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.

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.

A_1 Weights and d-Homogeneous Measures on Ahlfors d-Regular Space

Let X be an Ahlfors d-regular space and rn a d-regular measure on X. We prove that a measure μ on X is d-homogeneous if and only if μ is mutually absolutely continuous with respect to m and the derivative Dmμ（x） is an A1 weight. Also, we show by an example that every Ahlfors d-regular space carries a measure which is d-homogeneous but not d-regular.

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.

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.

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 → ∞.

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.

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.

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。

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.

公共安全与风险应对下的防护绿地类型、功能及效用研究

【目的】通过分析公共卫生事件发生期间防护绿地防灾功能的短板,探究城市化快速发展进程中防护绿地功能需求的演变,提出发挥防护绿地功能与效用的策略,有助于提升城市的公共安全和风险应对能力,为城市规划者和决策者提供实践指导。【方法】1)提升防护绿地应对风险的能力,包括评估防护绿地韧性水平、构建基本防灾单元、优化生态系统服务功能;2)拓展防护绿地的功能服务要素,覆盖平时服务功能与灾时服务功能;3)根据防护的时效原则,对平时、灾时2个时期的情景进行预判,实施弹性调控。【结果】构建了适合中国绿地系统规划编制的防护体系功能提升与布局优化方法,从而发挥绿地系统的多元功能,应对突发公共安全事件。【结论】在建设更完备积极的城市安全防护系统中,需提高对城市绿地系统中防护绿地时效的重视程度,使防护绿地真正成为城市防灾体系的一部分,并纳入国土空间规划编制体系,确保防护绿地的建设能够切实实施。

甘肃小柳沟钨钼矿成矿地质体补充研究及认识

依据小柳沟钨钼矿区勘查及生产中赋矿地质体所表现出的特征以及近年研究的新成果,在总结前人研究成果基础上,对小柳沟钨钼矿成矿规律进一步细化、补充、明确。通过地层及矿化的演化研究对比,认为小柳沟钨矿成矿地质体矽卡岩化有多期,前期矽卡岩化对成矿元素进一步富集起到了促进作用,后期的矽卡岩化才是主成矿期;认为钨钼成矿有时空交叉,两者成矿热液存在同步运移和富集的可能,钨钼的主矿化期极有可能均在闪长花岗岩活动时期。

基于自适应平滑度策略的三维模型分类神经架构搜索

针对人工设计三维模型分类网络架构过度依赖专家经验且泛化能力较差的问题,提出了一种自适应平滑度策略的神经架构搜索方法。首先,使用改进候选操作选择策略和连续松弛化方法将离散的搜索空间连续化,并利用权重共享机制提高搜索效率。其次,在损失函数中添加自适应平滑度策略的正则化,由温度参数控制损失函数的平滑程度。最后,使用指数归一化方法计算损失函数,以避免损失值溢出。在三维点云数据集和蛋白质间相互作用数据集上的实验结果表明,在相同的训练样本和迭代次数下,自适应平滑度策略的神经架构搜索方法的分类准确率更高,性能更稳定。

Besov Estimates for Sub-Elliptic Equations in the Heisenberg Group

In this article, we deal with weak solutions to non-degenerate sub-elliptic equations in the Heisenberg group, and study the regularities of solutions. We establish horizontal Calderón-Zygmund type estimate in Besov spaces with more general assumptions on coefficients for both homogeneous equations and non-homogeneous equations. This study of regularity estimates expands the Calderón-Zygmund theory in the Heisenberg group.

基于色度角信息的衡水湖富营养状态监测研究

【目的】营养状态作为评价湖库水环境变化特征的一个重要方面,实现对其准确、大范围的动态监测对于分析富营养化成因具有十分重要的作用。【方法】利用Landsat8遥感数据的色度角信息,构建了适用于衡水湖的叶绿素a浓度反演模型,并对其精度进行了检验,在此基础上,实现对衡水湖2013—2022年10 a间的营养状态监测,分析了其与气温和降水等气候因素的关系,对2018—2019年5次生态补水过程进行了遥感监测。【结果】结果表明:(1)该模型较为可靠,决定系数R^(2)为0.79,均方根误差和平均百分比误差分别为0.0018和4.5%;(2)近10 a衡水湖营养状态得到一定的改善,其空间变化呈现“北低南高”现象。其中,南关闸和南关新闸相对于其他湖体区域营养状态处于较高水平;(3)通过对5次生态补水过程的遥感监测发现,生态补水对于衡水湖营养状态改善具有一定的积极作用,尤其在进水口的王口闸附近,其对生态补水的响应最为及时。衡水湖营养状态是一个内在、外在、水动力等多因素影响的问题,对于个别区域存在些许波动,仍需进一步研究其内在关系。【结论】通过遥感手段实现对衡水湖营养状态的监测是可行的,能够较好揭示衡水湖营养状态变化整体规律,并实现对生态补水过程的有效监测,为衡水湖湿地水环境监测和营养状态治理提供重要的技术支撑。

分数阶Boussinesq-Coriolis方程在变指数Fourier-Besov空间中解的整体适定性和正则性

基于变指数Fourier-Besov函数空间理论,利用Littlewood-Paley分解工具、 Fourier局部化方法和Banach压缩映射原理,通过建立线性项与非线性项的估计,证明分数阶Boussinesq-Coriolis方程在临界变指数空间FB_(P(·),q)^(4-2a-3/p(·))(R^(3))中解的整体适定性和Gevrey类正则性.

Image decomposition using adaptive regularization and div(BMO)

In order to avoid staircasing effect and preserve small scale texture information for the classical total variation regularization, a new minimization energy functional model for image decomposition is proposed. Firstly, an adaptive regularization based on the local feature of images is introduced to substitute total variational regularization. The oscillatory component containing texture and/or noise is modeled in generalized function space div （BMO）. And then, the existence and uniqueness of the minimizer for proposed model are proved. Finally, the gradient descent flow of the Euler-Lagrange equations for the new model is numerically implemented by using a finite difference method. Experiments show that the proposed model is very robust to noise, and the staircasing effect is avoided efficiently, while edges and textures are well remained.

REGULARITY CRITERIA FOR WEAK SOLUTION TO THE 3D MAGNETOHYDRODYNAMIC EQUATIONS

In this article, regularity criteria for the 3D magnetohydrodynamic equations are investigated. Some sufficient integrability conditions on two components or the gradient of two components of u ＋ B and u - B in Morrey-Campanato spaces are obtained.

SOME DOUBLE SEQUENCE SPACES OF FUZZY NUMBERS DEFINED BY ORLICZ FUNCTIONS

In this article, we introduce some double sequence spaces of fuzzy real numbers defined by Orlicz function, study some of their properties like solidness, symmetricity, completeness etc, and prove some inclusion results.