辛普生公式中间点的渐近性(英文)

辛普生公式是数值积分中的著名公式.利用泰勒公式,讨论了当区间的两个端点都趋于其内一定点时辛普生公式中间点的渐近性,得到了具有一般性的结果.     

用贝叶斯公式解释化验结果

借助概率论中的贝叶斯公式理论和方法,对现实中人们对有关化验结果的疑惑进行了详细的解释,从而使人们能更科学地理解化验结果,深刻感知数学在解决实际问题的作用.     

Stochastic calculus for Markov processes associated with non-symmetric Dirichlet forms

Nakao’s stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the non-symmetric Dirichlet forms setting.It? ’s formula in terms of the extended stochastic integrals is obtained.     

On Connes’ trace formula for the Hankel transformation of order-1/2

A local Hankel transformation of order 1/2 is defined for every finite place of the field of rational numbers.Its inversion formula and the Plancherel type theorem are obtained.A Connes type trace formula is given for each local Hankel transformation of order 1/2.An S-local Connes type trace formula is derived for the S-local Hankel transformation of order 1/2.These formulas are generalizations of Connes’ corresponding trace formulas in 1999.     

Clifford分析中Cauchy型奇异积分算子的一些性质

First,we give a module estimation of the singular integral with a differential element.Then by proving the existences of Cauchy principal value we obtain the transformation formula of the Cauchy-type singular integrals with a parameter.     

$R^n$空间中的Cauchy积分公式

In this note p(D) = Dm+ b1Dm 1+···+ bmis a polynomial Dirac operator in R~n, where D =nj=1ej xjis a standard Dirac operator in Rn, bjare the complex constant coefficients. In this note we discuss all decompositions of p(D) according to its coefficients bj,and obtain the corresponding explicit Cauchy integral formulae of f which are the solution of p(D)f = 0.     

小湾水电站坝址区低高程岸坡表生改造特征及机制研究

摘要：小湾水电站坝基、水垫塘边坡及低高程排水洞系统广泛地揭示了低高程岸坡的地质特征。基于现场调查和二维弹塑性有限元分析,深化认识了低高程岸坡表生改造特征：（1）它是在建造和构造改造的基础上进行的：原构造缓倾角节理扩展、错动;陡倾角节理扩展、产状改变以及错动;新生了大量中缓倾角裂隙;表生改造程度向坡内减弱。（2）建立了低高程岸坡表生改造缓裂生成机制模型,分析了其生成过程。（3）在二维弹塑性有限元分析中,基于拉破坏区分布、剪应变和点安全度等指标,分析了低高程岸坡卸荷松弛范围,其中谷底表生改造明显影响深度为6~9m。     

Preliminary attempt on maximum likelihood tomosynthesis reconstruction of DEI data

Tomosynthesis is a three-dimension reconstruction method that can remove the effect of superimposition with limited angle projections. It is especially promising in mammography where radiation dose is concerned. In this paper, we propose a maximum likelihood tomosynthesis reconstruction algorithm (ML-TS) on the apparent absorption data of diffraction enhanced imaging (DEI). The motivation of this contribution is to develop a tomosynthesis algorithm in low-dose or noisy circumstances and make DEI get closer to clinic application. The theoretical statistical models of DEI data in physics are analyzed and the proposed algorithm is validated with the experimental data at the Beijing Synchrotron Radiation Facility (BSRF). The results of ML-TS have better contrast compared with the well known `shift-and-add' algorithm and FBP algorithm.

     

A formula used to subtract the effect of gamma-ray of the others to that of measured reaction in measurement of cross section of nuclear reaction and its application

Abstract According to the regulation of growing and decay of artificial radioactive nuclide, a formula used to subtract the effect of characteristic γ-ray of the others to that of measured reaction was deduced. And then the cross sections of 120Te (n, 2n)119mTe reaction induced by neutrons around 14 MeV were measured by activation relative to the 93Nb (n, 2n)92mNb. In the process of the cross sections measured to be calculated, it was subtracted that the effect of characteristic γ-ray of 126Te (n, p)126Sb to that of measured 120Te (n, 2n)119mTe reaction using the formula deduced. The experimental results were (689±37) and (750±41) mb at the neutron energies of (13.5±0.3) and (14.6±0.3) MeV, respectively. Measurements were carried out by γ-detection using a coaxial HPGe detector. As samples, spectroscopically pure tellurium powder has been used. The fast neutrons were produced by the T(d, n)4He reaction. The neutron energies in these measurements were determined by the method of cross-section ratios between 90Zr (n, 2n) 89m+gZr and 93Nb (n, 2n) 92mNb reactions.     

Lamb＇s integral formulas of two-phase saturated medium for soil dynamic with drainage

When dynamic force is applied to a saturated porous soil, drainage is common. In this paper, the saturated porous soil with a two-phase saturated medium is simulated, and Lamb＇s integral formulas with drainage and stress formulas for a two-phase saturated medium are given based on Biot＇s equation and Betti＇s theorem （the reciprocal theorem）. According to the basic solution to Biot＇s equation, Green＇s function Gij and three terms of Green＇s function G4i, Gi4, and G44 of a two-phase saturated medium subject to a concentrated force on a spherical coordinate are presented. The displacement field with drainage, the magnitude of drainage, and the pore pressure of the center explosion source are obtained in computation. The results of the classical Sharpe＇s solutions and the solutions of the two-phase saturated medium that decays to a single-phase medium are compared. Good agreement is observed.