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.

SLANT IMMERSIONS OF COMPLEX SPACE FORMS AND CHEN'S INEQUALITY

A submanifold in a complex space form is called slant if it has constant Wirtinger angles. B. Y. Chen and Y. Tazawa proved that there do not exist minimal proper slant surfaces in CP2 and CH2. So it seems that the slant immersion has some interesting properties. The authors have great interest to consider slant immersions satisfying some additional conditions, such as unfull first normal bundles or Chen’s equality holding. They prove that there do not exist n-dimensional Kaehlerian slant immersions in CPn and CHn with unfull first normal bundles. Next, it is seen that every Kaehlerian slant submanifold satisfying an equality of Chen is minimal which is similar to that of Lagrangian immersions. But in contrast, it is shown that a large class of slant immersions do not exist thoroughly. Finally, they give an application of Chen’s inequality to general slant immersions in a complex projective space, which generalizes a result of Chen.

On Intrinsic Rigidity for Submanifolds with Constant Scalar Curvature in Space Forms

Under the assumption that the normalized mean curvature vector is parallel in the normal bundle, by using the generalized ChengYau＇s self-adjoint differential operator, here we obtain some rigidity results for compact submanifolds with constant scalar curvature and higher codimension in the space forms.

Forming of Space Charge Wave with Broad Frequency Spectrum in Helical Relativistic Two-Stream Electron Beams

We elaborate a quadratic nonlinear theory of plural interactions of growing space charge wave （SCW） harmonics during the development of the two-stream instability in helical relativistic electron beams. It is found that in helical two-stream electron beams the growth rate of the two-stream instability increases with the beam entrance angle. An SCW with the broad frequency spectrum, in which higher harmonics have higher amplitudes, forms when the frequency of the first SCW harmonic is much less than the critical frequency of the two-stream instability. For helical electron beams the spectrum expands with the increase of the beam entrance angle. Moreover, we obtain that utilizing helical electron beams in multiharmonic two-stream superheterodyne free-electron lasers leads to the improvement of their amplification characteristics, the frequency spectrum broadening in multiharmonic signal generation mode, and the reduction of the overall system dimensions.

The Architectural Expression of Space and Form Created by the Light in the Works of Alvaro Siza

The light is an important element which helps people perceive objects. Therefore, it is important for architects to make the light and space be in harmony with each other. In this study, we analyzed the works of Alvaro Siza with a view to understand the conceptual value of the light expressed in his works and his principles in controlling it. According to the results of the study, the Siza’s architecture is not a mere theoretical one trapped inside formality, but is a sensual and experiential one based on the locality. He was willing to use void spaces to invite the light in free-flowing plans, in order to invigorate and extend architectural spatiality to create deeper visual effect. In addition, the refined light in his works helped visitors experience the continuous forms and spaces by their own movements, while using the changes of the light to stimulate the interest of visitors and highlight the sequence of spaces.

Some Inequalities for Submanifolds in Cosymplectic Space Forms

For submanifolds in a cosymplectic space form tangent to the structure vector field ξ, two important inequalities with Ricci curvature, scalar curvature and the squared mean curvature are obtained. These results are also applied to get corresponding consequences for anti-invariant submanifolds.

HYPERSURFACES IN SPACE FORMS WITH SCALAR CURVATURE CONDITIONS

Let f: Mn(?)Sn+1 C Rn+2 be an n-dimensional complete oriented Rieman-nian manifold minimally immersed in an (n+1)-dimensional unit sphere Sn+1. Denote by S_+~n+1 the upper closed hemisphere. If f(Mn)(?)_+~n+1, then under some curvature conditions the authors can get that the isometric immersion is a totally embedding. They also generalize a theorem of Li Hai Zhong on hypersurface of space form with costant scalar curvature.

Ricci Curvature of Certain Submanifolds in Kenmotsu Space Forms

In this paper, we obtain some sharp inequalities between the Ricci cur- vature and the squared mean curvature for bi-slant and semi-slant submanifolds in Kenmotsu space forms. Estimates of the scalar curvature and the k-Ricci curvature, in terms of the squared mean curvature, are also proved respectively.

RIGIDITY THEOREMS OF COMPLETE K?HLER-EINSTEIN MANIFOLDS AND COMPLEX SPACE FORMS

We concentrate on using the traceless Ricci tensor and the Bochner curvature tensor to study the rigidity problems for complete K?hler manifolds. We derive some elliptic differential inequalities from Weitzenb?ck formulas for the traceless Ricci tensor of K?hler manifolds with constant scalar curvature and the Bochner tensor of K?hler-Einstein manifolds respectively. Using elliptic estimates and maximum principle, several L^p and L~∞ pinching results are established to characterize K?hler-Einstein manifolds among K?hler manifolds with constant scalar curvature and complex space forms among K?hler-Einstein manifolds.Our results can be regarded as a complex analogues to the rigidity results for Riemannian manifolds. Moreover, our main results especially establish the rigidity theorems for complete noncompact K?hler manifolds and noncompact K?hler-Einstein manifolds under some pointwise pinching conditions or global integral pinching conditions. To the best of our knowledge,these kinds of results have not been reported.

Totally Real Sectional Curvature for Submanifolds in Sasakian Space Forms

By using the methods introduced by Chen[Chen Bang-yen,A series of Ka¨hlerian invarianrts and their applications to Khlerian geometry,Beitrge Algebra Geom,2001,42(1):165-178],we establish some inequalities for invariant submanifolds in a Sasakian space form involving totally real sectional curvature and the scalar curvature.Moreover,we consider the case of equalities.

