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.

Effects of film-stalk spaced dual mulching system on corn growth and yield

Film-stalk spaced dual mulching is a new type of cultivation measure that is increasingly highlighted in semi-arid areas in China.Despite its potential,there is limited understanding of how different mulching materials affect both soil quality and crop yield in these areas.To address this gap,we conducted a two-year(2020-2021)field experiment in central China to explore the yield-enhancing mechanisms and assess the impact of various mulching materials on soil and corn yield.The experiment comprised six treatments,i.e.,plastic film-whole stalk spaced mulching in fall(PSF),plastic film-whole stalk spaced mulching in spring(PSS),black and silver plastic film-whole stalk spaced mulching in spring(BPSS),biodegradable film-whole stalk spaced mulching in spring(BSS),liquid film-whole stalk spaced mulching in spring(LSS),and non-mulching cultivation(CK).Results revealed that BPSS demonstrated the most significant yield increase,surpassing CK by a notable 10.0%and other mulching treatments by 2.4%-5.9%.The efficacy of BPSS lied in its provision of favorable hydrothermal conditions for corn cultivation,particularly during hot season.Its cooling effect facilitated the establishment of optimal temperature conditions relative to transparent mulching,leading to higher root growth indices(e.g.,length and surface area),as well as higher leaf photosynthetic rate and dry matter accumulation per plant.Additionally,BPSS maintained higher average soil moisture content within 0-100 cm depth compared with biodegradable mulching and liquid mulching.As a result,BPSS increased activities of urease,catalase,and alkaline phosphatase,as well as the diversity and abundance of soil bacteria and fungi in the rhizosphere zone of corn,facilitating nutrient accessibility by the plant.These findings suggest that selecting appropriate mulching materials is crucial for optimizing corn production in drought-prone areas,highlighting the potential of BPSS cultivation.

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。

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

The main result of this paper is the identification of the sequential order dual [∧(X)]so containing sequentially order continuous linear functionals on the ordered generalized sequence space ∧(X) with its generalized Kothe dual ∧x(Xso), defined corresponding to the dual pair <X, Xso>.

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.

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 〈∞.

Classical Fourier Analysis over Homogeneous Spaces of Compact Groups

This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G and μ be the normalized G-invariant measure on G/H associated to the Weil＇s formula. Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space L^2 （G / H, μ）.

ON SIMULTANEOUS WEAKLY-CHEBYSHEV SUBSPACES

In this paper, we shall introduce and characterize simultaneous quasi-Chebyshev （and weakly-Chebyshev） subspaces of normed spaces with respect to a bounded set S by using elements of the dual space.

基于Dual-Mode MMA+MDD双模式T/2分数间隔盲均衡算法的研究

均衡技术是用来解决通信系统中码间干扰的常用方法.针对传统恒模算法的收敛速度和稳态剩余码间干扰大的缺点,将双模式多模算法和改进型判决引导算法结合起来,并且应用于分数间隔盲均衡器中.该算法初期用双模式算法收敛均衡器,然后切换到改进型判决引导算法中进一步收敛,由于分数间隔均衡器解决了波特间隔均衡器因抽样率不高带来的频谱混叠问题,从而进一步地提高了均衡效果.蒙特卡罗仿真表明,该算法不仅收敛速度快,而且得到较低的剩余码间干扰.

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.

A Note on Numerical Radius Operator Spaces

In this paper, we first study some -completely bounded maps between various numerical radius operator spaces. We also study the dual space of a numerical radius operator space and show that it has a dual realization. At last, we define two special numerical radius operator spaces and which can be seen as a quantization of norm space E.

ATOMIC DECOMPOSITION FOR B-VALUED R.V. SEQUENCE SPACES

In this article,atomic decompositions and the duals of some B-valued r.v.se- quence spaces are investigated.The results show that it closely depends on the geometrical properties of the sequence that take values in.

Curvature Motion on Dual Hyperbolic Unit Sphere H^(2)_(0)

In this paper, we define dual curvature motion on the dual hyperbolic unit sphere H2<sub style="margin-left:-8px;">0 in the dual Lorentzian space D31 with dual signature (+,+-) . We carry the obtained results to the Lorentzian line space R3<sub style="margin-left:-8px;">1 by means of Study mapping. Then we make an analysis of the orbits during the dual hyperbolic spherical curvature motion. Finally, we find some line congruences, the family of ruled surfaces and ruled surfaces in R3<sub style="margin-left:-8px;">1.