含k-次增生算子的Ishikawa迭代的收敛性问题

主要研究了非线性方程x Tx=f的Ishikawa迭代解．其中T为k-次增生的或增生的，并在一致光滑和任意的实Banach空间分别研究了上述方程的带误差的Ishikawa迭代解，从而推广了已知的一些结果。     

A purely algebraic characterization of the hyperreal numbers

The hyperreal numbers of nonstandard analysis are characterized in purely algebraic terms as homomorphic images of a suitable class of rings of functions.

     

Adsorption of argon and nitrogen in cylindrical pores of MCM-41 materials: application of density functional theory

Adsorption of argon and nitrogen at their respective boiling points in cylindrical pores of MCM-41 type silica-like adsorbents is studied by means of a non-local density functional theory (NLDFT), which is modified to deal with amorphous solids. By matching the theoretical results of the pore filling pressure versus pore diameter against the experimental data, we arrive at a conclusion that the adsorption branch (rather than desorption) corresponds to the true thermodynamic equilibrium. If this is accepted, we derive the optimal values for the solid-fluid molecular parameters for the system amorphous silica-Ar and amorphous silica-N₂, and at the same time we could derive reliably the specific surface area of non-porous and mesoporous silica-like adsorbents, without a recourse to the BET method. This method is then logically extended to describe the local adsorption isotherms of argon and nitrogen in silica-like pores, which are then used as the bases (kernel) to determine the pore size distribution. We test this with a number of adsorption isotherms on the MCM-41 samples, and the results are quite realistic and in excellent agreement with the XRD results, justifying the approach adopted in this paper.     

A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space

We provide a local as well as a semilocal convergence analysis for two-point Newton-like methods in a Banach space setting under very general Lipschitz type conditions. Our equation contains a Fréchet differentiable operator F and another operator G whose differentiability is not assumed. Using more precise majorizing sequences than before we provide sufficient convergence conditions for Newton-like methods to a locally unique solution of equation F(x)+G(x)=0. In the semilocal case we show under weaker conditions that our error estimates on the distances involved are finer and the information on the location of the solution at least as precise as in earlier results. In the local case a larger radius of convergence is obtained. Several numerical examples are provided to show that our results compare favorably with earlier ones. As a special case we show that the famous Newton-Kantorovich hypothesis is weakened under the same hypotheses as the ones contained in the Newton-Kantorovich theorem.     

A first-principles study of surface and subsurface H on and in Ni(1 1 1): diffusional properties and coverage-dependent behavior

Periodic, self-consistent, density functional theory (GGA-PW91) calculations are performed for both surface and subsurface atomic hydrogen on and in Ni(1 1 1). At a low coverage (θ=0.25 ML), the binding energies (BEs) of a hydrogen atom in surface fcc, subsurface octahedral (first layer), and subsurface octahedral (second layer) sites are −2.89, −2.18, and −2.11 eV, respectively. The activation energy barriers for hydrogen diffusion from the surface to the first subsurface layer and from the first to the second subsurface layer are estimated to be 0.88 and 0.52 eV, respectively. In the entire coverage range studied, hydrogen occupies surface fcc and hcp sites and subsurface octahedral sites. In addition, the magnitude of the BE per hydrogen atom and the magnetization of the nickel slabs both decrease as hydrogen coverage increases. Vibrational frequencies of hydrogen at various surface and subsurface sites are calculated and are in reasonable agreement with experimental data. A phase stability calculation with a 2 × 2 surface unit cell shows that a p(2 × 2)-2H overlayer structure (θ=0.5 ML) and a p(1 × 1)-1H structure (θ=1.0 ML) are stable at low hydrogen pressures, in agreement with numerous experimental results. A very large increase in pressure is required to populate subsurface sites. After such an increase occurs, the first subsurface layer is filled completely.     

Q-正则Loewner空间中的拟对称映射

本文在Q-正则Loewner空间中用环模不等式刻划了拟对称映射.另外,在 Q-维Ahlfors-David正则空间中建立了拟对称映射作用下的Grotzsch-Teichmuller型 模不等式,它是通过伸张系数的积分平均来表示.     

Spectral Analysis of Powers of the Operator (Vf)(x)=q(x)∫0 xw(t)f(t),dt

Mathematical Notes -     

B-Theory of Runge-Kutta methods for stiff volterra functional differential equations

B-stability andB-convergence theories of Runge-Kutta methods for nonlinear stiff Volterra functional differential equations (VFDEs) are established which provide unified theoretical foundation for the study of Runge-Kutta methods when applied to nonlinear stiff initial value problems (IVPs) in ordinary differential equations (ODEs), delay differential equations (DDEs), integro-differential equations (IDEs) and VFDEs of other type which appear in practice.     

高阶非线性波动方程的有限差分方法

本文研究一类广泛的高阶非线性波动方程组初边值问题的有限差分格式，用离散泛函分析方法和先验估计的技巧得到了有限差分格式的收敛性。     

The Module Structure Theorem for Sobolev Spaces on Open Manifolds

We prove a general embedding theorem for Sobolev spaces on open manifolds of bounded geometry and infer from this the module structure theorem. Thereafter we apply this to weighted Sobolev spaces.