This study aims to investigate the polar decomposition of tensors with the Einstein product for thefirst time.The polar decomposition of tensors can be computed using the singular value decomposition of the tensors wit...This study aims to investigate the polar decomposition of tensors with the Einstein product for thefirst time.The polar decomposition of tensors can be computed using the singular value decomposition of the tensors with the Einstein product.In the following,some iterative methods forfinding the polar decomposi-tion of matrices have been developed into iterative methods to compute the polar decomposition of tensors.Then,we propose a novel parametric iterative method tofind the polar decomposition of tensors.Under the obtained conditions,we prove that the proposed parametric method has the order of convergence four.In every iteration of the proposed method,only four Einstein products are required,while other iterative methods need to calculate multiple Einstein products and one tensor inversion in each iteration.Thus,the new method is superior in terms of efficiency index.Finally,the numerical comparisons performed among several well-known methods,show that the proposed method is remarkably efficient and accurate.展开更多
On the basis of the vector formula of the Newton’s law for a viscous liquid and the integrated vector form of the equation of an impulse for a viscous liquid for resistance and carrying power of a profile of any form...On the basis of the vector formula of the Newton’s law for a viscous liquid and the integrated vector form of the equation of an impulse for a viscous liquid for resistance and carrying power of a profile of any form and the big length dependences are found in a stream. Application of the found dependences at a circulating flow of the cylinder located across a stream is showed. The analysis of a tensor of viscosity for laminar and turbulent flow is carried out.展开更多
The arcuate fasciculus is a critical component of the neural substrate of human language function.Surgical resection of glioma adjacent to the arcuate fasciculus likely damages this region.In this study,we evaluated t...The arcuate fasciculus is a critical component of the neural substrate of human language function.Surgical resection of glioma adjacent to the arcuate fasciculus likely damages this region.In this study,we evaluated the outcome of surgical resection of glioma adjacent to the arcuate fasciculus under the guidance of magnetic resonance imaging and diffusion tensor imaging,and we aimed to identify the risk factors for postoperative linguistic deficit.In total,54 patients with primary glioma adjacent to the arcuate fasciculus were included in this observational study.These patients comprised 38 men and 16 women(aged 43±11 years).All patients underwent surgical resenction of glioma under the guidance of magnetic resonance imaging and diffusion tensor imaging.Intraoperative images were updated when necessary for further resection.The gross total resection rate of the 54 patients increased from 38.9%to 70.4%by intraoperative magnetic resonance imaging.Preoperative language function and glioma-to-arcuate fasciculus distance were associated with poor language outcome.Multivariable logistic regression analyses showed that glioma-to-arcuate fasciculus distance was the major independent risk factor for poor outcome.The cutoff point of glioma-to-arcuate fasciculus distance for poor outcome was 3.2 mm.These findings suggest that intraoperative magnetic resonance imaging combined with diffusion tensor imaging of the arcuate fasciculus can help optimize tumor resection and result in the least damage to the arcuate fasciculus.Notably,glioma-to-arcuate fasciculus distance is a key independent risk factor for poor postoperative language outcome.This study was approved by the Ethics Committee of the Chinese PLA General Hospital,China(approval No.S2014-096-01)on October 11,2014.展开更多
According to clinical statistics,the mortality of patients with early brainstem hemorrhage is high.In this study,we established rat models of brainstem hemorrhage by injecting type Ⅶ collagenase into the right basote...According to clinical statistics,the mortality of patients with early brainstem hemorrhage is high.In this study,we established rat models of brainstem hemorrhage by injecting type Ⅶ collagenase into the right basotegmental pontine and investigated the pathological changes of early brainstem hemorrhage using multi-sequence magnetic resonance imaging and histopathological methods.We found that brainstem hematoma gradually formed in the injured rats over the first 3 days and then reduced after 7 days.The edema that occurred was mainly of the vasogenic type.No complete myelin sheath structure was found around the focus of the brainstem hemorrhage.The integrity and continuity of nerve fibers gradually deteriorated over the first 7 days.Neuronal degeneration was mild in the first 3 days and then obviously aggravated on the 7^(th)day.Inflammatory cytokines,interleukin-1β,and tumor necrosis factorαappeared on the 1st day after intracerebral hemorrhage,reached peak levels on the 3^(rd)day,and decreased from the 7^(th)day.Our findings show the characteristics of the progression of early brainstem hemorrhage.展开更多
A study on the joint channel and symbol estimation issue is provided for two hop relay networks which employ the amplify-and-forward(AF)relaying approach.The encoding scheme at the source node introduces the time-doma...A study on the joint channel and symbol estimation issue is provided for two hop relay networks which employ the amplify-and-forward(AF)relaying approach.The encoding scheme at the source node introduces the time-domain spreading with a time-varying linear constellation precoding.Then,a set of amplifying factors matrices is utilized by the relays to amplify and forward the received data to the destination.The received signal at the destination can be construe ted as a fourth-order tensor model,which is referred to as the nested parallel factor(PARAFAC)model.And then,we present a novel Levenberg-Marquardt(LM)algorithm based on this tensor model.The proposed method does not require complex signal processing at the relay,which effectively reduces the burden of relay.As a semi-blind method,which does not require the pilot signal,the proposed receiver can jointly recover the channels and information symbols.Moreover,the proposed semi-blind receiver is robust as it can work in different wireless channel scenarios.Simulations are conducted to demonstrate the efficiency of the proposed semi-blind approach.展开更多
