In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise c...In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.展开更多
A simplified analytical approach is proposed for predicting the load-displacement behavior of single piles in unsaturated soils considering the contribution from the nonlinear shear strength and soil stiffness influen...A simplified analytical approach is proposed for predicting the load-displacement behavior of single piles in unsaturated soils considering the contribution from the nonlinear shear strength and soil stiffness influenced by matric suction.This approach includes a Modified Load Transfer Model(MLTM)that can predict the nonlinear relationships between the shear stress and pile-soil relative displacement along the pile shaft,and between the pile base resistance and base settlement.The proposed model is also extended for pile groups to incorporate the interaction effects between individual piles.The analytical approach is validated through a comparative analysis with the measurements from two single pile tests and one pile group test.In addition,a finite element analysis using 3D modeling is carried out to investigate the behavior of pile groups in various unsaturated conditions.This is accomplished with a user-defined subroutine that is written and implemented in ABAQUS to simulate the nonlinear mechanical behavior of unsaturated soils.The predictions derived from the proposed analytical and numerical methods compare well with the measurements of a published experimental study.The proposed methodologies have the potential to be applied in geotechnical engineering practice for the rational design of single piles and pile groups in unsaturated soils.展开更多
Potential games(PG)have attracted the attention of many researchers because of its excellent properties and multi-PG are more flexible and extensible,which greatly improve the application range of PG.Consider that wei...Potential games(PG)have attracted the attention of many researchers because of its excellent properties and multi-PG are more flexible and extensible,which greatly improve the application range of PG.Consider that weights and states to each player are common and practical in many application scenarios,and in this paper,by introducing weight value and state into multi-PG,q-weighted PG and q-state PG are systematically discussed and analyzed to expand the types of PG,respectively.First,using semi-tensor product of matrices(STP),a matrix approach to the modeling of weighted PG is investigated,and the verification method of weighted PG is proposed by defining three matrices,and the problem of how to detect weighted PG can be transformed to solve an algebraic equation,which is composed of the above three matrices.Next,by bringing weight values into multi-PG and detecting the weighted PG for each group,the verification method is extended to the q-weighted PG.Second,the model of state-based PG is constructed,and the problem of how to detect state-based PG can be transformed to solve another algebraic equation,which is seen as an extension of the verification method of weighted PG.Subsequently,the verification of q-state PG is discussed.Finally,we use two examples to demonstrate the validation of obtained results.展开更多
We display sharp bounds for upper and lower spectrum of a Hermitizable tridiagonal matrix.The representations are brought to light by exploiting the characteristic for eigenpairs(eigenvalue and its corresponding eigen...We display sharp bounds for upper and lower spectrum of a Hermitizable tridiagonal matrix.The representations are brought to light by exploiting the characteristic for eigenpairs(eigenvalue and its corresponding eigenvector)of tridiagonal matrices,isospectral transforms and sharp bounds for speed stability of birth-death processes.展开更多
High-performance lithium metal batteries benefit from the construction of composite polymer electrolytes(CPEs)which are synthesized by incorporating inorganic fillers into polymer matrices[1].However,the random distri...High-performance lithium metal batteries benefit from the construction of composite polymer electrolytes(CPEs)which are synthesized by incorporating inorganic fillers into polymer matrices[1].However,the random distribution of added fillers within the polymer matrix can lead to tortuous ion pathways and longer transmission distances(Fig.1).As a result,the ion transport capability of CPEs may decrease,while interface contact may deteriorate.Therefore,the organized arrangement of fillers emerges as a crucial consideration in constructing electrolyte membranes.One highly effective approach is the adoption of a vertically aligned filler configuration,where ceramic fillers are constructed to be perpendicular to the electrolyte membrane.If so,the filler/electrolyte interface impedance can be significantly reduced,while continuous ion transport channels along the specified direction are formed,thus significantly enhancing the ion conduction(Fig.1(a))[1].展开更多
Subcellular location is one of the key biological characteristics of proteins. Position-specific profiles （PSP） have been introduced as important characteristics of proteins in this article. In this study, to obtain...Subcellular location is one of the key biological characteristics of proteins. Position-specific profiles （PSP） have been introduced as important characteristics of proteins in this article. In this study, to obtain position-specific profiles, the Position Specific lterative-Basic Local Alignment Search Tool （PSI-BLAST） has been used to search for protein sequences in a database. Position-specific scoring matrices are extracted from the profiles as one class of characteristics. Four-part amino acid compositions and lst-7th order dipeptide compositions have also been calculated as the other two classes of characteristics. Therefore, twelve characteristic vectors are extracted from each of the protein sequences. Next, the characteristic vectors are weighed by a simple weighing function and inputted into a BP neural network predictor named PSP-Weighted Neural Network （PSP-WNN）. The Levenberg-Marquardt algorithm is employed to adjust the weight matrices and thresholds during the network training instead of the error back propagation algorithm. With a jackknife test on the RH2427 dataset, PSP-WNN has achieved a higher overall prediction accuracy of 88.4% rather than the prediction results by the general BP neural network, Markov model, and fuzzy k-nearest neighbors algorithm on this dataset. In addition, the prediction performance of PSP-WNN has been evaluated with a five-fold cross validation test on the PK7579 dataset and the prediction results have been consistently better than those of the previous method on the basis of several support vector machines, using compositions of both amino acids and amino acid pairs. These results indicate that PSP-WNN is a powerful tool for subcellular localization prediction. At the end of the article, influences on prediction accuracy using different weighting proportions among three characteristic vector categories have been discussed. An appropriate proportion is considered by increasing the prediction accuracy.展开更多
In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.
