In this paper,we propose a definition for eigenvalues of odd-order tensors based on some operators.Also,we define the Schur form and the Jordan canonical form of such tensors,and discuss commuting families of tensors....In this paper,we propose a definition for eigenvalues of odd-order tensors based on some operators.Also,we define the Schur form and the Jordan canonical form of such tensors,and discuss commuting families of tensors.Furthermore,we prove some eigenvalue ine-qualities for Hermitian tensors.Finally,we introduce characteristic polynomials of odd-order tensors.展开更多
Double perovskite matrix materials have recently attracted considerable interest due to their structural flexibility,ease of doping,and excellent thermal stability.While photoluminescence(PL)studies of rare-earth-dope...Double perovskite matrix materials have recently attracted considerable interest due to their structural flexibility,ease of doping,and excellent thermal stability.While photoluminescence(PL)studies of rare-earth-doped double perovskites are common,research on their thermoluminescence(TL)properties is less extensive.This study synthesized a series of Y_(2-x)Sm_(x)MgTiO_(6)(0≤x≤0.1)samples using a high-temperature solid-state method.X-ray diffraction(XRD)analysis confirmed a monoclinic crystal structure(space group P2_(1)∕n),with Sm^(3+)ions substituting for Y^(3+)ions in Y_(2)MgTiO_(6).The PL results indicated that the optimal doping concentration was Y_(1.95)Sm_(0.05)MgTiO_(6),exhibiting emission peaks at 568,605,652,and 715 nm under 409 nm blue light excitation.The TL measurements for different doping concentrations showed that the Y_(1.98)Sm_(0.02)MgTiO_(6)phosphors exhibited the strongest TL signals.The TL peaks observed at 530 and 610 K correspond to defects in the matrix and Sm^(3+)dopants,respectively.The T_(m)-T_(stop)analysis revealed that the TL curve of Y_(1.98)Sm_(0.02)MgTiO_(6)phosphors was a superposition of seven peaks.Computerized glow curve deconvolution(CGCD)was performed on the TL of the sample according to the results of three-dimensional thermoluminescence spectra(3D-TL)and T_(m)-T_(stop),and the trap depths in the sample were estimated to range from 0.69 to 1.49 eV.Additionally,the lifetimes of each overlapping peak were calculated using the fitting parameters.Furthermore,the dose-response test showed that the saturation dose of the sample was high(9956 Gy).Therefore,this material can serve as a thermoluminescent dosimeter for high-dose measurements.The saturation dose for the lowest-temperature overlapping peak was 102 Gy,which correlated with its specific energy-level lifetime,whereas the other overlapping peaks also exhibited favorable linear relationships.展开更多
