MAXIMAL ELEMENTS FOR G_B-MAJORIZED MAPPINGS IN PRODUCT G_CONVEX SPACES AND APPLICATIONS (Ⅱ)

A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set_valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature.

MAXIMAL ELEMENTS FOR G_B-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)

A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set_valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature.

Interpolating Isogeometric Boundary Node Method and Isogeometric Boundary Element Method Based on Parameter Space

In this paper,general interpolating isogeometric boundary node method(IIBNM)and isogeometric boundary element method(IBEM)based on parameter space are proposed for 2D elasticity problems.In both methods,the integral cells and elements are defined in parameter space,which can reproduce the geometry exactly at all the stages.In IIBNM,the improved interpolating moving leastsquare method(IIMLS)is applied for field approximation and the shape functions have the delta function property.The Lagrangian basis functions are used for field approximation in IBEM.Thus,the boundary conditions can be imposed directly in both methods.The shape functions are defined in 1D parameter space and no curve length needs to be computed.Besides,most methods for the treatment of the singular integrals in the boundary element method can be applied in IIBNM and IBEM directly.Numerical examples have demonstrated the accuracy of the proposed methods.

Exceptional family of elements and the solvability of complementarity problems in uniformly smooth and uniformly convex Banach spaces

The notion of “exceptional family of elements (EFE)” plays a very important role in solving complementarity prob- lems. It has been applied in finite dimensional spaces and Hilbert spaces by many authors. In this paper, by using the generalized projection defined by Alber, we extend this notion from Hilbert spaces to uniformly smooth and uniformly convex Banach spaces, and apply this extension to the study of nonlinear complementarity problems in Banach spaces.

THE SPACE-TIME FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS

Adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed. The approach is based on a combination of finite element and finite difference techniques. The existence and uniqueness of the weak solution are proved without any assumptions on choice of the spacetime meshes. Basic error estimates in L-infinity (L-2) norm, that is maximum-norm in time, L-2-norm in space are obtained. The numerical results are given in the last part and the analysis between theoretic and experimental results are obtained.

Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications(Ⅰ)

First, the notions of the measure of noncompactness and condensing setvalued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces. As applications, some new equilibrium existence theorems of generalized game involving condensing mappings are established in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper.

ON THE SELECTION OF SHAPE FUNCTION SPACES OF TRIANGULAR PLATE ELEMENTS

Using the method of undetermined coefficients, we construct a set of shape function spaces of nine-node triangular plate elements converging for any meshes, which generalize Spect's element and Veubeke's element.

MAXIMAL ELEMENTS OF CONDENSING PREFERENCE MAPS IN LOCALLY CONVEX HAUSDORFF SPACES

Two existence theorems of maximal elements of condensing preference maps in locally convex Hausdorff spaces are proved which generalize the recent results of Mehta. One of them positively answers the open problem mentioned by Mehta.

Design Elements of Urban Children' s Recreational Landscape Space Based on Genius Loci

Urban children's recreational landscape space is an organic component of urban children's recreational space,genius loci is both a result and a motive in its design.This paper interpreted the connotations of genius loci of urban children's recreational space,the correlation between both,and design elements of urban children's recreational landscape space,in order to provide theoretical support for the design of urban children's recreational landscape space.

Possibilities of mapping neotectonic elements based on the interpretation of space images:A study of Fergana Depression

For the current geological mapping of individual territories,remote sensing and geographic information system(GIS)technologies are widely used.Taking the Fergana depression as an example,this paper aims to determine the possibilities of using remote sensing materials for mapping structural and geomorphological elements.Landsat-8 satellite imagery obtained on 11 spectral channels was used to highlight the decoding features.Fault zones,lineament zones,various uplifts,depressions,and structural material complexes of different ages were identified.Based on the in-depth analysis of geological and geophysical data,a geological schematic map of the Fergana depression was developed.Using geological landscape and automated methods for deciphering space images,the main neotectonic elements of the Fergana depression were identified:the southern step,northern marginal slope,central graben-syncline,flexurefault zones,local anticlinal zones,individual uplifts/depressions,and local shear zones.The results show a neotectonic map of the study area,which can be used as a tectonic basis for prospecting,seismic zoning mapping,and geological engineering development.

Mixed time discontinuous space-time finite element method for convection diffusion equations

A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.

MAXIMAL ELEMENTS OF A FAMILY OF G_B-MAJORIZED MAPPINGS IN PRODUCT FC-SPACES AND APPLICATIONS

A new family of GB-majorized mappings from a topological space into a finite continuous topological spaces （in short, FC-space） involving a better admissible set-valued mapping is introduced. Some existence theorems of maximal elements for the family of GB-majorized mappings are proved under noncompact setting of product FCspaces. Some applications to fixed point and system of minimax inequalities are given in product FC-spaces. These theorems improve, unify and generalize many important results in recent literature.

A wideband fast multipole boundary element method for half-space/plane-symmetric acoustic wave problems

This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/planesymmetric acoustic wave problems.The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only.Moreover,a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived,and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating,translating and saving the multipole/local expansion coefficients of the image domain.The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems.As for exterior acoustic problems,the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method.Details on the implementation of the present method are described,and numerical examples are given to demonstrate its accuracy and efficiency.