A characteristic tensor is defined using stress tensor averaged in a small circular domain at the crack tip and multiplied by the root of domain radius.It possesses the original stress tensor characteristics and has a...A characteristic tensor is defined using stress tensor averaged in a small circular domain at the crack tip and multiplied by the root of domain radius.It possesses the original stress tensor characteristics and has a simple relationship with conventional fracture-mechanics parameters.Therefore,it can be used to estimate stress intensity factors(SIFs)for cracks of arbitrary shape subjected to multiaxial stress loads.A characteristic tensor can also be used to estimate SIFs for kinked cracks.This study examines the relation between a characteristic tensor and SIFs to demonstrate the correlation between the characteristic tensor and fracture-mechanics parameters.Consequently,a single straight crack and a kinked crack of finite length existing in a twodimensional,infinite isotropic elastic body in a plane stress state,were considered to investigate the properties of the characteristic tensor under mixed-mode loadings.To demonstrate the practical utility of the characteristic tensor,the stress distribution obtained through finite element analysis(FEA)was used to estimate mixed-mode SIFs,and the values of estimated SIFs were compared with those obtained using an analytical solution.Results demonstrate that SIFs estimated under mixed-mode loadings exhibit a good agreement with the analytical values.This indicates that the proposed characteristictensor-based approach is effective in extracting features of singular stress fields at crack tips,and can be employed to estimate values of fracture-mechanics parameters,such as SIFs.Owing to its simplicity,the proposed approach can be easily incorporated in commercial FE codes for practical applications to simulate the crack-growth problem under both static and dynamic loading scenarios.The excellent applicability of the characteristic tensor greatly contributes to efficiency of the design process in industries.展开更多
基金funded by Iran National Science Foundation(INSF)under project No.4013447.
文摘This study aims to investigate the polar decomposition of tensors with the Einstein product for thefirst time.The polar decomposition of tensors can be computed using the singular value decomposition of the tensors with the Einstein product.In the following,some iterative methods forfinding the polar decomposi-tion of matrices have been developed into iterative methods to compute the polar decomposition of tensors.Then,we propose a novel parametric iterative method tofind the polar decomposition of tensors.Under the obtained conditions,we prove that the proposed parametric method has the order of convergence four.In every iteration of the proposed method,only four Einstein products are required,while other iterative methods need to calculate multiple Einstein products and one tensor inversion in each iteration.Thus,the new method is superior in terms of efficiency index.Finally,the numerical comparisons performed among several well-known methods,show that the proposed method is remarkably efficient and accurate.
文摘On the basis of the vector formula of the Newton’s law for a viscous liquid and the integrated vector form of the equation of an impulse for a viscous liquid for resistance and carrying power of a profile of any form and the big length dependences are found in a stream. Application of the found dependences at a circulating flow of the cylinder located across a stream is showed. The analysis of a tensor of viscosity for laminar and turbulent flow is carried out.
基金Clinical Research Fostering Fund of Chinese PLA General Hospital in China,No.2017FC-TSYS-2012(to FYL)Youth Program of the Natural Science Foundation of Hainan Province of China,No.819QN378(to FYL)+2 种基金the National Natural Science Foundation of China,No.81771481(to XLC)China National Key R&D Program,No.2018YFC1312602(to XLC)National Clinical Research Center for Geriatric Diseases of China,No.NCRCGPLAGH-2017007(to XLC)。
文摘The arcuate fasciculus is a critical component of the neural substrate of human language function.Surgical resection of glioma adjacent to the arcuate fasciculus likely damages this region.In this study,we evaluated the outcome of surgical resection of glioma adjacent to the arcuate fasciculus under the guidance of magnetic resonance imaging and diffusion tensor imaging,and we aimed to identify the risk factors for postoperative linguistic deficit.In total,54 patients with primary glioma adjacent to the arcuate fasciculus were included in this observational study.These patients comprised 38 men and 16 women(aged 43±11 years).All patients underwent surgical resenction of glioma under the guidance of magnetic resonance imaging and diffusion tensor imaging.Intraoperative images were updated when necessary for further resection.The gross total resection rate of the 54 patients increased from 38.9%to 70.4%by intraoperative magnetic resonance imaging.Preoperative language function and glioma-to-arcuate fasciculus distance were associated with poor language outcome.Multivariable logistic regression analyses showed that glioma-to-arcuate fasciculus distance was the major independent risk factor for poor outcome.The cutoff point of glioma-to-arcuate fasciculus distance for poor outcome was 3.2 mm.These findings suggest that intraoperative magnetic resonance imaging combined with diffusion tensor imaging of the arcuate fasciculus can help optimize tumor resection and result in the least damage to the arcuate fasciculus.Notably,glioma-to-arcuate fasciculus distance is a key independent risk factor for poor postoperative language outcome.This study was approved by the Ethics Committee of the Chinese PLA General Hospital,China(approval No.S2014-096-01)on October 11,2014.
