Boundedness and compactness of an integral operator between <Emphasis Type="Italic">H</Emphasis><Superscript>∞</Superscript> and a mixed norm space on the polydisk

This addendum to [1] completely characterizes the boundedness and compactness of a recently introduced integral type operator from the space of bounded holomorphic functions H ^∞(\(\mathbb{D}^n \)) on the unit polydisk \(\mathbb{D}^n \) to the mixed norm space

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with p, q ∈ [1,∞) and α = (α₁, ..., α _n ) such that α _j > ?1 for every j = 1, ..., n. We show that the operator is bounded if and only if it is compact and if and only if g ∈

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, where \(\vec q\) = (q, ..., q).

     

On V-orthogonal projectors associated with a semi-norm

For any n ×  p matrix X and n ×  n nonnegative definite matrix V, the matrix X(X′V X)⁺ X′V is called a V-orthogonal projector with respect to the semi-norm , where (·)⁺ denotes the Moore-Penrose inverse of a matrix. Various new properties of the V-orthogonal projector were derived under the condition that rank(V X) =  rank(X), including its rank, complement, equivalent expressions, conditions for additive decomposability, equivalence conditions between two (V-)orthogonal projectors, etc.     

A mixed finite element method for a shallow shell problem with a stress function

In this paper we consider the problem of a deflected mode of a shallow shell. The stress function and the normal component of the displacement of the median surface of the shell are unknown functions. We propose a mixed variational statement of the problem, where the second derivatives of the stress function and the normal component of the displacement of the median surface are additional unknowns. This enables us to construct the finite element approximation of the initial problem. We prove the existence of a unique solution of the approximating problem and estimate the rate of convergence of the discrete solution.     

A minimum distance estimator in an imprecise probability model - Computational aspects and applications

The article considers estimating a parameter θ in an imprecise probability model which consists of coherent upper previsions . After the definition of a minimum distance estimator in this setup and a summarization of its main properties, the focus lies on applications. It is shown that approximate minimum distances on the discretized sample space can be calculated by linear programming. After a discussion of some computational aspects, the estimator is applied in a simulation study consisting of two different models. Finally, the estimator is applied on a real data set in a linear regression model.     

带有辅助信息的ROC曲线两种估计的比较

在医学研究中,常常使用受试者操作特性曲线(ROC)曲线来研究两样本的比较问题。Lloyd构造了ROC曲线的核平滑估计,并给出了其渐近偏差以及渐近标准差。此外,当还可以获悉某一处理组上的辅助信息时,Zhou,Zhou & Ma利用经验似然的方法构造了ROC曲线的核平滑经验似然估计。本文利用"亏量"这个概念比较了带有辅助信息的情况下,对核平滑经验似然估计与完全经验似然估计进行了比较。并给出了核平滑经验似然估计优于完全经验似然估计的结论,并且随着样本容量的增大,该亏量也是无限增大的。     

Weighted a priori estimates for solution of (−Δ)<Superscript><Emphasis Type="Italic">m</Emphasis></Superscript><Emphasis Type="Italic">u</Emphasis> = <Emphasis Type="Italic">f</Emphasis> with homogeneous dirichlet conditions

Let u be a weak solution of (-△)mu = f with Dirichlet boundary conditions in a smooth bounded domain Ω  Rn. Then, the main goal of this paper is to prove the following a priori estimate:‖u‖ Wω2 m,p(Ω) ≤ C ‖f‖ Lωp (Ω),where ω is a weight in the Muckenhoupt class Ap.     

对于金融资产波动率估计的双域组合方法

Time- and state-domain methods are two common approaches for nonparametrically estimating the volatility of financial assets. Economic conditions vary over time in real financial market. It is reasonable to expect that volatility depends on both time and price level for a given state variable. Recently, Fan, et al （2007） proposed the idea of dynamically integrated method in both time-and state domain. This idea has become an interesting topic in the estimation of volatility. In this paper, our purpose is to discuss the integrated method in the estimation of volatility. Simulations are conducted to demonstrate that the newly integrated method outperforms some old ones, and the results of simulations demonstrate this fact. Furthermore, we establish its asymptotic properties.     

