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Motion and Special Relativity in Complex Spaces
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作者 Jerzy K. Filus 《Journal of Applied Mathematics and Physics》 2024年第1期330-361,共32页
A natural extension of the Lorentz transformation to its complex version was constructed together with a parallel extension of the Minkowski M<sup>4</sup> model for special relativity (SR) to complex C<... A natural extension of the Lorentz transformation to its complex version was constructed together with a parallel extension of the Minkowski M<sup>4</sup> model for special relativity (SR) to complex C<sup>4</sup> space-time. As the [signed] absolute values of complex coordinates of the underlying motion’s characterization in C<sup>4</sup> one obtains a Newtonian-like type of motion whereas as the real parts of the complex motion’s description and of the complex Lorentz transformation, all the SR theory as modeled by M<sup>4</sup> real space-time can be recovered. This means all the SR theory is preserved in the real subspace M<sup>4</sup> of the space-time C<sup>4</sup> while becoming simpler and clearer in the new complex model’s framework. Since velocities in the complex model can be determined geometrically, with no primary use of time, time turns out to be definable within the equivalent theory of the reduced complex C<sup>4</sup> model to the C<sup>3</sup> “para-space” model. That procedure allows us to separate time from the (para)space and consider all the SR theory as a theory of C<sup>3</sup> alone. On the other hand, the complex time defined within the C<sup>3</sup> theory is interpreted and modeled by the single separate C<sup>1</sup> complex plane. The possibility for application of the C<sup>3</sup> model to quantum mechanics is suggested. As such, the model C<sup>3</sup> seems to have unifying abilities for application to different physical theories. 展开更多
关键词 Special Relativity complex space and Time Models and Dramatic SR Simplification complex Time and space Separation complex Time Interpretation
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SLANT IMMERSIONS OF COMPLEX SPACE FORMS AND CHEN'S INEQUALITY 被引量:10
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作者 李光汉 吴传喜 《Acta Mathematica Scientia》 SCIE CSCD 2005年第2期223-232,共10页
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 sla... 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. 展开更多
关键词 Slant immersion IDEAL Chen's inequality complex space form
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RIGIDITY THEOREMS OF COMPLETE K?HLER-EINSTEIN MANIFOLDS AND COMPLEX SPACE FORMS
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作者 Tian CHONG Yuxin DONG +1 位作者 Hezi LIN Yibin REN 《Acta Mathematica Scientia》 SCIE CSCD 2019年第2期339-356,共18页
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 form... 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. 展开更多
关键词 rigidity theorems Kahler-Einstein complex space forms
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Commuting Structure Jacobi Operator for Real Hypersurfaces in Complex Space Forms
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作者 U-Hang Ki Hiroyuki Kurihara 《Advances in Pure Mathematics》 2013年第2期264-276,共13页
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 com... 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. 展开更多
关键词 complex space Form Hopf HYPERSURFACE STRUCTURE JACOBI OPERATOR Shape OPERATOR RICCI Tensor
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Seismic identification and characterization of complex storage space oil and gas reservoirs
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作者 XiaoYu-Jiang Tao Song +5 位作者 Li Deng-Gan Xiao Yue-Zhou Jing Liang Lele-Wei Ming Zhang Xiaofeng-Dai 《Applied Geophysics》 SCIE CSCD 2024年第3期606-615,620,共11页
