Space Topologies and Their Dual Space Topologies for Conventional Functional Space Topologies

In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topological vector spaces and it is in this context that we have chosen to present this work. We are interested in the topology of its spaces and in the topologies of their dual spaces. The first part, we presented the fundamental topological properties of topological vector spaces. The second part, we studied Frechet spaces and particularly the space S(Rn) of functions of class C∞ on Rn which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn) the space of tempered distributions. The last part aims to define a topological structure on an increasing union of Frechet spaces called inductive limit of Frechet spaces. We study in particular the space D(Ω) of functions of class C∞ with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.

The Dual of the Two-Variable Exponent Amalgam Spaces (Lq(),lp())(Ω)

Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (Lq(),lp())(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.

The Dual Spaces of Sets of Difference Sequences of Order m and Matrix Transformations

Let p = （pk）k=0^∞ be a bounded sequence of positive reals, m C N and u be s sequence of nonzero terms. If x = （xk）k=0^∞ is any sequence of complex numbers we write Δ（m）x for the sequence of the m th order differences of x and Δu^（m）X = {x=（x）k=0^∞ uΔ（m）x ∈ X} for any set X of sequences. We determine the α-, β- and γ-duals of the sets Δμ^（m）X for X=co（p）,c（p）,l∞（p） and characterize some matrix transformations between these spaces Δ^（m）X.

THE DUAL OF NONCOMMUTATIVE LORENTZ SPACES

We prove some noncommutative analogues of the classical results about dual spaces of the classical Lorentz spaces.

Dual Space, Carleson Measure and Sequence Interpolation on A^p(φ)(0

Let D={z∈: |z|【1} and φ be a normal function on [0, 1). For p∈(0, 1) such a function φ is used to define a Bergman space A^p(φ) on D with weight φ~p(|·|)/(1-|·|~2). In this paper, the dual space of A^p(φ) is given, four characteristics of Carleson measure on A^p(φ) are obtained. Moreover, as an application, three sequence interpolation theorems in A^p(φ) are derived.

基于B-dual-space的摄像机标定

针对摄像机标定,提出了一种基于B-dual-space的改进型平面标定法。首先介绍了B-dual-space的概念和基本性质;并将B-dual-space与张正友的平板标定法相结合,提出了改进型的平面标定算法,这一方法继承了张的方法中二阶畸变模型的使用,相较Tsai的方法畸变模型更精细;然后,用棋盘标定平板实验验证了算法的有效性,通过与另外两种经典标定方法的标定结果比较,显示该方法的精度与张正友的方法接近。

A semantic and emotion-based dual latent variable generation model for a dialogue system

With the development of intelligent agents pursuing humanisation,artificial intelligence must consider emotion,the most basic spiritual need in human interaction.Traditional emotional dialogue systems usually use an external emotional dictionary to select appropriate emotional words to add to the response or concatenate emotional tags and semantic features in the decoding step to generate appropriate responses.However,selecting emotional words from a fixed emotional dictionary may result in loss of the diversity and consistency of the response.We propose a semantic and emotion-based dual latent variable generation model(Dual-LVG)for dialogue systems,which is able to generate appropriate emotional responses without an emotional dictionary.Different from previous work,the conditional variational autoencoder(CVAE)adopts the standard transformer structure.Then,Dual-LVG regularises the CVAE latent space by introducing a dual latent space of semantics and emotion.The content diversity and emotional accuracy of the generated responses are improved by learning emotion and semantic features respectively.Moreover,the average attention mechanism is adopted to better extract semantic features at the sequence level,and the semi-supervised attention mechanism is used in the decoding step to strengthen the fusion of emotional features of the model.Experimental results show that Dual-LVG can successfully achieve the effect of generating different content by controlling emotional factors.

SIR phasing by combination of SOLVE/RESOLVE and dual-space fragment extension involving OASIS

A new phasing procedure has been proposed for dealing with single isomorphous replacement （SIR） x-ray diffraction data. The procedure combines SOLVE/RESOLVE with the dual-space fragment extension involving OASIS. Two sets of SIR data at 0.28 nm resolution taken from the protein （R）-phycoerythrin （PDB code： 1LIA） were used in the test. For one of the two SIR data sets, a default run of SOLVE/RESOLVE based on the heavy-atom substructure found by SHLEXD led automatically to an interpretable electron density map. OASIS could not effectively improve the result. For the other set of SIR data, SOLVE/RESOLVE resulted in a fragmented model consisting of 454 of the total 668 residues, in which only 29 residues were docked into the sequence. Based on this model, 7 iteration cycles of OASIS-DM- RESOLVE （build only） yielded automatically a model of 547 residues with 133 residues docked into the sequence. The overall-averaged phase error decreased considerably and the quality of electron density map was improved significantly. Two more cycles of iterative OASIS-DM-RESOLVE were carried out, in which the output phases and figures of merit from DM were merged with that from the original run of SOLVE/RESOLVE before they were passed onto RESOLVE （build only）. This led automatically to a model containing 452 residues with 173 docked into the sequence. The resultant electron density map is manually traceable. It is concluded that when results of SOLVE/RESOLVE are not sufficiently satisfactory, the combination of SOLVE/RESOLVE and OASIS-DM-RESOLVE （build only） may significantly improve them.

