An exposition of the topological half of the Grothendieck–Hirzebruch–Riemann–Roch theorem in the fancy language of spectra

We give an informal exposition of pushforwards and orientations in generalized cohomology theories in the language of spectra. The whole note can be seen as an attempt at convincing the reader that Todd classes in Grothendieck–Hirzebruch–Riemann–Roch type formulas are not Devil’s appearances but rather that things just go in the most natural possible way.

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The local ultraconvergence of high‐order finite element method for second‐order elliptic problems with constant coefficients over a rectangular partition

In this article, we will discuss the local ultraconvergence of high‐degree finite element method based on a rectangular partition for the second‐degree elliptic problem with constant coefficients in Ω ? ?² , u( y ) = 0 on ?Ω . Based on suitable regularity, ultraconvergence of the displacement of the extrapolated kth (k ≥ 3) degree finite element solution has been obtained by an extrapolation technique. Finally, numerical experiments are applied to demonstrate our theoretical findings.     

Theoretical Studies on S-Phenyl-thiabenzene,S-Phenyl-thianaphthalene,and S-Phenyl-thiaanthracene

The molecular structures of S-phenyl-thiabenzene 1, S-phenyl-1-thianaphthalene 2, S-phenyl-2-thianaphthalene 3, and S-phenyl-9-thiaanthracene 4 are studied by ab initio calculations using HF as well as DFT methods at the 6–311+G? level of theory. The non-planar boat conformers of 1–4 with 6π electrons in the heterocyclic ring appear to be more stable than the corresponding planar conformers with 8π electrons in the ring. The activation energy for the inversion at the sulfur atom is compared for 1–4. Conformational flexibility of 1–4 is studied.     

A Spectroscopic Overview of Intramolecular Hydrogen Bonds of NH…O,S,N Type

Intramolecular NH…O,S,N interactions in non-tautomeric systems are reviewed in a broad range of compounds covering a variety of NH donors and hydrogen bond acceptors. ¹H chemical shifts of NH donors are good tools to study intramolecular hydrogen bonding. However in some cases they have to be corrected for ring current effects. Deuterium isotope effects on ¹³C and ¹⁵N chemical shifts and primary isotope effects are usually used to judge the strength of hydrogen bonds. Primary isotope effects are investigated in a new range of magnitudes. Isotope ratios of NH stretching frequencies, νNH/ND, are revisited. Hydrogen bond energies are reviewed and two-bond deuterium isotope effects on ¹³C chemical shifts are investigated as a possible means of estimating hydrogen bond energies.     

Single‐crystalline gold microplates grown on substrates by solution‐phase synthesis

Chemically synthesized single‐crystalline gold microplates have been attracting increasing interest because of their potential as high‐quality gold films for nanotechnology. We present the growth of tens of nanometers thick and tens of micrometers large single‐crystalline gold plates directly on solid substrates by solution‐phase synthesis. Compared to microplates deposited on substrates from dispersion phase, substrate‐grown plates exhibit significantly higher quality by avoiding severe small‐particle contamination and aggregation. Substrate‐grown gold plates also open new perspectives to study the growth mechanism via step‐growth and observation cycles of a large number of individual plates. Growth models are proposed to interpret the evolution of thickness, area and shape of the plates. It is found that the plate surface remains smooth after regrowth, implying the applicability of regrowth for producing giant plates as well as unique single‐crystalline nano‐structures.