To predict complex reservoir spaces(with developed caves,pores,and fractures),based on the results of full-azimuth depth migration processing,we adopted reverse weighted nonlinear inversion to improve the accuracy of ... To predict complex reservoir spaces(with developed caves,pores,and fractures),based on the results of full-azimuth depth migration processing,we adopted reverse weighted nonlinear inversion to improve the accuracy of porous reservoir prediction.Scattering imaging three-parameter wavelet transform technology was used to accurately predict small-scale cave bodies.The joint inversion method of velocity and amplitude anisotropy was developed to improve the accuracy of small and medium-sized fracture prediction.The results of multiscale fracture modeling and characterization,interwell connectivity analysis,and connection path prediction are consistent with the production condition.Finally,based on the above prediction findings,favorable reservoir development areas were predicted.The above ideas and strategies have great application value for the efficient exploration and development of complex storage space reservoirs and the optimization of high-yield well locations. 展开更多
关键词 complex storage space fracture prediction reservoir prediction cave prediction
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THE FEKETE-SZEG?INEQUALITY AND SUCCESSIVE COEFFICIENTS DIFFERENCE FOR A SUBCLASS OF CLOSE-TO-STARLIKE MAPPINGS IN COMPLEX BANACH SPACES 被引量:1
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作者 徐庆华 方炜康 +1 位作者 冯伟珩 刘太顺 《Acta Mathematica Scientia》 SCIE CSCD 2023年第5期2075-2088,共14页
Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 fo... Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space. 展开更多
关键词 Fekete and Szego inequality successive coefficients difference bound close-to-starlike mappings complex Banach space
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An experimental study on fire characteristics of urban complex underground space based on BIM
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作者 Jinrong Cui Hao Mei +3 位作者 Haosen Sun Ye Jingqi Wei Hu Yong Xu 《CAAI Transactions on Intelligence Technology》 SCIE EI 2023年第4期1403-1414,共12页
Compared with the space on the ground,if there is a fire in the urban complex underground space,the loss will be greatly harmful.In addition,the complex underground space is usually connected with other large space ar... Compared with the space on the ground,if there is a fire in the urban complex underground space,the loss will be greatly harmful.In addition,the complex underground space is usually connected with other large space areas and densely populated.Once a fire occurs in the complex underground space,it will cause huge property losses and casualties.In order to reduce the risk of fire,it is necessary to deeply understand the development rules and characteristics of fire in the complex underground space of the city.This article has mainly carried on the following work:(I)A particularly complex model of the multi‐storey subway station was built.On this basis,three groups of comparative experiments were conducted to study the effects of fire power,fire location and smoke control system on fire development,and the conclusion that fire location is the most important factor for fire development was obtained;(II)In order to explore the entire space fire and the local space fire,CFD(Computational Fluid Dynamics)is used to build a large‐size fire model and a small‐size fire model respectively;(III)Multiple detector data as temperature slices were built,and it is expected to make full use of the simulation data to deduce the important index of fire location in the early stage of fire.All of the works in this paper will provide reference experimental data for the prevention and firefighting of a sudden fire in the complex underground space. 展开更多
关键词 fire simulation underground multi‐storey subway station urban complex underground space
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基于CiteSpace的商业综合体公共空间研究现状综述
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作者 刘洋 刘彤彤 《建筑与文化》 2024年第1期147-149,共3页
随着城市化进程的不断推进,城市居民生活逐渐由物质层面向精神层面延伸。为满足城市商业发展和消费者对商业空间的多元化需求,商业综合体公共空间研究成为重要方面。文章基于中国知网(CNKI)数据库,整理相关文献,运用CiteSpace知识图谱... 随着城市化进程的不断推进,城市居民生活逐渐由物质层面向精神层面延伸。为满足城市商业发展和消费者对商业空间的多元化需求,商业综合体公共空间研究成为重要方面。文章基于中国知网(CNKI)数据库,整理相关文献,运用CiteSpace知识图谱量化文献计量软件,总结2005—2023年该领域发文量变化、关键词及聚类图谱等要素,对该领域的研究趋势进行分析,以期为商业综合体公共空间设计提供参考。 展开更多
关键词 CITEspace 商业综合体 公共空间 研究综述
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2-Harmonic Submanifolds in a Complex Space Form 被引量:12
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作者 ZHU Ye Cheng SONG Wei Dong 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2008年第3期727-732,共6页
In the present paper,the authors study totally real 2-harmonic submanifolds in a complex space form and obtain a Simons' type integral inequality of compact submanifolds as well as some relevant conclusions.
