相似非线性算子的谱相等

引进非线性算子相似的定义,证明了相似的非线性算子的谱相等。     

The Quantization Dimension of Self–Similar Probabilities

The quantization dimensions of self–similar probabilities satisfying the open set condition are determined.     

Very-high-order weno schemes

We study weno(2r − 1) reconstruction [D.S. Balsara, C.W. Shu, Monotonicity prserving weno schemes with increasingly high-order of accuracy, J. Comput. Phys. 160 (2000) 405–452], with the mapping (wenom) procedure of the nonlinear weights [A.K. Henrick, T.D. Aslam, J.M. Powers, Mapped weighted-essentially-non-oscillatory schemes: achieving optimal order near critical points, J. Comput. Phys. 207 (2005) 542–567], which we extend up to weno17 (r=9)$(r=9)$. We find by numerical experiment that these procedures are essentially nonoscillatory without any stringent cfl limitation (cfl∈[0.8,1])$(\text{<small-caps>cfl</small-caps>}\in [0.8\text{,}1])$, for scalar hyperbolic problems (both linear and scalar conservation laws), provided that the exponent p_β$p_{\beta }$ in the definition of the Jiang–Shu [G.S. Jiang, C.W. Shu, Efficient implementation of weighted eno schemes, J. Comput. Phys. 126 (1996) 202–228] nonlinear weights be taken as p_β=r$p_{\beta }=r$, as originally proposed by Liu et al. [X.D. Liu, S. Osher, T. Chan, Weighted essentially nonoscillatory schemes, J. Comput. Phys. 115 (1994) 200–212], instead of p_β=2$p_{\beta }=2$ (this is valid both for weno and wenom reconstructions), although the optimal value of the exponent is probably p_β(r)∈[2,r]$p_{\beta }(r)\in [2\text{,}r]$. Then, we apply the family of very-high-order wenom_pβ=r${\text{<small-caps>wenom</small-caps>}}_{p_{\beta }=r}$ reconstructions to the Euler equations of gasdynamics, by combining local characteristic decomposition [A. Harten, B. Engquist, S. Osher, S.R. Chakravarthy, Uniformly high-order accurate essentially nonoscillatory schemes iii, J. Comput. Phys. 71 (1987) 231–303], with recursive-order-reduction (ror) aiming at aleviating the problems induced by the nonlinear interactions of characteristic fields within the stencil. The proposed ror algorithm, which generalizes the algorithm of Titarev and Toro [V.A. Titarev, E.F. Toro, Finite-volume weno schemes for 3-D conservation laws, J. Comput. Phys. 201 (2004) 238–260], is free of adjustable parameters, and the corresponding rorwenom_pβ=r${\text{<small-caps>rorwenom</small-caps>}}_{p_{\beta }=r}$ schemes are essentially nonoscillatory, as Δx→0$\mathrm{\Delta }x\to 0$, up to r=9$r=9$, for all of the test-cases studied. Finally, the unsplit linewise 2-D extension of the schemes is evaluated for several test-cases.     

Application of bromine trifluoride for pre-concentration and determination of rare-earth elements in fuel uranium dioxide

Radioactive indicator's (¹⁵²Eu) method was used to study the behavior of rare-earth element (REE) micro-impurities at fluorination of fuel UO₂ with bromine trifluoride. The proposed process is very simple and carried out under a blanket layer of Freon-113 in the glassy carbon (vitreous) crucibles.It was shown that uranium matrix completely removes from reaction sphere in the form of UF₆ and REE contaminations quantitatively remain in crucible owing to practical non-volatility of their fluorides. High purity of fuel UO₂ causes small amount of the non-volatile rest (0.3-2 wt.% from initial weight) that considerably facilitates a problem of confident diagnostics of the strictly limited REE content in this material. Removal of uranium and concentration of REE from analyzed test samples via fluorination is several hundred times more rapid scheme of pre-sampling to atomic emission spectral determination of REE micro-quantities in UO₂ than traditionally used extraction and ion-exchange ways of the preliminary concentration of contaminations and removal of uranium.     