Singular perturbation composite control of a free-floating flexible dual-arm space robot

The Free-floating Flexible Dual-arm Space Robot is a highly nonlinear and coupled dynamics system. In this paper, the dynamic model is derived of a Free-floating Flexible Dual-arm Space Robot holding a rigid payload. Furthermore, according to the singular perturbation method, the system is separated into a slow subsystem representing rigid body motion of the robot and a fast subsystem representing the flexible link dynamics. For the slow subsystem, based on the second method of Lyapunov, using simple quantitative bounds on the model uncertainties, a robust tracking controller design is used during the trajectory tracking phase. The optimal control method is designed in the fast subsystem to guarantee the exponential stability. With the combination of the two above, the system can track the expected trajectory accurately, even though with uncertainty in model parameters, and its flexible vibration gets suppressed, too. Finally, some simulation tests have been conducted to verify the effectiveness of the proposed methods.

Adaptive neural network control for coordinated motion of a dual-arm space robot system with uncertain parameters

Control of coordinated motion between the base attitude and the arm joints of a free-floating dual-arm space robot with uncertain parameters is discussed. By combining the relation of system linear momentum conversation with the Lagrangian approach, the dynamic equation of a robot is established. Based on the above results, the free-floating dual-arm space robot system is modeled with RBF neural networks, the GL matrix and its product operator. With all uncertain inertial system parameters, an adaptive RBF neural network control scheme is developed for coordinated motion between the base attitude and the arm joints. The proposed scheme does not need linear parameterization of the dynamic equation of the system and any accurate prior-knowledge of the actual inertial parameters. Also it does not need to train the neural network offline so that it would present real-time and online applications. A planar free-floating dual-arm space robot is simulated to show feasibility of the proposed scheme.

Ordered Generalized Sequence Spaces and their Duals

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Study on Factors Influencing Urban-rural Dual Economic Structure of Chongqing Based on the State Space Variable Parameter Method

Firstly,this paper reviews and analyzes historic background of urban-rural integration of Chongqing,and the evolution and trend of urban and rural dual economic structure.On the basis of previous researches,it selects factors and variables influencing urban and rural dual economic structure,and establishes an econometric model.By state space Kalman filtering method,it analyzes dynamic influence of factors upon urban-rural dual economic intensity.According to empirical conclusion,it puts forward corresponding policy recommendations for promoting integrated urban and rural economic development of Chongqing.

用户资源创新能力、创业模式与创业绩效关系研究——基于众创空间的双重网络嵌入的调节作用

资源对用户开展创业活动至关重要,但对用户创业者资源创新能力影响创业模式选择以及关于创业绩效理论机制的探讨较少。通过构建不同资源创新能力、创业模式与创新绩效之间的匹配关系模型,对221家嵌入众创空间的用户创业企业进行实证研究。结果发现:①资源获取创新能力有助于用户创业者选择协同型创业模式并促进生存绩效提升;②资源利用创新能力有助于用户创业者选择自主型创业模式并促进成长绩效提升;③创业模式在资源创新能力对创业绩效影响中发挥部分中介作用;④众创空间双重网络嵌入对资源创新能力与创业模式关系以及创业模式与创业绩效关系发挥正向调节作用。

“双碳”目标下国土空间优化的挑战与应对

国土空间优化与调控始终是现代化建设面临的重大理论和实践问题。现有的国土空间规划研究多聚焦于对低碳空间治理思路、框架、工具的整体性把握,尚缺乏明确的碳约束目标及行动指南,亟待将“双碳”目标全面融入国土空间规划的目标体系、决策体系和保障体系,发挥规划在空间治理上的统筹引领作用。首先,国土空间优化光论“地”不谈“天”不行,也不能“就土论土、就地论地”;其次,低碳和“双碳”目标并不完全等同,要避免“双碳”研究中忽视国土,也要在研究国土问题中厘清“双碳”;再次,空间优化是个复杂动态过程,需要高度重视深度不确定性。因此,未来有必要建立国土空间抗解性识别分析范式和方法,开发应对深度不确定性的国土空间协同演化集成模型,构建国土空间多目标优化调控理论体系,并沿着科学认知、信息技术、智能规划、创新制度四个主轴展开深入研究和理论构建。

