Aqueous microwave-assisted DMAP catalyzed synthesis of β-phosphonomalonates and 2-amino-4H-chromen-4-ylphosphonates via a domino Knoevenagel-phospha-Michael reaction

An aqueous microwave (mw)-assisted DMAP catalyzed one-pot highly efficient route to synthesize β-phosphonomalonates and 2-amino-4H-chromen-4-yl phosphonates has been demonstrated via the domino Knoevenagel-phospha-Michael reaction of aryl aldehyde/salicylaldehyde, malononitrile/ethyl cyanoacetate and alkyl phosphite ester. Optimization of reaction conditions were performed by using conventional and microwave synthetic approaches. This conversion proceeded smoothly to deliver the desired product in good to excellent yields (75–95%) in a short reaction time (10–12 min). The present methodology is very simple, environmentally benign, high yielding and has very well demonstrated the synergistic effect of water and microwaves.     

Microbial desulfurization of waste latex rubber with Alicyclobacillus sp.

A microbe with desulfurizing capability, Alicyclobacillus sp., was selected to recycle waste latex rubber (WLR). The growth characteristics of the microorganism and the technical conditions in the co-culture desulfurization process were studied. The desulfurization effect of Alicyclobacillus sp. on the WLR was characterized, and the mechanism for the microbial desulfurization of WLR was tentatively explored. The results showed that adding 5% (w/v) WLR into medium had little effect on the growth of Alicyclobacillus sp. The surfactant polysorbate 80 (Tween 80) had a toxic effect on Alicyclobacillus sp., but the growth of the microbe was vigorous if the proper technique was used: the mixing of WLR with Tween 80, followed by the addition of the mixture into the culture media. With the increase of desulfurization time, the swelling value of desulfurizated waste latex rubber (DWLR) increased, but the crosslink density decreased. After co-culture desulfurization for 8–10 days, a DWLR with good desulfurization effect was obtained. The mechanical properties of natural rubber (NR)/DWLR composite improved significantly over those of NR/WLR composite. XPS and FTIR results revealed that Alicyclobacillus sp. could break the crosslinked sulfur bonds and oxidize them to sulfones groups. The increase of O element content on the surface of DWLR was confirmed by water contact angle measurements. The relationship between the crosslink density and sol fraction of DWLR with different desulfurization times agreed with the Horikx equation, an indication that the microorganisms could break the crosslinked sulfur bonds on the surface of WLR, but leaving the main chains intact.     

Efficient and Environmentally Friendly Approach to the Synthesis of Ferrocenyl‐Substituted 1,5‐Diketone Compounds Under Solvent‐Free Conditions

Abstract

This article describes a fast, efficient, economical, and environmentally friendly method for the preparation of a series of ferrocenyl‐substituted 1,5‐diketone compounds via Michael addition of ferrocenyl‐substituted chalcones with deoxybenzoin or dibenzyl ketone under solvent‐free conditions, and affords the corresponding Michael adducts with excellent yields of 77–93%.     

Innovative approach for the synthesis of N-substituted amides from nitriles and alcohols using propylphosphonic anhydride (T3P®) under solvent-free conditions

Novel and convenient methodology for the construction of N-substituted amide derivatives have been developed from nitriles and alcohols using propylphosphonic anhydride (T3P^®). This methodology is an alternate approach to the synthesis of amides via Ritter reaction, which is one of the classical methods for the synthesis of N-substituted amides from nitriles and alcohols. In this approach, first T3P^® activates the alcohol which is then attacked by nitrile to form N-substituted amides. This methodology can also apply for the synthesis of benzhydryl ether. This developed protocol is one of the novel applications of T3P^®.     

The Riemann–Hilbert Problem in Weighted Classes of Cauchy Type Integrals with Density from L P( · )(Γ)

We consider the Riemann–Hilbert problem in the following setting: find a function whose boundary values ϕ⁺(t) satisfy the condition a.e. on Γ. Here D is a simply connected domain bounded by a simple closed curve Γ, and K ^{p( · )}(D;ω) is the set of functions ϕ(z) representable in the form , where ω(z) is a weight function and (K _Γφ )(z) is a Cauchy type integral whose density φ is integrable with a variable exponent p(t). It is assumed that Γ is a piecewise-Lyapunov curve without zero angles, ω(z) is an arbitrary power function and p(t) satisfies the Log-H?lder condition. The solvability conditions are established and solutions are constructed. These solutions largely depend on the coefficients a, b, c, the weight ω, on the values of p(t) at the angular points of Γ and on the values of angles at these points. Submitted: May 13, 2007. Revised: August 8, 2007 and August 28, 2007. Accepted: November 8, 2007.     

The Schauder fixed point theorem in geodesic spaces

We give a direct proof of Schauder's fixed point theorem in the setting of geodesic metric spaces, generalizing the classical Schauder's theorem and improving a recent version of this theorem in CAT(κ)$\mathrm{CAT}(\kappa )$ spaces. As an application we prove an existence result for a variational inequality in the setting of CAT(κ)$\mathrm{CAT}(\kappa )$ spaces.     

Quasi-static Maxwell's equations with a dissipative non-linear boundary condition: Full discretization

We study a time dependent eddy current equation for the magnetic field H accompanied with a nonlinear boundary condition, which is a generalization of the classical Silver–Müller condition for a non-perfect conductor. More exactly, the relation between the normal components of electric (E) and magnetic (H  ) fields obeys the following power law (linearized for small and large values) ν×E=ν×(|H×ν|^α−1H×ν)$\mathit{\nu }\times \mathit{E}=\mathit{\nu }\times ({|\mathit{H}\times \mathit{\nu }|}^{\alpha -1}\mathit{H}\times \mathit{\nu })$ for some α∈(0,1]$\alpha \in (0,1]$. We design a linear fully discrete approximation scheme to solve this nonlinear problem. The convergence of the approximations to a weak solution is proved, error estimates describing the dependence of the error on discretization parameters are derived as well. The efficiency of the proposed method is supported by numerical experiments.     

拟线性方程非局部边值问题解的衰减估计

本文讨论一类源于拟静态热弹性力学和控制理论等领域的边值问题,通过构造适当的上下解得到拟线性方程解的衰减估计。     

Fundamental solutions of stochastic differential equations with drift

The paper deals with the pathwise uniqueness of solutions to one-dimensional time homogeneous stochastic differential equations with a diffusion coefficient σ satisfying the local time condition and measurable drift term b. We show that if the functions σ and b satisfy a non-degeneracy condition and fundamental solution to considered equation is unique in law, then pathwise uniqueness of solutions holds. Our result is in some sense negative, more precisely we give an example of an equation with Holder continuous diffusion coefficient and nondegenerate drift for which a fundamental solution is not unique in law and pathwise uniqueness of solutions does not hold.