关键词 2-HARMONIC MINIMAL totally geodesic complex space form.
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Classification of Lagrangian Surfaces of Curvatureε in Non-fiat Lorentzian Complex Space Form ■_1~2(4ε)
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作者 Bang Yen CHEN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2009年第12期1987-2022,共36页
It is well known that a totally geodesic Lagrangian surface in a Lorentzian complex space form M12(4ε) of constant holomorphic sectional curvature 4s is of constant curvature 6. A natural question is "Besides tota... It is well known that a totally geodesic Lagrangian surface in a Lorentzian complex space form M12(4ε) of constant holomorphic sectional curvature 4s is of constant curvature 6. A natural question is "Besides totally geodesic ones how many Lagrangian surfaces of constant curvature εin M12(46) are there?" In an earlier paper an answer to this question was obtained for the case e = 0 by Chen and Fastenakels. In this paper we provide the answer to this question for the case ε≠0. Our main result states that there exist thirty-five families of Lagrangian surfaces of curvature ε in M12(4ε) with ε ≠ 0. Conversely, every Lagrangian surface of curvature ε≠0 in M12(4ε) is locally congruent to one of the Lagrangian surfaces given by the thirty-five families. 展开更多
关键词 Lagrangian surfaces Lorentzian complex space form Legendre curve surfaces of constant curvature
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Conformally flat, minimal, Lagrangian submanifolds in complex space forms
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作者 Miroslava Antić Luc Vrancken 《Science China Mathematics》 SCIE CSCD 2022年第8期1641-1660,共20页
We investigate n-dimensional(n≥4),conformally flat,minimal,Lagrangian submanifolds of the n-dimensional complex space form in terms of the multiplicities of the eigenvalues of the Schouten tensor and classify those t... We investigate n-dimensional(n≥4),conformally flat,minimal,Lagrangian submanifolds of the n-dimensional complex space form in terms of the multiplicities of the eigenvalues of the Schouten tensor and classify those that admit at most one eigenvalue of multiplicity one.In the case where the ambient space is Cn,the quasi umbilical case was studied in Blair(2007).However,the classification there is not complete and several examples are missing.Here,we complete(and extend) the classification and we also deal with the case where the ambient complex space form has non-vanishing holomorphic sectional curvature. 展开更多
关键词 Lagrangian submanifolds conformally flat complex space form warped product submanifold
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Ruled Real Hypersurfaces of A Complex Space Form
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《Acta Mathematica Sinica,English Series》 SCIE CSCD 1994年第4期401-409,共9页
The purpose of this paper is to define a ruled real hypersurface of a complex space form M_n(c),c≠0,and to give characterizations of this hypersurface by the infinitesimal affine transformation of the structure vecto... The purpose of this paper is to define a ruled real hypersurface of a complex space form M_n(c),c≠0,and to give characterizations of this hypersurface by the infinitesimal affine transformation of the structure vector field induced on the hypersurface. 展开更多
关键词 MATH REAL Ruled Real Hypersurfaces of A complex space Form
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Some remarks on pseudo-umbilical totally real submanifolds in a complex projective space 被引量:3
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作者 ZHANG Liang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2008年第2期227-232,共6页
This paper studies the relationship between the pseudo-umbilical totally real submanifolds and the minimal totally real submanifolds in a complex projective space. Two theo- rems which claim that some types of pseudo-... This paper studies the relationship between the pseudo-umbilical totally real submanifolds and the minimal totally real submanifolds in a complex projective space. Two theo- rems which claim that some types of pseudo-umbilical totally real submanifolds must be minimal submanifolds are proved. 展开更多
关键词 complex projective space totally real submanifold pseudo-umbilical submanifold minimal submanifold.
