The vectorial evolution of light polarization can reveal the microstructure and anisotropy of a medium beyond what can be obtained from measuring light intensity alone.However,polarization imaging in reflection geomet...The vectorial evolution of light polarization can reveal the microstructure and anisotropy of a medium beyond what can be obtained from measuring light intensity alone.However,polarization imaging in reflection geometry,which is ubiquitous and often preferred in diverse applications,has often suffered from poor and even incorrect characterization of anisotropic media.We present reciprocal polarization imaging of complex media in reflection geometry with the reciprocal polar decomposition of backscattering Mueller matrices enforcing reciprocity.We demonstrate that reciprocal polarization imaging of complex chiral and anisotropic media ac-curately quantifies their anisotropic properties in reflection geometry,whereas traditional approaches encounter difficulties and produce inferior and often erroneous results from the violation of reciprocity.In particular,reciprocal polarization imaging provides a consistent characterization of complex media of different thicknesses,accurately measures the optical activity and glucose concentration of turbid media in reflection,and discriminates between cancerous and normal tissue with even stronger contrast than forward measurement.Reciprocal polarization imaging promises broad applications of polarization optics ranging from remote sensing to bio-medicine in reflection geometries,especially in in vivo biomedical imaging,where reflection is the only feasible geometry.展开更多
Soil moisture is a key parameter in the exchange of energy and water between the land surface and the atmosphere.This parameter plays an important role in the dynamics of permafrost on the Qinghai-Xizang Plateau,China...Soil moisture is a key parameter in the exchange of energy and water between the land surface and the atmosphere.This parameter plays an important role in the dynamics of permafrost on the Qinghai-Xizang Plateau,China,as well as in the related ecological and hydrological processes.However,the region's complex terrain and extreme climatic conditions result in low-accuracy soil moisture estimations using traditional remote sensing techniques.Thus,this study considered parameters of the backscatter coefficient of Sentinel-1A ground range detected(GRD)data,the polarization decomposition parameters of Sentinel-1A single-look complex(SLC)data,the normalized difference vegetation index(NDVI)based on Sentinel-2B data,and the topographic factors based on digital elevation model(DEM)data.By combining these parameters with a machine learning model,we established a feature selection rule.A cumulative importance threshold was derived for feature variables,and those variables that failed to meet the threshold were eliminated based on variations in the coefficient of determination(R^(2))and the unbiased root mean square error(ubRMSE).The eight most influential variables were selected and combined with the CatBoost model for soil moisture inversion,and the SHapley Additive exPlanations(SHAP)method was used to analyze the importance of these variables.The results demonstrated that the optimized model significantly improved the accuracy of soil moisture inversion.Compared to the unfiltered model,the optimal feature combination led to a 0.09 increase in R^(2)and a 0.7%reduction in ubRMSE.Ultimately,the optimized model achieved a R²of 0.87 and an ubRMSE of 5.6%.Analysis revealed that soil particle size had significant impact on soil water retention capacity.The impact of vegetation on the estimated soil moisture on the Qinghai-Xizang Plateau was considerable,demonstrating a significant positive correlation.Moreover,the microtopographical features of hummocks interfered with soil moisture estimation,indicating that such terrain effects warrant increased attention in future studies within the permafrost regions.The developed method not only enhances the accuracy of soil moisture retrieval in the complex terrain of the Qinghai-Xizang Plateau,but also exhibits high computational efficiency(with a relative time reduction of 18.5%),striking an excellent balance between accuracy and efficiency.This approach provides a robust framework for efficient soil moisture monitoring in remote areas with limited ground data,offering critical insights for ecological conservation,water resource management,and climate change adaptation on the Qinghai-Xizang Plateau.展开更多
