Heat Kernel and Number Theory on NC-Torus

The heat trace asymptotics on the noncommutative torus, where generalized Laplacians are made out of left and right regular representations, is fully determined. It turns out that this question is very sensitive to the number-theoretical aspect of the deformation parameters. The central condition we use is of a Diophantine type. More generally, the importance of number theory is made explicit in a few examples. We apply the results to the spectral action computation and revisit the UV/IR mixing phenomenon for a scalar theory. Although we find non-local counterterms in the NC theory on , we show that this theory can be made renormalizable at least at one loop, and maybe even beyond.     

Recent advances in honeycomb-structured porous polymer films prepared via breath figures

Since its introduction in 1994, the preparation of ordered porous polymer films by the breath figure (BF) method has received a considerable interest. The so-called “honeycomb” (HC) films exhibit a hexagonal array of micrometric pores obtained by water droplet condensation during the fast solvent evaporation performed under a humid flow. The main focus of this feature article is to describe the recent advances in the design of honeycomb polymer films by the BF process. We first review the recent studies related to the honeycomb film formation through the exploration of different parameters such as the relative humidity, the polymer concentration, the drying rate, the substrate or the role of interfacial tension. The influence of the architecture and microstructure of the polymer is examined through examples. In this contribution, a special attention is given to the recent articles focused on the preparation of elaborate functional honeycomb-structured polymer films obtained via the simple BF method. In this context, we review the preparation of hierarchical HC films showing either sub- or super-structure, the formation of hybrid HC films by self-assembly of nanoparticles or in situ generation of the inorganic matter, the fluorescence in HC films introduced either by a fluorescent polymer or by fluorescent chemical groups, the elaboration of biomaterials from HC films decorated by glycopolymer and/or showing sensing ability and finally the design of functional polymeric surfaces with either stimuli-responsive or superhydrophobic properties.     

A note on relatives to the Held and Karp 1-tree problem

We study a class of graph problems which includes as special cases the Held and Karp 1-tree problem, and the minimum spanning tree problem with one degree constraint studied by Glover and Klingman. For another special case, we note a mistake in a paper by Ramesh, Yoon and Karwan.     

A stabilized column generation scheme for the traveling salesman subtour problem

Given an undirected graph with edge costs and both revenues and weights on the vertices, the traveling salesman subtour problem is to find a subtour that includes a depot vertex, satisfies a knapsack constraint on the vertex weights, and that minimizes edge costs minus vertex revenues along the subtour.We propose a decomposition scheme for this problem. It is inspired by the classic side-constrained 1-tree formulation of the traveling salesman problem, and uses stabilized column generation for the solution of the linear programming relaxation. Further, this decomposition procedure is combined with the addition of variable upper bound (VUB) constraints, which improves the linear programming bound. Furthermore, we present a heuristic procedure for finding feasible subtours from solutions to the column generation problems. An extensive experimental analysis of the behavior of the computational scheme is presented.     

Magnetisch nichtäquivalente Methylenprotonen in einigen 2-substituierten 1,3-Benzodioxanen

Zusammenfassung Die magnetische Nichtäquivalenz der Methylenprotonen in 2-R-Benzo-1,3-dioxanen, mit R=C₆H₅,o-ClC₆H₄,m-ClC₆H₄,p-ClC₆H₄,o-BrC₆H₄,m-BrC₆H₄,p-BrC₆H₄,o-NO₂C₆H₄,m-NO₂C₆H₄,p-NO₂C₆H₄,o-CH₃OC₆H₄,m-CH₃OC₆H₄,p-CH₃OC₆H₄, -Naphthyl, -Naphthyl, -Thienyl und -Thienyl, wurde in (CD₃)₂CO, CDCl₃, CCl₄, CS₂ und C₆D₆ untersucht.

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Magnetic non equivalent methylenic protons of some 2-substituted 1.3-benzodioxanes

The magnetic non equivalence of the methylenic protons in 2-R-1.3-benzodioxanes, with R=C₆H₅,o-ClC₆H₄,m-ClC₆H₄,p-ClC₆H₄,o-BrC₆H₄,m-BrC₆H₄,p-BrC₆H₄,o-NO₂C₆H₄,m-NO₂C₆H₄,p-NO₂C₆H₄,o-CH₃OC₆H₄,m-CH₃OC₆H₄,p-CH₃OC₆H₄, -naphthyl, -naphthyl, -thienyl and -thienyl were studied in (CD₃)₂CO, CDCl₃, CCl₄, CS₂ and C₆D₆.

     

Nanospray analysis of the venom of the tarantula Theraphosa leblondi: a powerful method for direct venom mass fingerprinting and toxin sequencing

Mass spectrometric methods, including matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry (MALDI-TOFMS), on-line liquid chromatography/electrospray ionisation mass spectrometry (LC/ESI-MS), and nanospray ionisation/hybrid quadrupole time-of-flight mass spectrometry (nanoESI-QqTOFMS), were applied to characterize by mass fingerprinting the venom of the French Guyanese tarantula Theraphosa leblondi. Of these techniques direct nanoESI-QqTOFMS, which allowed the detection of 65 protonated molecules with high mass accuracy, appeared to give the best results. Three major peptides, TlTx1, TlTx2 and TlTx3, were sequenced using a combination of nanoESI-MS/MS and enzyme digestion/MS and MS/MS experiments. Each sequence was confirmed by automated Edman sequencing. In patch-clamp experiments these peptides were found to have a specific inhibitory effect on the voltage-dependent potassium channel, Kv4.2.     

Diastereotope Methylenprotonen und Methylgruppen in 2-Substituierten 1,6-Methano [10] Annulenen

The double magnetic non equivalence of the diastereotopic methylene protons resp. geminal methyl groups of 2-substituted 1,6-methano [10]annulenes were observed in five solvents. It was found that Δν_AB for one of the two methylene groups were much smaller than Δν_{A ‘B’} for the other and that Δν_A‘B’ was much more solvent dependent than Δν_AB. Δν_{A “B”} for the bridge protons varied very little with the solvent used.     

Trifluoromethyl radical triggered radical cyclization of N-benzoyl ynamides leading to isoindolinones

Science China Chemistry - Under photocatalytic reductive conditions, trifluoromethyl radical addition onto an ynamide followed by cyclization on a benzoyl moiety produces diverse isoindolinone...     

Recognition of enantiomers with chiral molecular tweezers derived from (+)- or (−)-usnic acid

The synthesis of four stereoisomers of a chiral molecular tweezer using trans-1,2-diaminocyclohexane as spacer and two molecules of usnic acid as pincers is reported. The behavior of these chiral tweezers as chiral complexing agents was evaluated in NMR with various chiral esters containing an electron-poor aromatic ring to allow non-covalent aromatic–aromatic interactions.