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51.
何松年 《高等学校计算数学学报》2006,28(3):202-208
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 相似文献
52.
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. 相似文献
53.
Sandro Faetti Leone Fronzoni Paolo Grigolini Riccardo Mannella 《Journal of statistical physics》1988,52(3-4):951-978
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. 相似文献
54.
55.
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. 相似文献
56.
Paul Geladi 《Mikrochimica acta》1995,120(1-4):211-230
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. 相似文献
57.
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. 相似文献
58.
Ioannis?Z.?EmirisEmail author Theodoros?G.?Nikitopoulos 《Journal of mathematical chemistry》2005,37(3):233-253
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 相似文献
59.
Wojciech Paszkowicz 《Analytica chimica acta》2006,566(1):81-98
Genetic algorithms represent a powerful global-optimisation tool applicable in solving tasks of high complexity in science, technology, medicine, communication, etc. The usual genetic-algorithm calculation scheme is extended here by introduction of a quadratic self-learning operator, which performs a partial local search for randomly selected representatives of the population. This operator is aimed as a minor deterministic contribution to the (stochastic) genetic search. The population representing the trial solutions is split into two equal subpopulations allowed to exhibit different mutation rates (so called asymmetric mutation). The convergence is studied in detail exploiting a crystallographic-test example of indexing of powder diffraction data of orthorhombic lithium copper oxide, varying such parameters as mutation rates and the learning rate. It is shown through the averaged (over the subpopulation) fitness behaviour, how the genetic diversity in the population depends on the mutation rate of the given subpopulation. Conditions and algorithm parameter values favourable for convergence in the framework of proposed approach are discussed using the results for the mentioned example. Further data are studied with a somewhat modified algorithm using periodically varying mutation rates and a problem-specific operator. The chance of finding the global optimum and the convergence speed are observed to be strongly influenced by the effective mutation level and on the self-learning level. The optimal values of these two parameters are about 6 and 5%, respectively. The periodic changes of mutation rate are found to improve the explorative abilities of the algorithm. The results of the study confirm that the applied methodology leads to improvement of the classical genetic algorithm and, therefore, it is expected to be helpful in constructing of algorithms permitting to solve similar tasks of higher complexity. 相似文献
60.
Hitoshi?MatsukiEmail author Michio?Yamanaka Hiroshi?Kamaya Shoji?Kaneshina Issaku?Ueda 《Colloid and polymer science》2005,283(5):512-520
The dissociation equilibrium between uncharged local anesthetic lidocaine (LC) and charged local anesthetic LC (LCH+) in a surface-adsorbed film was investigated by measuring the surface tension and pH of aqueous solutions of a mixture of hydrochloric acid and LC. The surface tension values decreased slightly with increasing total molality mt at 0X20.5, where X2 is the mole fraction of LC in the mixture, while they decreased rapidly with increasing mt at 0.5<X21. It was shown from the pH measurements that almost all LC molecules were changed into LCH+ ions by protonation at 0X20.5 and both forms coexisted only at 0.5<X21. The quantities of the respective LC and LCH+ transferred from the aqueous solution to the adsorbed film, i.e., their surface densities, were calculated by applying the thermodynamic equations derived to the surface tension and pH data. A greater quantity of LC than LCH+ existed in the adsorbed film at the coexisting composition. The partitioning behavior of LC and LCH+ in the adsorbed film was characterized by three composition regions: (1) slight partitioning of low surface-active LCH+ in the region at 0X20.5, (2) preferential partitioning of LC at 0.5<X2<around 0.7, and (3) negative partitioning of LCH+ at around 0.7X21. The present results clearly indicate that uncharged local anesthetics transfer into hydrophobic environments such as cell membranes more than charged ones. 相似文献