Exploring the Element Integration of Urban and Rural“Space of Flows”in the Context of Consumption Upgrading:A Case Study of Changsi Village in Anhui Province

The mobility and interaction between urban and rural areas are becoming more and more intensive,and their links and exchanges are increasingly closer due to constant flow of factors such as information,capital,personnel and technology.In this context,the element integration of urban and rural“space of flows”can promote the integrated development of urban and rural areas,improve the consumption environment and experience,and promote the industrial upgrading and technological progress.To realize the element integration of urban and rural“space of flows”,it is necessary to explore and innovate in infrastructure construction,information technology application,industrial cooperation and cultural exchanges.Government departments,enterprises and social organizations also need to work together to give play to their respective advantages and jointly promote the process of element integration of urban and rural“space of flows”.

Conservation-minded Urban Green Space System Planning in the Urban-rural Integration

Environmental and ecological problems in the urban-rural integration were analyzed, characteristics of urban green space system introduced, such as excellent landscape eco-structure, distinctive historical and humanistic features, and diversified natural landscape resources, and also challenges pointed out. Evolution, overall spatial structure and conservation concept of conservation-minded urban green space system planning were elaborated, on the basis of which the evaluation system of conservation-minded urban green space system was studied, and it was proposed that mutual relationship between impact factors of compound value and qualitative evaluation factors should be taken into consideration as a whole in evaluating conservation effects of green space system. Quantitative evaluation indexes and qualitative evaluation measures were analyzed, an objective and precise evaluation system for the conservation-minded urban green space system was established by combining qualitative and quantitative analysis to improve ecological environment during the urbanization, and fully show planning concepts of conservation-minded green space system.

PARAMETRIC EQUATIONS OF NONHOLONOMIC NONCONSERVATIVE SYSTEMS IN THE EVENT SPACE AND THE METHOD OF THEIR INTEGRATION

In this paper,the parametric equations with multipliers of nonholonomic nonconservative sys- tems in the event space are established,their properties are studied,and their explicit formulation is obtained. And then the field method for integrating these equations is given.Finally,an example illustrating the appli- cation of the integration method is given.

Poisson theory and integration method of Birkhoffian systems in the event space

This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space. The Birkhoff＇s equations in the event space are given. The Poisson theory of the Birkhoffian system in the event space is established. The definition of the Jacobi last multiplier of the system is given, and the relation between the Jacobi last multiplier and the first integrals of the system is discussed. The researches show that for a Birkhoffian system in the event space, whose configuration is determined by （2n ＋ 1） Birkhoff＇s variables, the solution of the system can be found by the Jacobi last multiplier if 2n first integrals are known. An example is given to illustrate the application of the results.

FEASIBLE STUDY ON THE INTEGRATION SYSTEM FOR THE SPACE MONITORING OF MAJOR EARTHQUAKES AND VOLCANOES IN TERRESTRIAL LAND

With the rapid development of space technology,earth observation tech nology and sky observatory technolo-gy,they have played a more and more im portant part in monitoring and predi cting of earthquakes and volcanoes i n the terres-trial land.In recent years,the rela ted agencies have done the experimen ts and researches on monitoring and p redicting of earthquakes and volcanoes in the forewarning period by means of many appr oaches,such as satellite thermal in frared re-mote sensing(TIRS),Global Positioning System(GPS),differential interferometric syn thesis aperture radar(D-INSAR),astronomical time-latitude residual anomaly,and Geographic Information Systems (GIS),etc.A quite large number of re-search foundation has been built in t he fundamental theories and applica tion methods.The experiments and re searches have shown that these technology is e fficient methods for high frequency crust movement.If the existed separate scientific forces and results are possibly asse mbled together to form a more complete integration monitoring system wit h the combina-tion of space,sky observation,grou nd,deep geology and macro anomaly,i t will come into a new stage of monitoring and predicting of earthquakes and volca nic eruptions.

A New Kind of Two-Fold Integration Transformation in Phase Space and Its Uses in Weyl Ordering of Operators

We propose a new two-fold integration transformation in p-q phase space∫∫^∞-∞dpdq/π e^2i（p-x）（q-y）f（p,q）≡G（x,y）,which possesses some well-behaved transformation properties. We apply this transformation to the Weyl ordering of operators, especially those Q-P ordered and P-Q ordered operators.

A Study on Internet Buzzwords in the Last Four Years Based on Conceptual Integration Theory

Internet buzzwords,as distinct forms of language,consist of short sentences yet carry rich meanings and spread rapidly.To better study this intriguing and unique linguistic phenomenon,this paper employed conceptual integration theory for its powerful explanatory capabilities to analyze the origins,composition,and emergence of meanings of internet buzzwords over the past four years.These 40 internet buzzwords can be categorized into five types:semantic derivation,generalization,abbreviation,metonymy,and compounding.Furthermore,this paper conducted cognitive analysis from different conceptual integration network perspectives,elucidating specific cognitive operations involved in the construction of meanings and revealing the emergence process of layered meanings in recent internet buzzwords over the past four years.

Study on the Integration and Optimization of Campus Spaces: A Case Study of Yaohu Campus of Jiangxi Normal University

In view of the problems brought by blind expansion of campus, such as lack of public spaces, oversized spaces, and improper traffic designs, this paper took Yaohu Campus of Jiangxi Normal University for example, proposed the methods for integrating and optimizing campus spaces, such as establishing artistic conception of campus space, improving campus traffic organization, creating and improving the external communication spaces, on the basis of analyzing evolution history of campus spaces.

