Conformational analysis of some C2-symmetric cyclic peptides containing tetrahydrofuran amino acids

Cyclic oligomers of tetrahydrofuran amino acids, cyclo-(Taa1-Leu-Val)2 (left), cyclo-(Taa2-Leu-Val)2 (middle), and cyclo-(Taa2-Phe-Leu)2 (right), displayed well-defined intramolecularly hydrogen-bonded structures with distorted "beta-beta corner" motifs similar to the tennis ball seam.     

Organocatalytic Asymmetric Mannich Cyclization of Hydroxylactams with Acetals: Total Syntheses of (−)‐Epilupinine, (−)‐Tashiromine,and (−)‐Trachelanthamidine

An asymmetric, organocatalytic, one‐pot Mannich cyclization between a hydroxylactam and acetal is described to provide fused, bicyclic alkaloids bearing a bridgehead N atom. Both aliphatic and aromatic substrates were used in this transformation to furnish chiral pyrrolizidinone, indolizidinone, and quinolizidinone derivatives in up to 89 % yield and 97 % ee. The total syntheses of (?)‐epilupinine, (?)‐tashiromine, and (?)‐trachelanthamidine also achieved to demonstrate the generality of the process.     

The palladium-catalyzed cross-coupling reaction of carboxylic anhydrides with arylboronic acids: a DFT study

The mechanism of the cross-coupling of phenylboronic acid with acetic anhydride, a viable model of the widely used Suzuki reaction, has been studied by DFT calculations at the BP86/6-31G level of theory. Two alternative catalytic cycles have been investigated, one starting from a neutral Pd(0)L(2) complex, the other from an anionic "Jutand-type" [Pd(0)L(2)X](-) species. The reaction profiles are in good agreement with the experimental findings, as both pathways require only moderate activation energies. Both pathways are dominated by cis-configured square-planar palladium(II)diphosphine intermediates. Despite careful investigations, we did not find in this model reaction any evidence for five-coordinate palladium(II) intermediates, which are commonly believed to cause the profound effects of counterions in palladium-catalyzed transformations. Instead, our calculations suggest that the higher catalytic activity of anionic complexes, such as [Pd(PMe(3))(2)OAc](-), may arise from their stronger ability to coordinate to carbon electrophiles. The transmetalation sequence is the same for both catalytic cycles, involving the dissociation of one phosphine ligand from the palladium. In the decisive transition state, in which the phenyl group is transferred from boron to palladium, the acetate base is found to be in a bridging coordination between these two atoms.     

Error estimate for a fully discrete spectral scheme for Korteweg-de Vries-Kawahara equation

We are concerned with convergence of spectral method for the numerical solution of the initial-boundary value problem associated to the Korteweg-de Vries-Kawahara equation (Kawahara equation, in short), which is a transport equation perturbed by dispersive terms of the 3rd and 5th order. This equation appears in several fluid dynamics problems. It describes the evolution of small but finite amplitude long waves in various problems in fluid dynamics. These equations are discretized in space by the standard Fourier-Galerkin spectral method and in time by the explicit leap-frog scheme. For the resulting fully discrete, conditionally stable scheme we prove an L ²-error bound of spectral accuracy in space and of second-order accuracy in time.     

Nondeterministic approach to tree-based jet substructure

Jet substructure is typically studied using clustering algorithms, such as k(T), which arrange the jets' constituents into trees. Instead of considering a single tree per jet, we propose that multiple trees should be considered, weighted by an appropriate metric. Then each jet in each event produces a distribution for an observable, rather than a single value. Advantages of this approach include (1) observables have significantly increased statistical stability, and (2) new observables, such as the variance of the distribution, provide new handles for signal and background discrimination. For example, we find that employing a set of trees substantially reduces the observed fluctuations in the pruned mass distribution, enhancing the likelihood of new particle discovery for a given integrated luminosity. Furthermore, the resulting pruned mass distributions for (background) QCD jets are found to be substantially wider than that for (signal) jets with intrinsic mass scales, e.g., boosted W jets. A cut on this width yields a substantial enhancement in significance relative to a cut on the standard pruned jet mass alone. In particular the luminosity needed for a given significance requirement decreases by a factor of 2 relative to standard pruning.     

Cu(II) catalyzed imine C-H functionalization leading to synthesis of 2,5-substituted 1,3,4-oxadiazoles

A direct access to symmetrical and unsymmetrical 2,5-disubstituted [1,3,4]-oxadiazoles has been accomplished through an imine C-H functionalization of N-arylidenearoylhydrazide using a catalytic quantity of Cu(OTf)(2). This is the first example of amidic oxygen functioning as a nucleophile in a Cu-catalyzed oxidative coupling of an imine C-H bond. These reactions can be performed in air atmosphere and moisture making it exceptionally practical for application in organic synthesis.     

Inverse Boundary Value Problem of Determining Up to a Second Order Tensor Appear in the Lower Order Perturbation of a Polyharmonic Operator

Journal of Fourier Analysis and Applications - We consider the following perturbed polyharmonic operator $$\mathcal {L}(x,D)$$ of order 2m defined in a bounded domain $$\Omega \subset \mathbb...     

Identifying shifts between two regression curves

Annals of the Institute of Statistical Mathematics - This article studies the problem whether two convex (concave) regression functions modelling the relation between a response and covariate in...     

Silanylidene and Germanylidene Anions: Valence‐Isoelectronic Species to the Well‐Studied Phosphinidene

The reduction of TipMCl₃ (Tip=2,4,6‐triisopropylphenyl) (M=Si, Ge) with KC₈ in the presence of cyclic alkyl(amino) carbene (cAAC) afforded the acyclic silanylidene and germanylidene anions in the form of potassium salt [K(cAAC)MTip]₂ (M=Si ( 1 ); Ge ( 2 )). The silanylidene and germanylidene anions are valence‐isoelectronic to the well‐studied phosphinidene and are a new class of acyclic anions of Group 14. Compounds 1 and 2 were isolated and well characterized by NMR and single‐crystal X‐ray structure analysis. Furthermore, the structure and bonding of compounds 1 and 2 was investigated by computational methods.     

Gram level synthesis of lead-free solder in the nanometer length scale obtained from tin and silver compounds using silicone oil

A straightforward route to gram level synthesis of a pure phase of the Sn-Ag nanoalloy in an eutectic composition (Sn/Ag 96.5:3.5) in silicone oil is reported. The composition, morphology, and microstructure of the alloy were fully characterized. In a mixture of ethylene glycol and silicone oil, direct reduction of Sn(II) acetate and Ag(I) nitrate gave the Sn-Ag nanoalloy. The nanoalloy disintegrates by sonication and reforms by heating, leading to smaller particles with a melting point as low as 128 degrees C.