Impact of geometry on the TM photonic band gaps of photonic crystals and quasicrystals

Here we demonstrate a novel quantitative procedure to pursue statistical studies on the geometric properties of photonic crystals and photonic quasicrystals (PQCs) which consist of separate dielectric particles. The geometric properties are quantified and correlated to the size of the photonic band gap (PBG) for wide permittivity range using three characteristic parameters: shape anisotropy, size distribution, and feature-feature distribution. Our concept brings statistical analysis to the photonic crystal research and offers the possibility to predict the PBG from a morphological analysis.     

Simulation of ion beam extraction and focusing system

The characteristics of ion beam extraction and focused to a volume as small as possible were investigated with the aid of computer code SIMION 3D version 7. This has been used to evaluate the extraction characteristics (accel-decel system) to generate an ion beam with low beam emittance and high brightness. The simulation process can provide a good study for optimizing the extraction and focusing system of the ion beam without any losses and transported to the required target. Also, a study of a simulation model for the extraction system of the ion source was used to describe the possible plasma boundary curvatures during the ion extraction that may be affected by the change in an extraction potential with a constant plasma density meniscus.     

A random coordinate descent algorithm for optimization problems with composite objective function and linear coupled constraints

In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz continuous gradient, then we prove that our method obtains an ?-optimal solution in $\mathcal{O}(n^{2}/\epsilon)$ iterations, where n is the number of blocks. For the class of problems with cheap coordinate derivatives we show that the new method is faster than methods based on full-gradient information. Analysis for the rate of convergence in probability is also provided. For strongly convex functions our method converges linearly. Extensive numerical tests confirm that on very large problems, our method is much more numerically efficient than methods based on full gradient information.     

Asymmetric synthesis of (−)-fosfomycin and its trans-(1S,2S)-diastereomer using a biocatalytic reduction as the key step

Fosfomycin is a gram positive and gram negative antibiotic that contains an asymmetric epoxide. An enzyme library was screened for its ability to reduce dimethyl(1-chloro-2-oxopropyl)phosphonate to the corresponding asymmetric chlorohydrin. Homology models were built in MOE, which were shown to accurately model the enzyme–substrate complex displaying the stereoselectivity that we observed. Two enzymes, YDR368w and YHR104w, were chosen for the scale up and synthesis of fosfomycin and its trans-(1S,2S)-diastereomer.     

Synthesis and Stereochemistry of Novel Dibrominated 1,5-Dioxaspiro[5.5]undecane Derivatives

 The synthesis and stereochemistry of new dibrominated spiro-1,3-dioxane derivatives are reported. Investigations by means of NMR methods and single crystal X-ray diffraction for two compounds revealed the high regio- and diastereoselectivity of the bromination reaction of some new spiro-1,3-dioxanes and the asymmetric induction of the chiral carbon atom located in the spiro skeleton.     

Enumerative Properties of NC (B) (p,q)

We determine the rank generating function, the zeta polynomial and the M?bius function for the poset NC ^(B) (p, q) of annular non-crossing partitions of type B, where p and q are two positive integers. We give an alternative treatment of some of these results in the case q = 1, for which this poset is a lattice. We also consider the general case of multiannular noncrossing partitions of type B, and prove that this reduces to the cases of non-crossing partitions of type B in the annulus and the disc.     

Synthesis and photophysical properties of some 6,6″-functionalized terpyridine derivatives

The synthesis and photophysical properties of several 6,6″ symmetrically substituted 4′-aryl-2,2′:6′,2″-terpyridine derivatives are reported herein. The UV-Vis spectra in acetonitrile as well as in dichloromethane show two intense bands in the UV areas 252–262 nm and 275–290 nm while the fluorescence emission spectra are only slightly influenced by chemical derivatization.     

Hexaaquacobalt(II) and hexaaquanickel(II) bis(μ‐pyridine‐2,6‐dicarboxylato)bis[(pyridine‐2,6‐dicarboxylato)bismuthate(III)] dihydrate

The title complexes, hexaaquacobalt(II) bis(μ‐pyridine‐2,6‐dicarboxylato)bis[(pyridine‐2,6‐dicarboxylato)bismuthate(III)] dihydrate, [Co(H₂O)₆][Bi₂(C₇H₄NO₄)₄]·2H₂O, (I), and hexaaquanickel(II) bis(μ‐pyridine‐2,6‐dicarboxylato)bis[(pyridine‐2,6‐dicarboxylato)bismuthate(III)] dihydrate, [Ni(H₂O)₆][Bi₂(C₇H₄NO₄)₄]·2H₂O, (II), are isomorphous and crystallize in the triclinic space group P. The transition metal ions are located on the inversion centre and adopt slightly distorted MO₆ (M = Co or Ni) octahedral geometries. Two [Bi(pydc)₂]⁻ units (pydc is pyridine‐2,6‐dicarboxylate) are linked via bridging carboxylate groups into centrosymmetric [Bi₂(pydc)₄]²⁻ dianions. The crystal packing reveals that the [M(H₂O)₆]²⁺ cations, [Bi₂(pydc)₄]²⁻ anions and solvent water molecules form multiple hydrogen bonds to generate a supramolecular three‐dimensional network. The formation of secondary Bi...O bonds between adjacent [Bi₂(pydc)₄]²⁻ dimers provides an additional supramolecular synthon that directs and facilitates the crystal packing of both (I) and (II).