Previous studies revealed that the error of pole coordinate prediction will significantly increase for a prediction period longer than 100 days, and this is mainly caused by short period oscillations. Empirical mode d...Previous studies revealed that the error of pole coordinate prediction will significantly increase for a prediction period longer than 100 days, and this is mainly caused by short period oscillations. Empirical mode decomposition （EMD）, which is increasingly popular and has advantages over classical wavelet decomposition, can be used to remove short period variations from observed time series of pole co- ordinates. A hybrid model combing EMD and extreme learning machine （ELM）, where high frequency signals are removed and processed time series is then modeled and predicted, is summarized in this paper. The prediction performance of the hybrid model is compared with that of the ELM-only method created from original time series. The results show that the proposed hybrid model outperforms the pure ELM method for both short-term and long-term prediction of pole coordinates. The improvement of prediction accuracy up to 360 days in the future is found to be 24.91% and 26.79% on average in terms of mean absolute error （MAE） for the xp and yp components of pole coordinates, respectively.展开更多
In this paper, the polar decomposition of a deformation gradient tensor is analyzed in detail. The four new methods for polar decompositioncomputation are given: (1) the iterated method, (2) the principal invariant...In this paper, the polar decomposition of a deformation gradient tensor is analyzed in detail. The four new methods for polar decompositioncomputation are given: (1) the iterated method, (2) the principal invariant's method, (3) the principal rotation axis' s method, (4) the coordinate transformation's method. The iterated method makes it possible to establish the nonlinear finite element method based on polar decomposition. Furthermore, the material time derivatives of the stretch tensor and the rotation tensor are obtained by explicit and simple expressions.展开更多
We developed a forest type classification technology for the Daxing＇an Mountains of northeast China using multisource remote sensing data.A SPOT-5 image and two temporal images of RADARSAT-2 full-polarization SAR wer...We developed a forest type classification technology for the Daxing＇an Mountains of northeast China using multisource remote sensing data.A SPOT-5 image and two temporal images of RADARSAT-2 full-polarization SAR were used to identify forest types in the Pangu Forest Farm of the Daxing＇an Mountains.Forest types were identified using random forest（RF） classification with the following data combination types： SPOT-5 alone,SPOT-5 and SAR images in August or November,and SPOT-5 and two temporal SAR images.We identified many forest types using a combination of multitemporal SAR and SPOT-5 images,including Betula platyphylla,Larix gmelinii,Pinus sylvestris and Picea koraiensis forests.The accuracy of classification exceeded 88% and improved by 12% when compared to the classification results obtained using SPOT data alone.RF classification using a combination of multisource remote sensing data improved classification accuracy compared to that achieved using single-source remote sensing data.展开更多
In this article, we give an operator transform T （＊） from class A operator to the class of hyponormal operators. It is different from the operator transform T defined by M. Ch and T. Yamazaki. Then, we show that σ...In this article, we give an operator transform T （＊） from class A operator to the class of hyponormal operators. It is different from the operator transform T defined by M. Ch and T. Yamazaki. Then, we show that σ（T ） = σ（ T （＊）） and σa（T ）／{0} = σa（ T （＊））／{0}, in case T belongs to class A. Next, we obtain some relations between T and T （9）.展开更多
Suppose A,B and C are the bounded linear operators on a Hilbert space H, when A has a generalized inverse A - such that (AA -) *=AA - and B has a generalized inverse B - such that (B -B) *=B -B,the general cha...Suppose A,B and C are the bounded linear operators on a Hilbert space H, when A has a generalized inverse A - such that (AA -) *=AA - and B has a generalized inverse B - such that (B -B) *=B -B,the general characteristic forms for the critical points of the map F p:X→‖ A X B-C ‖ p p (1<p<∞), have been obtained, it is a generalization for P J Maher's result about p=2. Similarly, the same question has been discussed for several operators.展开更多
In this paper,we give out a further extension of the relations between two famous inequalities(B r 2 A p B r 2) r p+r≥B r and Ap≥(A p 2 B r A p 2) p p+r,which can yield the result of Yamazaki and Yanagida's.