目的探讨基于MRI的脑白质纤维束T_(1)与T_(2)加权比(T_(1)W/T_(2)W)在0~8岁儿童脑白质髓鞘化发育进程评估中的应用价值。方法横断面研究。纳入2011年8月—2023年7月西安交通大学第一附属医院219例儿童的头颅MRI资料,其中男125例、女94例...目的探讨基于MRI的脑白质纤维束T_(1)与T_(2)加权比(T_(1)W/T_(2)W)在0~8岁儿童脑白质髓鞘化发育进程评估中的应用价值。方法横断面研究。纳入2011年8月—2023年7月西安交通大学第一附属医院219例儿童的头颅MRI资料,其中男125例、女94例,年龄0~8(3.5±2.4)岁。根据儿童发育阶段分类按年龄将219例儿童受检者分为6组:≤6个月组21例,>6个月~1岁组24例,>1~2岁组40例,>2~3岁组23例,>3~4岁组22例,>4~6岁组42例,>6~8岁组47例。应用3.0 T MR扫描仪采集儿童T_(1)加权像及T_(2)加权像,通过外部校准流程计算获得T_(1)W/T_(2)W图,并基于Johns Hopkins University Diffusion Tensor Imaging-81图谱提取联络束、边缘束、投射束、连合束、脑干束5束纤维束及其代表性白质纤维(左侧上纵束、左侧扣带回海马部、左侧内囊前肢、胼胝体膝部及左侧小脑上脚)的T_(1)W/T_(2)W值。观察指标:(1)观察不同年龄组儿童脑白质T_(1)W/T_(2)W图像信号强度的特点,比较各年龄组患儿不同白质纤维束T_(1)W/T_(2)W值的差异;(2)观察不同白质纤维束及其代表性白质纤维的T_(1)W/T_(2)W值随年龄变化的特点,采用局部加权回归散点平滑法(LOESS)绘制回归拟合曲线,确认不同白质纤维束T_(1)W/T_(2)W值随年龄变化的折点,并依此折点划分不同发育阶段,观察不同发育阶段中不同白质纤维束T_(1)W/T_(2)W值与年龄的相关性。结果(1)不同年龄组儿童T_(1)W/T_(2)W图像显示:≤6个月组仅脑桥背侧、内囊后肢及部分皮质脊髓束区域具有较高的信号强度,随着年龄增加,胼胝体压部、胼胝体膝部、皮质脊髓束等区域高信号的范围及强度逐渐增加,从>2~3岁组开始整个大脑皮层下白质区域均具有较高的信号强度。(2)各年龄组间白质纤维束T_(1)W/T_(2)W值比较:脑干束T_(1)W/T_(2)W值,≤6个月组及>6个月~1岁组均低于>2~3岁组及其后的各年龄组,>1~2岁组低于>2~3岁组和>3~4岁组,差异均有统计学意义(P值均<0.05);连合束的T_(1)W/T_(2)W值,≤6个月组和>6个月~1岁组均低于>1~2岁组及其后的各年龄组,>1~2岁组低于>2~3岁组,差异均有统计学意义(P值均<0.05);投射束、边缘束、联络束T_(1)W/T_(2)W值,≤6个月组和>6个月~1岁组均低于>1~2岁组及其后的各年龄组,差异均有统计学意义(P值均<0.05)。(3)不同白质纤维束及其代表性白质纤维的T_(1)W/T_(2)W值在儿童生后0~2岁期间迅速增加,2岁以后T_(1)W/T_(2)W值变化趋于平缓。LOESS回归拟合曲线显示:不同白质纤维束及其代表性白质纤维T_(1)W/T_(2)W值随年龄变化的折点均为2岁。依据折点将219例儿童划分2个脑白质髓鞘化发育阶段,其中0~2岁为快速发育阶段(85例),>2~8岁为缓慢发育阶段(134例)。不同白质纤维束T_(1)W/T_(2)W值在快速和缓慢发育阶段与年龄的相关性分析显示:在快速发育阶段,连合束、投射束、边缘束、联络束的T_(1)W/T_(2)W值均与年龄呈正相关(rs=0.71、0.60、0.53、0.61,P值均<0.001),而脑干束T_(1)W/T_(2)W值与年龄无相关性(rs=0.20,P>0.05);在缓慢发育阶段各白质纤维束T_(1)W/T_(2)W值与年龄均无相关性(P值均>0.05)。结论基于MRI的T_(1)W/T_(2)W值可用于量化评估儿童脑白质髓鞘化发育进程,可为2岁前儿童髓鞘损伤及发育异常的识别提供影像学参考。展开更多
大气加权平均温度T_(m)是GNSS探测大气可降水量PWV(Precipitable Water Vapor)的关键参数.目前,加权平均温度模型主要包括线性模型和非线性模型.本文基于2011—2015年期间的编号54511北京探空测站的有效探测资料,建立T_(m)与T_(s)的线...大气加权平均温度T_(m)是GNSS探测大气可降水量PWV(Precipitable Water Vapor)的关键参数.目前,加权平均温度模型主要包括线性模型和非线性模型.本文基于2011—2015年期间的编号54511北京探空测站的有效探测资料,建立T_(m)与T_(s)的线性和非线性(一阶傅里叶函数、一元二次函数)关系;利用2016年探空站实测资料对所建模型及常用模型进行对比分析,从RMSE、Bias及波动范围评价参数发现T_(m_G)模型精度高于常用模型,而再分析资料ERA-Interim建立的加权平温度T_(m)_ERA模型和新非线性T_(m)模型精度相差甚小,且误差概率分布趋近于正态分布;因此,新建模型能有效避免了通用Bevis全球模型在特定区域导致的区域性精度偏差问题,尤其在探空站缺乏的区域,可以采用ERA-Interim产品建立T_(m)模型.通过对不同T_(m)模型获取IGS站BJFS的PWV结果与相应时间54511探空站的实测PWV数据进行检验,结果表明不同T_(m)模型引起的PWV的偏差Bias范围在[-5,5]mm,均方根误差RMSE的差异甚小,Bias概率趋于正态分布,稳定性较强,尤其T_(m)_ERA、非线性加权平均温度T_(m_F)、T_(m_P)模型引起的PWV的Bias正态分布更强.展开更多
文摘In this paper,we propose a definition for eigenvalues of odd-order tensors based on some operators.Also,we define the Schur form and the Jordan canonical form of such tensors,and discuss commuting families of tensors.Furthermore,we prove some eigenvalue ine-qualities for Hermitian tensors.Finally,we introduce characteristic polynomials of odd-order tensors.
