Enantiocontrol in Macrocycle Formation from Catalytic Metal Carbene Transformations

The development of catalytic metal carbene transformations for the construction of macrocyclic lactones has dramatically increased their synthetic advantages. This is the first review of this Developing methodology. The research described in this review has been supported by the National Science Foundation, National Institutes of Health, and the Petroleum Research Fund of the American Chemical Society.     

Lower bounds for the blow-up time in a semilinear parabolic problem involving a variable source

This letter is concerned with the blow-up of the solutions to a semilinear parabolic problem with a reaction given by a variable exponent. Lower bounds for the time of blow-up are derived if the solutions blow up.     

On decomposition of strongly quasi-frobenius rings

We prove that the Nakayama permutation of a strongly quasi-Frobenius ring gives rise to a ring decomposition of the ring.     

Uniqueness of ϕ-minimal hypersurfaces in warped product manifolds

We show that (generalized) minimal graphs in a warped product with density over a parabolic manifold are fibers under appropriate conditions on the density. The proof employs appropriate test functions.     

基于电磁感应的脉冲功率发生器试验研究

为了验证基于电磁感应原理的脉冲发生器的可行性,设计了一种小型脉冲发生器试验模型。对发生器的初始磁场与磁芯转变过程进行了分析与计算,建立了发生器的等效电路模型,并结合试验测量的负载电阻电压得出发生器的感应电压。设计的发生器整体直径约70mm,长度约85mm,其中磁芯直径为25mm,长度为25mm,提供初始磁场的永磁体厚度为10mm,试验得出发生器感应电压峰值为784.5V,与理论计算结果基本吻合,验证了发生器的可行性。     

Thermomechanical Behavior of Electrically Conducting Solids Exposed to an External Electromagnetic Field

This paper describes a procedure for the mathematical and numerical modeling of the thermomechanical behavior of electrically conducting solid bodies exposed to an external electromagnetic field. The constitutive equations for the electromagnetic field are the Maxwell equations written for the region of the solid body and the ambient medium. The stress-strain state of the solid is described using the relations for nonisothermal elastoplastic flow. The effects of the electromagnetic field on the heat-transfer and deformation processes are taken into account via heat release and ponderomotive forces, respectively. The relations between the electric and magnetic inductions and the corresponding field strengths are considered nonlinear. All physicomechanical parameters of the body material are temperature dependent.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 14–26, September–October, 2005.     

Boundary Value Problems for Parabolic Operators in a Time-Varying Domain

We prove the existence of unique solutions to Dirichlet boundary value problems for linear second-order uniformly parabolic operators in either divergence or non-divergence form with boundary blowup low-order coefficients. The domain is possibly time varying, non-smooth, and satisfies an exterior measure condition.     

Global well-posedness and scattering for a nonlinear Klein–Gordon system in low dimensions

This article investigates the global well-posedness and the scattering for a nonlinear Klein–Gordon system in spatial dimensions 1 and 2. We establish a Morawetz estimate for this system which is similar to the Morawetz estimate established by Nakanishi [K. Nakanishi, Energy scattering for nonlinear Klein–Gordon and Schrödinger equations in spatial dimensions 1 and 2, J. Funct. Anal. 169(1), pp. 201–225], combining this Morawetz estimate with the induction on energy argument developed by Bourgain [J. Bourgain, Global well-posedness of defocusing 3D critical NLS in the radial case, J. Am. Math. Soc. 12 (1999), pp. 145–171], the bound of a certain space-time norm and scattering result are obtained.