In this paper, we prove that the norm closure of all linear combinations of two unitary operators is equal to the norm closure of all invertible operators in B(H). We apply the results to frame representations and giv...In this paper, we prove that the norm closure of all linear combinations of two unitary operators is equal to the norm closure of all invertible operators in B(H). We apply the results to frame representations and give some simple and alternative proofis of the propositions in 'P. G. Casazza, Every frame is a sum of three (but not two) orthonormal bases-and other frame representations, J. Fourier Anal. Appl., 4(6)(1998), 727-732.'展开更多
In this paper,we propose a general algorithmic framework to solve a class of optimization problems on the product of complex Stiefel manifolds based on the matrix polar decomposition.We establish the weak convergence,...In this paper,we propose a general algorithmic framework to solve a class of optimization problems on the product of complex Stiefel manifolds based on the matrix polar decomposition.We establish the weak convergence,global convergence and linear convergence properties,respectively,of this general algorithmic approach using theŁojasiewicz gradient inequality and the Morse–Bott property.This general algorithmic approach and its convergence results are applied to the simultaneous approximate tensor diagonalization problem and the simultaneous approximate tensor compression problem,which include as special cases the low rank orthogonal approximation,best rank-1 approximation and low multilinear rank approximation for higher order complex tensors.We also present a variant of this general algorithmic framework to solve a symmetric version of this class of optimization models,which essentially optimizes over a single Stiefel manifold.We establish its weak convergence,global convergence and linear convergence properties in a similar way.This symmetric variant and its convergence results are applied to the simultaneous approximate symmetric tensor diagonalization,which includes as special cases the low rank symmetric orthogonal approximation and best symmetric rank-1 approximation for higher order complex symmetric tensors.It turns out that well-known algorithms such as LROAT,S-LROAT,HOPM and S-HOPM are all special cases of this general algorithmic framework and its symmetric variant,and our convergence results subsume the results found in the literature designed for those special cases.All the algorithms and convergence results in this paper are straightforwardly applicable to the real case.展开更多
In this paper,a new matrix decomposition called the weighted polar decomposition is considered.Two uniqueness theorems of weighted polar decomposition are presented,and the best approximation property of weighted unit...In this paper,a new matrix decomposition called the weighted polar decomposition is considered.Two uniqueness theorems of weighted polar decomposition are presented,and the best approximation property of weighted unitary polar factor and perturbation bounds for weighted polar decomposition are also studied.展开更多
This study explored different methodologiesusing a C-band RADARSAT-2 quad-polarized SyntheticAperture Radar （SAR） image located over China＇s YellowSea to investigate polarization decomposition parametersfor identif...This study explored different methodologiesusing a C-band RADARSAT-2 quad-polarized SyntheticAperture Radar （SAR） image located over China＇s YellowSea to investigate polarization decomposition parametersfor identifying mixed floating pollutants from a complexocean background. It was found that solitary polarizationdecomposition did not meet the demand for detecting andclassifying multiple floating pollutants, even after applyinga polarized SAR image. Furthermore, considering thatYamaguchi decomposition is sensitive to vegetation andthe algal variety Enteromorpha prolifera, while H/A/alphadecomposition is sensitive to oil spills, a combination ofparameters which was deduced from these two decom-positions was proposed for marine environmental mon-itoring of mixed floating sea surface pollutants. Acombination of volume scattering, surface scattering, andscattering entropy was the best indicator for classifyingmixed floating pollutants from a complex ocean back-ground. The Kappa coefficients for Enteromorpha pro-lifera and oil spills were 0.7514 and 0.8470, respectively,evidence that the composite polarized parameters based onquad-polarized SAR imagery proposed in this research isan effective monitoring method for complex marinepollution.展开更多
