Cross-Project Defect Prediction(CPDP)is a method that utilizes historical data from other source projects to train predictive models for defect prediction in the target project.However,existing CPDP methods only consi...Cross-Project Defect Prediction(CPDP)is a method that utilizes historical data from other source projects to train predictive models for defect prediction in the target project.However,existing CPDP methods only consider linear correlations between features(indicators)of the source and target projects.These models are not capable of evaluating non-linear correlations between features when they exist,for example,when there are differences in data distributions between the source and target projects.As a result,the performance of such CPDP models is compromised.In this paper,this paper proposes a novel CPDP method based on Synthetic Minority Oversampling Technique(SMOTE)and Deep Canonical Correlation Analysis(DCCA),referred to as S-DCCA.Canonical Correlation Analysis(CCA)is employed to address the issue of non-linear correlations between features of the source and target projects.S-DCCA extends CCA by incorporating the MlpNet model for feature extraction from the dataset.The redundant features are then eliminated by maximizing the correlated feature subset using the CCA loss function.Finally,cross-project defect prediction is achieved through the application of the SMOTE data sampling technique.Area Under Curve(AUC)and F1 scores(F1)are used as evaluation metrics.This paper conducted experiments on 27 projects from four public datasets to validate the proposed method.The results demonstrate that,on average,our method outperforms all baseline approaches by at least 1.2%in AUC and 5.5%in F1 score.This indicates that the proposed method exhibits favorable performance characteristics.展开更多
Grand canonical Monte Carlo simulation(GCMCs)is utilized for studying hydrogen storage gravimetric density by pha-graphene at different metal densities,temperatures and pressures.It is demonstrated that the optimum ad...Grand canonical Monte Carlo simulation(GCMCs)is utilized for studying hydrogen storage gravimetric density by pha-graphene at different metal densities,temperatures and pressures.It is demonstrated that the optimum adsorbent location for Li atoms is the center of the seven-membered ring of pha-graphene.The binding energy of Li-decorated phagraphene is larger than the cohesive energy of Li atoms,implying that Li can be distributed on the surface of pha-graphene without forming metal clusters.We fitted the force field parameters of Li and C atoms at different positions and performed GCMCs to study the absorption capacity of H_(2).The capacity of hydrogen storage was studied by the differing density of Li decoration.The maximum hydrogen storage capacity of 4Li-decorated pha-graphene was 15.88 wt%at 77 K and100 bar.The enthalpy values of adsorption at the three densities are in the ideal range of 15 kJ·mol^(-1)-25 kJ·mol^(-1).The GCMC results at different pressures and temperatures show that with the increase in Li decorative density,the hydrogen storage gravimetric ratio of pha-graphene decreases but can reach the 2025 US Department of Energy's standard(5.5 wt%).Therefore,pha-graphene is considered to be a potential hydrogen storage material.展开更多
Biometric gait recognition is a lesser-known but emerging and effective biometric recognition method which enables subjects’walking patterns to be recognized.Existing research in this area has primarily focused on fe...Biometric gait recognition is a lesser-known but emerging and effective biometric recognition method which enables subjects’walking patterns to be recognized.Existing research in this area has primarily focused on feature analysis through the extraction of individual features,which captures most of the information but fails to capture subtle variations in gait dynamics.Therefore,a novel feature taxonomy and an approach for deriving a relationship between a function of one set of gait features with another set are introduced.The gait features extracted from body halves divided by anatomical planes on vertical,horizontal,and diagonal axes are grouped to form canonical gait covariates.Canonical Correlation Analysis is utilized to measure the strength of association between the canonical covariates of gait.Thus,gait assessment and identification are enhancedwhenmore semantic information is available through CCA-basedmulti-feature fusion.Hence,CarnegieMellon University’s 3D gait database,which contains 32 gait samples taken at different paces,is utilized in analyzing gait characteristics.The performance of Linear Discriminant Analysis,K-Nearest Neighbors,Naive Bayes,Artificial Neural Networks,and Support Vector Machines was improved by a 4%average when the CCA-utilized gait identification approachwas used.Asignificant maximumaccuracy rate of 97.8%was achieved throughCCA-based gait identification.Beyond that,the rate of false identifications and unrecognized gaits went down to half,demonstrating state-of-the-art for gait identification.展开更多
