一维问题的一种积分形式的流量重构算法

1引言我们考虑如下一维二阶椭圆边界值问题(-(β(x)p′)(x))′=f(x),x∈(a,b) p(a)=p(b)=0(1))其中β=β(x)是一恒正函数,且β∈H~1(a,b),f∈L~2(a,b)．事实上,在此条件下,我们可保证p∈H~2(a,b)(见[1],[2])．(1)之弱形式为：求p∈H_0~1(a,b)使得a(p,q)=(f,q),(?)q∈H_0~1(a,b),(2)其中a(p,q)=(?)_a~bβp′q′dx,(f,g)=(?)_a~bfqdx．给定(a,b)的一个分割α=x_0＜x_1＜…＜x_(n-1)＜x_n=b,令h=(?)(x_i-x_(i-1)),(?)_i表示通常相应于节点x_i的形状函数,即(?)_i是连续的分段线性函数且满足(?)_i(x_k)=δ_(ik),这里δ_(ik)=(?)i,k=0,1,…,n．又记V_h~0=span{(?)_1,(?)_2,…,(?)_(n-1)),取V_h~0作为p的逼近空间,则求解(1)的标准有限元格式为：求ph∈V_h~0使得     

活动课与地方课程资源的开发和利用

历史课程标准特别强调要培养学生的实践活动能力，全国各地出版的九年义务教育历史课本，每一种版本都安排了“活动课”，并将作为必修课内容。“活动课”就其教学内容而言，具有极大的开放性，不仅涉及历史课本上的内容，而且涉及到课本以外的教学内容，涉及整个社会现实和学生的生活实践，所以活动课与地方历史课程紧密相关。因此，教师在教学过程中，要充分开发和利用地方历史课程资源，把地方历史课程资源作为“活动课”的教学资源，使“活动课”教学更加丰富多彩，更加贴近学生的生活，充分展示“活动课”的教学功能。     

浅析科技英语句法特点

科技英语表达科学技术内容，适应科技人员交际的需要。文体要求是条理清晰，准确凝练，叙述客观。科技英语虽然有明显的特点，但都在英语语法规则的范围之内，并没有构成新的语法规则。     

Multiple local solutions to nonlinear control processes

We use the topological tool of Nielsen fixed-point theory to study the controllability of perturbed linear control processes whose control space can be reduced to a finite-dimensional one. These methods produce a lower bound on the number of controls that achieve a given target. We concentrate particularly on the case where the perturbation has sublinear growth, and we exhibit examples of multiple controls of various types that are detected by the Nielsen theory method.This research was partly supported by the Research Grant Teoria del Controllo dei Sistemi Dinamici, Ministero della Pubblica Istruzione, Roma, Italy.     

The projection approach to the Fokker-Planck equation. I. Colored Gaussian noise

It is shown that the Fokker-Planck operator can be derived via a projection-perturbation approach, using the repartition of a more detailed operator into a perturbation ₁ and an unperturbed part ₀. The standard Fokker-Planck structure is recovered at the second order in ₁, whereas the perturbation terms of higher order are shown to provoke the breakdown of this structure. To get rid of these higher order terms, a key approximation, local linearization (LL), is made. In general, to evaluate at the second order in ₁ the exact expression of the diffusion coefficient which simulates the influence of a Gaussian noise with a finite correlation time, a resummation up to infinite order in must be carried out, leading to what other authors call the best Fokker-Planck approximation (BFPA). It is shown that, due to the role of terms of higher order in ₁, the BFPA leads to predictions on the equilibrium distributions that are reliable only up to the first order in t. The LL, on the contrary, in addition to making the influence of terms of higher order in ₁ vanish, results in a simple analytical expression for the term of second order that is formally coincident with the complete resummation over all the orders in t provided by the Fox theory. The corresponding diffusion coefficient in turn is shown to lead in the limiting case to exact results for the steady-state distributions. Therefore, over the whole range 0 the LL turns out to be an approximation much more accurate than the global linearization proposed by other authors for the same purpose of making the terms of higher order in ₁ vanish. In the short- region the LL leads to results virtually coincident with those of the BFPA. In the large- region the LL is a more accurate approximation than the BFPA itself. These theoretical arguments are supported by the results of both analog and digital simulation.     

