Abstract:
Non-point source pollution (NPS) besides point source pollution (PS) has contributed to pollutant loading into natural receiving water bodies. Due to the nature of NPS, the quantification of pollutant loading from NPS is very challenging but crucial to riverine water quality management, especially for the river reach flowing through urban areas. The water quality in the river reach of the Bow River flowing through the City of Calgary in Alberta, Canada, is affected by both PS and NPS. Thus, understanding and characterizing water quality of discharges (affected by NPS) into the river reach is necessary for better managing riverine water quality and preventing water quality degradation. In the paper, monitored event mean concentrations (EMCs) of stormwater runoff and mean concentrations of snowmelt and baseflow of seven common pollutants from sub-catchments, which are categorized into four land use types including commercial, industrial, residential and on-going development land uses, were used to investigate the linkage between land use and water quality. Statistical analysis techniques were adopted to identify differences or similarities in water quality among different flow types, different land use types, and among/between catchments of same land use. The results indicated that EMCs of many water quality parameters vary among different land use types and among/between catchments of same land use. The results also showed median EMCs of pollutants of snowmelt and baseflow are, in general, lower than those of stormwater runoff. In addition, Stormwater Management Model was employed to investigate the physical process that would affect water quality response to storm events for two typical land uses, industrial and residential land uses. The modeling results supported that wash-off of particulate matters might primarily affect water quality response of catchments between different land uses. All the results shed the light on the necessity of quantifying pollutant loading considering the characteristics of land uses.

Abstract:
Let a =(1,2,…,)∈？ be an m-dimensional vector. Then, it can be identified with an × circulant matrix. By using the theory of matrix-valued wavelet analysis (Walden and Serroukh, 2002), we discuss the vector-valued multiresolution analysis. Also, we derive several different designs of finite length of vector-valued filters. The corresponding scaling functions and wavelet functions are given. Specially, we deal with the construction of filters on symmetric matrix-valued functions space.

Abstract:
The relation between Riesz potential and heat kernel on the Heisenberg group is studied. Moreover, the Hardy-Littlewood-Sobolev inequality is established.

Abstract:
Let be the generalized Heisenberg group. In this paper, we study the inversion of the Radon transforms on . Several kinds of inversion Radon transform formulas are established. One is obtained from the Euclidean Fourier transform; the other is derived from the differential operator with respect to the center variable . Also by using sub-Laplacian and generalized sub-Laplacian we deduce an inversion formula of the Radon transform on . 1. Introduction In the past decade the research of Radon transform on the Euclidean space has made considerable progress due to its wide applications to partial differential equations, X-ray technology, radio astronomy, and so on. The basic theory and some new developments can be found in [1] by Helgason and the references therein. The combination of Radon transform and wavelet transform has proved to be very useful both on pure mathematics and its applications. Therefore, it is very meaningful to give the inversion formula of the Radon transforms by using various ways. The first result in the area is due to Holschneider who considered the classical Radon transform on the two-dimensional plane (see [2]). Rubin in [3, 4] extended the results in [2] to the -dimensional Radon transform on and totally geodesic Radon transforms on the sphere and hyperbolic space. Heisenberg group is a vital Lie group with the underlying . Strichartz [5] discussed the Radon transform on the Heisenberg group. Nessibi and Trimèche [6] obtained an inversion formula of the Radon transform on the Laguerre hypergroup by using the generalized wavelet transform. Afterwards, He and Liu studied the analogous problems on the Heisenberg group and Siegel type Lie group (see [7, 8]), and Rubin [9] achieved some new progress of the Radon transform on . In [10] the authors gave the definition of generalized Heisenberg group denoted by and dealt with some problems related to geometric analysis. In this paper, we investigate the inversion formulas of the Radon transform on the generalized Heisenberg group. From the Euclidean Fourier transform and group Fourier transform, we deduce inversion formulas of the Radon transform on associated with differential operators and generalized sub-Laplacian. Let be an -dimensional vector, where are positive real constants for . We can turn into a non-Abelian group by defining the group operation as This group is called the generalized Heisenberg group and is denoted by . It is obvious that the generalized Heisenberg group becomes ordinary Heisenberg group if all for . For any -dimensional vectors , , we define For , , the

Abstract:
Let $\mathscr Q$ be the quaternion Heisenberg group, and let $\mathbf P$ be the affine automorphism group of $\mathscr Q$. We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary representations of $\mathbf P$ on $L^2(\mathscr Q)$. A class of radial wavelets is constructed. The inverse wavelet transform is simplified by using radial wavelets. Then we investigate the Radon transform on $\mathscr Q$. A Semyanistri-Lizorkin space is introduced, on which the Radon transform is a bijection. We deal with the Radon transform on $\mathscr Q$ both by the Euclidean Fourier transform and the group Fourier transform. These two treatments are essentially equivalent. We also give an inversion formula by using wavelets, which does not require the smoothness of functions if the wavelet is smooth.

Abstract:
In this paper, one considers the change of orbifold Gromov-Witten invariants under weighted blow-up at smooth points. Some blow-up formula for Gromov-Witten invariants of symplectic orbifolds is proved. These results extend the results of manifolds case to orbifold case.