Powers of Hamilton cycles in random graphs and tight Hamilton cycles in random hypergraphs

We show that for every there exists C > 0 such that if then asymptotically almost surely the random graph contains the k^th power of a Hamilton cycle. This determines the threshold for appearance of the square of a Hamilton cycle up to the logarithmic factor, improving a result of Kühn and Osthus. Moreover, our proof provides a randomized quasi‐polynomial algorithm for finding such powers of cycles. Using similar ideas, we also give a randomized quasi‐polynomial algorithm for finding a tight Hamilton cycle in the random k‐uniform hypergraph for . The proofs are based on the absorbing method and follow the strategy of Kühn and Osthus, and Allen et al. The new ingredient is a general Connecting Lemma which allows us to connect tuples of vertices using arbitrary structures at a nearly optimal value of p. Both the Connecting Lemma and its proof, which is based on Janson's inequality and a greedy embedding strategy, might be of independent interest.     

Solvent Effects on the Structure-Activity Relationship of Phenytoin-like Anticonvulsant Drugs

The absorption spectra of nine compounds structurally related to phenytoin (5,5-diphenylhydantoin) were recorded in twelve solvents over the range of 200 to 400 nm. The effects of solvent dipolarity/polarizability and solvent/solute hydrogen bonding interactions were analyzed by means of the linear solvation energy relationship (LSER) concept proposed by Kamlet and Taft. The lipophilic activity of the investigated hydantoins was estimated by calculation of their log ₁₀ P values. The calculated values of log ₁₀ P were correlated with the ratio of the contributions of specific and non-specific solute/solvent interactions. The correlation equations were combined with the corresponding ED₅₀ values to generate new equations that demonstrate exact relationship between solute/solvent interactions and the structure-activity parameters.     

Multiband processing of multimode light: combining 3D photonic lanterns with waveguide Bragg gratings

The first demonstration of narrowband spectral filtering of multimode light on a 3D integrated photonic chip using photonic lanterns and waveguide Bragg gratings is reported. The photonic lanterns with multi‐notch waveguide Bragg gratings were fabricated using the femtosecond direct‐write technique in boro‐aluminosilicate glass (Corning, Eagle 2000). Transmission dips of up to 5 dB were measured in both photonic lanterns and reference single‐mode waveguides with 10.4‐mm‐long gratings. The result demonstrates efficient and symmetrical performance of each of the gratings in the photonic lantern. Such devices will be beneficial to space‐division multiplexed communication systems as well as for units for astronomical instrumentation for suppression of the atmospheric telluric emission from OH lines.     

Brane-induced-gravity shock waves

We construct exact gravitational field solutions for a relativistic particle localized on a tensional brane in brane-induced gravity. They are a generalization of gravitational shock waves in 4D de Sitter space. We provide the metrics for both the normal branch and the self-inflating branch Dvali-Gabadadze-Porrati brane worlds, and compare them to the 4D Einstein gravity solution and to the case when gravity resides only in the 5D bulk, without any brane-localized curvature terms. At short distances the wave profile looks the same as in four dimensions. The corrections appear only far from the source, where they differ from the long distance corrections in 4D de Sitter space. We also discover a new nonperturbative channel for energy emission into the bulk from the self-inflating [corrected] branch, when gravity is modified at the de Sitter radius.     

Linear Free‐Energy Relationships Applied to the 13C NMR Chemical Shifts in 4‐Substituted N‐[1‐(Pyridine‐3‐ and ‐4‐yl)ethylidene]anilines

Two series of 4‐substituted N‐[1‐(pyridine‐3‐ and ‐4‐yl)ethylidene]anilines have been synthesized using different methods of conventional and microwave‐assisted synthesis, and linear free‐energy relationships have been applied to the ¹³C NMR chemical shifts of the carbon atoms of interest. The substituent‐induced chemical shifts have been analyzed using single substituent parameter and dual substituent parameter methods. The presented correlations describe satisfactorily the field and resonance substituent effects having similar contributions for C1 and the azomethine carbon, with exception of the carbon atom in para position to the substituent X. In both series, negative ρ values have been found for C1′ atom (reverse substituent effect). Quantum chemical calculations of the optimized geometries at MP2/6‐31G++(d,p) level, together with ¹³C NMR chemical shifts, give a better insight into the influence of the molecular conformation on the transmission of electronic substituent effects. The comparison of correlation results for different series of imines with phenyl, 4‐nitrophenyl, 2‐pyridyl, 3‐pyridyl, 4‐pyridyl group attached at the azomethine carbon with the results for 4‐substituted N‐[1‐(pyridine‐3‐ and ‐4‐yl)ethylidene]anilines for the same substituent set (X) indicates that a combination of the influences of electronic effects of the substituent X and the π₁‐unit can be described as a sensitive balance of different resonance structures.     

Carbonised polyaniline and polypyrrole: towards advanced nitrogen-containing carbon materials

Polyaniline (PANI) and polypyrrole (PPY) undergo carbonisation in an inert/reduction atmosphere and vacuum, yielding different nitrogen-containing carbon materials. This contribution reviews various procedures for the carbonisation of PANI and PPY precursors, and the characteristics of obtained carbonised PANI (C-PANI) and carbonised PPY (C-PPY). Special attention is paid to the role of synthetic procedures in tailoring the formation of C-PANI and C-PPY nanostructures and nanocomposites. The review considers the importance of scanning and transmission electron microscopies, XPS, FTIR, Raman, NMR, and EPR spectroscopies, electrical conductivity and adsorption/desorption measurements, XRD, and elemental analyses in the characterisation of C-PANIs and C-PPYs. The application of C-PANI and C-PPY in various fields of modern technology is also reviewed.     

Preconditioning of Krylov subspace methods using recycling in Lattice QCD computations

Many applications in computational science and engineering require the solution of sequences of slowly changing linear systems. We focus on problems arising in Lattice QCD simulations. In order to generate an ensemble of configurations from which the values of physical observables can be obtained, we have to solve a linear system with a Dirac operator in each time step of the hybrid Monte-Carlo simulations. This operator changes just slightly from time step to time step. While recycling subspace information from the previous system like described in [1] reduces the number of necessary matrix-vector multiplications, the systems are still expensive to solve. To overcome this limitation, we include preconditioning in our implementation. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)