基金supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region, No. 2020D01A13 (to CWW)Chengdu Science and Technology Bureau, No. 2019-YF05-00511-SN (to MT)1.3.5 Project for Disciplines of Excellence, West China Hospital, Sichuan University, Nos. ZY2016102 (to MT), and ZY2016203 (to CY)
文摘According to clinical statistics,the mortality of patients with early brainstem hemorrhage is high.In this study,we established rat models of brainstem hemorrhage by injecting type Ⅶ collagenase into the right basotegmental pontine and investigated the pathological changes of early brainstem hemorrhage using multi-sequence magnetic resonance imaging and histopathological methods.We found that brainstem hematoma gradually formed in the injured rats over the first 3 days and then reduced after 7 days.The edema that occurred was mainly of the vasogenic type.No complete myelin sheath structure was found around the focus of the brainstem hemorrhage.The integrity and continuity of nerve fibers gradually deteriorated over the first 7 days.Neuronal degeneration was mild in the first 3 days and then obviously aggravated on the 7^(th)day.Inflammatory cytokines,interleukin-1β,and tumor necrosis factorαappeared on the 1st day after intracerebral hemorrhage,reached peak levels on the 3^(rd)day,and decreased from the 7^(th)day.Our findings show the characteristics of the progression of early brainstem hemorrhage.
基金the National Natural Science Foundation of China(Nos.61601414 and 61701448)the National Key Research and Development Program of China(No.2016YFB0502001)the Fundamental Research Fund for the Central Universities(Nos.2018CUCTJ082 and CUC18A007)。
文摘A study on the joint channel and symbol estimation issue is provided for two hop relay networks which employ the amplify-and-forward(AF)relaying approach.The encoding scheme at the source node introduces the time-domain spreading with a time-varying linear constellation precoding.Then,a set of amplifying factors matrices is utilized by the relays to amplify and forward the received data to the destination.The received signal at the destination can be construe ted as a fourth-order tensor model,which is referred to as the nested parallel factor(PARAFAC)model.And then,we present a novel Levenberg-Marquardt(LM)algorithm based on this tensor model.The proposed method does not require complex signal processing at the relay,which effectively reduces the burden of relay.As a semi-blind method,which does not require the pilot signal,the proposed receiver can jointly recover the channels and information symbols.Moreover,the proposed semi-blind receiver is robust as it can work in different wireless channel scenarios.Simulations are conducted to demonstrate the efficiency of the proposed semi-blind approach.
文摘A characteristic tensor is defined using stress tensor averaged in a small circular domain at the crack tip and multiplied by the root of domain radius.It possesses the original stress tensor characteristics and has a simple relationship with conventional fracture-mechanics parameters.Therefore,it can be used to estimate stress intensity factors(SIFs)for cracks of arbitrary shape subjected to multiaxial stress loads.A characteristic tensor can also be used to estimate SIFs for kinked cracks.This study examines the relation between a characteristic tensor and SIFs to demonstrate the correlation between the characteristic tensor and fracture-mechanics parameters.Consequently,a single straight crack and a kinked crack of finite length existing in a twodimensional,infinite isotropic elastic body in a plane stress state,were considered to investigate the properties of the characteristic tensor under mixed-mode loadings.To demonstrate the practical utility of the characteristic tensor,the stress distribution obtained through finite element analysis(FEA)was used to estimate mixed-mode SIFs,and the values of estimated SIFs were compared with those obtained using an analytical solution.Results demonstrate that SIFs estimated under mixed-mode loadings exhibit a good agreement with the analytical values.This indicates that the proposed characteristictensor-based approach is effective in extracting features of singular stress fields at crack tips,and can be employed to estimate values of fracture-mechanics parameters,such as SIFs.Owing to its simplicity,the proposed approach can be easily incorporated in commercial FE codes for practical applications to simulate the crack-growth problem under both static and dynamic loading scenarios.The excellent applicability of the characteristic tensor greatly contributes to efficiency of the design process in industries.
