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41.
A nonhomogeneous boundary value problem for the Kuramoto–Sivashinsky equation in a quarter plane 下载免费PDF全文
Jing Li Bing‐Yu Zhang Zhixiong Zhang 《Mathematical Methods in the Applied Sciences》2017,40(15):5619-5641
We study the initial boundary value problem for the one‐dimensional Kuramoto–Sivashinsky equation posed in a half line with nonhomogeneous boundary conditions. Through the analysis of the boundary integral operator, and applying the known results of the Cauchy problem of the Kuramoto–Sivashinsky equation posed on the whole line , the initial boundary value problem of the Kuramoto–Sivashinsky equation is shown to be globally well‐posed in Sobolev space for any s >?2. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
42.
Aditya Mishra Dipak K. Dey Kun Chen 《Journal of computational and graphical statistics》2017,26(4):814-825
In multivariate regression models, a sparse singular value decomposition of the regression component matrix is appealing for reducing dimensionality and facilitating interpretation. However, the recovery of such a decomposition remains very challenging, largely due to the simultaneous presence of orthogonality constraints and co-sparsity regularization. By delving into the underlying statistical data-generation mechanism, we reformulate the problem as a supervised co-sparse factor analysis, and develop an efficient computational procedure, named sequential factor extraction via co-sparse unit-rank estimation (SeCURE), that completely bypasses the orthogonality requirements. At each step, the problem reduces to a sparse multivariate regression with a unit-rank constraint. Nicely, each sequentially extracted sparse and unit-rank coefficient matrix automatically leads to co-sparsity in its pair of singular vectors. Each latent factor is thus a sparse linear combination of the predictors and may influence only a subset of responses. The proposed algorithm is guaranteed to converge, and it ensures efficient computation even with incomplete data and/or when enforcing exact orthogonality is desired. Our estimators enjoy the oracle properties asymptotically; a non-asymptotic error bound further reveals some interesting finite-sample behaviors of the estimators. The efficacy of SeCURE is demonstrated by simulation studies and two applications in genetics. Supplementary materials for this article are available online. 相似文献
43.
We prove new results regarding the existence of positive solutions for a nonlinear periodic boundary value problem related to the Liebau phenomenon. As a consequence we obtain new sufficient conditions for the existence of a pump in a simple model. Our methodology relies on the use of classical fixed point index. Some examples are provided to illustrate our theory. We improve and complement previous results in the literature. 相似文献
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45.
Maximum likelihood estimation for stochastic volatility in mean models with heavy‐tailed distributions 下载免费PDF全文
Carlos A. Abanto‐Valle Roland Langrock Ming‐Hui Chen Michel V. Cardoso 《商业与工业应用随机模型》2017,33(4):394-408
In this article, we introduce a likelihood‐based estimation method for the stochastic volatility in mean (SVM) model with scale mixtures of normal (SMN) distributions. Our estimation method is based on the fact that the powerful hidden Markov model (HMM) machinery can be applied in order to evaluate an arbitrarily accurate approximation of the likelihood of an SVM model with SMN distributions. Likelihood‐based estimation of the parameters of stochastic volatility models, in general, and SVM models with SMN distributions, in particular, is usually regarded as challenging as the likelihood is a high‐dimensional multiple integral. However, the HMM approximation, which is very easy to implement, makes numerical maximum of the likelihood feasible and leads to simple formulae for forecast distributions, for computing appropriately defined residuals, and for decoding, that is, estimating the volatility of the process. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
46.
微分达布定理表明区间内的导函数具有介值性,这使得我们在考虑一些数学分析问题时,往往可以不需要最高阶导函数的连续性.而在微分方程理论中,比较定理的思想对于解的估计非常重要.本文利用比较定理的思想将中值定理类问题转化为微分方程解的估计问题,对于在数学分析的学习中提高学生的认识和兴趣很有意义. 相似文献
47.
基于格林函数理论,主要利用Lerray-Schauder抉择定理和上下解方法针对半正定条件下,奇异超线性二阶周期边值问题正解的存在性进行推理证明,获取了奇异超线性二阶周期边值问题的一个正解. 相似文献
48.
将194例小肝癌患者纳入小肝癌组,185例肝细胞结节患者纳入结节组,所有患者均行MRI扩散加权成像(DWI-MRI),评估患者在DWI-MRI上的形态学表现及ADC值,检测患者血清AFP水平,比较不同检测方法诊断小肝癌的准确度、灵敏度、特异度。结果显示,应用DWI-MRI联合血清AFP诊断小肝癌的特异度、灵敏度和准确度均显著高于单独应用DWI-MRI,或血清AFP(P<0.05)。表明DWI-MRI联合血清AFP对小肝癌的诊断价值显著,可为病情评估提供切实可行的参考。 相似文献
49.
选取我院60例腰椎管狭窄症(LSS)患者作为研究组,同期健康者60例作为对照组,探究CT检查参数对LSS的诊断价值及与疗效、腰椎功能改善的相关性。结果显示,研究组椎管面积、硬膜囊面积、椎管矢径、椎管横径、侧隐窝矢径、侧隐窝角小于对照组(P<0.05);CT各参数联合诊断LSS的AUC值大于任一参数单独诊断;疗效优良患者术后3个月椎管面积、硬膜囊面积、椎管矢径、侧隐窝矢径、侧隐窝角大于治疗前及非优良患者(P<0.05);经偏相关性分析发现,CT检查参数与疗效显著相关(P<0.05)。说明LSS疗效、腰椎功能改善情况与椎管面积、硬膜囊面积、椎管矢径等关系密切,CT检查对指导临床完善手术方案有重要意义。 相似文献
50.