基金supported by the Zhanjiang Science and Technology Plan Project(No.2022A05022)Science and Technology Development Special Project of Zhanjiang(No.2023A21616)Research Project of Guangdong Ocean University(No.060302112102).
文摘Double perovskite matrix materials have recently attracted considerable interest due to their structural flexibility,ease of doping,and excellent thermal stability.While photoluminescence(PL)studies of rare-earth-doped double perovskites are common,research on their thermoluminescence(TL)properties is less extensive.This study synthesized a series of Y_(2-x)Sm_(x)MgTiO_(6)(0≤x≤0.1)samples using a high-temperature solid-state method.X-ray diffraction(XRD)analysis confirmed a monoclinic crystal structure(space group P2_(1)∕n),with Sm^(3+)ions substituting for Y^(3+)ions in Y_(2)MgTiO_(6).The PL results indicated that the optimal doping concentration was Y_(1.95)Sm_(0.05)MgTiO_(6),exhibiting emission peaks at 568,605,652,and 715 nm under 409 nm blue light excitation.The TL measurements for different doping concentrations showed that the Y_(1.98)Sm_(0.02)MgTiO_(6)phosphors exhibited the strongest TL signals.The TL peaks observed at 530 and 610 K correspond to defects in the matrix and Sm^(3+)dopants,respectively.The T_(m)-T_(stop)analysis revealed that the TL curve of Y_(1.98)Sm_(0.02)MgTiO_(6)phosphors was a superposition of seven peaks.Computerized glow curve deconvolution(CGCD)was performed on the TL of the sample according to the results of three-dimensional thermoluminescence spectra(3D-TL)and T_(m)-T_(stop),and the trap depths in the sample were estimated to range from 0.69 to 1.49 eV.Additionally,the lifetimes of each overlapping peak were calculated using the fitting parameters.Furthermore,the dose-response test showed that the saturation dose of the sample was high(9956 Gy).Therefore,this material can serve as a thermoluminescent dosimeter for high-dose measurements.The saturation dose for the lowest-temperature overlapping peak was 102 Gy,which correlated with its specific energy-level lifetime,whereas the other overlapping peaks also exhibited favorable linear relationships.
