Shintani lifts and fractional derivatives for harmonic weak Maass forms

In this paper, we construct Shintani lifts from integral weight weakly holomorphic modular forms to half-integral weight weakly holomorphic modular forms. Although defined by different methods, these coincide with the classical Shintani lifts when restricted to the space of cusp forms. As a side effect, this gives the coefficients of the classical Shintani lifts as new cycle integrals. This yields new formulas for the L-values of Hecke eigenforms. When restricted to the space of weakly holomorphic modular forms orthogonal to cusp forms, the Shintani lifts introduce a definition of weakly holomorphic Hecke eigenforms. Along the way, auxiliary lifts are constructed from the space of harmonic weak Maass forms which yield a “fractional derivative” from the space of half-integral weight harmonic weak Maass forms to half-integral weight weakly holomorphic modular forms. This fractional derivative complements the usual ξ-operator introduced by Bruinier and Funke.     

Tribological durability of silane monolayers on silicon

We report the frictional performance and long-term tribological stability of various alkyl silane monolayer films on silicon by using pin-on-disk tribometry at ambient conditions. We show that the durability of monolayers derived from n-alkyltrichlorosilanes on silicon increases exponentially with the chain length of the silane precursor, which we relate to the cohesive energy of these monolayers through molecular dynamics simulations. X-ray photoelectron spectroscopy (XPS) was used to show that tribological damage consisted of the loss of molecular components that could be partially replaced upon exposure to a solution containing perfluorinated silane precursors. For monolayers derived from n-octadecyltrichlorosilane, a critical load was identified to be approximately 250 mN (200 MPa), above which failure of films occurred within 100 cycles of testing. Monolayers with hydroxyl surfaces exhibited reduced stabilities due to stronger tip-surface interactions. Monolayers with the capability for cross-linking exhibited much greater stabilities than monolayers where cross-linking was limited or prevented. Collectively, these results demonstrate that the mechanical durability of monolayers when subjected to a tribological load is greatly enhanced by maximizing dispersional interactions and cross-linking and minimizing tip-surface interactions.     

Total synthesis of iejimalide B

Iejimalide B, a structurally unique 24-membered polyene macrolide having a previously underutilized mode of anticancer activity, was synthesized according to a strategy employing Julia-Kocienski olefinations, a palladium-catalyzed Heck reaction, a palladium-catalyzed Marshall propargylation, a Keck-type esterification, and a palladium-catalyzed macrolide-forming, intramolecular Stille coupling of a highly complex cyclization substrate. The overall synthesis is efficient (19.5% overall yield for 15 linear steps) and allows for more practical scaled-up synthesis than previously reported strategies that differed in the order of assembly of key subunits and in the method of macrocyclization. The present synthesis paves the way for efficient preparation of analogues for drug development efforts.     

Failure criteria with unilateral conditions for simulation of plate perforation

Finite element analysis of plate perforation is performed using a thermoelastic–thermoviscoplastic constitutive model and two uncoupled damage criteria with unilateral conditions. The first criterion is based on continuum damage mechanics, while the second is the Cockcroft–Latham criterion. Fracture is assumed to occur at a critical damage, and crack propagation is modelled with element erosion. The identification of the material parameters is based on inverse modelling of a uniaxial tension test. The constitutive model and damage criteria are applied in explicit finite element analysis of the perforation of a 12 mm thick steel plate struck by a blunt projectile in the sub-ordinance velocity regime. The results show the importance of the unilateral conditions in obtaining accurate prediction of the adiabatic shear banding process. The two fracture criteria have comparable dependence on the stress triaxiality and the Lode parameter when the microcrack-closure parameter is set to zero in the criterion based on continuum damage mechanics, and give similar failure mode and ballistic limit in the plate perforation problem.     

A microfocus X‐ray fluorescence beamline at Indus‐2 synchrotron radiation facility

A microfocus X‐ray fluorescence spectroscopy beamline (BL‐16) at the Indian synchrotron radiation facility Indus‐2 has been constructed with an experimental emphasis on environmental, archaeological, biomedical and material science applications involving heavy metal speciation and their localization. The beamline offers a combination of different analytical probes, e.g. X‐ray fluorescence mapping, X‐ray microspectroscopy and total‐external‐reflection fluorescence characterization. The beamline is installed on a bending‐magnet source with a working X‐ray energy range of 4–20 keV, enabling it to excite K‐edges of all elements from S to Nb and L‐edges from Ag to U. The optics of the beamline comprises of a double‐crystal monochromator with Si(111) symmetric and asymmetric crystals and a pair of Kirkpatrick–Baez focusing mirrors. This paper describes the performance of the beamline and its capabilities with examples of measured results.     

The homotopy types of compact lie groups

Hans Scheerer proved that if two simply connected compact Lie groups are homotopically equivalent, then the groups are isomorphic. We give a conceptually simpler proof which shows that the result depends only on the 2 and 3 primary homotopy of the Lie groups.     

Dynamic nuclear magnetic resonance and empirical force field studies of cannabidiol

Internal rotation of cannabidiol (1), its mono-(2) and dimethyl (3) derivatives has been studied by ¹H and ¹³C dynamic NMR spectroscopy. The free energy of activation for the rotation of C₃-C₂, bond that we have observed for cannabidiol of 14.7 kcal/mol at 22° in CDCl₃ is in contrast with values previously reported in the literature. Molecular mechanics simulation of the rotation of C₃-C₂, bond of a model structure (4) well reproduced the presently determined barrier height. Analysis of the calculated rotational transition state structure revealed severe nonbonded C₂H/O and C ₈/O interactions as the source of barrier. Calculations of other model structures indicate general occurrence of restricted rotation about the pivot bond of phenylcyclohexanes appropriately substituted at β-carbon of cyclohexane ring and at ortho position of phenyl ring. The fully substituted 2,6-dimethyl-1-(o,o'-dimethylphenyl) cyclohexane (10) is predicted to show atropisomerism.     

The synthesis of cyclopropyl analogues of precocene I

A new, short synthesis of precocene I is described together with the syntheses of two cyclopropyl analogues. One of these compounds showed interesting biological activity against the bean aphid, $\text{Aphis fabae}$