Let T = U｜T｜ be the polar decomposition of a bounded linear operator T on a Hilbert space. The transformation T = ｜T｜^1/2 U｜T｜^1/2 is called the Aluthge transformation and Tn means the n-th Aluthge transformatio...Let T = U｜T｜ be the polar decomposition of a bounded linear operator T on a Hilbert space. The transformation T = ｜T｜^1/2 U｜T｜^1/2 is called the Aluthge transformation and Tn means the n-th Aluthge transformation. Similarly, the transformation T（＊）=｜T＊｜^1/2 U｜T＊｜＆1/2 is called the ＊-Aluthge transformation and Tn^（＊） means the n-th ＊-Aluthge transformation. In this paper, firstly, we show that T（＊） = UV｜T^（＊）｜ is the polar decomposition of T（＊）, where ｜T｜^1/2 ｜T^＊｜^1/2 = V｜｜T｜^1/2 ｜T^＊｜^1/2｜ is the polar decomposition. Secondly, we show that T（＊） = U｜T^（＊）｜ if and only if T is binormal, i.e., [｜T｜, ｜T^＊｜]=0, where [A, B] = AB - BA for any operator A and B. Lastly, we show that Tn^（＊） is binormal for all non-negative integer n if and only if T is centered, and so on.展开更多
Conversion of the Reed–Muller（RM） expansion between two different polarities is an important step in the synthesis and optimization of RM circuits. By investigating XOR decomposition, a new conversion algorithm is ...Conversion of the Reed–Muller（RM） expansion between two different polarities is an important step in the synthesis and optimization of RM circuits. By investigating XOR decomposition, a new conversion algorithm is proposed to convert MPRM expansion from one polarity to another. First, the relationship between XOR decomposition and mixed polarity is set up. Second, based on this, the operation relation of term coefficients between the two polarities is derived to realize MPRM expansion conversion. And finally, with the MCNC Benchmark, the resultsofouralgorithmshowthatitismoresuitablefordealingwithMPRMexpansionwithmoreterms.Compared to the previous tabular technique, the conversion efficiency is improved up to approximately 44.39%.展开更多
This paper presents a spectral approach to compress dynamic animation consisting of a sequence of homeomorphic manifold meshes. Our new approach directly compresses the field of deformation gradient defined on the sur...This paper presents a spectral approach to compress dynamic animation consisting of a sequence of homeomorphic manifold meshes. Our new approach directly compresses the field of deformation gradient defined on the surface mesh, by decomposing it into rigid-body motion （rotation） and non-rigid-body deformation （stretching） through polar decomposition. It is known that the rotation group has the algebraic topology of 3D ring, which is different from other operations like stretching. Thus we compress these two groups separately, by using Manifold Harmonics Transform to drop out their high-frequency details. Our experimental result shows that the proposed method achieves a good balance between tile reconstruction quality and the compression ratio. We compare our results quantitatively with other existing approaches on animation compression, using standard measurement criteria.展开更多
In this note we present a perturbation bound of unitary polar factors.We add the orthogonalprojectors into the bound;as a result,a uniform perturbation bound of Q-factors is obtained,and the previousbounds are improved.
基金upported by the Natural Science Foundation of Zhejiang Province(Grant No.LZ16H180002)the National Natural Science Foundation of China(Grant No.61905181)+1 种基金the Wenzhou Municipal Science and Technology Bureau(Grant No.ZS2017022)the National Science Foundation of the U.S.(Grant No.1607664).
文摘The vectorial evolution of light polarization can reveal the microstructure and anisotropy of a medium beyond what can be obtained from measuring light intensity alone.However,polarization imaging in reflection geometry,which is ubiquitous and often preferred in diverse applications,has often suffered from poor and even incorrect characterization of anisotropic media.We present reciprocal polarization imaging of complex media in reflection geometry with the reciprocal polar decomposition of backscattering Mueller matrices enforcing reciprocity.We demonstrate that reciprocal polarization imaging of complex chiral and anisotropic media ac-curately quantifies their anisotropic properties in reflection geometry,whereas traditional approaches encounter difficulties and produce inferior and often erroneous results from the violation of reciprocity.In particular,reciprocal polarization imaging provides a consistent characterization of complex media of different thicknesses,accurately measures the optical activity and glucose concentration of turbid media in reflection,and discriminates between cancerous and normal tissue with even stronger contrast than forward measurement.Reciprocal polarization imaging promises broad applications of polarization optics ranging from remote sensing to bio-medicine in reflection geometries,especially in in vivo biomedical imaging,where reflection is the only feasible geometry.
基金supported by the Scientific Research Foundation for High-level Talents of Anhui University of Science and Technology(13230550)the Coal Industry Engineering Research Center of Mining Area Environmental and Disaster Cooperative Monitoring,Anhui University of Science and Technology(KSXTJC202305)+1 种基金the State Key Laboratory of Geodesy and Earth's Dynamics,Innovation Academy for Precision Measurement Science and Technology(SKLGED2023-5-1)the China Postdoctoral Science Foundation(2023M733604).