On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial ...On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.展开更多
An approach for generating test problems by a computer using the Monte Carlo method based upon user-given characterizations is described.A single point X~* is prespocified by the user to be a solution of the test prob...An approach for generating test problems by a computer using the Monte Carlo method based upon user-given characterizations is described.A single point X~* is prespocified by the user to be a solution of the test problems.The approach is flex- ible enough to specify function values,gradients,Hesse,degeneracy degree and ill- conditioned degree at the point X~*.Other numerical features such as indefiniteness, convexity are also under user's control.展开更多
In today's aircraft,the hardware redundancy is driven by the critical surfaces resulting in single point-failures.Reconfiguration technology remoVes the single surface criticality by employing control surfaces wit...In today's aircraft,the hardware redundancy is driven by the critical surfaces resulting in single point-failures.Reconfiguration technology remoVes the single surface criticality by employing control surfaces with aerodynamic redundancy.This paper studies a control reconfiguration scheme based on Control Mixer Concept.A technique for the design of a control mixer for an aircraft with damaged surfaces/actuators using the pseudo-inverse is developed and applied.This paper discusses its applications and limitations based on linear analysis and computer simulation.展开更多
The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability ...The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability of the problem is given. A numerical algorithm for solving the problem is provided and a numerical example is presented.展开更多
Melanocytic matricoma is a very rare adnexal tumor that recapitulates the anagen hair follicle bulb. Few cases of malignant melanocytic matricoma have been reported, thus criteria for malignant potential have not been...Melanocytic matricoma is a very rare adnexal tumor that recapitulates the anagen hair follicle bulb. Few cases of malignant melanocytic matricoma have been reported, thus criteria for malignant potential have not been previously reviewed. We report a case of an 81 year old male that was originally diagnosed as atypical melanocytic matricoma. The site was re-excised with a small focus of residual tumor, but all margins were negative. The re-excision site healed without complication. However, two years after the original biopsy, a new 8 mm firm nodule appeared at the re-excision site, which was subsequently diagnosed as malignant melanocytic matricoma (MMM). In the following paper we will report a new case of MMM and review potential criteria that could be used in the future to establish malignant potential.展开更多
As it is well known,it is difficult to identify a nonlinear time varying system using traditional identification approaches,especially under unknown nonlinear function.Neural networks have recently emerged as a succes...As it is well known,it is difficult to identify a nonlinear time varying system using traditional identification approaches,especially under unknown nonlinear function.Neural networks have recently emerged as a successful tool in the area of identification and control of time invariant nonlinear systems.However,it is still difficult to apply them to complicated time varying system identification.In this paper we present a learning algorithm for identification of the nonlinear time varying system using feedforward neural networks.The main idea of this approach is that we regard the weights of the network as a state of a time varying system,then use a Kalman filter to estimate the state.Thus the network implements nonlinear and time varying mapping.We derived both the global and local learning algorithms.Simulation results demonstrate the effectiveness of this approach.展开更多
A systematic geometric model has been presented for calibration of a newly designed 5-axis turbine blade grinding machine. This machine is designed to serve a specific purpose to attain high accuracy and high efficien...A systematic geometric model has been presented for calibration of a newly designed 5-axis turbine blade grinding machine. This machine is designed to serve a specific purpose to attain high accuracy and high efficiency grinding of turbine blades by eliminating the hand grinding process. Although its topology is RPPPR （P： prismatic; R： rotary）, its design is quite distinct from the competitive machine tools. As error quantification is the only way to investigate, maintain and improve its accuracy, calibra- tion is recommended for its performance assessment and acceptance testing. Systematic geometric error modeling technique is implemented and 52 position dependent and position independent errors are identified while considering the machine as five rigid bodies by eliminating the set-up errors of workpiece and cutting tool. 39 of them are found to have influential errors and are accommodated for finding the resultant effect between the cutting tool and the workpiece in workspace volume. Rigid body kinematics techniques and homogenous transformation matrices are used for error synthesis.展开更多