(TiNi)_x(x=2~4)团簇结构和电子结构

从团簇角度对TiNi形状记忆合金进行了量子化学从头算研究。设计并优化了等原子比(TiNi)x(x=2~4)簇的多种可能几何结构,并对较稳定构型进行电子结构的分析。结果表明,等原子比的(TiNi)n团簇以TiNi成键为主要分子骨架,小团簇有较多能量接近的异构体,TiTi成键对能量降低有较大贡献。     

Local and non-local sources of airborne particulate pollution at Beijing--The ratio of Mg/Al as an element tracer for estimating the contributions of mineral aerosols from outside Beijing

A new element tracer technique has firstly been established to estimate the contributions of mineral aerosols from both inside and outside Beijing. The ratio of Mg/Al in aerosol is a feasible element tracer to distinguish between the sources of inside and outside Beijing. Mineral aerosol, inorganic pollution aerosol mainly as sulfate and nitrate, and organic aerosol are the major components of airborne particulates in Beijing, of which mineral aerosol accounted for 32%―67% of total suspended particles (TSP), 10%―70% of fine particles (PM2.5), and as high as 74% and 90% of TSP and PM2.5, respectively, in dust storm. The sources from outside Beijing contributed 62% (38%―86%) of the total mineral aerosols in TSP, 69% (52%―90%) in PM10, and 76% (59%―93%) in PM2.5 in spring, and 69% (52%―83%), 79% (52%―93%), and 45% (7%―79%) in TSP, PM10, and PM2.5, respectively, in winter, while only ～20% in summer and autumn. The sources from outside Beijing contributed as high as 97% during dust storm and were the dominant source of airborne particulates in Beijing. The contributions from outside Beijing in spring and winter are higher than those in summer, indicating clearly that it was related to the various meteorological factors.     

Sampling and local models for multivariate image analysis

Local models are a very important concept for microscopic and macroscopic imaging. Different methods of sub-sampling a multivariate image are described both in general and for three examples. The need for sub-sampling and its influence on multivariate image analysis and visualization are studied. Examples from MRI (256 × 256), satellite imaging (7 × 512 × 512) and biofuel studies (6 × 512 × 512) are used to illustrate some of the principles involved.     

Linear scaling local correlation approach for solving the coupled cluster equations of large systems

A linear scaling local correlation approach is proposed for approximately solving the coupled cluster doubles (CCD) equations of large systems in a basis of orthogonal localized molecular orbitals (LMOs). By restricting double excitations from spatially close occupied LMOs into their associated virtual LMOs, the number of significant excitation amplitudes scales only linearly with molecular size in large molecules. Significant amplitudes are obtained to a very good approximation by solving the CCD equations of various subsystems, each of which is made up of a cluster associated with the orbital indices of a subset of significant amplitudes and the local environmental domain of the cluster. The combined effect of these two approximations leads to a linear scaling algorithm for large systems. By using typical thresholds, which are designed to target an energy accuracy, our numerical calculations for a wide range of molecules using the 6-31G or 6-31G* basis set demonstrate that the present local correlation approach recovers more than 98.5% of the conventional CCD correlation energy.     

Molecular conformation search by distance matrix perturbations

Three-dimensional molecular structure is fundamental in chemical function identification and computer-aided drug design. The enumeration of a small number of feasible conformations provides a rigorous way to determine the optimal or a few acceptable conformations. Our contribution concerns a heuristic enhancement of a method based on distance geometry, typically in relation with experiments of the NMR type. Distance geometry has been approached by different viewpoints; ours is expected to help in several subtasks arising in the process that determines 3D structure from distance information. More precisely, the input to our algorithm consists of a set of approximate distances of varying precision; some are specified by the covalent structure and others by Nuclear Magnetic Resonance (NMR) experiments (or X-ray crystallography which, however, requires crystallization). The output is a valid tertiary structure in a specified neighborhood of the input. Our approach should help in detecting outliers of the NMR experiments, and handles inputs with partial information. Moreover, our technique is able to bound the number of degrees of freedom of the conformation manifold. We have used numerical linear algebra algorithms for reasons of speed, and because they are well-implemented, fully documented and widely available. Our main tools include, besides distance matrices, structure-preserving matrix perturbations for minimizing singular values. Our MATLAB (or SCILAB) implementation is described and illustrated.AMS subject Classification: 92E10 Molecular structure, 92C40 Biochemistry, molecular biology, 65F15 Eigenvalues, eigenvectors, 15A18 Eigenvalues, singular values, and eigenvectors