Let M be a semifinite von Neumann algebra.We equip the associated noncommutative Lp-spaces with their natural operator space structure introduced by Pisier via complex interpolation.On the other hand,for L_(p),p(M)=(...Let M be a semifinite von Neumann algebra.We equip the associated noncommutative Lp-spaces with their natural operator space structure introduced by Pisier via complex interpolation.On the other hand,for L_(p),p(M)=(L_(∞)(M),L_(1)(M)_(1/p,p)be equipped with the operator space structure via real interpolation as defined by the second named author(J.Funct.Anal.139(1996),500–539).We show that Lp,p(M)=Lp(M)completely isomorphically if and only if M is finite dimensional.This solves in the negative the three problems left open in the quoted work of the second author.We also show that for 1<p<∞and 1≤q≤∞with p 6=q,(L_(∞)(M;l_(q)),L_(1)(M;l_(q)_(1/p,p)=L_(p)(M;l_(q)with equivalent norms,i.e.,at the Banach space level if and only if M is isomorphic,as a Banach space,to a commutative von Neumann algebra.Our third result concerns the following inequality:||(∑iixtq)^(1/q)||lp(M)≤||(∑iixit)^(1/q)||lp(M),for any finite sequence(xi)⊂L+p(M),where 0<r<q<∞and 0<p≤∞.If M is not isomorphic,as a Banach space,to a commutative von Meumann algebra,then this inequality holds if and only if p≥r.展开更多
In this paper,we introduce a special class of nilpotent Lie groups defined by hermitian maps,which includes all the groups of affine holomorphic automorphisims of Siegel domains of type Ⅱ,in particular,the Heisenberg...In this paper,we introduce a special class of nilpotent Lie groups defined by hermitian maps,which includes all the groups of affine holomorphic automorphisims of Siegel domains of type Ⅱ,in particular,the Heisenberg group.And we study harmonic analysis on these groups as spectral theory of the associated Sub-Laplacian instead of the group representation theory in usual way.展开更多
In this paper, some results concerning the relationship between the bounded-ness of some spheres and the local boundedness of the .F*-space are presented. Moreover, some results about the compactness are also given.
In this article,we discuss the stability ofε-isometries for L∞,λ-spaces.Indeed,we first study the relationship among separably injectivity,injectivity,cardinality injectivity and universally left stability of L∞,...In this article,we discuss the stability ofε-isometries for L∞,λ-spaces.Indeed,we first study the relationship among separably injectivity,injectivity,cardinality injectivity and universally left stability of L∞,λ-spaces as well as we show that the second duals of universally left-stable spaces are injective,which gives a partial answer to a question of Bao-Cheng-Cheng-Dai,and then we prove a sharpen quantitative and generalized Sobczyk theorem which gives examples of nonseparable L∞-spaces X(but not injective)such that the couple(X,Y)is stable for every separable space Y.This gives a new positive answer to Qian's problem.展开更多
In this paper we prove the existence of conditional expectations in the noncom- mutative Lp（M, Ф）-spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the ...In this paper we prove the existence of conditional expectations in the noncom- mutative Lp（M, Ф）-spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the obtained results, we establish the norm convergence of weighted averages of martingales in noncommutative Lp（M, Ф）-spaces.展开更多
Several theorems on closed (resp. open) covering properties of H-spaces are obtained which improve and generalize the corresponding results of Sperner, Klee, Alexandroff-Pasynkoff, Berge, Ghouila-Houri, Danzer-Grunbau...Several theorems on closed (resp. open) covering properties of H-spaces are obtained which improve and generalize the corresponding results of Sperner, Klee, Alexandroff-Pasynkoff, Berge, Ghouila-Houri, Danzer-Grunbaum-Klee, Ky Fan, Shih-Tan, Horvath and Lassonde. As application an almost fixed point theorem for lower semi-continuous map in l.c.-spaces and a generalization of Tychonoffs fixed point theorem are proved in l.c.-spaces which improve those results of Ky Fan and Horvath.展开更多
An (LF)-space (E, t) = md(En, tn) satisfying Retakh's condition (M0) needn't be regular[7]. D. Vogt[7] proved that if every step (En, tn) is reflealve then it is regular.By using the fort that the biduals of F...An (LF)-space (E, t) = md(En, tn) satisfying Retakh's condition (M0) needn't be regular[7]. D. Vogt[7] proved that if every step (En, tn) is reflealve then it is regular.By using the fort that the biduals of Frechet spaces are weakdy sequentially complete.the authors give some weaker conditions for (LF)-spaces satisfying condition (M0) to be regular, which improve the ah ore Vogt's result.展开更多