In the past few decades, the increase in grazing intensity has led to soil degradation and desertification in Inner Mongolia grassland, China, due to population growth and shift in the socio-economic system. Two sites...In the past few decades, the increase in grazing intensity has led to soil degradation and desertification in Inner Mongolia grassland, China, due to population growth and shift in the socio-economic system. Two sites with different grazing intensities, continuous grazing site （CG） with 1.2 sheep ha-1 year-1 and heavy grazing site （HG） with 2.0 sheep ha-1 year-1, were investigated at the Inner Mongolia Grassland Ecosystem Research Station （43° 37′ 50″ N, 116° 42′ 18″ E） situated in the northern China to i） characterize the temporal distribution of soil water content along soil profile; and ii） quantify the water fluxes as affected by grazing intensity. Soil water content was monitored by time domain refiectometry （TDR） probes. Soil water retention curves were determined by pressure membrane extractor, furthermore processed by RETC （RETention Curve） software. Soil matric potential, plant available water and water flux were calculated using these data. Both sites showed an identical seasonal soil water dynamics within four defined hydraulic periods： i） wetting transition coincided with a dramatic water increase due to snow and frozen soil thawing from March to April; 2） wet summer, rainfall in accordance with plant growth from May to September; 3） drying transition, a decrease of soil water from October to November due to rainfall limit; and 4） dry winter, freezing from December to next February. Heavy grazing largely reduced soil water content by 43%-48% and plant available water by 46%-61% as compared to the CG site. During growing season net water flux was nearly similar between HG （242 mm） and CG （223 mm） sites between 5 and 20 cm depths. However, between 20 and 40 cm depths, the upward flux was more pronounced at HG site than at CG site, indicating that water was depleted by root uptake at HG site but stored at CG site. In semi-arid grassland ecosystem, grazing intensity can affect soil water regime and flux, particularly in the growing season.展开更多
Using semi-tensor product of matrices, the controllability and stabilizability of finite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions ar...Using semi-tensor product of matrices, the controllability and stabilizability of finite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions are represented in matrix forms.Based on this algebraic description, a necessary and sufficient condition is proposed for checking whether a state is controllable to another one. By this condition, an algorithm is established to find all the control sequences of an arbitrary length. Moreover, the stabilizability of finite automata is considered, and a necessary and sufficient condition is presented to examine whether some states can be stabilized. Finally, the study of illustrative examples verifies the correctness of the presented results/algorithms.展开更多
文摘In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.
基金financially supported by NSERC,CanadaDiscovery Grant 2020(Grant No.5808).
文摘A simplified analytical approach is proposed for predicting the load-displacement behavior of single piles in unsaturated soils considering the contribution from the nonlinear shear strength and soil stiffness influenced by matric suction.This approach includes a Modified Load Transfer Model(MLTM)that can predict the nonlinear relationships between the shear stress and pile-soil relative displacement along the pile shaft,and between the pile base resistance and base settlement.The proposed model is also extended for pile groups to incorporate the interaction effects between individual piles.The analytical approach is validated through a comparative analysis with the measurements from two single pile tests and one pile group test.In addition,a finite element analysis using 3D modeling is carried out to investigate the behavior of pile groups in various unsaturated conditions.This is accomplished with a user-defined subroutine that is written and implemented in ABAQUS to simulate the nonlinear mechanical behavior of unsaturated soils.The predictions derived from the proposed analytical and numerical methods compare well with the measurements of a published experimental study.The proposed methodologies have the potential to be applied in geotechnical engineering practice for the rational design of single piles and pile groups in unsaturated soils.