文摘Soil moisture is a key parameter in the exchange of energy and water between the land surface and the atmosphere.This parameter plays an important role in the dynamics of permafrost on the Qinghai-Xizang Plateau,China,as well as in the related ecological and hydrological processes.However,the region's complex terrain and extreme climatic conditions result in low-accuracy soil moisture estimations using traditional remote sensing techniques.Thus,this study considered parameters of the backscatter coefficient of Sentinel-1A ground range detected(GRD)data,the polarization decomposition parameters of Sentinel-1A single-look complex(SLC)data,the normalized difference vegetation index(NDVI)based on Sentinel-2B data,and the topographic factors based on digital elevation model(DEM)data.By combining these parameters with a machine learning model,we established a feature selection rule.A cumulative importance threshold was derived for feature variables,and those variables that failed to meet the threshold were eliminated based on variations in the coefficient of determination(R^(2))and the unbiased root mean square error(ubRMSE).The eight most influential variables were selected and combined with the CatBoost model for soil moisture inversion,and the SHapley Additive exPlanations(SHAP)method was used to analyze the importance of these variables.The results demonstrated that the optimized model significantly improved the accuracy of soil moisture inversion.Compared to the unfiltered model,the optimal feature combination led to a 0.09 increase in R^(2)and a 0.7%reduction in ubRMSE.Ultimately,the optimized model achieved a R²of 0.87 and an ubRMSE of 5.6%.Analysis revealed that soil particle size had significant impact on soil water retention capacity.The impact of vegetation on the estimated soil moisture on the Qinghai-Xizang Plateau was considerable,demonstrating a significant positive correlation.Moreover,the microtopographical features of hummocks interfered with soil moisture estimation,indicating that such terrain effects warrant increased attention in future studies within the permafrost regions.The developed method not only enhances the accuracy of soil moisture retrieval in the complex terrain of the Qinghai-Xizang Plateau,but also exhibits high computational efficiency(with a relative time reduction of 18.5%),striking an excellent balance between accuracy and efficiency.This approach provides a robust framework for efficient soil moisture monitoring in remote areas with limited ground data,offering critical insights for ecological conservation,water resource management,and climate change adaptation on the Qinghai-Xizang Plateau.
基金supported by Chinese Academy of Sciences(No.201491)“Light of West China” Program(201491)
文摘Previous studies revealed that the error of pole coordinate prediction will significantly increase for a prediction period longer than 100 days, and this is mainly caused by short period oscillations. Empirical mode decomposition （EMD）, which is increasingly popular and has advantages over classical wavelet decomposition, can be used to remove short period variations from observed time series of pole co- ordinates. A hybrid model combing EMD and extreme learning machine （ELM）, where high frequency signals are removed and processed time series is then modeled and predicted, is summarized in this paper. The prediction performance of the hybrid model is compared with that of the ELM-only method created from original time series. The results show that the proposed hybrid model outperforms the pure ELM method for both short-term and long-term prediction of pole coordinates. The improvement of prediction accuracy up to 360 days in the future is found to be 24.91% and 26.79% on average in terms of mean absolute error （MAE） for the xp and yp components of pole coordinates, respectively.
基金the National Natural Science Foundation of Chinathe Natural Science Foundation of Jiangxi of China in 1998.
文摘In this paper, the polar decomposition of a deformation gradient tensor is analyzed in detail. The four new methods for polar decompositioncomputation are given: (1) the iterated method, (2) the principal invariant's method, (3) the principal rotation axis' s method, (4) the coordinate transformation's method. The iterated method makes it possible to establish the nonlinear finite element method based on polar decomposition. Furthermore, the material time derivatives of the stretch tensor and the rotation tensor are obtained by explicit and simple expressions.
