Magnetic resonance image reconstruction using trained geometric directions in 2D redundant wavelets domain and non-convex optimization

Reducing scanning time is significantly important for MRI. Compressed sensing has shown promising results by undersampling the k-space data to speed up imaging. Sparsity of an image plays an important role in compressed sensing MRI to reduce the image artifacts. Recently, the method of patch-based directional wavelets (PBDW) which trains geometric directions from undersampled data has been proposed. It has better performance in preserving image edges than conventional sparsifying transforms. However, obvious artifacts are presented in the smooth region when the data are highly undersampled. In addition, the original PBDW-based method does not hold obvious improvement for radial and fully 2D random sampling patterns. In this paper, the PBDW-based MRI reconstruction is improved from two aspects: 1) An efficient non-convex minimization algorithm is modified to enhance image quality; 2) PBDW are extended into shift-invariant discrete wavelet domain to enhance the ability of transform on sparsifying piecewise smooth image features. Numerical simulation results on vivo magnetic resonance images demonstrate that the proposed method outperforms the original PBDW in terms of removing artifacts and preserving edges.     

Mathematical models for the elastic beam with structural damping

In this paper the existence, regularity and sharp estimates for the solutions of an abstract second order evolution equation are proved and applications to models of a (possibly non homogeneous) elastic beam with a frequency-proportional damping are given.     

On the *-Polynomial Identities of a Class of *-Minimal Algebras

Let F be an infinite field. We consider certain block-triangular algebras with involution U _n , with n ∈ ?, having minimal *-exponent. We describe their *-polynomial identities, and in case char.F = 0, their structure as a T _*-ideal under the action of general linear groups. These goals are achieved by means of Y-proper polynomials. We also compute explicitly the irreducible modules occurring in the decomposition of B _Y (U ₃) and their multiplicities.     

基于因子分析模型的土壤重金属污染成因分析

应用因子分析模型针对不同的污染区逐一分析其污染源,应用spss软件确定主要影响因子,给各污染源确定名称.结果表明,低污染区受人类活动影响较小,在中污染区和高污染区以混合污染源为主,其中主干道路区和工业区属于较重污染,交通污染和冶炼厂、化工厂工业废气影响较为突出,建议采取有效措施减少其对土壤重金属污染.     

Endpoint Bounds for the Quartile Operator

It is a result by Lacey and Thiele (Ann. of Math. (2) 146(3):693–724, 1997; ibid. 149(2):475–496, 1999) that the bilinear Hilbert transform maps $L^{p_{1}}(\mathbb{R}) \times L^{p_{2}}(\mathbb{R}) $ into $L^{p_{3}}(\mathbb{R})$ whenever (p ₁,p ₂,p ₃) is a Hölder tuple with p ₁,p ₂>1 and $p_{3}>\frac{2}{3}$ . We study the behavior of the quartile operator, which is the Walsh model for the bilinear Hilbert transform, when $p_{3}=\frac{2}{3}$ . We show that the quartile operator maps $L^{p_{1}}(\mathbb{R}) \times L^{p_{2}}(\mathbb{R}) $ into $L^{\frac{2}{3},\infty}(\mathbb{R})$ when p ₁,p ₂>1 and one component is restricted to subindicator functions. As a corollary, we derive that the quartile operator maps $L^{p_{1}}(\mathbb{R}) \times L^{p_{2},\frac{2}{3}}(\mathbb{R}) $ into $L^{\frac{2}{3},\infty}(\mathbb{R})$ . We also provide weak type estimates and boundedness on Orlicz-Lorentz spaces near p ₁=1,p ₂=2 which improve, in the Walsh case, the results of Bilyk and Grafakos (J. Geom. Anal. 16 (4):563–584, 2006) and Carro et al. (J. Math. Anal. Appl. 357(2):479–497, 2009). Our main tool is the multi-frequency Calderón-Zygmund decomposition from (Nazarov et al. in Math. Res. Lett. 17(3):529–545, 2010).     

Global estimates for nonlinear parabolic equations

We consider nonlinear parabolic equations of the type $$u_t - {\rm div}a(x, t, Du)= f(x, t) \quad {\rm on}\quad \Omega_T =\Omega\times (-T,0),$$ under standard growth conditions on a, with f only assumed to be integrable. We prove general decay estimates up to the boundary for level sets of the solutions u and the gradient Du which imply very general estimates in Lebesgue and Lorentz spaces. Assuming only that the involved domains satisfy a mild exterior capacity density condition, we provide global regularity results.     

武汉市在校大学生数与经济增长的协整分析

近二十年来,我国高等教育规模不断扩大,高校在校生数不断增加,其中武汉市位居全国前列．为了研究高校在校生数对当地经济发展的影响,本文利用武汉市1992—2012年在校大学生人数数据,通过建立合适的模型,来定量探讨武汉市在校大学生数与经济增长的内在关系．结果表明,武汉市经济增长与武汉在校大学生人数模型之间存在着长期均衡关系且互为格兰杰因果关系．     

水资源短缺的一种综合加权评价模型

从水资源量、暴露性、脆弱性、人口、工程技术5方面着手,根据14个二级指标,应用层次分析模型和综合加权法对北京水资源短缺风险进行综合评价.结果表明,北京水资源处于高风险阶段,属于严重缺水.     

Complementary Lidstone interpolation on scattered data sets

Recently we have introduced a new technique for combining classical bivariate Shepard operators with three point polynomial interpolation operators (Dell’Accio and Di Tommaso, On the extension of the Shepard-Bernoulli operators to higher dimensions, unpublished). This technique is based on the association, to each sample point, of a triangle with a vertex in it and other ones in its neighborhood to minimize the error of the three point interpolation polynomial. The combination inherits both degree of exactness and interpolation conditions of the interpolation polynomial at each sample point, so that in Caira et al. (J Comput Appl Math 236:1691–1707, 2012) we generalized the notion of Lidstone Interpolation (LI) to scattered data sets by combining Shepard operators with the three point Lidstone interpolation polynomial (Costabile and Dell’Accio, Appl Numer Math 52:339–361, 2005). Complementary Lidstone Interpolation (CLI), which naturally complements Lidstone interpolation, was recently introduced by Costabile et al. (J Comput Appl Math 176:77–90, 2005) and drawn on by Agarwal et al. (2009) and Agarwal and Wong (J Comput Appl Math 234:2543–2561, 2010). In this paper we generalize the notion of CLI to bivariate scattered data sets. Numerical results are provided.