Research on Improvement of Utilization of Open Space: Through Demonstration Experiment Focusing on Spatial Elements

Along with the rise of buildings, a large number of public open spaces have been created for the purpose of mitigating hatching restrictions and the like. However, many of them are used at low levels, and there remain very few known public open spaces. In this research, we set up a resting place to demonstrate the effect of elements and placement in order to obtain knowledge for appropriately managing and utilizing such low use open public spaces. The survey means analyzed the presence/absence of the attraction/retention degree based on the cross-sectional traffic volume by video analysis and a hearing questionnaire survey for the users of the resting place. From the results, we have found that placement methods and effects that exceed the expectation value of each element, regionality, and attachment, occur by continuing experiments.

Finite Element Method for a Kind of Two-Dimensional Space-Fractional Diffusion Equation with Its Implementation

In this article, we consider a two-dimensional symmetric space-fractional diffusion equation in which the space fractional derivatives are defined in Riesz potential sense. The well-posed feature is guaranteed by energy inequality. To solve the diffusion equation, a fully discrete form is established by employing Crank-Nicolson technique in time and Galerkin finite element method in space. The stability and convergence are proved and the stiffness matrix is given analytically. Three numerical examples are given to confirm our theoretical analysis in which we find that even with the same initial condition, the classical and fractional diffusion equations perform differently but tend to be uniform diffusion at last.

SPACE-TIME FINITE ELEMENT METHOD FOR SCHRDINGER EQUATION AND ITS CONSERVATION

Energy conservation of nonlinear Schrodinger ordinary differential equation was proved through using continuous finite element methods of ordinary differential equation; Energy integration conservation was proved through using space-time continuous fully discrete finite element methods and the electron nearly conservation with higher order error was obtained through using time discontinuous only space continuous finite element methods of nonlinear Schrodinger partial equation. The numerical results are in accordance with the theory.

Finite Element Orthogonal Collocation Approach for Time Fractional Telegraph Equation with Mamadu-Njoseh Polynomials

Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a variational form over a given space, say a Hilbert space, are better numerically handled with the FEM. The FEM algorithm is used in various applications which includes fluid flow, heat transfer, acoustics, structural mechanics and dynamics, electric and magnetic field, etc. Thus, in this paper, the Finite Element Orthogonal Collocation Approach (FEOCA) is established for the approximate solution of Time Fractional Telegraph Equation (TFTE) with Mamadu-Njoseh polynomials as grid points corresponding to new basis functions constructed in the finite element space. The FEOCA is an elegant mixture of the Finite Element Method (FEM) and the Orthogonal Collocation Method (OCM). Two numerical examples are experimented on to verify the accuracy and rate of convergence of the method as compared with the theoretical results, and other methods in literature.

吴文化元素在苏州地铁公共空间中的表达与应用

[目的]以城市地域文化传承为背景,探讨吴文化元素在苏州地铁公共空间中的融合与运用,总结吴文化元素在地铁公共空间的应用价值及策略。[方法]由吴文化兼收并蓄、崇文重教、柔中蓄劲、人巧天工等内涵出发,从典型性提炼、抽象化法则、文化符号重构三方面提出了吴文化元素的提取方法;利用案例分析法从设计说明、材料工艺、工艺施工及技术要求层面对苏州地铁出入口、站内公共艺术、车厢厢体吴文化元素的运用展开分析,详细介绍了吴文化建筑元素、园林元素、文化性格、餐饮文化、宗教信仰、语言文化、戏曲文化等方面对构建独特苏州地铁文化景观的具体做法。[结果及结论]通过吴文化元素提取的法则,建立吴文化符号设计系统、赋予吴文化符号功能及文化语义、运用现代设计手段实现传统文化在地铁公共空间转译传达,对传承城市文脉、塑造新时代城市精神,提升城市文化软实力具有推动意义。

从空间规划体系到国土空间体系——兼析国土空间体系构建下的国土空间治理趋向

研究目的:分析国家治理体系和治理能力现代化背景下,国土空间体系表述的形成脉络及内在逻辑,并从国土空间体系构建视角探讨国土空间治理的未来趋向。研究方法:综合分析法与对比分析法。研究结果:国土空间具有“区域”和“要素”双重特性,建立空间规划体系旨在解决传统国土空间治理的“区域”“要素”缺乏统筹问题。从空间规划体系、国土空间规划体系到国土空间体系的演变,实质上是不断推进迈向高质量发展、强化“区域—要素”统筹的国土空间治理。在构建国土空间体系的指引下,国土空间治理既要聚焦国土空间的高质量发展,绘就国土空间协调发展蓝图,又要完善主体功能区战略和制度,做好国土空间治理的“区域—要素”统筹。研究结论:面向国土空间体系构建,国土空间治理未来应做好国土空间高质量发展导向下的“区域—要素”统筹治理。

地月空间全球治理规则框架构成要素研究

地月空间全球治理规则框架是构建地月空间治理规则体系的顶层指导,是争夺地月空间治理规则制定主导权的“先手棋”和关键所在,其构成要素研究具有重要意义。对政府间国际组织、重大国际合作项目、机构间和非政府3类不同平台的地月空间治理规则制定现状进行了综述,对《月球协定》《阿尔忒弥斯协定》等6个相关规则框架构成要素进行了研究,提出了涵盖4项基本原则和9类具体规则的地月空间全球治理规则框架构成要素,并给出了后续工作建议。