Greedy wavelet projections are bounded on BV

Let be the space of functions of bounded variation on with . Let , , be a wavelet system of compactly supported functions normalized in , i.e., , . Each has a unique wavelet expansion with convergence in . If is the set of indicies for which are largest (with ties handled in an arbitrary way), then is called a greedy approximation to . It is shown that with a constant independent of . This answers in the affirmative a conjecture of Meyer (2001).

     

estimates for overdetermined Radon transforms

We prove several variations on the results of F. Ricci and G. Travaglini (2001), concerning bounds for convolution with all rotations of arc length measure on a fixed convex curve in . Estimates are obtained for averages over higher-dimensional convex (nonsmooth) hypersurfaces, smooth -dimensional surfaces, and nontranslation-invariant families of surfaces. We compare Ricci and Travaglini's approach, based on average decay of the Fourier transform, with an approach based on boundedness of Fourier integral operators, and show that essentially the same geometric condition arises in proofs using the two techniques.

     

General solution of A 2-D weak singular integral equation with constraint and its applications

Hertz'ssolutionTheProjectsupportedbytheNaturalScienceFoundationofGuangdongProvinceofChina[.IntroductionTheintegralequationsubjecttoconstraintp(s,te)=o,for(s,W)-(r,o)6Q={(r,O)lF(r,o)>c.}'(l.2)hasbeenstudiedin[l].Themultipleintegrationsimilartothelefthandsi…     

Application of SSNTD for maintenance of radiation and nuclear safety of the Sarcophagus

Object “Shelter” (known world-wide as the Sarcophagus) is a source of very high radiological and nuclear hazard. Transfer of the Sarcophagus into an ecologically safe site is a task not only for Ukraine but also for the world community. A composite approach to maintenance of radiation and nuclear safety of the Sarcophagus applying spectrometric methods using solid state nuclear track detectors (SSNTD) is suggested in this paper. The aspects are: (1) monitoring of transuranium element inhalation intake to a human body of nuclear workers; (2) neutron flux evaluation in some premises of the Sarcophagus; (3) fuel hot particle detection in air of working zones; (4) radon and thoron simultaneous measurements.     

HELP法在中草药分析中的应用研究-冬虫夏草的化学成分测定

基于直观推导式演进特征投影（ＨＥＬＰ）法,对冬虫夏草子座和虫体分别进行了多组分同时定性定量测定．结果表明,ＨＥＬＰ法能减少样本提取分离的步骤,降低色谱分离条件的要求,提高检测准确度．联用色谱检测与化学计量学解析法相结合将为复杂中草药分析提供一种全新手段     

A Reflection Principle and an Orthogonal Decomposition Concernig Hypoelliptic Equations

A jump relation for a boundary integral representation of solutions of hypoelliptic equations is described by a reflection principle. An orthogonal decomposition of L² can be proved by the jump relation. In the orthogonal complement of the space of regular functions, i.e. the space of solutions of the homogeneous equation, the inhomogeneous adjoint equation has a solution with homogeneous boundary values. As a conclusion, one obtains Sobolev's regularity theorem. Furthermore it will be proved that the existence of the orthogonal decomposition and Sobolev's regularity theorem are equivalent. Theorems of Runge's type will be proved in order to determine countable dense subsets of the space of regular functions.     

Radon transforms on Siegel-type nilpotent Lie groups

Let \mathfrak{N}:={{\displaystyle H}}_n\times {ℂ}^n be the Siegel-type nilpotent group, which can be identified as the Shilov boundary of Siegel domain of type II, where {{\displaystyle H}}_n denotes the set of all n\times n Hermitian matrices. In this article, we use singular convolution operators to define Radon transform on \mathfrak{N} and obtain the inversion formulas of Radon transforms. Moveover, we show that Radon transform on \mathfrak{N} is a unitary operator from Sobolev space W^n;2 into L²(\mathfrak{N}):     

多重集非凸分裂可行问题的非精确均值投影算法

在本文中,我们引入了非精确均值投影算法来求解多重集非凸分裂可行问题,其中这些非凸集合为半代数邻近正则集合.通过借助著名的Kurdyka-Lojasiewicz不等式理论,我们建立了算法的收敛性.     

基于脊波变换的渐变镜头转场检测算法

分析了脊波变换在处理含“线奇异”信号上的优势.提出用脊波变换后的各高频系数和作为图像的特征量.渐变镜头脊波变换的实现分两步：首先,对图像帧进行一定方向参量的Radon变换;其次,对Radon变换得到各数组进行Haar小波二级分解,采用分解后的高频系数和描述图像.在检测窗内,计算连续帧间脊波变换系数和之间的欧式距离判别渐变转场的边界.     

Variation of radon concentrations in soil and groundwater and its correlation with radon exhalation rate from soil in Budhakedar, Garhwal Himalaya

Radon was measured in soil-gas and groundwater in the Budhakedar area of Tehri Garhwal, India in summer and winter to obtain the seasonal variation and its correlation with radon exhalation rate. The environmental surface gamma dose rate was also measured in the same area. The radon exhalation rate in the soil sample collected from different geological unit of Budhakedar area was measured using plastic track detector (LR-115 type II) technique. The variation in the radon concentration in soil-gas was found to vary from 1098 to 31,776 Bq.m⁻³ with an average of 7456 Bq.m⁻³ in summer season and 3501 to 42883 Bq.m⁻³ with an average of 17148 Bq.m⁻³ in winter season. In groundwater, it was found to vary from 8 to 3047 Bq.l⁻¹ with an average value 510 Bq.l⁻¹ in summer and 26 to 2311 Bq.l⁻¹ with an average value 433 Bq.L⁻¹ in winter. Surface gamma dose rate in the study area varied from 32.4 to 83.6 μR.h⁻¹ with an overall mean of 58.7 μ-R.h⁻¹ in summer and 34.6 to 79.3 μR.h⁻¹ with an average value 58.2 μR.h⁻¹ in winter. Radon exhalation rate from collected soil samples was found to vary from 0.1 × 10⁻⁵ to 5.7 × 10⁻⁵ Bq.kg⁻¹.h⁻¹ with an average of 1.5 × 10⁻⁵ Bq.kg⁻¹.h⁻¹ in summer season and 1.7 × 10⁻⁵ to 9.6 × 10⁻⁵ Bq.kg⁻¹.h⁻¹ with an average of 5.5 × 10⁻⁵ Bq.kg⁻¹.h⁻¹. A weak negative correlation was observed between radon exhalation rate from soil and radon concentration in the soil. Radon exhalation rate from the soil was also not found to be correlated with the gamma dose rate, while it shows a positive correlation with radon concentration in water in summer season. Inter-correlations among various parameters are discussed in detail.