An interpolating reproducing kernel particle method for two-dimensional scatter points

An interpolating reproducing kernel particle method for two-dimensional(2D) scatter points is introduced. It eliminates the dependency of gridding in numerical calculations. The interpolating shape function in the interpolating reproducing kernel particle method satisfies the property of the Kronecker delta function. This method offers a mathematics basis for recognition technology and simulation analysis, which can be expressed as simultaneous differential equations in science or project problems. Mathematical examples are given to show the validity of the interpolating reproducing kernel particle method.     

An improved interpolating element-free Galerkin method with nonsingular weight function for two-dimensional potential problems

In this paper, an improved interpolating moving least-square (IIMLS) method is presented. The shape function of the IIMLS method satisfies the property of Kronecker δ function. The weight function used in the IIMLS method is nonsingular. Then the IIMLS method can overcome the difficulties caused by the singularity of the weight function in the IMLS method. And the number of unknown coefficients in the trial function of the IIMLS method is less than that of the moving least-square (MLS) approximation. Then by combining the IIMLS method with the Galerkin weak form of the potential problem, the improved interpolating element-free Galerkin (IIEFG) method for two-dimensional potential problems is presented. Compared with the conventional element-free Galerkin (EFG) method, the IIEFG method can directly use the essential boundary conditions. Then the IIEFG method has a higher accuracy. For demonstration, three numerical examples are solved using the IIEFG method.     

光谱辐射照度标准灯的数据插值与曲线拟合方法研究

介绍了多种插值方法与曲线拟合方法,对光谱辐射照度标准灯在所需波长间隔上的照度值进行内插运算,包括这些方法的模型建立、参数计算及误差分析过程。得到了效果较好的插值方法及分段普朗克曲线拟合模型,其中拟合模型较好地体现了光谱辐射照度标准灯的灯丝发射率及灯壳的光谱透射比。最终结果的相对偏差接近国家级计量院提供标准灯的最佳不确定度0.2%。     

An improved interpolating element-free Galerkin method for elasticity

Based on the improved interpolating moving least-squares （ⅡMLS） method and the Galerkin weak form, an improved interpolating element-free Galerkin （ⅡEFG） method is presented for two-dimensional elasticity problems in this paper. Compared with the interpolating moving least-squares （IMLS） method presented by Lancaster, the ⅡMLS method uses the nonsingular weight function. The number of unknown coefficients in the trial function of the ⅡMLS method is less than that of the MLS approximation and the shape function of the ⅡMLS method satisfies the property of Kronecker δ function. Thus in the ⅡEFG method, the essential boundary conditions can be applied directly and easily, then the numerical solutions can be obtained with higher precision than those obtained by the interpolating element-free Galerkin （IEFG） method. For the purposes of demonstration, four numerical examples are solved using the ⅡEFG method.     

Some remarks on radiation gauges in general relativity

We prove that it is possible to specify the shift vector field for a given foliation in such a way as to provide automatically the transverse-traceless part of the second fundamental form K associated with the slices of the foliation. We interpret this particular specification as providing a simple way for characterizing the dynamical degrees of freedom of the gravitational field. The resulting gauge is not the minimal distortion gauge devised by Smarr and York. In numerical relativity it permits the maintenance in time of the difference equations associated with the divergence constraint.     

Renormalizability of a generalized gauge fixing interpolating among the Coulomb, Landau and maximal Abelian gauges

A detailed discussion of the renormalization properties of a class of gauges which interpolates among the Landau, Coulomb and maximal Abelian gauges is provided in the framework of the algebraic renormalization in Euclidean Yang-Mills theories in four dimensions.     

An improved interpolating element-free Galerkin method with a nonsingular weight function for two-dimensional potential problems

In this paper, an improved interpolating moving least-square (IIMLS) method is presented. The shape function of the IIMLS method satisfies the property of the Kronecker δ function. The weight function used in the IIMLS method is nonsingular. Then the IIMLS method can overcome the difficulties caused by the singularity of the weight function in the IMLS method. The number of unknown coefficients in the trial function of the IIMLS method is less than that of the moving least-square (MLS) approximation. Then by combining the IIMLS method with the Galerkin weak form of the potential problem, the improved interpolating element-free Galerkin (IIEFG) method for two-dimensional potential problems is presented. Compared with the conventional element-free Galerkin (EFG) method, the IIEFG method can directly use the essential boundary conditions. Then the IIEFG method has higher accuracy. For demonstration, three numerical examples are solved using the IIEFG method.     