目的探讨磁共振三维可变翻转角快速自旋回波成像技术(SPACE)在显示肺球形病灶内部血管的临床应用价值。方法搜集拟进行胸部CT增强扫描的患者30例,所有患者均在接受CT增强检查后24 h内进行MR检查。扫描序列包括T1WI 3D Star VIBE序列、T2...目的探讨磁共振三维可变翻转角快速自旋回波成像技术(SPACE)在显示肺球形病灶内部血管的临床应用价值。方法搜集拟进行胸部CT增强扫描的患者30例,所有患者均在接受CT增强检查后24 h内进行MR检查。扫描序列包括T1WI 3D Star VIBE序列、T2WI HASTE序列以及T2-SPACE FLOW序列。由2名具有10年以上工作经验的放射科医师采用盲法先对MRI图像上所有病灶中肺血管的显示度进行主观评价,再观察与之对应的CT增强图像上肺血管的显示能力(CT增强图像作为参考标准),评分标准采用4分法(4分:边缘非常清晰,3分:边缘较清晰,2分:边缘不清晰,1分:不可见)。结果 CT增强图像上共检出48个肺球形病灶(大小1.0~5.6 cm),69支肺血管,另于MRI T2-SPACE FLOW序列上,检出48个球形病灶64支肺血管,检出率为94.3%。两名医师对CT增强图像和MRI图像上对肺球形病变内部血管形态显示度的主观评分分别为(3.59±0.46)分和(3.42±0.39)分(医师1)、(3.61±0.22)分和(3.49±0.68)分(医师2),差异均无统计学意义(P>0.05)。结论在显示肺球形病变内部血管中,T2-SPACE FLOW序列具有较高的敏感度及准确率,同时可以提供和CT增强扫描同等效能的肺血管显示度,具有重要的临床价值。展开更多
In this paper, the source localization by utilizing the measurements of a single electromagnetic （EM） vector-sensor is investigated in the framework of the geometric algebra of Euclidean 3-space. In order to describ...In this paper, the source localization by utilizing the measurements of a single electromagnetic （EM） vector-sensor is investigated in the framework of the geometric algebra of Euclidean 3-space. In order to describe the orthogonality among the electric and magnetic measurements, two multivectors of the geometric algebra of Euclidean 3-space （G3） are used to model the outputs of a spatially collocated EM vector-sensor. Two estimators for the wave propagation vector estimation are then formulated by the inner product between a vector and a bivector in the G3. Since the information used by the two estimators is different, a weighted inner product estimator is then proposed to fuse the two estimators together in the sense of the minimum mean square error （MMSE）. Analytical results show that the statistical performances of the weighted inner product estimator are always better than its traditional cross product counterpart. The efficacy of the weighted inner product estimator and the correctness of the analytical predictions are demonstrated by simulation results.展开更多
In this paper,we study the pseudo-spherical evolutes of curves in three dimensional hyperbolic space.We use techniques from singularity theory to investigate the singularities of pseudo-spherical evolutes and establis...In this paper,we study the pseudo-spherical evolutes of curves in three dimensional hyperbolic space.We use techniques from singularity theory to investigate the singularities of pseudo-spherical evolutes and establish some relationships between singularities of these curves and geometric invariants of curves under the action of the Lorentz group.Besides,we defray with illustration some computational examples in support our main results.展开更多
We will introduce a new connection between some transformations and some aspects of differential geometry of some curves in Minkowski space. The concept of folding, retractions and contraction on some curves in Minkow...We will introduce a new connection between some transformations and some aspects of differential geometry of some curves in Minkowski space. The concept of folding, retractions and contraction on some curves in Minkowski space will be characterized by using some aspects of differential geometry. Types of the deformation retracts of some curves in Minkowski 3-space are obtained. The relations between the foldings and the deformation retracts of some curves are deduced. The connections between some transformations and time like, space like, light like of some curves in Minkowski 3-space are also presented.展开更多
This paper is a continuation of[Erguang YANG.On some generalized countably compact spaces.J.Math.Res.Appl.,2019,39(5):540–550]in which characterizations of some generalized countably compact spaces such as quasi-γsp...This paper is a continuation of[Erguang YANG.On some generalized countably compact spaces.J.Math.Res.Appl.,2019,39(5):540–550]in which characterizations of some generalized countably compact spaces such as quasi-γspaces,quasi-Nagata spaces,wN-spaces and wM-spaces in terms of real-valued functions were obtained.In this paper,we shall present some other forms of characterizations of the spaces mentioned above.展开更多
In Minkowski 3-space,we construct a surfaces family interpolating the involute of a spacelike curve as a common line of curvature,geodesic or asymptotic curve.Moreover,the conditions are examined for the ruled surface...In Minkowski 3-space,we construct a surfaces family interpolating the involute of a spacelike curve as a common line of curvature,geodesic or asymptotic curve.Moreover,the conditions are examined for the ruled surface to be developable.And we support our conclusion with some examples.展开更多