Decision implication is a form of decision knowledge represen-tation,which is able to avoid generating attribute implications that occur between condition attributes and between decision attributes.Compared with other...Decision implication is a form of decision knowledge represen-tation,which is able to avoid generating attribute implications that occur between condition attributes and between decision attributes.Compared with other forms of decision knowledge representation,decision implication has a stronger knowledge representation capability.Attribute granularization may facilitate the knowledge extraction of different attribute granularity layers and thus is of application significance.Decision implication canonical basis(DICB)is the most compact set of decision implications,which can efficiently represent all knowledge in the decision context.In order to mine all deci-sion information on decision context under attribute granulating,this paper proposes an updated method of DICB.To this end,the paper reduces the update of DICB to the updates of decision premises after deleting an attribute and after adding granulation attributes of some attributes.Based on this,the paper analyzes the changes of decision premises,examines the properties of decision premises,designs an algorithm for incrementally generating DICB,and verifies its effectiveness through experiments.In real life,by using the updated algorithm of DICB,users may obtain all decision knowledge on decision context after attribute granularization.展开更多
Triple Negative Breast Cancer (TNBC) is a malignant form of cancer with very high mortality and morbidity. Epithelial to Mesenchymal Transition (EMT) is the most common pathophysiological change observed in cancer cel...Triple Negative Breast Cancer (TNBC) is a malignant form of cancer with very high mortality and morbidity. Epithelial to Mesenchymal Transition (EMT) is the most common pathophysiological change observed in cancer cells of epithelial origin that promotes metastasis, drug resistance and cancer stem cell formation. Since the information regarding differential gene expression in TNBC cells and cell signaling events leading to EMT is limited, this investigation was done by comparing transcriptomic data generated by RNA isolation and sequencing of a EMT model TNBC cell line in comparison to regular TNBC cells. RNA sequencing and Ingenuity Pathway Software Analysis (IPA) of the transcriptomic data revealed several upregulated and downregulated gene expressions along with novel core canonical pathways including Sirtuin signaling, Oxidative Phosphorylation and Mitochondrial dysfunction events involved in EMT changes of the TNBC cells.展开更多
Linear canonical transformation(LCT)is a generalization of the Fourier transform and fractional Fourier transform.The recent research has shown that the LCT is widely used in signal processing and applied mathematics,...Linear canonical transformation(LCT)is a generalization of the Fourier transform and fractional Fourier transform.The recent research has shown that the LCT is widely used in signal processing and applied mathematics,and the discretization of the LCT becomes vital for the applic-ations of LCT.Based on the development of discretization LCT,a review of important research progress and current situation is presented,which can help researchers to further understand the discretization of LCT and can promote its engineering application.Meanwhile,the connection among different discretization algorithms and the future research are given.展开更多
Adipose-derived stromal cells(ASCs) have gained great attention in regenerative medicine. Progress in our understanding of adult neovascularization further suggests the potential of ASCs in promoting vascular regenera...Adipose-derived stromal cells(ASCs) have gained great attention in regenerative medicine. Progress in our understanding of adult neovascularization further suggests the potential of ASCs in promoting vascular regeneration, although the specific cues that stimulate their angiogenic behavior remain controversial. In this study, we established a three-dimensional(3D) angiogenesis model by co-culturing ASCs and endothelial cells(ECs) in collagen gel and found that ASC-EC-instructed angiogenesis was regulated by the canonical Wnt pathway. Furthermore, the angiogenesis that occurred in implants collected after injections of our collagen gelbased 3D angiogenesis model into nude mice was confirmed to be functional and also regulated by the canonical Wnt pathway. Wnt regulation of angiogenesis involving changes in vessel length, vessel density,vessel sprout, and connection numbers occurred in our system. Wnt signaling was then shown to regulate ASCmediated paracrine signaling during angiogenesis through the nuclear translocation of β-catenin after its cytoplasmic accumulation in both ASCs and ECs. This translocation enhanced the expression of nuclear cofactor Lef-1 and cyclin D1 and activated the angiogenic transcription of vascular endothelial growth factor A(VEGFA), basic fibroblast growth factor(bF GF), and insulin-like growth factor 1(IGF-1). The angiogenesis process in the 3D collagen model appeared to follow canonical Wnt signaling, and this model can help us understand the importance of the canonical Wnt pathway in the use of ASCs in vascular regeneration.展开更多
