a powerful method for element distribution examination of conducting and semi-conducting surfaces at high spatial resolution and with a high sensitivity. Routine surface analysis produces about 8 to 15 images in a short time, each of which displays the intensity distribution of one mass, thus generating a multispectral SIMS image. Formation of occlusions, segregations, and the overall location of the elements relative to each other, are difficult to recognise when looking at n separate 2-D images. Image fusion is a process whereby images obtained from various sensors, or at different moments of time, or under different conditions, are combined together to provide a more complete picture of the object under investigation. The process of combining SIMS images may be viewed as an attempt to compensate for the inherent effect of SIMS to channel the information obtained from the sample into different images, corresponding to different element phases. The wavelet transform is a powerful method for fusion of images. This work covers the use of wavelet based fusion algorithms on multispectral SIMS images, evaluating the performance of different wavelet based fusion rules on different type of image systems and comparing the results to conventional fusion techniques. An aim of this study is to increase the information, i.e. the number of masses, which can be merged into one image in order to enhance the perception and interpretation of the SIMS surface images.     

gem-Bromochlorospiropentane reactivity toward methyllithium: an unusual carbenoid rearrangement

A skeletal carbenoid rearrangement of the gem-bromochlorospiropentanes in the presence of methyllithium has been studied. The synthetic and mechanistic aspects of this rearrangement as well as the influence of the halogen atom nature on the reaction pathway are discussed.     

Tensor train completion: Local recovery guarantees via Riemannian optimization

In this work, we estimate the number of randomly selected elements of a tensor that with high probability guarantees local convergence of Riemannian gradient descent for tensor train completion. We derive a new bound for the orthogonal projections onto the tangent spaces based on the harmonic mean of the unfoldings' singular values and introduce a notion of core coherence for tensor trains. We also extend the results to tensor train completion with auxiliary subspace information and obtain the corresponding local convergence guarantees.     

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.     

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)