Hybrid Meta-Model Based Design Space Differentiation Method for Expensive Problems

In this work,a hybrid meta-model based design space differentiation（HMDSD）method is proposed for practical problems.In the proposed method,an iteratively reduced promising region is constructed using the expensive points,with two different search strategies respectively applied inside and outside the promising region.Besides,the hybrid meta-model strategy applied in the search process makes it possible to solve the complex practical problems.Tested upon a serial of benchmark math functions,the HMDSD method shows great efficiency and search accuracy.On top of that,a practical lightweight design demonstrates its superior performance.

Spatio-temporal Differentiation of Residential Land for Coastal Town: A Case Study of Dalian Jinshitan

Based on SPOT5 satellite remote sensing images and land use data in five time phases covering the period 1988–2012, the distribution characteristics, spatial differentiation processes, and driving mechanisms affecting the residential land of the Jinshitan Tourist Resort were studied. The work included a combination of GIS technology, adoption of the differentiation index D, and the multi-group differentiation-measure model D(m). The results provided a basis for the following conclusions: 1) From 1988 to 2012, the degree of differentiation of the rural residential land first decreased, and then increased. The general residential, commercial residential and garden-house land-types all showed declining trends, of which the garden-house type presented the most intense volatility. 2) The overall background of the traditional residential land type was gradually replaced by a new residential land type, and the total area of residential land increased year by year, significantly improving the overall residential conditions. The areas of the new residential land type showed growth, and were increasingly widely distributed in the coastal tourist resorts, transportation corridors, and scenic areas. 3) Government policy, social differentiation, market mechanisms, and individual choices(along with other factors) were mutually promoted, although still restrained. However, all of these factors interacted to constrain the developmental direction and the processes affecting tourism real estate in the Dalian Jinshitan Tourist Resort.

Spatial Differentiation and Influencing Factors of Poverty Alleviation Performance Under the Background of Sustainable Development:A Case Study of Contiguous Destitute Areas in Hunan Province,China

Poverty eradication is a realistic requirement for the addressing of the urban-rural development imbalance.It consolidates the achievements of the poverty alleviation,and accelerates the realization of the United Nations Sustainable Development Goals.In research that deals with poverty,qualitative analysis is often used to study the connection between a single influencing factor and poverty reduction,and to solve regional poverty through government measures.However,these studies usually ignore the multidimensional nature of poverty,and the fact that poverty alleviation also needs to be approached from multiple perspectives.By constructing a theoretical framework of poverty alleviation performance from the perspective of sustainable development,this study selects contiguous poverty-stricken areas in the Hunan Province,China as the empirical study area,constructs an evaluation index system from the three dimensions of economic development,infrastructure and people’s livelihood security,and selects influencing factors from three aspects of‘population’,‘land’and‘industry’.The spatial differentiation characteristics and influencing factors of poverty alleviation performance in poverty-stricken areas were studied by using the methods of entropy weight method and geodetector.The results show:firstly,in the concentrated and contiguous poverty-stricken areas of the Hunan Province,the performance of poverty alleviation in the economic development makes little difference,showing a‘high-medium-low’cross-distribution pattern.The poverty alleviation performance of the infrastructure presents a distribution pattern of‘low in the middle and high on both sides.The poverty alleviation performance of people’s livelihood security has significant spatial differentiation characteristics,which all present a reunion distribution.The overall poverty alleviation performance varies greatly,showing a funnel-shaped distribution in space.Secondly,the spatial differentiation of poverty alleviation performance in the concentrated and contiguous poverty-stricken areas of the Hunan Province is the result of the combined effects of multiple factors.‘Population’is the dominant factor affecting the performance of poverty alleviation,‘land’is the basic factor that causes the spatial differentiation of poverty alleviation performance,and‘industry’is the key factor for the improvement of the poverty alleviation ability.

ON THE PRODUCT OF GTEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES

A locally convex space is said to be a Gateaux differentiability space (GDS) provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in .D.This paper shows that the product of a GDS and a family of separable Prechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.

