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
This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers...This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.展开更多
1. Introduction In application of nonlinear boundary value problems, it is sometimes important to know that L~2-boundedness of a class of pseudo-differential operators with symbols whioh have nonsmooth coefficients. I...1. Introduction In application of nonlinear boundary value problems, it is sometimes important to know that L~2-boundedness of a class of pseudo-differential operators with symbols whioh have nonsmooth coefficients. In [2], Coifman and Meyer proved that the operator σ(x, D) is bounded in L~2(R~n) if its symbold (x, ξ) satisfies:展开更多
目的评价MRI 3D T2-SPACE诊断大脑中动脉及基底动脉狭窄的价值。方法选取2019年11月至2020年10月在南京医科大学附属淮安第一医院就诊的40例脑血管狭窄患者为研究对象,选取符合研究要求的大脑中动脉及基底动脉共120根。在入院1周内完成...目的评价MRI 3D T2-SPACE诊断大脑中动脉及基底动脉狭窄的价值。方法选取2019年11月至2020年10月在南京医科大学附属淮安第一医院就诊的40例脑血管狭窄患者为研究对象,选取符合研究要求的大脑中动脉及基底动脉共120根。在入院1周内完成颅颈动脉MRI 3D T2-SPACE和数字减影血管造影(DSA)检查,分别评估动脉狭窄程度。按狭窄程度分成轻度(1%~49%)、中度(50%~69%)、重度(70%~99%)和闭塞(100%),和金标准DSA检查对照,计算灵敏度、特异度,并分析MRI 3D T2-SPACE和DSA诊断结果的一致性。结果MRI 3D T2-SPACE诊断大脑中动脉及基底动脉狭窄/闭塞的灵敏度、特异度结果如下,轻度狭窄分别为90.0%、96.4%,中度狭窄分别为77.8%、98.2%,重度狭窄分别为96.7%、97.8%,闭塞分别为87.5%、100.0%。MRI 3D T2-SPACE与DSA检查诊断大脑中动脉及基底动脉轻、中、重度狭窄及闭塞的一致性分别为0.760、0.760、0.934、0.929。结论MRI 3D T2-SPACE能够较准确地评估大脑中动脉及基底动脉狭窄程度,特别是对重度狭窄及闭塞的诊断与DSA检查结果高度一致,作为血管检查的一种全新技术,其将会在临床发挥重要作用。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
We consider the problem of packing d-dimensional cubes into the minimum number of 2-space bounded unit cubes. Given a sequence of items, each of which is a d-dimensional （d ≥ 3） hypercube with side length not great...We consider the problem of packing d-dimensional cubes into the minimum number of 2-space bounded unit cubes. Given a sequence of items, each of which is a d-dimensional （d ≥ 3） hypercube with side length not greater than 1 and an infinite number of d-dimensional （d ≥ 3） hypercube bins with unit length on each side, we want to pack all of the items in the sequence into the minimum number of bins. The constraint is that only two bins are active at anytime during the packing process. Each item should be orthogonally packed without overlapping other items. Items are given in an online manner without the knowledge of or information about the subsequent items. We extend the technique of brick partitioning for square packing and obtain two results： a three-dimensional box and d-dimensional hyperbox partitioning schemes for cube and hypercube packing, respectively. We design 32 5.43-competitive and 32/21·2d-competitive algorithms for cube and hypercube packing, respectively. To the best of our knowledge these are the first known results on 2-space bounded cube and hypercube packing.展开更多
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supported by the Graduate Education Innovation Funds(2022CXZZ088)at Central China Normal University in Chinasupported by the NSFC(12225106,11931012)the Fundamental Research Funds(CCNU22LJ002)for the Central Universities in China。
文摘This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.
基金Project supported by the Science Fund of the Chinese Academy of Sciences.
文摘1. Introduction In application of nonlinear boundary value problems, it is sometimes important to know that L~2-boundedness of a class of pseudo-differential operators with symbols whioh have nonsmooth coefficients. In [2], Coifman and Meyer proved that the operator σ(x, D) is bounded in L~2(R~n) if its symbold (x, ξ) satisfies:
文摘目的评价MRI 3D T2-SPACE诊断大脑中动脉及基底动脉狭窄的价值。方法选取2019年11月至2020年10月在南京医科大学附属淮安第一医院就诊的40例脑血管狭窄患者为研究对象,选取符合研究要求的大脑中动脉及基底动脉共120根。在入院1周内完成颅颈动脉MRI 3D T2-SPACE和数字减影血管造影(DSA)检查,分别评估动脉狭窄程度。按狭窄程度分成轻度(1%~49%)、中度(50%~69%)、重度(70%~99%)和闭塞(100%),和金标准DSA检查对照,计算灵敏度、特异度,并分析MRI 3D T2-SPACE和DSA诊断结果的一致性。结果MRI 3D T2-SPACE诊断大脑中动脉及基底动脉狭窄/闭塞的灵敏度、特异度结果如下,轻度狭窄分别为90.0%、96.4%,中度狭窄分别为77.8%、98.2%,重度狭窄分别为96.7%、97.8%,闭塞分别为87.5%、100.0%。MRI 3D T2-SPACE与DSA检查诊断大脑中动脉及基底动脉轻、中、重度狭窄及闭塞的一致性分别为0.760、0.760、0.934、0.929。结论MRI 3D T2-SPACE能够较准确地评估大脑中动脉及基底动脉狭窄程度,特别是对重度狭窄及闭塞的诊断与DSA检查结果高度一致,作为血管检查的一种全新技术,其将会在临床发挥重要作用。
基金supported by the National Natural Science Foundation of China (No. 61170232)the 985 Project funding of Sun Yat-sen UniversityState Key Laboratory of Rail Traffic Control and Safety independent research (No. RS2012K011)
文摘We consider the problem of packing d-dimensional cubes into the minimum number of 2-space bounded unit cubes. Given a sequence of items, each of which is a d-dimensional （d ≥ 3） hypercube with side length not greater than 1 and an infinite number of d-dimensional （d ≥ 3） hypercube bins with unit length on each side, we want to pack all of the items in the sequence into the minimum number of bins. The constraint is that only two bins are active at anytime during the packing process. Each item should be orthogonally packed without overlapping other items. Items are given in an online manner without the knowledge of or information about the subsequent items. We extend the technique of brick partitioning for square packing and obtain two results： a three-dimensional box and d-dimensional hyperbox partitioning schemes for cube and hypercube packing, respectively. We design 32 5.43-competitive and 32/21·2d-competitive algorithms for cube and hypercube packing, respectively. To the best of our knowledge these are the first known results on 2-space bounded cube and hypercube packing.
