Geometric Integration Methods that Preserve Lyapunov Functions

We consider ordinary differential equations (ODEs) with a known Lyapunov function V. To ensure that a numerical integrator reflects the correct dynamical behaviour of the system, the numerical integrator should have V as a discrete Lyapunov function. Only second-order geometric integrators of this type are known for arbitrary Lyapunov functions. In this paper we describe projection-based methods of arbitrary order that preserve any given Lyapunov function. AMS subject classification (2000) 65L05, 65L06, 65L20, 65P40     

Gap Functions for Equilibrium Problems

The theory of gap functions, developed in the literature for variational inequalities, is extended to a general equilibrium problem. Descent methods, with exact an inexact line-search rules, are proposed. It is shown that these methods are a generalization of the gap function algorithms for variational inequalities and optimization problems.     

Robust hierarchical a posteriori error estimators for stabilized convection–diffusion problems

We construct a hierarchical a posteriori error estimator for a stabilized finite element discretization of convection‐diffusion equations with height Péclet number. The error estimator is derived without the saturation assumption and without any comparison with the classical residual estimator. Besides, it is robust, such that the equivalence between the norm of the exact error and the error estimator is independent of the meshsize or the diffusivity parameter. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012     

一类新共轭梯度法的全局收敛性

共轭梯度法是求解无约束最优化问题的有效方法.本文在βkDY的基础上对βk引入参数,提出了一类新共轭梯度法,并证明其在强Wolfe线性搜索条件下具有充分下降性和全局收敛性.     

Analytical Methods for the Determination of 90Sr and 239,240Pu in Environmental Samples

Artificial long-lived radionuclides such as ⁹⁰Sr and ^239,240Pu have been long released into the environment by human nuclear activities, which have a profound impact on the ecological environment. It is of great significance to monitor the concentration of these radionuclides for environmental safety. This paper summarizes and critically discusses the separation and measurement methods for ultra-trace determination of ⁹⁰Sr, ²³⁹Pu, and ²⁴⁰Pu in the environment. After selecting the measurement method, it is necessary to consider the decontamination of the interference from matrix elements and the key elements, and this involves the choice of the separation method. Measurement methods include both radiometric methods and non-radiometric methods. Radiometric methods, including alpha spectroscopy, liquid scintillation spectrometry, etc., are commonly used methods for measuring ^239+240Pu and ⁹⁰Sr. Mass spectrometry, as the representative of non-radiometric measurement methods, has been regarded as the most promising analytical method due to its high absolute sensitivity, low detection limit, and relatively short sample-analysis time. Through the comparison of various measurement methods, the future development trend of radionuclide measurement is prospected in this review. The fully automatic and rapid analysis method is a highlight. The new mass spectrometer with ultra-high sensitivity shows strong analytical capabilities for extremely low concentrations of ⁹⁰Sr, ²³⁹Pu, and ²⁴⁰Pu, and it is expected to develop determination methods with higher sensitivity and lower detection limit.     

Stereoisomeric Tris-BINOL-Menthol Bulky Monophosphites: Synthesis,Characterisation and Application in Rhodium-Catalysed Hydroformylation

Four stereoisomeric monoether derivatives, based on axially chiral (R)- or (S)-BINOL bearing a chiral (+)- or (−)-neomenthyloxy group were synthesised and fully characterised by NMR spectroscopy and X-ray crystallography. The respective tris-monophosphites were thereof prepared and fully characterised. The coordination ability of the new bulky phosphites with Rh(CO)₂(acac), was attested by ³¹P NMR, which presented a doublet in the range of δ = 120 ppm, with a ¹J(¹⁰³Rh-³¹P) coupling constant of 290 Hz. The new tris-binaphthyl phosphite ligands were further characterised by DFT computational methods, which allowed us to calculate an electronic (CEP) parameter of 2083.2 cm⁻¹ and an extremely large cone angle of 345°, decreasing to 265° upon coordination with a metal atom. Furthermore, the monophosphites were applied as ligands in rhodium-catalysed hydroformylation of styrene, leading to complete conversions in 4 h, 100% chemoselectivity for aldehydes and up to 98% iso-regioselectivity. The Rh(I)/phosphite catalytic system was also highly active and selective in the hydroformylation of disubstituted olefins, including (E)-prop-1-en-1-ylbenzene and prop-1-en-2-ylbenzene.     

Differential Entropy and Dynamics of Uncertainty

We analyze the functioning of Gibbs-type entropy functionals in the time domain, with emphasis on Shannon and Kullback-Leibler entropies of time-dependent continuous probability distributions. The Shannon entropy validity is extended to probability distributions inferred from L ²(R ⁿ ) quantum wave packets. In contrast to the von Neumann entropy which simply vanishes on pure states, the differential entropy quantifies the degree of probability (de)localization and its time development. The associated dynamics of the Fisher information functional quantifies nontrivial power transfer processes in the mean, both in dissipative and quantum mechanical cases. PACS NUMBERS: 05.45.+b, 02.50.-r, 03.65.Ta, 03.67.-a     

Cu(1 1 1) and Cu(0 0 1) surface electronic states. Comparison between theory and experiment

Recent advances in both the experimental resolution and in the computational capabilities motivate new studies of surface properties. In particular, a detailed comparison between theoretical and experimental data is expected to provide a better insight into surface and image states. In this work we present a joint effort analyzing such features of the Cu(1 1 1) and Cu(0 0 1) surfaces. The experiments are performed by using both linear and non-linear angle-resolved photoemission. From the theoretical point of view, we make use of the Green function embedding technique within density functional theory. We are able to account for the image states by suitably modifying the effective potential in the Kohn-Sham equation and the generalized boundary conditions on the Green function. Comprehensive theoretical and experimental results on the effective mass and the binding energy of the Shockley state and the first image states are reported.     

Accurate and analytical strain mapping at the surface of Ge/Si(0 0 1) islands by an improved flat-island approximation

We propose an extension of the well-known flat-island approximation in (1 + 1) dimensions which, while keeping simple analytical relations, allows one to better describe the strain field on the facets of steeper islands, and on the wetting layer between them. The results of atomistic molecular dynamics simulations using the Tersoff potential are used as a benchmark. The simple continuum approach is also shown to predict the correct trend of the strain gradients characterizing closely-spaced interacting islands, which has been recently observed to produce lateral motion of large Ge dots on Si(0 0 1).