ODEs IN BANACH SPACES AND FIXED POINTS OF WEAKLY INWARD MAPS

This paper is an attempt to investigate systematically fixed points of weakly inward maps by using some basic results from differential equations in Banach spaces. By investigating the Poincare operators for such differential equations, we establish a fixed point index theory for two classes of weakly inward maps.

Tracing the Holistic Voice in Ecological Space： Exploring Theodore Roszak＇s Ecopsychology in Henri Lefebvre＇s ＂Differential Space＂

The goal of ecopsychology is to awaken the inherent sense of environmental reciprocity that lies within the ecological unconsciousness. Proclaiming the spirit of ecopsychology, Theodore Roszak argues that psychotherapy is an urban movement, but human beings can never heal themselves until they reconnect with nature. Other therapies aim at healing the alienation between person and person, person and family, person and society; ecopsychology intends to heal the more primary alienation between the person and the natural environment. Henri Lefebvre＇s work has revitalized urban studies, geography and planning via concepts like the social production of space. Lefebvre claims that space is not an inert, neutral, and pre-existing given, but rather, an on-going production of spatial relations. According to Lefebvre, space is produced by three types of practice： spatial practices of physical transformation of the environment, practices of representation of space, and everyday practices of representational space. Lefebvre further presents a ＂differential space,＂ named as such for its dialectical resistance to the forces of homogenization present in ＂abstract space.＂ The aim of this paper is to trace the ecological voice from Roszak＇s The Voice of the Earth in Henri Lefebvre＇s ＂differential space.＂ Roszak＇s ecopsychology has formed a differential space, acknowledging that the boundaries of dualism and separations such as mind and body, man and nature should be finally dissolved in terms of ecological sustainability. Within this space, a holistic approach and thinking are created and required to take into account perception of the inextricable relationship between all life and all phenomena.

Differentiability of Convex Functions in Locally Convex Spaces(Ⅱ)──Frechet

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On Differential Equations Describing 3-Dimensional Hyperbolic Spaces

In this paper, we introduce the notion of a （2＋1）-dimenslonal differential equation describing three-dimensional hyperbolic spaces （3-h.s.）. The （2＋1）-dimensional coupled nonlinear Schrodinger equation and its sister equation, the （2＋1）-dimensional coupled derivative nonlinear Schrodinger equation, are shown to describe 3-h.s, The （2 ＋ 1 ）-dimensional generalized HF model：St=（1/2i[S,Sy]＋2iσS）x,σx=-1/4i tr（SSxSy）, in which S ∈ GLc（2）/GLc（1）×GLc（1）,provides another example of （2＋1）-dimensional differential equations describing 3-h.s. As a direct con-sequence, the geometric construction of an infinire number of conservation lairs of such equations is illustrated. Furthermore we display a new infinite number of conservation lairs of the （2＋1）-dimensional nonlinear Schrodinger equation and the （2＋1）-dimensional derivative nonlinear Schrodinger equation by a geometric way.

FIXED POINT INDEX THEORY FOR WEAKLY INWARD MAPPINGS

In this paper we define a fixed point index theory for locally Lip., completely continuous and weakly inward mappings defined on closed convex sets in general Banach spaces where no other artificial conditions are imposed. This makes ns to deal with these kinds of mappings more easily. As obvious applications, some results in [3],[5],[7],[9],[10] are deepened and extended.

Differential Groupoids

The basic properties and some examples of the differential groupoids are studied.

Space diversification process and evolution mechanism of typical village in the suburbs of Guangzhou:A case study of Beicun