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B-Implicit Contractive Conditions and Unique(Common) Fixed Points on Complex Valued Metric Spaces 被引量:2
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作者 PIAO Yong-jie 《Chinese Quarterly Journal of Mathematics》 2018年第2期212-220,共9页
A class B of complex functions is introduced and several existence theorems of unique(common) fixed points for mappings satisfying a B-implicit contraction are presented.Moreover, the existence results of common fixed... A class B of complex functions is introduced and several existence theorems of unique(common) fixed points for mappings satisfying a B-implicit contraction are presented.Moreover, the existence results of common fixed points for two mappings on a nonempty set with two complex valued metrics are provided. Our outcomes generalize and improve some known results, especially, for instance, Banach contraction principle, Chatterjea-type fixed point theorem and the corresponding fixed point theorems. 展开更多
关键词 complex valued metric space (Common) Fixed point B-implicit contraction
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One Roper-Suffridge Extension Operator in Complex Banach Spaces 被引量:1
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作者 WANG Xiao-feng XU Yi-fei 《Chinese Quarterly Journal of Mathematics》 CSCD 2013年第3期468-474,共7页
In this paper, by the definition of almost spirallike mappings of type β and order α and the geometric property of the spirallike mapping of type β, we prove that the generalized Roper-Suffridge extension operator ... In this paper, by the definition of almost spirallike mappings of type β and order α and the geometric property of the spirallike mapping of type β, we prove that the generalized Roper-Suffridge extension operator preserves almost spirallikeness of type β and order α in complex Banach spaces. Key words: 展开更多
关键词 Roper-Suffridge extension operator Reinhardt domains complex Banach spaces
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THE MAIN INVARIANTS OF A COMPLEX FINSLER SPACE
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作者 Nicoleta ALDEA Gheorghe MUNTEANU 《Acta Mathematica Scientia》 SCIE CSCD 2014年第4期995-1011,共17页
In this paper we extend the results obtained in [3], where are investigated the general settings of the two-dimensional complex Finsler manifolds, with respect to a local complex Berwahl frame. The geometry of such ma... In this paper we extend the results obtained in [3], where are investigated the general settings of the two-dimensional complex Finsler manifolds, with respect to a local complex Berwahl frame. The geometry of such manifolds is controlled by three real invari- ants which live on T'M: two horizontal curvature invariants K and W and one vertical curvature invariant I. By means of these invariants are defined both the horizontal and the vertical holomorphic sectional curvatures. The complex Landsberg and Berwald spaces are of particular into, rest. Complex Berwald spaces coincide with K/ihler spaces, in the two - dimensional case, We establish the necessary and sufficient condition under which K is a constant and we obtain a characterization for the Kghler purely Hermitian spaces by the fact K = W=constant and I = 0. For the class of complex Berwald spaces we have K =W = 0. Finally, a classitication of two-dimensional complex Finsler spaces for which the horizontal curvature satisfies a special property is obtained. 展开更多
关键词 Berwald frame complex Landsberg space complex Berwald space holomorphic sectional curvature
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Lagrangian Bonnet Problems in Complex Space Forms
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作者 Hui Xia HE Hui MA Er Xiao WANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2019年第8期1357-1366,共10页
In this note we consider Lagrangian Bonnet problem for Lagrangian surfaces in complex space forms. We first give a Bonnet type theorem for conformal Lagrangian surfaces in complex space forms, then we show that any co... In this note we consider Lagrangian Bonnet problem for Lagrangian surfaces in complex space forms. We first give a Bonnet type theorem for conformal Lagrangian surfaces in complex space forms, then we show that any compact Lagrangian surface in the complex space form admits at most one other global isometric Lagrangian surface with the same mean curvature form, unless the Maslov form is conformal. These two Lagrangian surfaces are then called Lagrangian Bonnet pairs. We also studied Lagrangian Bonnet surfaces in complex space forms, and obtain some characterizations of such surfaces. 展开更多
关键词 LAGRANGIAN SUBMANIFOLDS complex space forms. BONNET PAIRS
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Points of Coincidence and Common Fixed Points for Ⅱ-Expansive Mappings on Complex Valued Metric Spaces
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作者 Yongjie Piao 《Analysis in Theory and Applications》 CSCD 2017年第4期366-374,共9页
Abstract. We use the two mappings satisfying II-expansive conditions on complex valued metric spaces to construct the convergent sequences and prove that the unique limit of the sequences is the point of coincidence o... Abstract. We use the two mappings satisfying II-expansive conditions on complex valued metric spaces to construct the convergent sequences and prove that the unique limit of the sequences is the point of coincidence or common fixed point of the two mappings. Also, we discuss the uniqueness of points of coincidence or common fixed points and give the existence theorems of unique fixed points. The obtained results generalize and improve the corresponding conclusions in references. 展开更多
关键词 complex valued metric space II-expansive mapping Cauchy sequence point ofcoincidence common fixed point.