This paper takes some investigations on generalized topological spaces with some μ- separations. Some characterizations of μTi-spaces for i = 0, 1, 2, 3, 4, μTn-spaces and μR0-spaces are obtained and some relation...This paper takes some investigations on generalized topological spaces with some μ- separations. Some characterizations of μTi-spaces for i = 0, 1, 2, 3, 4, μTn-spaces and μR0-spaces are obtained and some relations among these spaces are established.展开更多
Recently, the notion of an S-metric space is defined and extensively studied as a generalization of a metric space. In this paper, we define the notion of the S∞-space and prove its completeness. We obtain a new gene...Recently, the notion of an S-metric space is defined and extensively studied as a generalization of a metric space. In this paper, we define the notion of the S∞-space and prove its completeness. We obtain a new generalization of the classical ＂Picard Theorem＂.展开更多
In this paper, we mainly discuss the class of charming spaces. First, we show that there exists a charming space such that the Tychonoff product is not a charming space. Then we discuss some properties of charming spa...In this paper, we mainly discuss the class of charming spaces. First, we show that there exists a charming space such that the Tychonoff product is not a charming space. Then we discuss some properties of charming spaces and give some characterizations of some class of charming spaces. Finally, we show that the Suslin number of an arbitrary charming rectifiable space is countable.展开更多
基金the French ANR project(ANR-19-CE40-0002)the Natural Science Foundation of China(12031004).
文摘Let M be a semifinite von Neumann algebra.We equip the associated noncommutative Lp-spaces with their natural operator space structure introduced by Pisier via complex interpolation.On the other hand,for L_(p),p(M)=(L_(∞)(M),L_(1)(M)_(1/p,p)be equipped with the operator space structure via real interpolation as defined by the second named author(J.Funct.Anal.139(1996),500–539).We show that Lp,p(M)=Lp(M)completely isomorphically if and only if M is finite dimensional.This solves in the negative the three problems left open in the quoted work of the second author.We also show that for 1<p<∞and 1≤q≤∞with p 6=q,(L_(∞)(M;l_(q)),L_(1)(M;l_(q)_(1/p,p)=L_(p)(M;l_(q)with equivalent norms,i.e.,at the Banach space level if and only if M is isomorphic,as a Banach space,to a commutative von Neumann algebra.Our third result concerns the following inequality:||(∑iixtq)^(1/q)||lp(M)≤||(∑iixit)^(1/q)||lp(M),for any finite sequence(xi)⊂L+p(M),where 0<r<q<∞and 0<p≤∞.If M is not isomorphic,as a Banach space,to a commutative von Meumann algebra,then this inequality holds if and only if p≥r.
文摘In this paper,we introduce a special class of nilpotent Lie groups defined by hermitian maps,which includes all the groups of affine holomorphic automorphisims of Siegel domains of type Ⅱ,in particular,the Heisenberg group.And we study harmonic analysis on these groups as spectral theory of the associated Sub-Laplacian instead of the group representation theory in usual way.
基金This research is supported by National Natural Science Foundation of China(19971046) RFDP(2001005513)
文摘In this paper, some results concerning the relationship between the bounded-ness of some spheres and the local boundedness of the .F*-space are presented. Moreover, some results about the compactness are also given.
基金supported by the Natural Science Foundation of China(11601264)the Natural Science Foundation of Fujian Province of China(2019J05103)+1 种基金the Outstanding Youth Scientific Research Personnel Training Program of Fujian Provincethe High level Talents Innovation and Entrepreneurship Project of Quanzhou City(2017Z032)
文摘In this article,we discuss the stability ofε-isometries for L∞,λ-spaces.Indeed,we first study the relationship among separably injectivity,injectivity,cardinality injectivity and universally left stability of L∞,λ-spaces as well as we show that the second duals of universally left-stable spaces are injective,which gives a partial answer to a question of Bao-Cheng-Cheng-Dai,and then we prove a sharpen quantitative and generalized Sobczyk theorem which gives examples of nonseparable L∞-spaces X(but not injective)such that the couple(X,Y)is stable for every separable space Y.This gives a new positive answer to Qian's problem.