The reform of global production mode and social system accelerate the process of urbanization,and the urban-rural factors accelerate rural space diversification.Based on the space production theory and game theory,this paper analyzed the space diversification process and its influence on Beicun village.The results show that:(1)In the past 30 years,the development of Beicun has experienced three stages:agricultural development,industrial development,and service industrial development.The industrial structure has changed from single to diverse.The transformation of agricultural decentralization to rural community has been realized.(2)Accompanying the rural economic development transformation,the land use type and structure of Beicun has diversified.The spatial relationship of various types of land use was complicated and gave rise to new characteristics of mixed land for commercial and residential use,and industrial and commercial use,gradually forming a circular spatial layout structure model of public service facilities,traditional residential areas and modern residential areas,commercial areas,agricultural and industrial areas.(3)Rural space diversification was mainly due to the intervention of new industries and the transformation of leading industries.The endogenous land transferring mechanism and exogenous urban capital jointly promoted the industrialization process,and the market power promoted the transformation of industry into the service industry.(4)The industrialization process promoted the functional replacement of historical buildings by village organizations.It changed the social relations of the village with the blood clan and geography oriented,and produced the occupational relation between migrant workers and urban low-income groups.(5)The multi-differentiation of suburban rural space followed the game logic of capital and land interests.The rural community played a key mediation in the competition for space and the game of interests among local villagers,farmers,economic cooperation,industrial operators,and service owners.

REMARKS OF DIFFERENTIAL EQUATIONS ON CLOSED SUBSETS IN A BANACH SPACE

We give some extensions of Monch-Harton inequalities with respect to measures of noncompactness. As an example of the application, we obtain two existencetheorems of solutions for Cauchy problems of differential equations on closed setsunder weaker compactness conditions.

Ball-covering property of Banach spaces that is not preserved under linear isomorphisms

By a ball-covering B of a Banach space X, we mean that it is a collection of open balls off the origin whose union contains the sphere of the unit ball of X. The space X is said to have a ball-covering property, if it admits a ball-covering consisting of countably many balls. This paper, by constructing the equivalent norms on l~∞, shows that ball-covering property is not invariant under isomorphic mappings, though it is preserved under such mappings if X is a Gateaux differentiability space; presents that this property of X is not heritable by its closed subspaces; and the property is also not preserved under quotient mappings.

The isometrical extensions of 1-Lipschitz mappings on Gteaux differentiability spaces

Let X and Y be real Banach spaces.Suppose that the subset sm[S1(X)] of the smooth points of the unit sphere [S1(X)] is dense in S1(X).If T0 is a surjective 1-Lipschitz mapping between two unit spheres,then,under some condition,T0 can be extended to a linear isometry on the whole space.

NUMERICAL SOLUTION OF THE SPACE FRACTIONAL DIFFERENTIAL EQUATION

In this paper, a space fractional differential equation is considered. The equation is obtained from the parabolic equation containing advection, diffusion and reaction terms by replacing the second order derivative in space by a fractional derivative in space of order. An implicit finite difference approximation for this equation is presented. The stability and convergence of the finite difference approximation are proved. A fractional-order method of lines is also presented. Finally, some numerical results are given.

Solving systems of multi-term fractional PDEs:Invariant subspace approach

In the present paper,invariant subspace method has been extended for solving systems of multi-term fractional partial differential equations(FPDEs)involving both time and space fractional derivatives.Further,the method has also been employed for solving multi-term fractional PDEs in(1+n)dimensions.A diverse set of examples is solved to illustrate the method.

Weak Convergence Theorems for Strict Pseudo-contractions in Banach Spaces

In this paper, it is shown that there is a gap in the paper [Chidume, C. E., Shahzad, N.： Weak convergence theorems for a finite family of strict pseudo-contractions. Nonlinear Anal., 72, 1257–1265（2010）], consequently, the main results of the paper do not hold in uniformly smooth Banach spaces. Meanwhile, it is also shown that the main results（Lemma 3.4, Theorems 3.5–3.6, 3.8–3.9） in the paper [Cholamjiak, P., Suantai, S.： Weak convergence theorems for a countable family of strict pseudo-contractions in Banach spaces. Fixed Point Theory Appl., 2010, Article ID 632137, 16 pages（2010）] do not hold in Lpfor p 〉 3. Finally, some modified results are presented in the setting of uniformly smooth and uniformly convex Banach spaces which include Lpfor p ≥ 2 as special cases. Furthermore, our arguments are also different from the ones given by the authors above.

Error Analysis on Hérmite Learning with Gradient Data

This paper deals with Hermite learning which aims at obtaining the target function from the samples of function values and the gradient values. Error analysis is conducted for these algorithms by means of approaches from convex analysis in the frame- work of multi-task vector learning and the improved learning rates are derived.