Approximation of Functions by the Szász-Mirakjan-Kantorovich Operator

We characterize the approximation of functions in the L_p-norm by the Szász-Mirakjan-Kantorovich operator. We prove a direct and a strong converse inequality of type B in terms of an appropriate K-functional.     

On local strong solutions to the Cauchy problem of the two-dimensional full compressible magnetohydrodynamic equations with vacuum and zero heat conduction

This paper concerns the Cauchy problem of the two-dimensional full compressible magnetohydrodynamic equations with zero heat-conduction and vacuum as far field density. In particular, the initial density can have compact support. We prove that the Cauchy problem admits a local strong solution provided both the initial density and the initial magnetic field decay not too slow at infinity.     

Existence and uniqueness of maximal strong solution of a 1D blood flow in a network of vessels

We study the well-posedness of a system of one-dimensional partial differential equations modeling blood flows in a network of vessels with viscoelastic walls. We prove the existence and uniqueness of maximal strong solution for this type of hyperbolic/parabolic model. We also prove a stability estimate under suitable nonlinear Robin boundary conditions.     

Optical spectra of organic quantum dots in the strong coupling regime

We analyze the emission spectrum of a single organic quantum dot coupled to a microcavity in the strong coupling regime. We take into account non-linearities arising from both exciton–exciton interactions and the Pauli exclusion principle. We apply the recently developed Pade approximation for regular truncation of Green functions to calculate the emission spectrum. We show that as the number of excitations in the quantum dot increases the Rabi doublet evolves into a more complicated triplet structure.     

On strong solutions to the compressible Hall-magnetohydrodynamic system

In this paper, we consider strong/classical solutions to the 3D compressible Hall-magnetohydrodynamic system. First, we prove the existence of local strong solutions with positive density. Then the existence of global small solutions with small initial data is proved. Optimal time decay rate is also established.     

Strong solutions to the equations of electrically conductive magnetic fluids

We study the equations of flow of an electrically conductive magnetic fluid, when the fluid is subjected to the action of an external applied magnetic field. The system is formed by the incompressible Navier–Stokes equations, the magnetization relaxation equation of Bloch type and the magnetic induction equation. The system takes into account the Kelvin and Lorentz force densities. We prove the local-in-time existence of the unique strong solution to the system equipped with initial and boundary conditions. We also establish a blow-up criterion for the local strong solution.     

Ground-state correlation energy of counterions at a charged planar wall: Gibbs-Bogoliubov lower-bound approach

Recent simulation results imply the lowering of the ground-state correlation energy per counterion at a charged planar wall, compared with that of the 2D and 3D one-component plasma systems. Our aim is to correctly evaluate the ground-state energy of strongly-coupled counterion systems by considering a quasi-2D bound state where bound counterions are confined to a layer of molecular thickness. We use a variational approach based on the Gibbs-Bogoliubov inequality for the lower-bound free energy so that the liquid-state theory can be incorporated into the formulations. The soft mean spherical approximation demonstrates that the lowered ground-state energy can be reproduced by the obtained analytical form of a quasi-2D bound state.     

WO3/ZrO2固体强酸催化剂上异丁烷-丁烯烷基化反应研究(Ⅰ)--钨负载量和焙烧温度的影响

制备了系列 WO3/ Zr O2 固体强酸催化剂 ,用 XRD,DTA-TG,H2 -TPR,Raman光谱和酸性测定等方法测定其晶型结构、表面状态和酸性 .结果表明 ,WO3/ Zr O2 中的 Zr O2 基本以 T晶相存在 ,WO3对稳定 T晶相有重要作用 ,样品具有较大的表面积 .分散于 Zr O2 表面上的 WO3主要以单层分散和析出的 WO3晶粒形式存在 ,部分可能与 Zr O2 作用形成 Zr— O—W键并起强酸作用 .研究了各种实验条件下的异丁烷 -丁烯烷基化反应 .与其它固体酸相比 ,具有较高的起始活性和 i-C08选择性 ,且与酸强度和酸量有较好的对应关系