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The influence of pore structure on P-& S-wave velocities in complex carbonate reservoirs with secondary storage space 被引量:10
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作者 Wang Haiyang Sam Zandong Sun +3 位作者 Yang Haijun Gao Hongliang Xiao Youjun Hu Hongru 《Petroleum Science》 SCIE CAS CSCD 2011年第4期394-405,共12页
Secondary storage spaces with very complex geometries are well developed in Ordovician carbonate reservoirs in the Tarim Basin,which is taken as a study case in this paper.It is still not clear how the secondary stora... Secondary storage spaces with very complex geometries are well developed in Ordovician carbonate reservoirs in the Tarim Basin,which is taken as a study case in this paper.It is still not clear how the secondary storage space shape influences the P-& S-wave velocities (or elastic properties) in complex carbonate reservoirs.In this paper,three classical rock physics models (Wyllie timeaverage equation,Gassmann equation and the Kuster-Toks z model) are comparably analyzed for their construction principles and actual velocity prediction results,aiming at determining the most favourable rock physics model to consider the influence of secondary storage space shape.Then relationships between the P-& S-wave velocities in carbonate reservoirs and geometric shapes of secondary storage spaces are discussed from different aspects based on actual well data by employing the favourable rock physics model.To explain the influence of secondary storage space shape on V P-V S relationship,it is analyzed for the differences of S-wave velocities between derived from common empirical relationships (including Castagna's mud rock line and Greenberg-Castagna V P-V S relationship) and predicted by the rock physics model.We advocate that V P-V S relationship for complex carbonate reservoirs should be built for different storage space types.For the carbonate reservoirs in the Tarim Basin,the V P-V S relationships for fractured,fractured-cavernous,and fractured-hole-vuggy reservoirs are respectively built on the basis of velocity prediction and secondary storage space type determination.Through the discussion above,it is expected that the velocity prediction and the V P-V S relationships for complex carbonate reservoirs should fully consider the influence of secondary storage space shape,thus providing more reasonable constraints for prestack inversion,further building a foundation for realizing carbonate reservoir prediction and fluid prediction. 展开更多
关键词 complex carbonate reservoir secondary storage space velocity prediction V P-V S relationships
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2-Harmonic Totally Real Submanifolds in a Complex Projective Space
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作者 孙弘安 《Chinese Quarterly Journal of Mathematics》 CSCD 1995年第3期37-41,共5页
In this paper, we discuss the relations between the 2-harmornic totally real submsnifold and the minimal totall real submanifold in the complex protective spsace, and obtain the pinching conductions for the second fu... In this paper, we discuss the relations between the 2-harmornic totally real submsnifold and the minimal totall real submanifold in the complex protective spsace, and obtain the pinching conductions for the second fundamental form and the Rieci curature of the 2-harmornic totally real submanifold in the complex projective space. 展开更多
关键词 complex projective space totally real 2-HARMONIC MINIMAL
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