The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems o...The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems of continuous systems and discrete systems as well as other complex systems.In this paper,the theory of generalized canonical transformation for second-order Birkhoffian systems on time scales is proposed and studied,which extends the canonical transformation theory of Hamilton canonical equations.First,the condition of generalized canonical transformation for the second-order Birkhoffian system on time scales is established.Second,based on this condition,six basic forms of generalized canonical transformation for the second-order Birkhoffian system on time scales are given.Also,the relationships between new variables and old variables for each of these cases are derived.In the end,an example is given to show the application of the results.展开更多
In this paper,we investigate the tensor similarity and propose the T-Jordan canonical form and its properties.The concepts of the T-minimal polynomial and the T-characteristic polynomial are proposed.As a special case...In this paper,we investigate the tensor similarity and propose the T-Jordan canonical form and its properties.The concepts of the T-minimal polynomial and the T-characteristic polynomial are proposed.As a special case,we present properties when two tensors commute based on the tensor T-product.We prove that the Cayley-Hamilton theorem also holds for tensor cases.Then,we focus on the tensor decompositions:T-polar,T-LU,T-QR and T-Schur decompositions of tensors are obtained.When an F-square tensor is not invertible with the T-product,we study the T-group inverse and the T-Drazin inverse which can be viewed as the extension of matrix cases.The expressions of the T-group and T-Drazin inverses are given by the T-Jordan canonical form.The polynomial form of the T-Drazin inverse is also proposed.In the last part,we give the T-core-nilpotent decomposition and show that the T-index and T-Drazin inverses can be given by a limit process.展开更多
An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the pola...An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the polar coordinate form of quaternion-valued signals,the UP of the two-sided quaternion linear canonical transform(QLCT)is strengthened in terms of covariance.The condition giving rise to the equal relation of the derived result is obtained as well.The novel UP with covariance can be regarded as one in a tighter form related to the QLCT.It states that the product of spreads of a quaternion-valued signal in the spatial domain and the QLCT domain is bounded by a larger lower bound.展开更多
A deeper understanding of the biological events occurring when bioprocess parameters changed will be of great value in improving the monoclonal antibodies (mAbs) production. Design of experiment (DoE) was applied to i...A deeper understanding of the biological events occurring when bioprocess parameters changed will be of great value in improving the monoclonal antibodies (mAbs) production. Design of experiment (DoE) was applied to investigate the effect of process parameters (pH, temperature shift and dissolve oxygen (DO)) on protein titer. The key metabolites connecting the critical process parameters (CPPs) with monoclonal antibody production were identified by different chemometrics tools. Finally, the biological events of marker metabolites relating with titer improvement were concluded. pH and temperature shift were identified as CPPs that affect the target protein titer. A series of metabolites influenced by the altered CPPs and correlated with protein titer were screened by principal component analysis (PCA) and Pearson' correlation test. The marker metabolites and their pathways linking CPPs to target protein titer in different culture phases were summarized. Metabolomics and chemometrics are promising data-driven tools to shine light into the biological black box between the bioprocess parameters and process performance.展开更多
This paper introduces the canonical coordinates method to obtain the first integral of a single-degree freedom constraint mechanical system that contains conservative and non-conservative constraint homonomic systems....This paper introduces the canonical coordinates method to obtain the first integral of a single-degree freedom constraint mechanical system that contains conservative and non-conservative constraint homonomic systems. The definition and properties of canonical coordinates are introduced. The relation between Lie point symmetries and the canonical coordinates of the constraint mechanical system are expressed. By this relation, the canonical coordinates can be obtained. Properties of the canonical coordinates and the Lie symmetry theory are used to seek the first integrals of constraint mechanical system. Three examples are used to show applications of the results.展开更多
In this paper,the GH-congruence canonical forms of positive semidefinite and definte inite and definite(need not be self-conjugate)quaternion matrices are given,and a neccessary and sufficientcondition of GH-congruenc...In this paper,the GH-congruence canonical forms of positive semidefinite and definte inite and definite(need not be self-conjugate)quaternion matrices are given,and a neccessary and sufficientcondition of GH-congruence for two positive semidifinite(definite)quaternion matrices isgiven also.Then simultaneous GH-congruence reduced forms for two self-conjugate matri-ces and some result about the simultaneous GH-congruence diagonalization of quaternionmatrices are obtained.展开更多
基金NationalNatural Science Foundation of China,Grant/AwardNumber:61867004National Natural Science Foundation of China Youth Fund,Grant/Award Number:41801288.
