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 ...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.展开更多
Let T be a mapping from the unit sphere S[l^p（Г）] into S[l^p（△）] of two atomic AL^p- spaces. We prove that if T is a 1-Lipschitz mapping such that -T[S[l^p（Г）]] belong to T[S[l^p（Г）]], then T can be linear...Let T be a mapping from the unit sphere S[l^p（Г）] into S[l^p（△）] of two atomic AL^p- spaces. We prove that if T is a 1-Lipschitz mapping such that -T[S[l^p（Г）]] belong to T[S[l^p（Г）]], then T can be linearly isometrically extended to the whole space for p 〉 2; if T is injective and the inverse mapping T^-1 is a 1-Lipschitz mapping, then T can be extended to be a linear isometry from l^p（Г） into l^p（△） for 1 〈 p ≤ 2.展开更多
目的探讨心脏磁共振组织追踪(cardiac magnetic resonance tissue tracing,CMR-TT)技术及T1 mapping技术在2型糖尿病(type 2 diabetes mellitus,T2DM)患者心肌损伤评估中的应用价值。材料与方法前瞻性收集2023年12月至2025年4月在我院...目的探讨心脏磁共振组织追踪(cardiac magnetic resonance tissue tracing,CMR-TT)技术及T1 mapping技术在2型糖尿病(type 2 diabetes mellitus,T2DM)患者心肌损伤评估中的应用价值。材料与方法前瞻性收集2023年12月至2025年4月在我院进行心脏磁共振检查的T2DM患者64例,健康对照(healthy controls,HC)32例。所有心脏磁共振图像数据导入专用软件进行分析,获取全心心肌应变参数、双心室功能参数以及左心室T1 mapping参数,采用t检验,Mann-Whitney U检验及卡方检验对两组间上述参数进行比较,采用Pearson及Spearman相关性分析心肌结构、功能与心肌应变的关联。结果T2DM组左心室心肌质量指数(left ventricular myocardial mass index,LVMI)、左心室重塑指数(left ventricular remodeling index,LVRI)增加(均P<0.001),左心室全局纵向应变(global longitudinal peak strain in the left ventricle,LV GLS)、右心室全局纵向应变降低(均P<0.05),T2DM组周向左心室收缩期峰值应变率(peak systolic strain rate of the left ventricle,LV PSSR)、纵向LV PSSR及左心室舒张期峰值应变率(diastolic peak strain rate of the left ventricle,LV PDSR)绝对值均降低(均P<0.019)。T2DM患者左心房/右心房(leftatrium/rightatrium,LA/RA)储存应变、LA/RA导管应变均降低(均P<0.001)。T2DM患者的细胞外容积(extracellular volume,ECV)较HC组升高(P<0.001)。双心室射血分数、收缩末期容积指数与双心室应变功能均相关(均P<0.003)。LVMI与左心室全局径向应变(global radial strain of the left ventricle,LV GRS)、左心室全局周向应变(global circumferential strain of the left ventricle,LV GCS)、LV GLS、周向LV PSSR、纵向LV PSSR、径向LV PDSR、周向LV PDSR、纵向LV PDSR相关(均P<0.021)。左心室舒张末期容积指数与LV GCS、LV GLS、周向LV PSSR、纵向LV PSSR、周向LV PDSR相关(均P<0.044)。右心室舒张末期容积指数与右心室全局周向应变相关(r=0.331,P=0.007)。LVRI与LV GLS及纵向LV PDSR相关(均P<0.01),且与径向LV PSSR弱相关(r=0.266,P=0.034)。结论T2DM患者全心心肌应变较对照组降低,ECV值升高,双心室心肌结构、功能与心肌应变相互关联,CMR-TT及T1 mapping技术可以有效检测糖尿病心肌损伤。展开更多
基金supported by National Natural Science Foundation of China (Grant No.10871101)the Research Fund for the Doctoral Program of Higher Education (Grant No. 20060055010)
文摘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.
基金the Natural Science Foundation of the Education Department of Jiangsu Province (No.06KJD110092)
文摘Let T be a mapping from the unit sphere S[l^p（Г）] into S[l^p（△）] of two atomic AL^p- spaces. We prove that if T is a 1-Lipschitz mapping such that -T[S[l^p（Г）]] belong to T[S[l^p（Г）]], then T can be linearly isometrically extended to the whole space for p 〉 2; if T is injective and the inverse mapping T^-1 is a 1-Lipschitz mapping, then T can be extended to be a linear isometry from l^p（Г） into l^p（△） for 1 〈 p ≤ 2.
文摘目的探讨心脏磁共振组织追踪(cardiac magnetic resonance tissue tracing,CMR-TT)技术及T1 mapping技术在2型糖尿病(type 2 diabetes mellitus,T2DM)患者心肌损伤评估中的应用价值。材料与方法前瞻性收集2023年12月至2025年4月在我院进行心脏磁共振检查的T2DM患者64例,健康对照(healthy controls,HC)32例。所有心脏磁共振图像数据导入专用软件进行分析,获取全心心肌应变参数、双心室功能参数以及左心室T1 mapping参数,采用t检验,Mann-Whitney U检验及卡方检验对两组间上述参数进行比较,采用Pearson及Spearman相关性分析心肌结构、功能与心肌应变的关联。结果T2DM组左心室心肌质量指数(left ventricular myocardial mass index,LVMI)、左心室重塑指数(left ventricular remodeling index,LVRI)增加(均P<0.001),左心室全局纵向应变(global longitudinal peak strain in the left ventricle,LV GLS)、右心室全局纵向应变降低(均P<0.05),T2DM组周向左心室收缩期峰值应变率(peak systolic strain rate of the left ventricle,LV PSSR)、纵向LV PSSR及左心室舒张期峰值应变率(diastolic peak strain rate of the left ventricle,LV PDSR)绝对值均降低(均P<0.019)。T2DM患者左心房/右心房(leftatrium/rightatrium,LA/RA)储存应变、LA/RA导管应变均降低(均P<0.001)。T2DM患者的细胞外容积(extracellular volume,ECV)较HC组升高(P<0.001)。双心室射血分数、收缩末期容积指数与双心室应变功能均相关(均P<0.003)。LVMI与左心室全局径向应变(global radial strain of the left ventricle,LV GRS)、左心室全局周向应变(global circumferential strain of the left ventricle,LV GCS)、LV GLS、周向LV PSSR、纵向LV PSSR、径向LV PDSR、周向LV PDSR、纵向LV PDSR相关(均P<0.021)。左心室舒张末期容积指数与LV GCS、LV GLS、周向LV PSSR、纵向LV PSSR、周向LV PDSR相关(均P<0.044)。右心室舒张末期容积指数与右心室全局周向应变相关(r=0.331,P=0.007)。LVRI与LV GLS及纵向LV PDSR相关(均P<0.01),且与径向LV PSSR弱相关(r=0.266,P=0.034)。结论T2DM患者全心心肌应变较对照组降低,ECV值升高,双心室心肌结构、功能与心肌应变相互关联,CMR-TT及T1 mapping技术可以有效检测糖尿病心肌损伤。