Pediatric abdominal masses: diagnostic accuracy of diffusion weighted MRI

Purpose

To retrospectively identify apparent diffusion coefficient (ADC) values of pediatric abdominal mass lesions, to determine whether measured ADC of the lesions and signal intensity on diffusion-weighted (DW) images allow discrimination between benign and malignant mass lesions.

Materials and Methods

Approval for this retrospective study was obtained from the institutional review board. Children with abdominal mass lesions, who were examined by DW magnetic resonance imaging (MRI) were included in this study. DW MR images were obtained in the axial plane by using a non breath-hold single-shot spin-echo sequence on a 1.5-T MR scanner. ADCs were calculated for each lesion. ADC values were compared with Mann–Whitney U test. Receiver operating characteristic curve analysis was performed to determine cut-off values for ADC. The results of visual assessment on b800 images and ADC map images were compared with chi-square test.

Results

Thirty-one abdominal mass lesions (16 benign, 15 malignant) in 26 patients (15 girls, 11 boys, ranging from 2 days to 17 years with 6.9 years mean) underwent MRI. Benign lesions had significantly higher ADC values than malignant ones (P<.001). The mean ADCs of malignant lesions were 0.84±1.7×10⁻³ mm²/s, while the mean ADCs of the benign ones were 2.28±1.00×10⁻³ mm²/s. With respect to cutoff values of ADC: 1.11×10⁻³ mm²/s, sensitivity and negative predictive values were 100%, specificity was 78.6% and positive predictive value was 83.3%. For b800 and ADC map images, there were statistically significant differences on visual assessment. All malignant lesions had variable degrees of high signal intensity whereas eight of the 16 benign ones had low signal intensities on b800 images (P<.001). On ADC map images, all malignant lesions were hypointense and most of the benign ones (n=11, 68.7%) were hyperintense (P<.001).

Conclusion

DW imaging can be used for reliable discrimination of benign and malignant pediatric abdominal mass lesions based on considerable differences in the ADC values and signal intensity changes.     

元胞自动机混合交通流模型的能耗研究

基于元胞自动机交通流NaSch模型,提出元胞自动机混合交通流能耗公式,对混合交通流的能耗进行研究,通过数值模拟研究不同最大速度、不同车长的混合交通流的能耗;研究表明不同车长、不同最大速度以及混合比对混合交通流能耗均有不同的影响. 关键词： 交通流 元胞自动机 能耗 混合交通     

An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection–diffusion equations

In this paper, we present hybridizable discontinuous Galerkin methods for the numerical solution of steady and time-dependent nonlinear convection–diffusion equations. The methods are devised by expressing the approximate scalar variable and corresponding flux in terms of an approximate trace of the scalar variable and then explicitly enforcing the jump condition of the numerical fluxes across the element boundary. Applying the Newton–Raphson procedure and the hybridization technique, we obtain a global equation system solely in terms of the approximate trace of the scalar variable at every Newton iteration. The high number of globally coupled degrees of freedom in the discontinuous Galerkin approximation is therefore significantly reduced. We then extend the method to time-dependent problems by approximating the time derivative by means of backward difference formulae. When the time-marching method is (p+1)$(p+1)$th order accurate and when polynomials of degree p?0$p?0$ are used to represent the scalar variable, each component of the flux and the approximate trace, we observe that the approximations for the scalar variable and the flux converge with the optimal order of p+1$p+1$ in the L²$L^2$-norm. Finally, we apply element-by-element postprocessing schemes to obtain new approximations of the flux and the scalar variable. The new approximate flux, which has a continuous interelement normal component, is shown to converge with order p+1$p+1$ in the L²$L^2$-norm. The new approximate scalar variable is shown to converge with order p+2$p+2$ in the L²$L^2$-norm. The postprocessing is performed at the element level and is thus much less expensive than the solution procedure. For the time-dependent case, the postprocessing does not need to be applied at each time step but only at the times for which an enhanced solution is required. Extensive numerical results are provided to demonstrate the performance of the present method.