Design Strategy of Underground Space of Urban Rail Transit Complex Based on Integration Concept

With the accelerated development and utilization of urban underground space,the underground space design of complex based on rail transit has attracted much attention.By sorting out the integration concept and constructing the logical framework of integrated design,the integrated design strategy is proposed from the aspects of function,transportation,space and environment on the urban scale,and the evaluation points of integrated design effect are put forward from the aspects of accessibility,coordination,openness and symbolism.

Lorentz Transform in Multi-Dimensional Space

It is shown that in Euclidean space with any number of spatial dimensions more than three, the Lorentz transform holds true if the proper time of each elementary particle is proportional to the length of its path in the extra-dimensional subspace, and all elementary particles move at the speed of light in the complete space. The six-dimensional treatment of the Coulomb force of interaction between two charges is given. The electric force is due to the motion of charges in the extra-dimensional subspace and is equal to the corresponding Lorentz force.

Study on the Current Situation of Urban Integration of Aboveground Space and Underground Space:Under the Background of China’s Land Spatial Planning

Urban underground public space has a synergistic effect with its surrounding urban aboveground functions or facilities,which reflects the complementarity between underground functions and urban functions.The research analyses the degree of integration through the case study of urban aboveground space and underground space in China.The research method of this paper will give different evaluation criteria to public transport and public space and the influencing factors of space integration.The indicators of public transport include the number of subway lines and underground parking spaces.The evaluation standard of public space is the area of underground space and the number of floors of underground space.The subway entrance and exits are selected as the evaluation index for the aboveground and underground transition space.Through the specific analysis of 7 selected cases,it provides arguments for the research.The average rent in the case is taken as the dependent variable.Through the regression model,the influencing factors of the integration of aboveground and underground space are determined.The purpose of the study is to explore the influencing factors of the integration of aboveground space and underground space,and how to optimize the integration of aboveground and underground space.

RETRACTED: Disintegration of Group Representations on Direct Integrals of Banach Spaces

Short Retraction Notice? The paper does not meet the standards of "Advances in Pure Mathematics".? This article has been retracted to straighten the academic record. In making this decision the Editorial Board follows COPE's Retraction Guidelines. The aim is to promote the circulation of scientific research by offering an ideal research publication platform with due consideration of internationally accepted standards on publication ethics. The Editorial Board would like to extend its sincere apologies for any inconvenience this retraction may have caused.? Editor guiding this retraction: Editorial Board (EIC of APM).? Please see the article page for more details. The full retraction notice in PDF is preceding the original paper which is marked "RETRACTED".

AN INTEGRATION METHOD WITH FITTING CUBIC SPLINE FUNCTIONS TO A NUMERICAL MODEL OF 2ND-ORDER SPACE-TIME DIFFERENTIAL REMAINDER——FOR AN IDEAL GLOBAL SIMULATION CASE WITH PRIMITIVE ATMOSPHERIC EQUATIONS

In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.

THE BASIC THEORY OF SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH BOUNDED DELAY IN THE SPACE OF INTEGRABLE FUNCTIONS

在可积函数空间中讨论有界滞量泛函微分方程，建立其解的基本理论，包括解的存在性，唯一性及延展性。

A NEW INTEGRATION WITH RESPECT TO A VECTOR MEASURE AND ITS PROPERTIES

We introduce a new integration with respect to a vector measure, which may be considered the generalization of a line integration with respect to coordinates in classical calculus, we disscuss its properties and investigate the relationship between an integration with respect to a vector measure and one with respect to the variation of the vector measure, which is similar to the relationship between a line integration.with respect to coordinates and one with respect to arc length.

Multilinear singular integrals and commutators in variable exponent Lebesgue spaces

Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.

INTERIOR ESTIMATES IN MORREY SPACES FOR SOLUTIONS OF ELLIPTIC EQUATIONS AND WEIGHTED BOUNDEDNESS FOR COMMUTATORS OF SINGULAR INTEGRAL OPERATORS

It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp, (w).

BOUNDEDNESS OF COMMUTATORS RELATED TO MARCINKIEWICZ INTEGRALS ON HARDY TYPE SPACES

In this paper, the authors study the boundedness of the operator [μΩ,b], the commutator generated by a function b ∈ Lipβ(Rn)(0 <β≤1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω ∈ Lipα(Sn-1)(0 <α≤ 1).

System Integration of Terrestrial Mobile Communication and Satellite Communication——The Trends, Challenges and Key Technologies in B5G and 6G

Mobile communication standards have been developed into a new era of B5G and 6G.In recent years,low earth orbit(LEO)satellites and space Internet have become hot topics.The integrated satellite and terrestrial systems have been widely discussed by industries and academics,and even are expected to be applied in those huge constellations in construction.This paper points out the trends of two stages towards system integration of the terrestrial mobile communication and the satellite communications:to be compatible with 5G,and to be integrated within 6G.Based on analysis of the challenges of both stages,key technologies are thereafter analyzed in detail,covering both air interface currently discussed in 3GPP for B5G and also novel network architecture and related transmission technologies toward future 6G.

AN INTEGRAL ESTIMATE AND THE EQUIVALENT NORMS ON F(p, q, s, k) SPACES IN THE UNIT BALL

In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.