A semi-analytical finite element formulation for modeling stress wave propagation in axisymmetric damped waveguides

A semi-analytical finite element (SAFE) method is presented for analyzing the wave propagation in viscoelastic axisymmetric waveguides. The approach extends a recent study presented by the authors, in which the general SAFE method was extended to account for material damping. The formulation presented in this paper uses the cylindrical coordinates to reduce the finite element discretization over the waveguide cross-section to a mono-dimensional mesh. The algorithm is validated by comparing the dispersion results with viscoelastic cases for which a Superposition of Partial Bulk Waves solution is known. The formulation accurately predicts dispersion properties and does not show any missing root. Applications to viscoelastic axisymmetric waveguides with varying mechanical and geometrical properties are presented.     

Reversible Activation of Water by an Air- and Moisture-Stable Frustrated Rhodium Nitrogen Lewis Pair

[Cp*Rh(κ³N,N′,P- L )][SbF₆] (Cp*=C₅Me₅), bearing a guanidine-derived phosphano ligand L , behaves as a “dormant” frustrated Lewis pair and activates H₂ and H₂O in a reversible manner. When D₂O is employed, a facile H/D exchange at the Cp* ring takes place through sequential C(sp³)−H bond activation.     

Nonlinear corrector for Reynolds-averaged Navier-Stokes equations

The scope of this paper is to present a nonlinear error estimation and correction for Navier-Stokes and Reynolds-averaged Navier-Stokes equations. This nonlinear corrector enables better solution or functional output predictions at fixed mesh complexity and can be considered in a mesh adaptation process. After solving the problem at hand, a corrected solution is obtained by solving again the problem with an added source term. This source term is deduced from the evaluation of the residual of the numerical solution interpolated on the h/2 mesh. To avoid the generation of the h/2 mesh (which is prohibitive for realistic applications), the residual at each vertex is computed by local refinement only in the neighborhood of the considered vertex. One of the main feature of this approach is that it automatically takes into account all the properties of the considered numerical method. The numerical examples point out that it successfully improves solution predictions and yields a sharp estimate of the numerical error. Moreover, we demonstrate the superiority of the nonlinear corrector with respect to linear corrector that can be found in the literature.     

Divergent Synthesis of Bioactive Dithiodiketopiperazine Natural Products Based on a Double C(sp3)−H Activation Strategy

This article provides a detailed report of our efforts to synthesize the dithiodiketopiperazine (DTP) natural products (−)-epicoccin G and (−)-rostratin A using a double C(sp³)−H activation strategy. The strategy's viability was first established on a model system lacking the C8/C8’ alcohols. Then, an efficient stereoselective route including an organocatalytic epoxidation was secured to access a key bis-triflate substrate. This bis-triflate served as the functional handles for the key transformation of the synthesis: a double C(sp³)−H activation. The successful double activation opened access to a common intermediate for both natural products in high overall yield and on a multigram scale. After several unsuccessful attempts, this intermediate was efficiently converted to (−)-epicoccin G and to the more challenging (−)-rostratin A via suitable oxidation/reduction and protecting group sequences, and via a final sulfuration that occurred in good yield and high diastereoselectivity. These efforts culminated in the synthesis of (−)-epicoccin G and (−)-rostratin A in high overall yields (19.6 % over 14 steps and 12.7 % over 17 steps, respectively), with the latter being obtained on a 500 mg scale. Toxicity assessments of these natural products and several analogues (including the newly synthesized epicoccin K) in the leukemia cell line K562 confirmed the importance of the disulfide bridge for activity and identified dianhydrorostratin A as a 20x more potent analogue.     

Retracted: The Manganese(I)-Catalyzed Asymmetric Transfer Hydrogenation of Ketones: Disclosing the Macrocylic Privilege

The bis(carbonyl) manganese(I) complex [Mn(CO)₂( 1 )]Br ( 2 ) with a chiral (NH)₂P₂ macrocyclic ligand ( 1 ) catalyzes the asymmetric transfer hydrogenation of polar double bonds with 2-propanol as the hydrogen source. Ketones (43 substrates) are reduced to alcohols in high yields (up to >99 %) and with excellent enantioselectivities (90–99 % ee). A stereochemical model based on attractive CH–π interactions is proposed.     

Exciton Interactions,Excimer Formation,and [2π+2π] Photodimerization in Nonconjugated Curcuminoid-BF2 Dimers

We describe the synthesis of a series of covalently linked dimers of quadrupolar curcuminoid-BF₂ dyes and the detailed investigation of their solvent-dependent spectroscopic and photophysical properties. In solvents of low polarity, intramolecular folding induces the formation of aggregated chromophores, the UV/Vis absorption spectra of which display the optical signature characteristic of weakly-coupled H-aggregates. The extent of folding and, in turn, of ground-state aggregation is strongly dependent on the nature of the flexible linker. Steady-state and time-resolved fluorescence emission spectroscopies show that the Frenkel exciton relaxes into a fluorescent symmetrical excimer state with a long lifetime. Furthermore, our in-depth studies show that a weakly emitting excimer lies on the pathway toward a photocyclomer. Two-dimensional ¹H NMR spectroscopy and density functional theory (DFT) allowed the structure of the photoproduct to be established. To our knowledge, this represents the first example of a [2π+2π] photodimerization of the curcuminoid chromophore.     

Product measures and convergence theorems for product integrals in integration theory for semigroup valued functions

In [11] Sion has investigated measures and integrals having values in uniform semigroups. In this paper a result which gives sufficient conditions for the existence of a unique product of semigroup valued measures is established. Moreover a convergence theorem for product integrals of semigroup valued functions is proved.     

On chaotic extensions of dynamical systems

In this paper, inspired by some results in linear dynamics, we will show that every dynamical system (X,f), where f is a continuous self-map on a separable metric space X, can be extended to a chaotic (in the sense of Devaney) dynamical system in an isometric way.