Some observations on degenerate metrics

There are some polynomial formulations of Einstein's equations in which the metric is allowed to become degenerate. We examine some known exact solutions to see whether they may be smoothly joined to solutions with degenerate metrics. If one uses a lapse function which is a spatial scalar, this is very easy. If the lapse function has a small and negative tensor density weight, the joining together may take place across the horizons in the Schwarzschild and Kerr solutions. For large and negative weights, we have been unable to find any examples.     

Some observations on cochlear mechanics.

A set of experiments was conducted using the M?ssbauer effect to determine the vibratory characteristics of the basilar membrane, Reissner's membrane, the malleus, incus, and oval window in squirrel monkey. A few measurements were also made in guinea pig in the basal cochlear region. The nonlinear vibration properties of the basilar membrane are described in detail for the midfrequency region in the squirrel monkey. Only in this region have nonlinear effects been observed. A comparison of mechanical and neural data indicates good qualitative agreement.     

Some observations on models of absorption spectra

The question of models of absorption spectra as applied to the problems which arise in investigations of the propagation of infrared radiation in the atmosphere is discussed. The general and asymptotic formulas for the absorption function of individual lines, models of equidistant lines of equal intensity and statistical models are considered successively. Certain new formulas are introduced without mathematical derivation. Inaccuracies and errors in the literature are corrected, and the square-toot law is considered critically. The general conclusions resulting from the investigations into spectral models are analyzed.     

Some observations on the development of anticipatory coarticulation

The influence of vocalic context on various temporal and spectral properties of preceding acoustic segments was investigated in utterances containing [schwa No. CV] sequences produced by two girls aged 4;8 and 9;5 years and by their father. The younger (but not the older) child's speech showed a systematic lowering of [s] noise and [th] release burst spectra before [u] as compared to [i] and [ae]. The older child's speech, on the other hand, showed an orderly relationship of the second-formant frequency in [] to the transconsonantal vowel. Both children tended to produce longer [s] noises and voice onset times as well as higher second-formant peaks at constriction noise offset before [i] than before [u] and [ae]. All effects except the first were shown by the adult who, in addition, produced first-formant frequencies in [] that anticipated the transconsonantal vowel. These observations suggest that different forms of anticipatory coarticulation may have different causes and may follow different developmental patterns. A strategy for future research is suggested.     

Some observations on uncertainty propagation through a simple nonlinear system

This paper discusses a number of issues relating to the analysis of uncertain systems or data in the context of (low-frequency) structural dynamics. In order to illustrate potential problems in applying ‘classical’ uncertainty analysis methods to nonlinear systems, a simple nonlinear system is simulated and the breakdown of two standard approaches is demonstrated on data from the system. By relaxing the requirements of the analysis, it is shown that an alternative uncertainty theory gives useful qualitative information about the system. This motivates a discussion of how uncertainty frameworks should be chosen to suit the problem in hand and leads to a clustering of uncertainty problems in structural dynamics into three types: quantification, fusion and propagation.     