文摘In this paper we prove the existence of conditional expectations in the noncom- mutative Lp（M, Ф）-spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the obtained results, we establish the norm convergence of weighted averages of martingales in noncommutative Lp（M, Ф）-spaces.
基金This project partially supported by National Natural Science Foundation of ChinaThis work was partially supported by NSERC of Canada under grant A-8096
文摘Several theorems on closed (resp. open) covering properties of H-spaces are obtained which improve and generalize the corresponding results of Sperner, Klee, Alexandroff-Pasynkoff, Berge, Ghouila-Houri, Danzer-Grunbaum-Klee, Ky Fan, Shih-Tan, Horvath and Lassonde. As application an almost fixed point theorem for lower semi-continuous map in l.c.-spaces and a generalization of Tychonoffs fixed point theorem are proved in l.c.-spaces which improve those results of Ky Fan and Horvath.
文摘An (LF)-space (E, t) = md(En, tn) satisfying Retakh's condition (M0) needn't be regular[7]. D. Vogt[7] proved that if every step (En, tn) is reflealve then it is regular.By using the fort that the biduals of Frechet spaces are weakdy sequentially complete.the authors give some weaker conditions for (LF)-spaces satisfying condition (M0) to be regular, which improve the ah ore Vogt's result.
基金National Natural Science Foundation of China(61171127)National Basic Research Program of China(2011CB302903)
文摘In this paper, the source localization by utilizing the measurements of a single electromagnetic （EM） vector-sensor is investigated in the framework of the geometric algebra of Euclidean 3-space. In order to describe the orthogonality among the electric and magnetic measurements, two multivectors of the geometric algebra of Euclidean 3-space （G3） are used to model the outputs of a spatially collocated EM vector-sensor. Two estimators for the wave propagation vector estimation are then formulated by the inner product between a vector and a bivector in the G3. Since the information used by the two estimators is different, a weighted inner product estimator is then proposed to fuse the two estimators together in the sense of the minimum mean square error （MMSE）. Analytical results show that the statistical performances of the weighted inner product estimator are always better than its traditional cross product counterpart. The efficacy of the weighted inner product estimator and the correctness of the analytical predictions are demonstrated by simulation results.
文摘In this paper,we study the pseudo-spherical evolutes of curves in three dimensional hyperbolic space.We use techniques from singularity theory to investigate the singularities of pseudo-spherical evolutes and establish some relationships between singularities of these curves and geometric invariants of curves under the action of the Lorentz group.Besides,we defray with illustration some computational examples in support our main results.
文摘We will introduce a new connection between some transformations and some aspects of differential geometry of some curves in Minkowski space. The concept of folding, retractions and contraction on some curves in Minkowski space will be characterized by using some aspects of differential geometry. Types of the deformation retracts of some curves in Minkowski 3-space are obtained. The relations between the foldings and the deformation retracts of some curves are deduced. The connections between some transformations and time like, space like, light like of some curves in Minkowski 3-space are also presented.
文摘This paper is a continuation of[Erguang YANG.On some generalized countably compact spaces.J.Math.Res.Appl.,2019,39(5):540–550]in which characterizations of some generalized countably compact spaces such as quasi-γspaces,quasi-Nagata spaces,wN-spaces and wM-spaces in terms of real-valued functions were obtained.In this paper,we shall present some other forms of characterizations of the spaces mentioned above.
文摘In Minkowski 3-space,we construct a surfaces family interpolating the involute of a spacelike curve as a common line of curvature,geodesic or asymptotic curve.Moreover,the conditions are examined for the ruled surface to be developable.And we support our conclusion with some examples.
基金Supported by the National Natural Science Foundation of China(10971185)
文摘This paper takes some investigations on generalized topological spaces with some μ- separations. Some characterizations of μTi-spaces for i = 0, 1, 2, 3, 4, μTn-spaces and μR0-spaces are obtained and some relations among these spaces are established.
文摘Recently, the notion of an S-metric space is defined and extensively studied as a generalization of a metric space. In this paper, we define the notion of the S∞-space and prove its completeness. We obtain a new generalization of the classical ＂Picard Theorem＂.
基金The NSF(11571158,11471153 and 11201414) of Chinathe NSF(2017J01405,2016J05014,2016J01671 and 2016J01672) of Fujian Province of China
文摘In this paper, we mainly discuss the class of charming spaces. First, we show that there exists a charming space such that the Tychonoff product is not a charming space. Then we discuss some properties of charming spaces and give some characterizations of some class of charming spaces. Finally, we show that the Suslin number of an arbitrary charming rectifiable space is countable.
