On Liouville type theorems for fully nonlinear elliptic equations with gradient term

In this paper, we prove a Hadamard property and Liouville type theorems for viscosity solutions of fully nonlinear elliptic partial differential equations with a gradient term, both in the whole space and in an exterior domain.     

Interpretation of vicinal proton–proton coupling constants of heteroaromatic molecules in terms of topological electron density descriptors

The indirect vicinal proton–proton coupling constants for pyrrole, furan, thiophene and 15 related heteroaromatic compounds were calculated using the Khon–Sham approximation. An analysis of the four Ramsey contributions to the coupling constants was carried out showing that the Fermi contact term is always positive and dominant, although the remaining contributions have a nonnegligible net negative contribution. The trends observed for the proton–proton coupling constants were rationalized in terms of the properties of the electron density. It was found that electron delocalization between the corresponding hydrogen atoms plays a major role on the observed behavior with the charges of the carbon atoms bonded to them and the accompanying geometric variations being also of importance in the coupling mechanism. Copyright © 2010 John Wiley & Sons, Ltd.     

Term rank preservers of Boolean matrices

We obtain some characterizations of linear operators that preserve the term rank of Boolean matrices. That is, a linear operator over Boolean matrices preserves the term rank if and only if it preserves the term ranks 1 and k(≠1) if and only if it preserves the term ranks 2 and l(≠2). Other characterizations of term rank preservers are given.     

On the stability and dissipation of wall boundary conditions for compressible flows

Characteristic formulations for boundary conditions have demonstrated their effectiveness to handle inlets and outlets, especially to avoid acoustic wave reflections. At walls, however, most authors use simple Dirichlet or Neumann boundary conditions, where the normal velocity (or pressure gradient) is set to zero. This paper demonstrates that there are significant differences between characteristic and Dirichlet methods at a wall and that simulations are more stable when using walls modelled with a characteristic wave decomposition. The derivation of characteristic methods yields an additional boundary term in the continuity equation, which explains their increased stability. This term also allows to handle the two acoustic waves going towards and away from the wall in a consistent manner. Those observations are confirmed by stability matrix analysis and one‐ and two‐dimensional simulations of acoustic modes in cavities. Copyright © 2009 John Wiley & Sons, Ltd.     

与Euler函数有关的误差项均值估计

设ψ(n)是Euler函数,r是正实数.以E(x,r)表示和式的渐近公式中的误差项,本文研究了E(x,r)的算术均值和积分均值.     

带常数项的最优加权组合预测

We propose a model based on the optimal weighted combinational forecasting with constant terms,give formulae of the weights and the average errors as well as a rela- tion of the model and the corresponding model without constant terms,and compare these models.Finally an example was given,which showed that the fitting precision has been enhanced.     

Spin States of Iron(III) in Highly Saddled Dodecaphenylporphyrin Complexes

The alignment correlation term in the β-decay angular distribution from purely nuclear spin aligned ²⁰Na has been measured for the first time. The final objective is to test the G parity symmetry, one of the fundamental symmetry in the weak nucleon current. For artificial creation of the alignment, the knowledge of the hyperfine interaction of ²⁰Na implanted in a single-crystal ZnO was utilized. *Research Abroad, Japan Society for the Promotion of Science     

Ground state solutions for the singular Lane-Emden-Fowler equation with sublinear convection term

We are concerned with singular elliptic equations of the form −Δu=p(x)(g(u)+f(u)+a|∇u|) in RN (N?3), where p is a positive weight and 0<a<1. Under the hypothesis that f is a nondecreasing function with sublinear growth and g is decreasing and unbounded around the origin, we establish the existence of a ground state solution vanishing at infinity. Our arguments rely essentially on the maximum principle.     

Estimation over Curves of the Functions Given by Dirichlet Series on a Half-Plane

We study the maximal term of the Hadamard composition of Dirichlet series with real exponents. We obtain a lower estimate for the sum of a Dirichlet series over a curve arbitrarily approaching the convergence line.     

无简并微扰论公式的研究

本文介绍了Ｗｉｇｎｅｒ公式，Ｇｏｌｄｓｔｏｎｅ公式与Ｓｃｈｒｏｄｉｎｇｅｒ公式及其递推形式，比较表明，Ｓｃｈｒｏｄｉｎｇｅｒ公式的递推形式更容易利用计算机程序实现。文中还给出了逐级计算非连通项到任意级的方法。