SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION

This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.

Enhanced Differentiable Architecture Search Based on Asymptotic Regularization

In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search space with different complexity according to various operations.Meanwhile rationalizing the search strategies to explore the well-defined search space will further improve the speed and efficiency of architecture search.With this in mind,we propose a faster and more efficient differentiable architecture search method,AllegroNAS.Firstly,we introduce a more efficient search space enriched by the introduction of two redefined convolution modules.Secondly,we utilize a more efficient architectural parameter regularization method,mitigating the overfitting problem during the search process and reducing the error brought about by gradient approximation.Meanwhile,we introduce a natural exponential cosine annealing method to make the learning rate of the neural network training process more suitable for the search procedure.Moreover,group convolution and data augmentation are employed to reduce the computational cost.Finally,through extensive experiments on several public datasets,we demonstrate that our method can more swiftly search for better-performing neural network architectures in a more efficient search space,thus validating the effectiveness of our approach.

Solving Neumann Boundary Problem with Kernel-Regularized Learning Approach

We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.

Generalized regular points of a C^1 map between Banach spaces

Let f be a C^1 map between two Banach spaces E and F. It has been proved that the concept of generalized regular points of f, which is a generalization of the notion of regular points of f, has some crucial applications in nonlinearity and global analysis. We characterize the generalized regular points of f using the three integer-valued （or infinite） indices M（x0）, Mc（x0） and Mr（x0） at x0 ∈ E generated by f and by analyzing generalized inverses of bounded linear operators on Banach spaces, that is, iff ＇（x0） has a generalized inverse in the Banach space B（E, F） of all bounded linear operators on E into F and at least one of the indices M（x0）, Mc（x0） and Mr（x0） is finite, then xo is a generalized regular point off if and only if the multi-index （M（x）, Me（x）, Mr（x）） is continuous at X0.

LAVRENTIEV'S REGULARIZATION METHOD FOR NONLINEAR ILL-POSED EQUATIONS IN BANACH SPACES

In this paper, we deal with nonlinear ill-posed problems involving m-accretive mappings in Banach spaces. We consider a derivative and inverse free method for the imple- mentation of Lavrentiev regularization method. Using general HSlder type source condition we obtain an optimal order error estimate. Also we consider the adaptive parameter choice strategy proposed by Pereverzev and Schock （2005） for choosing the regularization parameter.

THE PRODUCT OPERATOR BETWEEN BLOCH-TYPE SPACES OF SLICE REGULAR FUNCTIONS

There is little work concerning the properties of quaternionic operators acting on slice regular function spaces defined on quaternions.In this paper,we present an equivalent characterization for the boundedness of the product operator C_(φ)D^(m) acting on Bloch-type spaces of slice regular functions.After that,an equivalent estimation for its essential norm is established,which can imply several existing results on holomorphic spaces.

A Regularity Criterion Via the Pressure On the Three-dimensional Micropolar Fluid Equations in Besov Space

In this paper,we investigate the regularity criterion via the pressure of weak solutions to the micropolar fluid equations in three dimensions.We obtain that for 0<α<1 if p€L^(2/a)(0,T;B^α∞,∞),then the weak solution(u,ω)is regular on(0,T).

Some Properties of Regular and α-Regular (LM)-Spaces

In this paper, we give some properties of regular (LM)-spaces and α-regular (LM)-spaces and investigate the relationship among them.

Regularity of Continuous Linear Operators on Banach Function Spaces

In this paper we present some characterizations of Banach function spaces on which every continuous linear operator is regular.

Regularity Criterion of Weak Solutions to the 3D Micropolar Fluid Equations in Besov Space

This paper studies the regularity criterion of weak solutions to the micropolarfluid equations in three dimensions. Let (■u∈L2/2-γ(0,T;B^-γ∞,∞),■ω∈L^2(0,T;B^-1∞,∞)),it is showed that the weak solution(u,ω) is globally regular for the case 0 < γ < 2.

Gevrey Regularity and Time Decay of Fractional Porous Medium Equation in Critical Besov Spaces

In this paper, we show the existence and regularity of mild solutions depending on the small initial data in Besov spaces to the fractional porous medium equation. When 1 < α ≤ 2, we prove global well-posedness for initial data with 1 ≤ p < ∞, 1 ≤ q ≤ ∞, and analyticity of solutions with 1 < p < ∞, 1 ≤ q ≤ ∞. In particular, we also proved that when α = 1, both u and belong to . We solve this equation through the contraction mapping method based on Littlewood-Paley theory and Fourier multiplier. Furthermore, we can get time decay estimates of global solutions in Besov spaces, which is as t → ∞.

On Ws-Regular Spaces

In the present, the authors investigate a new type of separation axioms, which they call it w s-regular. The authors obtained some of its basic properties and its characterizations. Also, the authors notice that the axiom of tO s-regularity is weaker than the regularity, stronger than s-regularity and it is independent of w -regularity. However, the authors showed that the w s-regularity and regularity are identical on the class of all locally countable spaces, while the concepts ofw s-regularity and s-regularity are same on the class of anti-locally countable spaces：; furthermore, they proved that the three concepts w s-regularity, s-regularity and w s-regularity are same on the class of extremally disconnected spaces. The authors characterized w s-regular Trspaces by g-open sets, and they proved that the w s-regularity is an open hereditary property and it is also a topologizal property. The w s-closure of subsets of topological spaces are investigated and characterized. The authors used the concepts w s-closure to obtain some characterizations of the w s-regular spaces. Behind those, the authors obtained some properties and characterizations of w -semi open sets.