基金supported by the National Natural Science Foundation of China(Nos.31500518,31500519,and 31470640)
文摘We developed a forest type classification technology for the Daxing＇an Mountains of northeast China using multisource remote sensing data.A SPOT-5 image and two temporal images of RADARSAT-2 full-polarization SAR were used to identify forest types in the Pangu Forest Farm of the Daxing＇an Mountains.Forest types were identified using random forest（RF） classification with the following data combination types： SPOT-5 alone,SPOT-5 and SAR images in August or November,and SPOT-5 and two temporal SAR images.We identified many forest types using a combination of multitemporal SAR and SPOT-5 images,including Betula platyphylla,Larix gmelinii,Pinus sylvestris and Picea koraiensis forests.The accuracy of classification exceeded 88% and improved by 12% when compared to the classification results obtained using SPOT data alone.RF classification using a combination of multisource remote sensing data improved classification accuracy compared to that achieved using single-source remote sensing data.
基金supported by Science Foundation of Ministry of Education of China (208081)Technology and pioneering project in Henan Provice (102300410012)Education Foundation of Henan Province (2007110016, 2008B110006)
文摘In this article, we give an operator transform T （＊） from class A operator to the class of hyponormal operators. It is different from the operator transform T defined by M. Ch and T. Yamazaki. Then, we show that σ（T ） = σ（ T （＊）） and σa（T ）／{0} = σa（ T （＊））／{0}, in case T belongs to class A. Next, we obtain some relations between T and T （9）.
文摘Suppose A,B and C are the bounded linear operators on a Hilbert space H, when A has a generalized inverse A - such that (AA -) *=AA - and B has a generalized inverse B - such that (B -B) *=B -B,the general characteristic forms for the critical points of the map F p:X→‖ A X B-C ‖ p p (1<p<∞), have been obtained, it is a generalization for P J Maher's result about p=2. Similarly, the same question has been discussed for several operators.
基金Supported by the Natural Science Foundation of the Department of Education of Henan Province（2011A110009）
文摘In this paper,we give out a further extension of the relations between two famous inequalities(B r 2 A p B r 2) r p+r≥B r and Ap≥(A p 2 B r A p 2) p p+r,which can yield the result of Yamazaki and Yanagida's.
文摘In this paper, we prove that the norm closure of all linear combinations of two unitary operators is equal to the norm closure of all invertible operators in B(H). We apply the results to frame representations and give some simple and alternative proofis of the propositions in 'P. G. Casazza, Every frame is a sum of three (but not two) orthonormal bases-and other frame representations, J. Fourier Anal. Appl., 4(6)(1998), 727-732.'
基金supported by the National Natural Science Foundation of China(No.11601371)the Guangdong Basic and Applied Basic Research Foundation(No.2021A1515010232).
文摘In this paper,we propose a general algorithmic framework to solve a class of optimization problems on the product of complex Stiefel manifolds based on the matrix polar decomposition.We establish the weak convergence,global convergence and linear convergence properties,respectively,of this general algorithmic approach using theŁojasiewicz gradient inequality and the Morse–Bott property.This general algorithmic approach and its convergence results are applied to the simultaneous approximate tensor diagonalization problem and the simultaneous approximate tensor compression problem,which include as special cases the low rank orthogonal approximation,best rank-1 approximation and low multilinear rank approximation for higher order complex tensors.We also present a variant of this general algorithmic framework to solve a symmetric version of this class of optimization models,which essentially optimizes over a single Stiefel manifold.We establish its weak convergence,global convergence and linear convergence properties in a similar way.This symmetric variant and its convergence results are applied to the simultaneous approximate symmetric tensor diagonalization,which includes as special cases the low rank symmetric orthogonal approximation and best symmetric rank-1 approximation for higher order complex symmetric tensors.It turns out that well-known algorithms such as LROAT,S-LROAT,HOPM and S-HOPM are all special cases of this general algorithmic framework and its symmetric variant,and our convergence results subsume the results found in the literature designed for those special cases.All the algorithms and convergence results in this paper are straightforwardly applicable to the real case.
文摘In this paper,a new matrix decomposition called the weighted polar decomposition is considered.Two uniqueness theorems of weighted polar decomposition are presented,and the best approximation property of weighted unitary polar factor and perturbation bounds for weighted polar decomposition are also studied.