文摘Cross-Project Defect Prediction(CPDP)is a method that utilizes historical data from other source projects to train predictive models for defect prediction in the target project.However,existing CPDP methods only consider linear correlations between features(indicators)of the source and target projects.These models are not capable of evaluating non-linear correlations between features when they exist,for example,when there are differences in data distributions between the source and target projects.As a result,the performance of such CPDP models is compromised.In this paper,this paper proposes a novel CPDP method based on Synthetic Minority Oversampling Technique(SMOTE)and Deep Canonical Correlation Analysis(DCCA),referred to as S-DCCA.Canonical Correlation Analysis(CCA)is employed to address the issue of non-linear correlations between features of the source and target projects.S-DCCA extends CCA by incorporating the MlpNet model for feature extraction from the dataset.The redundant features are then eliminated by maximizing the correlated feature subset using the CCA loss function.Finally,cross-project defect prediction is achieved through the application of the SMOTE data sampling technique.Area Under Curve(AUC)and F1 scores(F1)are used as evaluation metrics.This paper conducted experiments on 27 projects from four public datasets to validate the proposed method.The results demonstrate that,on average,our method outperforms all baseline approaches by at least 1.2%in AUC and 5.5%in F1 score.This indicates that the proposed method exhibits favorable performance characteristics.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11904175,11804169,and 11804165)the Graduate Innovation Project of Jiangsu Province,China(Grant No.KYCX210700)。
文摘Grand canonical Monte Carlo simulation(GCMCs)is utilized for studying hydrogen storage gravimetric density by pha-graphene at different metal densities,temperatures and pressures.It is demonstrated that the optimum adsorbent location for Li atoms is the center of the seven-membered ring of pha-graphene.The binding energy of Li-decorated phagraphene is larger than the cohesive energy of Li atoms,implying that Li can be distributed on the surface of pha-graphene without forming metal clusters.We fitted the force field parameters of Li and C atoms at different positions and performed GCMCs to study the absorption capacity of H_(2).The capacity of hydrogen storage was studied by the differing density of Li decoration.The maximum hydrogen storage capacity of 4Li-decorated pha-graphene was 15.88 wt%at 77 K and100 bar.The enthalpy values of adsorption at the three densities are in the ideal range of 15 kJ·mol^(-1)-25 kJ·mol^(-1).The GCMC results at different pressures and temperatures show that with the increase in Li decorative density,the hydrogen storage gravimetric ratio of pha-graphene decreases but can reach the 2025 US Department of Energy's standard(5.5 wt%).Therefore,pha-graphene is considered to be a potential hydrogen storage material.
基金supported by Istanbul University Scientific Research Project Department with IRP-51706 Project Number.
文摘Biometric gait recognition is a lesser-known but emerging and effective biometric recognition method which enables subjects’walking patterns to be recognized.Existing research in this area has primarily focused on feature analysis through the extraction of individual features,which captures most of the information but fails to capture subtle variations in gait dynamics.Therefore,a novel feature taxonomy and an approach for deriving a relationship between a function of one set of gait features with another set are introduced.The gait features extracted from body halves divided by anatomical planes on vertical,horizontal,and diagonal axes are grouped to form canonical gait covariates.Canonical Correlation Analysis is utilized to measure the strength of association between the canonical covariates of gait.Thus,gait assessment and identification are enhancedwhenmore semantic information is available through CCA-basedmulti-feature fusion.Hence,CarnegieMellon University’s 3D gait database,which contains 32 gait samples taken at different paces,is utilized in analyzing gait characteristics.The performance of Linear Discriminant Analysis,K-Nearest Neighbors,Naive Bayes,Artificial Neural Networks,and Support Vector Machines was improved by a 4%average when the CCA-utilized gait identification approachwas used.Asignificant maximumaccuracy rate of 97.8%was achieved throughCCA-based gait identification.Beyond that,the rate of false identifications and unrecognized gaits went down to half,demonstrating state-of-the-art for gait identification.