Remark on Regularity of Continuous Operators on AL-Spaces

Let E and F be Banach lattices. It is known that if every continuous linear operator from E into F is regular, then, under some mild assumptions on E or F, either E is lattice isomorphic to an AL-space or F is lattice isomorphic to an AM-space. Here we present a characterization on an AL-space E such that every bounded linear operator from E into a Banach lattice is regular. A counterexample is also provided, which shows that the results are unexpected even if the domain is an AL-space or the range space is an AM-space.

Near-Vector Spaces Constructed over Zp, for p a Prime

The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Zp for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we focus on those studied by André [1]. These near-vector spaces have recently proven to be very useful in finite linear games. We will discuss the construction and properties, give examples of these near-vector spaces and give its application in finite linear games.

We Live on a Small Space Comet: The Third Extraordinary Motion of Earth towards the North Pole and Its Various Effects

The idea of research started with a crazy imaginary theory in the field of astrogeography, saying: We often taught ourselves and then convinced the students that the planet Earth moves despite not feeling the vibrations of traffic, and we listed successive scientific confirmations to indicate the rotation of the planet in a regular movement around its axis once every 24 hours, and it is running in another second movement around the sun once every 365¼ days, so are they only two movements, no more?! Is it possible for him to run at a regular speed in an additional direction?

高斯感知约束空间异常的相关滤波目标跟踪

针对目标在复杂场景运动过程中容易出现跟踪丢失问题,提出一种高斯感知约束空间异常的目标跟踪算法。以高斯均匀分布为分布规律建立目标特征采样点,采用卷积结构提取目标的外观模型以及权重模型;为了约束空间异常,在目标函数中构建空间正则项,同时更新目标权重模型,减小空间过拟合的产生,增强跟踪器的空间异常适应性;应用加权最小二乘法思想,获得权重响应模型中心,确定目标中心,更新跟踪位置,增强跟踪器鲁棒性。使用OTB2015和UAV20L数据集,与其他主流相关滤波算法相比,该算法在目标运动导致低分辨率、遮挡等复杂条件下,跟踪成功率以及跟踪精度较高。

基于核机器的加速失效时间模型及其应用

加速失效时间模型是一种应用广泛的生存分析模型。本文借助LASSO惩罚剔除冗余预测变量,构建基于核机器的加速失效时间模型,用以刻画预测变量与生存期间的复杂关系。此外,提出一种新的正则化Garrotized核机器估计方法,可以较好地刻画预测变量与生存期潜在的非线性关系,实现非参数分量中预测变量间交互作用的自动建模,提升模型预测精度。模拟研究表明,与已有的代表性方法相比,本文提出的方法对生存期的预测精度更高,特别是在复杂关系情形下优势更为显著。最后,将该方法应用于胃癌数据分析,利用临床信息和基因表达预测生存期和风险评分。实证结果显示,该方法能为病例基于风险分层的临床精准诊疗方案设计提供有益的参考。

AM-FM算子分解方法在滚动轴承故障诊断中的应用

基于算子的零空间追踪算法能够实现复杂信号的自适应分解,其关键在于信号模型的构造与求解。通过定义一种新的可完全消除调幅调频信号的调幅调频算子(AFO),进一步建立了一种基于AFO的信号分解新模型。为了提高参数对信号分解的鲁棒性,将非参数正则化(NPR)方法用于解决上述模型的约束优化问题,提出了一种基于NPR的自适应信号分解方法——NPR-AFO。论文将NPR-AFO方法引入到机械故障诊断中,并通过仿真和滚动轴承局部故障实测数据分析,与现有的其他分解方法进行了对比。结果表明:所提方法不仅可以有效的提取故障特征,而且状态故障特征更加明显。

速度零耗散且温度分数阶扩散的二维微极Rayleigh-Bénard对流系统的全局正则性

该文研究速度零耗散,微旋转速度拉普拉斯耗散且温度分数阶扩散的二维微极Rayleigh-Bénard对流系统的全局正则性问题.通过构建两个组合量和使用Littlewood-Paley分解技术,该文建立了该系统解的全局正则性结果.

改进Tikhonov正则化方法在结构激励识别与响应重构中的应用

为了改善传递矩阵的病态性,实现利用结构有限测量信息对结构外部激励与未知响应的有效重构,提出了一种用于结构激励识别与响应重构的改进Tikhonov正则化方法。首先,基于状态空间模型构建传递矩阵,并推导结构外部激励识别与响应重构方程。其次,采用改进Tikhonov正则化方法改善传递矩阵的病态性,得到激励方程的正则化解,并结合结构需重构位置对应的传递矩阵重构未知加速度响应。最后,分别对平面二维桁架和简支梁进行数值仿真和试验分析,验证所提方法的可行性。结果表明所提方法能够改善传递矩阵的病态性,提高结构激励识别与响应重构的精度。