PHOBOS at RHIC: Some global observations

Particle production in Au+Au collisions has been measured in the PHOBOS experiment at RHIC for a range of collision energies for a large span of pseudorapidities, |η| < 5.4. Three empirical observations have emerged from this data set which require theoretical examination. First, there is clear evidence of limiting fragmentation. Namely, particle production in central Au + Au collisions, when expressed as dN/dη′ ( η′ ≡ – y_beam), becomes energy independent at high energy for a broad region of η′ around η′ = 0. This energy-independent region grows with energy, allowing only a limited region (if any) of longitudinal boost-invariance. Second, there is a striking similarity between particle production in e⁺e⁻and Au + Au collisions (scaled by the number of participating nucleon pairs). Both the total number of produced particles and the longitudinal distribution of produced particles are approximately the same in e⁺e⁻and in scaled Au + Au. This observation This presentation is based in large part on the PHOBOS summary talk by M Baker at the16th Int. Conf. on Ultrarelativistic Nucleus- Nucleus Collisions, Quark Matter 2002, Nantes, France was not predicted and has not been explained. Finally, particle production has been found to scale approximately with the number of participating nucleon pairs for (N _part ) > 65. This scaling occurs both for the total multiplicity and for highp _T particles (3 <p _T < 4.5 GeV/c). This presentation is based in large part on the PHOBOS summary talk by M Baker at the16th Int. Conf. on Ultrarelativistic Nucleus-Nucleus Collisions, Quark Matter 2002, Nantes, France     

Some observations on Levy stability and intermittency in nucleus-nucleus interactions at SPS energies

The power law relation between higher order and second order scaled factorial moments is studied in one dimensional pseudo-rapidity phase (η) space in the interactions of ³²S beam with CNO, AgBr and Emulsion at incident energy of 200 AGeV. Observation for such a power law may indicate a self similar cascade mechanism in multiparticle production process. The values of slope, β_q are found to be independent of target size. The value of the scaling exponent υ = 1.412 obtained is higher than the critical value υ = 1.304, indicating that no second order phase transition exists in our data. The ratio of anomalous fractal dimensions, d_q/d₂ is found to increase with increase in the order of moments, q. The dependence of d_q/d₂ on q indicates a multifractal structure and the presence of self-similar cascading mechanism in our data. The d_q/d₂ values are well described by the Levy-stable distribution with Levy index μ = 1.562 which is consistent with and lies within the Levy stable region (0 ≤ μ ≤ 2). The multifractal spectrum is concave downward with a maximum at q = 0. The decrease in D_q with increasing q shows that there is a self affine multifractal behaviour in multiparticle production in our data.     

Super-symmetric V-A gauges and fermion number

The problem of fermion-number conservation can be solved in a supersymmetric gauge theory provided both vector and axial-vector interactions are admitted.     

Some leed and electron spectroscopic observations on disordered EuO(100) surfaces

Three vacuum-cleaved surfaces of EuO have been studied using LEED, Auger electron spectroscopy, electron loss spectrocopy and mass spectroscopy. The (100) surface is stable in the electron beam but is disordered after cleavage at room temperature. The Auger spectrum below 150 eV is assigned to initial state holes in the 4d shell of europium and to autoionisation processes. The consequences of the observation of disorder upon the interpretation of various magnetic and optical experiments are discussed.     

X-ray and microscope observations on the texture and stability of polyethylene crystallized under pressure: Some new observations on the triclinic crystal form

It is known that linear polyethylene, which has been crystallized from the melt under hydrostatic pressures above 4000 atm, has properties that are distinctly different from the usual melt crystallized polyethylene [1]. The examination of replicas of fracture surfaces of such material under the electron and optical microscopes reveals a texture on an unusually large scale [2, 2a]. Bands several microns in width were observed that were concluded to be the edge-on views of large lamellae. A fine structure of continuous striations was also observed running perpendicular to the broad faces of the lamellae. It was shown that the molecules lie perpendicular to the band or lamellar surfaces and parallel to the striations. As the band width is comparable with the average chain length, it was concluded that the molecules are in an extended state or, at any rate, that they cannot fold back on themselves any appreciable number of times. Even greater extension of the crystalline order is implied by the lateral dimension of the bands, if the fine structure is ignored. There is strong support for the contention that this fine structure is not intrinsic but merely the expected result of fracturing an intrinsically fibrillating material [3]. In addition, it must be remembered that surface replication does not lend itself to unique interpretations of the texture of a material and is inherently incapable of defining the extension of a uniformly diffracting crystal area.     

Gauge transformation between retarded and multipolar gauges

The gauge function, expressed in terms of the sources, required for a gauge transformation between the retarded electromagnetic gauge and the three-vector version of the multipolar gauge is obtained.