Some small ball probabilities for Gaussian processes under nonuniform norms

We establish lower and upper bounds for the small ball probability of a centered Gaussian process(X(t)) _t[0,1] ^N under Hölder-type norms as well as upper bounds for some more general functionals. This extends recently established results for the uniform norm. In addition, our proof of the lower bound is considerably simpler. In the special caseN=1 we establish precise estimates under a wider class of norms including in particular the Besov norms.     

Elementary reverse Hölder type inequalities with application to operator interpolation theory

We give a very elementary proof of the reverse Hölder type inequality for the classes of weights which characterize the boundedness on of the Hardy operator for nonincreasing functions. The same technique is applied to Calderón operator involved in the theory of interpolation for general Lorentz spaces. This allows us to obtain further consequences for intermediate interpolation spaces.

     

Quadratic forms for the 1-D semilinear Schrödinger equation

This paper is concerned with 1-D quadratic semilinear
Schrödinger equations. We study local well posedness in classical Sobolev space of the associated initial value problem and periodic boundary value problem. Our main interest is to obtain the lowest value of which guarantees the desired local well posedness result. We prove that at least for the quadratic cases these values are negative and depend on the structure of the nonlinearity considered.

     

Lamperti-type operators on a weighted space of continuous functions

For a locally convex Hausdorff topological vector space and for a system of weights vanishing at infinity on a locally compact Hausdorff space , let be the weighted space of -valued continuous functions on with the locally convex topology derived from the seminorms which are weighted analogues of the supremum norm. A characterization of the orthogonality preserving (Lamperti-type) operators on is presented in this paper.

     

A posteriori error estimate for the mixed finite element method

A computable error bound for mixed finite element methods is established in the model case of the Poisson-problem to control the error in the H(div,) -norm. The reliable and efficient a posteriori error estimate applies, e.g., to Raviart-Thomas, Brezzi-Douglas-Marini, and Brezzi-Douglas-Fortin-Marini elements.

     

MRI增强扫描联合DWI检测在乳腺癌诊断中的应用

本文探究了MRI增强扫描(DCE-MRI)联合磁共振扩散加权成像(DWI)检测对乳腺癌的诊断效果。回顾性分析2015年8月~2017年8月本院收治的经手术病理证实的乳腺癌患者81例,术前均行DCE-MRI和DWI检查,根据数据绘制时间-信号强度曲线(TIC),并计算扩散系数(ADC)值。以病理结果为金标准,计算单一检测及联合检测的诊断准确率,并采用ROC分析ADC值诊断乳腺癌良/恶性的效能。结果显示,81例患者经手术病理诊断显示良性37例、恶性44例;DCE-MRI与DWI联合检测的敏感度与准确度显著高于单一检测(P<0.05);良、恶性病灶的TIC分型分布比较,差异具有统计学意义(P<0.05);恶性病灶ADC值较良性病灶低(P<0.05);ADC值诊断乳腺癌良/恶性最佳界限值为1.28×10-3 mm 2/s,灵敏度和特异度分别为86.5%和90.9%。因此,DCE-MRI与DWI联合检测可明显提高乳腺癌良/恶性病变诊断的准确度,为临床诊断提供可靠影像学依据。     

粘性不可压缩流体定常层流管流及柱体的扭转

本文用加权残数法求得了任意等腰三角形及矩形截面的柱体的扭转问题以及和柱体形状相同的等截面长管的不可压缩粘性流体的定常层流问题的近似解.近似解有较高的精确度.另外,文中还提出了变率配域法的概念.     

Statistical forecasting for stochastic processes

The main purpose of this paper is to review the efficiency properties of least-squares predictors when the parameters are estimated. It is shown that the criterion of asymptotic best unbiased predictors for general stochastic models is a natural analogue of the minimum mean-square error criterion used traditionally in linear prediction for linear models. The results are applied to log-linear models and autoregressive processes. Both stationary and non-stationary processes are considered.This paper is based on a key note lecture given at the meeting of The Institute of Management Sciences and the Operations Research Society of America, held in Williamsburg, Virginia, January 7–9, 1985.     

Characterization of coalitionally ordered games

Summary In the sequel we will derive sufficient and necessary conditions for the existence of certain numeric representations of simple games. In § 2 the above mentioned representation is given by a so called, coalitionally ordered function, i.e. a numeric function representing the desirability of each coalition in the class of all coalitions. Simple games which possess a c.o.f are called coalitionally ordered games. Sufficient and necessary criteria are given for a simple game to be a c.o.g. Analogously weighted majority games are characterized in § 3. The criteria to be presented are linked by properties of the desirability relation of a simple game. The concept of a desirability relation was introduced by Peleg 1978.

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Zusammenfassung Im folgenden werden wir hinreichende und notwendige Bedingungen zur Existenz von gewissen numerischen Darstellungen einfacher Spiele (simple games) herleiten. Diese oben genannte Darstellung wird in § 2 durch eine sogenannte coalitionally ordered function, gegeben, wobei wir darunter eine numerische Funktion verstehen, die die Desirability, jeder Koalition innerhalb der Klasse aller Koalitionen beschreibt. Einfache Spiele, die eine c.o.f besitzen, werden coalitionally ordered games genannt. Es werden hinreichende und notwendige Bedingungen dafür genannt, daß ein einfaches Spiel ein c.o.g ist. Analog werden gewichtete Abstimmungsspiele (weighted majority games) in § 3 charakterisiert. Die angegebenen Kriterien werden mit Eigenschaften der sogenannten desirability relation eines einfachen Spieles in Verbindung gebracht. Das Konzept einer desirability relation wurde von Peleg 1978 verwendet.

     

Asymptotic profile of solutions for some wave equations with very strong structural damping

We consider the Cauchy problem in R ⁿ for some types of damped wave equations. We derive asymptotic profiles of solutions with weighted L^1,1( R ⁿ) initial data by using a simple method introduced in by the first author. The obtained results will include regularity loss type estimates, which are essentially new in this kind of equation.