基金supported by the National Natural Science Foundation of China (Nos.61972238,62072294).
文摘Decision implication is a form of decision knowledge represen-tation,which is able to avoid generating attribute implications that occur between condition attributes and between decision attributes.Compared with other forms of decision knowledge representation,decision implication has a stronger knowledge representation capability.Attribute granularization may facilitate the knowledge extraction of different attribute granularity layers and thus is of application significance.Decision implication canonical basis(DICB)is the most compact set of decision implications,which can efficiently represent all knowledge in the decision context.In order to mine all deci-sion information on decision context under attribute granulating,this paper proposes an updated method of DICB.To this end,the paper reduces the update of DICB to the updates of decision premises after deleting an attribute and after adding granulation attributes of some attributes.Based on this,the paper analyzes the changes of decision premises,examines the properties of decision premises,designs an algorithm for incrementally generating DICB,and verifies its effectiveness through experiments.In real life,by using the updated algorithm of DICB,users may obtain all decision knowledge on decision context after attribute granularization.
文摘Triple Negative Breast Cancer (TNBC) is a malignant form of cancer with very high mortality and morbidity. Epithelial to Mesenchymal Transition (EMT) is the most common pathophysiological change observed in cancer cells of epithelial origin that promotes metastasis, drug resistance and cancer stem cell formation. Since the information regarding differential gene expression in TNBC cells and cell signaling events leading to EMT is limited, this investigation was done by comparing transcriptomic data generated by RNA isolation and sequencing of a EMT model TNBC cell line in comparison to regular TNBC cells. RNA sequencing and Ingenuity Pathway Software Analysis (IPA) of the transcriptomic data revealed several upregulated and downregulated gene expressions along with novel core canonical pathways including Sirtuin signaling, Oxidative Phosphorylation and Mitochondrial dysfunction events involved in EMT changes of the TNBC cells.
基金supported by the National Natural Science Found-ation of China(No.62001193).
文摘Linear canonical transformation(LCT)is a generalization of the Fourier transform and fractional Fourier transform.The recent research has shown that the LCT is widely used in signal processing and applied mathematics,and the discretization of the LCT becomes vital for the applic-ations of LCT.Based on the development of discretization LCT,a review of important research progress and current situation is presented,which can help researchers to further understand the discretization of LCT and can promote its engineering application.Meanwhile,the connection among different discretization algorithms and the future research are given.
基金funded by the National Natural Science Foundation of China(81771125,81471803,81671031)the Sichuan Province Youth Science and Technology Innovation Team(2014TD0001)
文摘Adipose-derived stromal cells(ASCs) have gained great attention in regenerative medicine. Progress in our understanding of adult neovascularization further suggests the potential of ASCs in promoting vascular regeneration, although the specific cues that stimulate their angiogenic behavior remain controversial. In this study, we established a three-dimensional(3D) angiogenesis model by co-culturing ASCs and endothelial cells(ECs) in collagen gel and found that ASC-EC-instructed angiogenesis was regulated by the canonical Wnt pathway. Furthermore, the angiogenesis that occurred in implants collected after injections of our collagen gelbased 3D angiogenesis model into nude mice was confirmed to be functional and also regulated by the canonical Wnt pathway. Wnt regulation of angiogenesis involving changes in vessel length, vessel density,vessel sprout, and connection numbers occurred in our system. Wnt signaling was then shown to regulate ASCmediated paracrine signaling during angiogenesis through the nuclear translocation of β-catenin after its cytoplasmic accumulation in both ASCs and ECs. This translocation enhanced the expression of nuclear cofactor Lef-1 and cyclin D1 and activated the angiogenic transcription of vascular endothelial growth factor A(VEGFA), basic fibroblast growth factor(bF GF), and insulin-like growth factor 1(IGF-1). The angiogenesis process in the 3D collagen model appeared to follow canonical Wnt signaling, and this model can help us understand the importance of the canonical Wnt pathway in the use of ASCs in vascular regeneration.
