Accelerating light beams along arbitrary convex trajectories

We demonstrate, theoretically and experimentally, nonbroadening optical beams propagating along any arbitrarily chosen convex trajectory in space. We present a general method to construct such beams, and demonstrate it by generating beams following polynomial and exponential trajectories. We find that all such beams, accelerating along any convex trajectory, display the same universal intensity cross section, irrespective of their acceleration. The universal features of these beams are explored using catastrophe theory.     

Robust Synthesis of Gold Nanotriangles and their Self-Assembly into Vertical Arrays

We report an efficient, seed-mediated method for the synthesis of gold nanotriangles (NTs) which can be used for controlled self-assembly. The main advantage of the proposed synthetic protocol is that it relies on using stable (over the course of several days) intermediate seeds. This stability translates into increasing time efficiency of the synthesis and makes the protocol experimentally less demanding (‘fast addition’ not required, tap water can be used in the final steps) as compared to previously reported procedures, without compromising the size and shape monodispersity of the product. We demonstrate high reproducibility of the protocol in the hands of different researchers and in different laboratories. Additionally, this modified seed-mediated method can be used to produce NTs with edge lengths between ca. 45 and 150 nm. Finally, the high ‘quality’ of NTs allows the preparation of long-range ordered assemblies with vertically oriented building blocks, which makes them promising candidates for future optoelectronic technologies.     

Interactions of (MY)6 (M = Zn,Cd; Y = O,S, Se) quantum dots with N-bases

Structural Chemistry - (MY)6 clusters, with M = Zn and Cd and Y = O, S, Se, form double-layer drum-like structures containing M–Y covalent bonds. The positive regions near the M atoms attract...     

Two-dimensional Fourier transform of arbitrarily sampled NMR data sets

A new procedure for Fourier transform with respect to more than one time variable simultaneously is proposed for NMR data processing. In the case of two-dimensional transform the spectrum is calculated for pairs of frequencies, instead of conventional sequence of one-dimensional transforms. Therefore, it enables one to Fourier transform arbitrarily sampled time domain and thus allows for analysis of high dimensionality spectra acquired in a short time. The proposed method is not limited to radial sampling, it requires only to fulfill the Nyquist theorem considering two or more time domains at the same time. We show the application of new approach to the 3D HNCO spectrum acquired for protein sample with radial and spiral time domain sampling.     

Polygon vertex extremality and decomposition of polygons

In this paper, we show that if we decompose a polygon into two smaller polygons, then by comparing the number of extremal vertices in the original polygon versus the sum of the two smaller polygons, we can gain at most two globally extremal vertices in the smaller polygons, as well as at most two locally extremal vertices. We then will derive two discrete Four-Vertex Theorems from our results.     

Zur elektrographischen Bestimmung von Blei in Legierungen

Zusammenfassung Die elektrographische Methode wurde zur Bestimmung von Pb in Pb-Sn-Legierungen verwendet. Die Fehler überschreiten nicht ±0,6%. Es wurde auch der Einfluß der Spannung, der Zeitdauer, der Konzentration des Elektrolyten sowie der Oberfläche der untersuchten Proben auf die entstandene Menge an Pb²⁺-Ionen untersucht.

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Summary The electrographic method has been applied to the determination of Pb in Pb-Sn alloys. The error is smaller than ±0,6%. The effects of voltage, time, electrolyte concentration and surface area of the sample on the amount of Pb²⁺ ions formed has been investigated.

     

The DQ-HN[CACB] and DQ-HN(CO)[CACB] sequences with evolution of double quantum Calpha-Cbeta coherences

The new variant of known HNCACB and HN(CO)CACB techniques is proposed that employs excitation and evolution of double quantum Calpha-Cbeta coherences. The most important features of the new method are: increased signal dispersion, lack of splittings due to 1J(Calpha-Cbeta) spin-spin couplings, and absence of accidental cancellations of positive and negative signals. The acquisition of both DQ-HN[CACB] and DQ-HN(CO)[CACB] techniques enables sequential assignment of protein backbone, using only Calpha-Cbeta DQ-frequencies. The determination of all Calpha and Cbeta chemical shifts requires, however, a comparison with HN(CO)CA or HNCA spectra. Examples of applications of the DQ-HN[CACB] and DQ-HN(CO)[CACB] experiments are presented, employing the 2D Reduced Dimensionality approach for 13C, 15N-labeled ubiquitin, and the 3D acquisition for 13C, 15N-double labeled Ca2+ -binding bovine S100A1 protein in the apo state (21 kDa) with overall correlation time of 8.1 ns.