<i>L^pp</i>-Harmonic 1-Forms on <i>δ</i>-Stable Hypersurface in Space Form with Nonnegative Bi-Ricci Curvature

In this paper, we investigate the space of Lp p-harmonic 1-forms on a complete noncompact orientable δ-stable hypersurface Mm that is immersed in space form with nonnegative BiRic curvature. We prove the nonexistence of Lp p-harmonic 1-forms on Mm. Moreover, we obtain some vanishing properties for this class of harmonic 1-forms.

Commuting Structure Jacobi Operator for Real Hypersurfaces in Complex Space Forms

Let M be a real hypersurface of a complex space form with almost contact metric structure (φ,ξ,η,g). In this paper, we prove that if the structure Jacobi operator Rξ=(·,ξ) ξ is φ▽ξξ-parallel and Rξ commute with the shape operator, then M is a Hopf hypersurface. Further, if Rξ is φ▽ξξ-parallel and Rξ commute with the Ricci tensor, then M is also a Hopf hypersurface provided that TrRξ is constant.

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

In this paper,we study the Noether-form invariance of nonholonomic mechanical controllable systems inphase space.Equations of motion of the controllable mechanical systems in phase space are presented.The definitionand the criterion for this system are presented.A new conserved quantity and the Noether conserved quantity deducedfrom the Noether-form invariance are obtained.An example is given to illustrate the application of the results.

Chen’s Inequalities for Submanifolds in (<i>&kgreen;, &#181</i>)-Contact Space Form with a Semi-Symmetric Non-Metric Connection

In this paper, we obtain Chen’s inequalities in (k,?μ)-contact space form with a semi-symmetric non-metric connection. Also we obtain the inequalites for Ricci and K-Ricci curvatures.

Model-Following Designs Using Direct State Derivative Measurement Feedback in Novel Reciprocal State Space Form

The paper introduces effective and straightforward algorithms of both explicit and implicit model-following designs with state derivative measurement feedback in novel reciprocal state space form (RSS) to handle state derivative related performance output and state related performance output design cases. Applying proposed algorithms, no integrators are required. Consequently, implementation is simple and low-cost. Simulation has also been carried out to verify the proposed algorithms. Since acceleration can only be modeled as state derivative in state space form and micro-accelerometer which is the state derivative sensor is getting more and more attentions in many microelectromechanical and nanoelectromechanical systems (MEMS/NEMS) applications, the proposed algorithms are suitable for MEMS/NEMS systems installed with micro-accelerometers.

基于Space Syntax与GIS的城市历史文化街区空间形态分析——以成都市少城片区为例

文章以成都市少城片区历史文化街区为例,总结归纳相关文献,运用空间句法与GIS相结合的方法,对少城片区的空间形态进行量化分析研究,选取整合度、协同度、选择度、商业POI等4个参数,探究其空间形态特征。结果表明,少城片区呈现出整体与局部相协调的空间形态,空间结构层次分明,特殊的鱼骨形路网具有较高的向心性和聚合性,展现出了一定的历史文化吸引力,商业业态分布与人群的聚集呈现出一定的相关性,以期为今后城市空间与历史文化的融合更新提供参考。

基于遗传算法的自由曲面单层空间结构网格参数化自动生成及方向优化

自由曲面空间网格结构的力学性能和网格方向之间的联系复杂,难以快速直接地找到最优方向,若对结构网格方向进行多角度建模分析,则存在工作量大且准确性不易保证等问题。为了快速确定自由曲面空间网格结构的最优网格方向,提出一种基于遗传算法的自由曲面空间结构网格方向优化方法,以结构网格方向为优化变量,结合参数化建模软件Grasshopper和有限元分析软件SAP2000实现参数化分析,以结构应变能和结构最大位移两项力学指标作为优化目标,通过最小化目标函数实现结构网格方向优化。通过参数化编程,可实现快速自动优化,并结合工程案例,应用自动优化方法进行网格优化。结果表明:基于遗传算法的自由曲面空间结构网格方向自动优化法具有实用性和高效性,具有较高的工程应用价值。

A NON－INCREMENTAL TIME－SPACE ALGORITHM FOR NUMERICAL SIMULATION OF FORMING PROCESS

A non-incremental time-space algorithm is proposed for numerical. analysis of forming process with the inclusion of geometrical, material, contact-frictional nonlinearities. Unlike the widely used Newton-Raphson counterpart, the present scheme features an iterative solution procedure on entire time and space domain. Validity and feasibility of foe present scheme are further justiced by the numerical investigation herewith presented.

山西省煤矿采空地下空间评估与再利用研究

山西省煤炭资源丰富,年煤炭产量占全国产量的近1/4,煤炭资源开采形成大量的采空地下空间。随着碳中和目标的提出和山西风电、光伏发电的大力发展,如何合理利用煤矿采空地下空间,尤其是将地下空间与新能源结合将成为煤炭产业低碳发展的关键。本次研究运用比例系数法和采空地下空间守恒定律,测算出2022年山西省开采煤矿井巷可利用空间为1.54亿m^(3),“十五”到“十三五”期间关闭/退出煤矿的井巷可利用空间为1.05亿m^(3),估算1949至2021年山西省煤矿因工作面开采形成的采空地下空间约38.98亿m3,预测到2030年山西省煤矿工作面开采还可形成采空地下空间约19.56亿m^(3)。根据山西省能源低碳发展需求提出了山西省煤矿采空地下空间未来可利用的四种模式:煤矿地下旅游或地下仓储、煤矿地下抽水蓄能、煤矿地下压缩空气储能和煤矿地下封存二氧化碳等。