基金supported by the National Natural Science Foundation of China(Grants 11972241 and 11572212)
文摘The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems of continuous systems and discrete systems as well as other complex systems.In this paper,the theory of generalized canonical transformation for second-order Birkhoffian systems on time scales is proposed and studied,which extends the canonical transformation theory of Hamilton canonical equations.First,the condition of generalized canonical transformation for the second-order Birkhoffian system on time scales is established.Second,based on this condition,six basic forms of generalized canonical transformation for the second-order Birkhoffian system on time scales are given.Also,the relationships between new variables and old variables for each of these cases are derived.In the end,an example is given to show the application of the results.
基金the National Natural Science Foundation of China(Grant No.11771099)the Hong Kong Research Grant Council(Grant Nos.PolyU 15302114,15300715,15301716 and 15300717)the Innovation Program of Shanghai Municipal Education Commission.
文摘In this paper,we investigate the tensor similarity and propose the T-Jordan canonical form and its properties.The concepts of the T-minimal polynomial and the T-characteristic polynomial are proposed.As a special case,we present properties when two tensors commute based on the tensor T-product.We prove that the Cayley-Hamilton theorem also holds for tensor cases.Then,we focus on the tensor decompositions:T-polar,T-LU,T-QR and T-Schur decompositions of tensors are obtained.When an F-square tensor is not invertible with the T-product,we study the T-group inverse and the T-Drazin inverse which can be viewed as the extension of matrix cases.The expressions of the T-group and T-Drazin inverses are given by the T-Jordan canonical form.The polynomial form of the T-Drazin inverse is also proposed.In the last part,we give the T-core-nilpotent decomposition and show that the T-index and T-Drazin inverses can be given by a limit process.
基金supported by Startup Foundation for Phd Research of Henan Normal University(No.5101119170155).
文摘An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the polar coordinate form of quaternion-valued signals,the UP of the two-sided quaternion linear canonical transform(QLCT)is strengthened in terms of covariance.The condition giving rise to the equal relation of the derived result is obtained as well.The novel UP with covariance can be regarded as one in a tighter form related to the QLCT.It states that the product of spreads of a quaternion-valued signal in the spatial domain and the QLCT domain is bounded by a larger lower bound.
基金Foundation item： Supported by the National Natural Science Foundation of China（11471333） Supported by the Basic and Advanced Technology Research Project of Henan Province（142300410449）
文摘All monomials with t-value ≤ 6 in Canonical basis of quantized enveloping algebra of type B3 are determined in this paper.
基金Supported by the Science and Technology Development Program of Zhejiang Province(2017C03003)
文摘A deeper understanding of the biological events occurring when bioprocess parameters changed will be of great value in improving the monoclonal antibodies (mAbs) production. Design of experiment (DoE) was applied to investigate the effect of process parameters (pH, temperature shift and dissolve oxygen (DO)) on protein titer. The key metabolites connecting the critical process parameters (CPPs) with monoclonal antibody production were identified by different chemometrics tools. Finally, the biological events of marker metabolites relating with titer improvement were concluded. pH and temperature shift were identified as CPPs that affect the target protein titer. A series of metabolites influenced by the altered CPPs and correlated with protein titer were screened by principal component analysis (PCA) and Pearson' correlation test. The marker metabolites and their pathways linking CPPs to target protein titer in different culture phases were summarized. Metabolomics and chemometrics are promising data-driven tools to shine light into the biological black box between the bioprocess parameters and process performance.
基金Project supported by the National Natural Science Foundation of China(Nos.11072218 and 11272287)the Program for Changjiang Scholars and Innovative Research Team in University(PCSIRT)(No.IRT13097)
文摘This paper introduces the canonical coordinates method to obtain the first integral of a single-degree freedom constraint mechanical system that contains conservative and non-conservative constraint homonomic systems. The definition and properties of canonical coordinates are introduced. The relation between Lie point symmetries and the canonical coordinates of the constraint mechanical system are expressed. By this relation, the canonical coordinates can be obtained. Properties of the canonical coordinates and the Lie symmetry theory are used to seek the first integrals of constraint mechanical system. Three examples are used to show applications of the results.
文摘In this paper,the GH-congruence canonical forms of positive semidefinite and definte inite and definite(need not be self-conjugate)quaternion matrices are given,and a neccessary and sufficientcondition of GH-congruence for two positive semidifinite(definite)quaternion matrices isgiven also.Then simultaneous GH-congruence reduced forms for two self-conjugate matri-ces and some result about the simultaneous GH-congruence diagonalization of quaternionmatrices are obtained.