文摘目的探讨基于MRI的脑白质纤维束T_(1)与T_(2)加权比(T_(1)W/T_(2)W)在0~8岁儿童脑白质髓鞘化发育进程评估中的应用价值。方法横断面研究。纳入2011年8月—2023年7月西安交通大学第一附属医院219例儿童的头颅MRI资料,其中男125例、女94例,年龄0~8(3.5±2.4)岁。根据儿童发育阶段分类按年龄将219例儿童受检者分为6组:≤6个月组21例,>6个月~1岁组24例,>1~2岁组40例,>2~3岁组23例,>3~4岁组22例,>4~6岁组42例,>6~8岁组47例。应用3.0 T MR扫描仪采集儿童T_(1)加权像及T_(2)加权像,通过外部校准流程计算获得T_(1)W/T_(2)W图,并基于Johns Hopkins University Diffusion Tensor Imaging-81图谱提取联络束、边缘束、投射束、连合束、脑干束5束纤维束及其代表性白质纤维(左侧上纵束、左侧扣带回海马部、左侧内囊前肢、胼胝体膝部及左侧小脑上脚)的T_(1)W/T_(2)W值。观察指标:(1)观察不同年龄组儿童脑白质T_(1)W/T_(2)W图像信号强度的特点,比较各年龄组患儿不同白质纤维束T_(1)W/T_(2)W值的差异;(2)观察不同白质纤维束及其代表性白质纤维的T_(1)W/T_(2)W值随年龄变化的特点,采用局部加权回归散点平滑法(LOESS)绘制回归拟合曲线,确认不同白质纤维束T_(1)W/T_(2)W值随年龄变化的折点,并依此折点划分不同发育阶段,观察不同发育阶段中不同白质纤维束T_(1)W/T_(2)W值与年龄的相关性。结果(1)不同年龄组儿童T_(1)W/T_(2)W图像显示:≤6个月组仅脑桥背侧、内囊后肢及部分皮质脊髓束区域具有较高的信号强度,随着年龄增加,胼胝体压部、胼胝体膝部、皮质脊髓束等区域高信号的范围及强度逐渐增加,从>2~3岁组开始整个大脑皮层下白质区域均具有较高的信号强度。(2)各年龄组间白质纤维束T_(1)W/T_(2)W值比较:脑干束T_(1)W/T_(2)W值,≤6个月组及>6个月~1岁组均低于>2~3岁组及其后的各年龄组,>1~2岁组低于>2~3岁组和>3~4岁组,差异均有统计学意义(P值均<0.05);连合束的T_(1)W/T_(2)W值,≤6个月组和>6个月~1岁组均低于>1~2岁组及其后的各年龄组,>1~2岁组低于>2~3岁组,差异均有统计学意义(P值均<0.05);投射束、边缘束、联络束T_(1)W/T_(2)W值,≤6个月组和>6个月~1岁组均低于>1~2岁组及其后的各年龄组,差异均有统计学意义(P值均<0.05)。(3)不同白质纤维束及其代表性白质纤维的T_(1)W/T_(2)W值在儿童生后0~2岁期间迅速增加,2岁以后T_(1)W/T_(2)W值变化趋于平缓。LOESS回归拟合曲线显示:不同白质纤维束及其代表性白质纤维T_(1)W/T_(2)W值随年龄变化的折点均为2岁。依据折点将219例儿童划分2个脑白质髓鞘化发育阶段,其中0~2岁为快速发育阶段(85例),>2~8岁为缓慢发育阶段(134例)。不同白质纤维束T_(1)W/T_(2)W值在快速和缓慢发育阶段与年龄的相关性分析显示:在快速发育阶段,连合束、投射束、边缘束、联络束的T_(1)W/T_(2)W值均与年龄呈正相关(rs=0.71、0.60、0.53、0.61,P值均<0.001),而脑干束T_(1)W/T_(2)W值与年龄无相关性(rs=0.20,P>0.05);在缓慢发育阶段各白质纤维束T_(1)W/T_(2)W值与年龄均无相关性(P值均>0.05)。结论基于MRI的T_(1)W/T_(2)W值可用于量化评估儿童脑白质髓鞘化发育进程,可为2岁前儿童髓鞘损伤及发育异常的识别提供影像学参考。
文摘大气加权平均温度T_(m)是GNSS探测大气可降水量PWV(Precipitable Water Vapor)的关键参数.目前,加权平均温度模型主要包括线性模型和非线性模型.本文基于2011—2015年期间的编号54511北京探空测站的有效探测资料,建立T_(m)与T_(s)的线性和非线性(一阶傅里叶函数、一元二次函数)关系;利用2016年探空站实测资料对所建模型及常用模型进行对比分析,从RMSE、Bias及波动范围评价参数发现T_(m_G)模型精度高于常用模型,而再分析资料ERA-Interim建立的加权平温度T_(m)_ERA模型和新非线性T_(m)模型精度相差甚小,且误差概率分布趋近于正态分布;因此,新建模型能有效避免了通用Bevis全球模型在特定区域导致的区域性精度偏差问题,尤其在探空站缺乏的区域,可以采用ERA-Interim产品建立T_(m)模型.通过对不同T_(m)模型获取IGS站BJFS的PWV结果与相应时间54511探空站的实测PWV数据进行检验,结果表明不同T_(m)模型引起的PWV的偏差Bias范围在[-5,5]mm,均方根误差RMSE的差异甚小,Bias概率趋于正态分布,稳定性较强,尤其T_(m)_ERA、非线性加权平均温度T_(m_F)、T_(m_P)模型引起的PWV的Bias正态分布更强.