m分Cantor尘的Hausdorff测度

为得到一类相似分形的Hausdorff测度准确值．给出了m分Cantor尘的几何结构,利用几何度量关系对m分Cantor尘的Hausdorff测度准确值进行研究．证明了m分Cantor尘的Hausdorff测度准确为H^s（E）=1/（m-1）^s[（m-2k＋1）^2＋（m-1）^2]^s/2,其中s=logm4,m≥4,1≤k≤m．结果表明它是Cantor尘和Sierpinski地毯的Hausdorff测度的准确值的推广,4分Cantor尘和4分Sierpinski地毯的Hausdorff测度的准确值是其特例．     

Representations of Some Hopf Algebras Associated to the Symmetric Group S n

We prove that all irreducible representations of the bismash product have Frobenius–Schur indicator +1, where k is an algebraically closed field of characteristic 0. If n = p, a prime, we find all indicators for . We also study more general bismash products. Both authors were supported by NSF grants DMS-07-01291 and DMS-04-01399.     

一种基于三角形区域生长的图像篡改检测方法

针对现有的多数图像篡改检测算法中存在着的对旋转、缩放等篡改失效和计算量大等问题,利用三角形具有抗平移、旋转、尺度缩放的优越特性,提出了一种新的图像篡改检测算法.首先,利用Delaunay三角剖分算法对提取的Harris特征角点进行三角剖分,进行相似三角形的初始匹配.然后,以匹配的相似三角形顶点为种子点,建立三角形组,再进行一次相似三角形的匹配,实现对篡改区域的三角形生长.最后,利用区域面积阈值和数学形态学准确定位出篡改区域.实验结果表明,该算法与同类算法相比不仅能有效地对抗旋转、缩放,噪声等后期处理操作,而且对篡改区域有很好的检测和定位效果并具有计算复杂度低的特点.     

裂缝性应力敏感油藏流固耦合的数值模拟

以裂缝各向异性全张量渗透率动态耦合渗流模型为基础,建立三维三相裂缝各向异性特低渗透油藏流固耦合数学模型,并运用模块化显示耦合迭代求解建立流固耦合渗流数值模拟方法,编制耦合求解程序.研究表明:对于裂缝性油藏,随着油藏开采过程中压力的变化,岩石变形和储层介质的各向异性应变特性使开发过程中多组裂缝的变形程度不同,引起裂缝渗透率的非线性变化,进而使油藏裂缝渗透率张量主值发生旋转,改变液流方向、影响油藏开发效果.     

基于软件接收机的卫星导航信号模拟器性能指标测试

针对卫星导航信号模拟器的性能指标测试评估问题,提出了基于软件接收机的性能指标测试方法;通过分析模拟器性能,包括对动态性能、相位噪声、通道间时延一致性和静态定位精度的综合分析,给出了相应的测试方法和测试流程,并结合卫星导航信号模拟器产生的实际信号对各项性能指标的测试结果进行分析;经测试结果表明,软件接收机可以有效地对卫星导航信号模拟器各项性能指标进行测试,测试结果符合理论预期,满足模拟器性能指标测试评估的需求。     

Measurement network for urban noise assessment: Comparison of mobile measurements and spatial interpolation approaches

This paper investigates the relevance of different interpolation techniques to improve the spatial resolution of urban noise maps, in complement to measurements achieved at fixed stations. Interpolation techniques based on mobile measurements are compared to usual spatial interpolations techniques, namely Inverse Distance Weighting and Kriging. The analyses rely on a measurement campaign, which consisted of nearly 8 h of geo-referenced mobile noise measurements performed at random moments of the day, conducted simultaneously with continuous measurements collected at five fixed stations located on the inner city of Gent, Belgium.Firstly, a procedure is proposed to build a noise map with a high spatial resolution (one point every 5 m). The procedure relies on both mobile and fixed measurements: the mobile measurements are used to capture spatial variations on the network, and the measurements at fixed stations are used to capture the temporal variations. The map produced is then used as reference to compare the interpolation techniques based on a significantly more sparse measurement set.The spatial interpolation techniques tested fail in predicting accurately the noise level variations within streets. The explanation given is that they do not offer a sufficient covering of the network, and assume spatial variations which are not coherent with traffic dynamics or street configurations. Inversely, mobile measurements cover the entire network. As a result, they allow a more accurate prediction of noise levels even if very short samples are used, provided that the procedure used to estimate noise levels includes a spatial aggregation, which aims at smoothing the high spatial variations inevitable with short samples. Moreover, mobile measurements can advantageously be used to optimize, through a Genetic Algorithm, the locations where to install fixed stations, promising an efficient noise monitoring at reduced operational costs.