Direct cyclopropanation of 1-alkynylphosphonates by Cp2ZrCl2/2EtMgBr/2AlCl3 to afford cyclopropylmethylphosphonates

[reaction: see text] The reagent system Cp2ZrCl2/2EtMgBr/2AlCl3 converts 1-alkynylphosphonates into cyclopropylmethylphosphonates 3 in good isolated yields. Ethers, chlorides, and other cyclopropyl groups are compatible with the reaction conditions. Deuterium labeling is consistent with the formation of stable cyclopropylmethylbimetallic phosphonates by ring contraction of the corresponding aluminacyclopentenylphosphonate. Temperature is crucial; apparently, the cyclopropylmethylbimetallic phosphonates are in equilibrium with the aluminacyclopentenylphosphonates. Low temperature favors the former. We surmise that the negative charges of the intermediate are stabilized by the phosphonate group. Thus, diphenylacetylene and 3-hexyne failed to give cyclopropyl products under the same reaction conditions.     

An autoxidation study of C2 substituted pyrimidine amino reductones

Three pyrimidine derivatives (8a-c), differing from isouramil and divicine at C2, have been synthesized and their autoxidation rates measured spectrophotometrically. The autoxidation rates of all five pyrimidines (8a-c, isouramil and divicine) were correlated with values (rho=−1.28, r²=0.949).     

Spray algorithm without interface construction

This research is aimed to create a new and robust family of convective schemes to capture the interface between the dispersed and the carrier phases in a spray without the need to build up the interface boundary. The selection of the Weighted Average Flux (WAF) scheme is due to this scheme being designed to deal with random flux scheme which is second-order accurate in space and time. The convective flux in each cell face utilizes the WAF scheme blended with Switching Technique for Advection and Capturing of Surfaces (STACS) scheme for high resolution flux limiters. In the next step, the high resolution scheme is blended with the WAF scheme to provide the sharpness and boundedness of the interface by using switching strategy. In this work, the Eulerian–Eulerian framework of non-reactive turbulent spray is set in terms of theoretical proposed methodology namely spray moments of drop size distribution, presented by Beck and Watkins [1]. The computational spray model avoids the need to segregate the local droplet number distribution into parcels of identical droplets. The proposed scheme is tested on capturing the spray edges in modelling hollow cone sprays without need to reconstruct two-phase interface. A test is made on simple comparison between TVD scheme and WAF scheme using the same flux limiter on convective flow hollow cone spray. Results show the WAF scheme gives a better prediction than TVD scheme. The only way to check the accuracy of the presented models is by evaluating the spray sheet thickness.     

On vanishing patterns in <Emphasis Type="Italic">j</Emphasis>-strands of edge ideals

We consider two problems regarding vanishing patterns in the Betti table of edge ideals I over any fixed field. First, we show that the j-strand is connected if \(j=3\) (for \(j=2\) this is easy and known), and give examples where the j-strand is not connected for any \(j>3\). Next, we apply our result on strand connectivity to establish the subadditivity conjecture for edge ideals, \(t_{a+b}(I)\le t_a(I)+t_b(I)\), in case \(b=2,3\) (the case \(b=1\) is known). Here \(t_i(I)\) denote the maximal shifts in the minimal free resolution of S / I over its polynomial algebra.     

Enantioselective Crystallization of Chiral Inorganic Crystals of ϵ-Zn(OH)2 with Amino Acids

Many inorganic materials can form crystals, but little is known about their enantioselective crystallization. Herein, we report on the enantioselective crystallization of ϵ-Zn(OH)₂ (Wulfingite) chiral crystals by using amino acids. Crystals of ϵ-Zn(OH)₂ were crystallized from supersaturated sodium hydroxide and zinc nitrate aqueous solutions in the presence of l - or d -arginine. All of the chiral measurements, such as selective chiral adsorption by circular dichroism (CD), chiral chromatography, and polarimetry measurements, clearly show chiral discrimination during the crystallization of ϵ-Zn(OH)₂. In addition, a new method has been developed for identifying chirality in crystals by using electron paramagnetic resonance (EPR). Although the values of chiral induction of the ϵ-Zn(OH)₂ crystals obtained are somewhat low, these values are still significant because they demonstrate that enantioselectivity during the crystallization of chiral inorganic crystals with chiral additives can be achieved. The method can be applied to many chiral inorganic systems. Understanding and controlling the crystallization of chiral inorganic crystals is important for gaining knowledge on the interaction of chiral molecules with inorganic surfaces. This knowledge can lead to an understanding of basic scientific questions such as the evolution of homochirality in biomolecules and the development of chiral inorganic crystals for a variety of purposes such as asymmetric catalysis and optical applications.     

On the stability of Langmuir films of pyramidic mesogens

Abstract

Pyramidic mesogens forming thermotropic liquid crystal bulk phases were spread in an air-water interface. Pressure surface measurements and polarizing microscopy on the Langmuir films were used to characterize the various states of these pyramidic-like molecules. For two compounds bearing short lateral aliphatic chains, the surface pressure isotherms exhibit a large plateau region corresponding to a metastable monolayer in which the molecules may adopt an ‘edge-on’ arrangement. The coexistence of multilayered, anisotropic, slowly growing domains with the monolayer in the plateau region has been observed at long time scale. The film area relaxation kinetics at constant surface pressure show the existence of two nucleation mechanisms for the formation of these domains.     

Optimal Stability and Instability for Near-Linear Hamiltonians

In this paper, we will prove a very general result of stability for perturbations of linear integrable Hamiltonian systems, and we will construct an example of instability showing that both our result and our example are optimal. Moreover, in the same spirit as the notion of KAM stable integrable Hamiltonians, we will introduce a notion of effectively stable integrable Hamiltonians, conjecture a characterization of these Hamiltonians and show that our result proves this conjecture in the linear case.     

The classical KAM theorem for Hamiltonian systems via rational approximations

In this paper, we give a new proof of the classical KAM theorem on the persistence of an invariant quasi-periodic torus, whose frequency vector satisfies the Bruno-Rüssmann condition, in real-analytic non-degenerate Hamiltonian systems close to integrable. The proof, which uses rational approximations instead of small divisors estimates, is an adaptation to the Hamiltonian setting of the method we introduced in [4] for perturbations of constant vector fields on the torus.     

Ergodization time for linear flows on tori via geometry of numbers

In this paper, we give a new, short, simple, and geometric proof of the optimal ergodization time for linear flows on tori. This result was first obtained by Bourgain et al. (Comm Math Phys 190:491–508, 1998) using Fourier analysis. Our proof uses geometry of numbers: it follows trivially from a Diophantine duality that was established by Bounemoura and Fischler (Math 275:1135–1167, 2013).