职住学空间测度及儿童通学决策的影响机理——以昆明市双职工家庭为例

当代城市家庭选择居住地时往往将临近学校作为重要参考,在缩小学住距离的同时加剧了职住分离。选取昆明市561个有学龄儿童的双职工家庭为研究对象,分析家庭空间分异对儿童通学决策的影响。首先,基于时间地理学理论构建考虑职住学三个锚点的家庭活动空间及测度理论模型。其次,根据测度结果将家庭活动空间划分为职住学就近型和职住学分离型两类。最后,建立结构方程模型分别探究两种模式下父母工作时长以及父母儿童组合时间窗对儿童通学时空行为的影响。研究结果表明:相对于学住距离,父母的职住距离和工作时长对通学行为的影响更为显著,因此就近入学政策对于促进儿童步行上学的作用有限;对于职住学分离型家庭,父母下班与儿童放学组合时间窗的宽裕程度对儿童出行影响显著,组合时间窗越宽裕,儿童小汽车出行的可能越大,因此弹性放学时间的效果也有待商榷;儿童在通学行为中的性别差异主要在职住学分离型家庭中体现。

基于虚拟电压矢量的双三相直线磁通切换永磁电机容错SVPWM策略

高可靠性是电梯驱动系统的首要指标。针对双三相直线磁通切换永磁(dual-three-phase linear flux switching permanent magnet,DTP-LFSPM)电机单相开路故障,提出一种基于虚拟电压矢量的容错空间矢量脉宽调制策略。首先,基于单相开路故障下的五维变换矩阵计算得到故障后的32个空间电压矢量分布。然后,筛选部分空间电压矢量,以z子空间电压幅值为零且每个扇区产生对称的脉宽调制波形为目标,重构得到12个虚拟电压矢量,相邻的2个虚拟电压矢量都由3个基本电压矢量组成,并用于合成参考电压矢量,不仅可以减少单相开路故障容错控制时的电流谐波,而且具有计算简单,易于硬件实现等优点。最后,搭建DTP-LFSPM电机驱动控制系统仿真与实验平台,仿真和实验测试结果证明所提容错策略的正确性和有效性。

基于KA-SRCN-pSTAP的低空风切变风速估计方法

针对由于独立同分布(IID)样本严重不足,导致极化空时自适应(pSTAP)处理性能下降,进而导致低空风切变风速估计不准确的问题,本文提出了一种基于知识辅助的稀疏表示杂波零陷极化空时自适应(KA-SRCN-pSTAP)的低空风切变风速估计方法。该方法首先利用杂波脊的先验知识辅助构造极化空时稀疏字典,然后利用极化空时稀疏字典,通过SRCN算法挑选原子并对到杂波线性子空间补空间上的投影矩阵进行估计,从而得到pSTAP权矢量,最后构造pSTAP滤波器对地杂波进行抑制,准确估计低空风切变风速。该方法仅使用少量IID样本,将SRCN算法与极化-空时域相结合,完成对风切变风速的有效估计。仿真实验结果证明该方法可以有效实现少样本情况下的风速准确估计。

一种动态锁定式多星协同任务规划的A2C算法

提出了一种基于强化学习算法的多星协同任务规划方法。该方法将多星协同任务规划视为多个双星协同规划,采用相邻双星锁定的方式来共享双星任务规划结果信息,基于A2C(优势动作评价)强化学习算法对双星任务规划的结果进行再调整。针对多星协同任务规划状态空间复杂且变化的问题,设计了两级状态空间和价值评价函数决策的方法,对强化学习所依赖的状态空间进行维度限制,确保智能体对任务进行调整的过程不影响状态空间维度。算法设计过程考虑了多种约束条件,设置了天气、成像质量和成像优先级等可调参数作为强化学习A2C算法的评价参数,这些可调参数有助于用户自定义决策评价体系。最后,通过仿真验证了算法的可行性。仿真结果表明,该算法多星协同任务规划的组合任务抛弃率小于10%。

Fock正交补空间上亚正规对偶Toeplitz算子

Fock空间是由整函数构成的一类重要解析函数空间.由于与量子力学中的海森堡群表示理论相关,所以不仅在函数空间算子理论有着重要研究意义,还与量子力学的研究紧密相关.对偶Toeplitz算子也是算子理论研究内容之一,且与Toeplitz算子相互影响.算子的亚正规性,起源于Halmos的Hilbert空间问题集中的第5个问题,一直都是算子理论的重点研究内容之一.主要利用函数空间的结构和对偶Toeplitz算子的性质,刻画Fock空间的正交补空间上以(z-a)(z-b)为符号的对偶Toeplitz算子亚正规性,并得出其亚正规性等价于正规性,同时也探究了以调和多项式为符号的对偶Toeplitz算子是亚正规的一些必要条件.

Fock-Sobolev Spaces and Weighted Composition Operators among Them

Abstract： We characterize the boundedness and compactness of weighted compo-sition operators among some Fock-Sobolev spaces. We also estimate the norm and essential norm of these operators. Furthermore, we discuss the duality spaces of Fock-Sobolev spaces Fs^p,mwhen 0 〈 p 〈∞.