文摘This study explored different methodologiesusing a C-band RADARSAT-2 quad-polarized SyntheticAperture Radar （SAR） image located over China＇s YellowSea to investigate polarization decomposition parametersfor identifying mixed floating pollutants from a complexocean background. It was found that solitary polarizationdecomposition did not meet the demand for detecting andclassifying multiple floating pollutants, even after applyinga polarized SAR image. Furthermore, considering thatYamaguchi decomposition is sensitive to vegetation andthe algal variety Enteromorpha prolifera, while H/A/alphadecomposition is sensitive to oil spills, a combination ofparameters which was deduced from these two decom-positions was proposed for marine environmental mon-itoring of mixed floating sea surface pollutants. Acombination of volume scattering, surface scattering, andscattering entropy was the best indicator for classifyingmixed floating pollutants from a complex ocean back-ground. The Kappa coefficients for Enteromorpha pro-lifera and oil spills were 0.7514 and 0.8470, respectively,evidence that the composite polarized parameters based onquad-polarized SAR imagery proposed in this research isan effective monitoring method for complex marinepollution.
基金Science Foundation of Minisitry of Education of China (No.208081)
文摘Let T = U｜T｜ be the polar decomposition of a bounded linear operator T on a Hilbert space. The transformation T = ｜T｜^1/2 U｜T｜^1/2 is called the Aluthge transformation and Tn means the n-th Aluthge transformation. Similarly, the transformation T（＊）=｜T＊｜^1/2 U｜T＊｜＆1/2 is called the ＊-Aluthge transformation and Tn^（＊） means the n-th ＊-Aluthge transformation. In this paper, firstly, we show that T（＊） = UV｜T^（＊）｜ is the polar decomposition of T（＊）, where ｜T｜^1/2 ｜T^＊｜^1/2 = V｜｜T｜^1/2 ｜T^＊｜^1/2｜ is the polar decomposition. Secondly, we show that T（＊） = U｜T^（＊）｜ if and only if T is binormal, i.e., [｜T｜, ｜T^＊｜]=0, where [A, B] = AB - BA for any operator A and B. Lastly, we show that Tn^（＊） is binormal for all non-negative integer n if and only if T is centered, and so on.
基金Project supported by the National Natural Science Foundation of China(Nos.61076032,61234002)the Natural Science Foundation of Zhejiang Province(Nos.Z1111219,LY12D06002,LY13F040003)K.C.Wong Magna Fund in Ningbo University
文摘Conversion of the Reed–Muller（RM） expansion between two different polarities is an important step in the synthesis and optimization of RM circuits. By investigating XOR decomposition, a new conversion algorithm is proposed to convert MPRM expansion from one polarity to another. First, the relationship between XOR decomposition and mixed polarity is set up. Second, based on this, the operation relation of term coefficients between the two polarities is derived to realize MPRM expansion conversion. And finally, with the MCNC Benchmark, the resultsofouralgorithmshowthatitismoresuitablefordealingwithMPRMexpansionwithmoreterms.Compared to the previous tabular technique, the conversion efficiency is improved up to approximately 44.39%.
基金Chao Wang, Xiaohu Guo, and Zichun Zhong are partially supported by the National Science Foundation under Grant Nos. IlS- 1149737 and CNS-1012975.
文摘This paper presents a spectral approach to compress dynamic animation consisting of a sequence of homeomorphic manifold meshes. Our new approach directly compresses the field of deformation gradient defined on the surface mesh, by decomposing it into rigid-body motion （rotation） and non-rigid-body deformation （stretching） through polar decomposition. It is known that the rotation group has the algebraic topology of 3D ring, which is different from other operations like stretching. Thus we compress these two groups separately, by using Manifold Harmonics Transform to drop out their high-frequency details. Our experimental result shows that the proposed method achieves a good balance between tile reconstruction quality and the compression ratio. We compare our results quantitatively with other existing approaches on animation compression, using standard measurement criteria.
基金Supported in part by Guangdong Provincial Natural Science Foundation (No.31496)Nature Science Foundation of Guangdong Provincial University Teachers (No.0119)Guangdong Provincial Excellent Talent Foundation (No.Q02084)
文摘In this note we present a perturbation bound of unitary polar factors.We add the orthogonalprojectors into the bound;as a result,a uniform perturbation bound of Q-factors is obtained,and the previousbounds are improved.