基金supported by the National Natural Science Foundation of China Grant No.62203328.
文摘Potential games(PG)have attracted the attention of many researchers because of its excellent properties and multi-PG are more flexible and extensible,which greatly improve the application range of PG.Consider that weights and states to each player are common and practical in many application scenarios,and in this paper,by introducing weight value and state into multi-PG,q-weighted PG and q-state PG are systematically discussed and analyzed to expand the types of PG,respectively.First,using semi-tensor product of matrices(STP),a matrix approach to the modeling of weighted PG is investigated,and the verification method of weighted PG is proposed by defining three matrices,and the problem of how to detect weighted PG can be transformed to solve an algebraic equation,which is composed of the above three matrices.Next,by bringing weight values into multi-PG and detecting the weighted PG for each group,the verification method is extended to the q-weighted PG.Second,the model of state-based PG is constructed,and the problem of how to detect state-based PG can be transformed to solve another algebraic equation,which is seen as an extension of the verification method of weighted PG.Subsequently,the verification of q-state PG is discussed.Finally,we use two examples to demonstrate the validation of obtained results.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11771046,12101186)Beijing Natural Science Foundation(Grant No.1254039).
文摘We display sharp bounds for upper and lower spectrum of a Hermitizable tridiagonal matrix.The representations are brought to light by exploiting the characteristic for eigenpairs(eigenvalue and its corresponding eigenvector)of tridiagonal matrices,isospectral transforms and sharp bounds for speed stability of birth-death processes.
基金supported by the National Natural Science Foundation of China(No.51972293)Hangzhou Key Research Program Project(2023SZD0099)LingYan Project(2024C01090).
文摘High-performance lithium metal batteries benefit from the construction of composite polymer electrolytes(CPEs)which are synthesized by incorporating inorganic fillers into polymer matrices[1].However,the random distribution of added fillers within the polymer matrix can lead to tortuous ion pathways and longer transmission distances(Fig.1).As a result,the ion transport capability of CPEs may decrease,while interface contact may deteriorate.Therefore,the organized arrangement of fillers emerges as a crucial consideration in constructing electrolyte membranes.One highly effective approach is the adoption of a vertically aligned filler configuration,where ceramic fillers are constructed to be perpendicular to the electrolyte membrane.If so,the filler/electrolyte interface impedance can be significantly reduced,while continuous ion transport channels along the specified direction are formed,thus significantly enhancing the ion conduction(Fig.1(a))[1].
基金the National Natural Science Foundation of China (No. 60471003).
文摘Subcellular location is one of the key biological characteristics of proteins. Position-specific profiles （PSP） have been introduced as important characteristics of proteins in this article. In this study, to obtain position-specific profiles, the Position Specific lterative-Basic Local Alignment Search Tool （PSI-BLAST） has been used to search for protein sequences in a database. Position-specific scoring matrices are extracted from the profiles as one class of characteristics. Four-part amino acid compositions and lst-7th order dipeptide compositions have also been calculated as the other two classes of characteristics. Therefore, twelve characteristic vectors are extracted from each of the protein sequences. Next, the characteristic vectors are weighed by a simple weighing function and inputted into a BP neural network predictor named PSP-Weighted Neural Network （PSP-WNN）. The Levenberg-Marquardt algorithm is employed to adjust the weight matrices and thresholds during the network training instead of the error back propagation algorithm. With a jackknife test on the RH2427 dataset, PSP-WNN has achieved a higher overall prediction accuracy of 88.4% rather than the prediction results by the general BP neural network, Markov model, and fuzzy k-nearest neighbors algorithm on this dataset. In addition, the prediction performance of PSP-WNN has been evaluated with a five-fold cross validation test on the PK7579 dataset and the prediction results have been consistently better than those of the previous method on the basis of several support vector machines, using compositions of both amino acids and amino acid pairs. These results indicate that PSP-WNN is a powerful tool for subcellular localization prediction. At the end of the article, influences on prediction accuracy using different weighting proportions among three characteristic vector categories have been discussed. An appropriate proportion is considered by increasing the prediction accuracy.
文摘In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.
文摘On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.
文摘An approach for generating test problems by a computer using the Monte Carlo method based upon user-given characterizations is described.A single point X~* is prespocified by the user to be a solution of the test problems.The approach is flex- ible enough to specify function values,gradients,Hesse,degeneracy degree and ill- conditioned degree at the point X~*.Other numerical features such as indefiniteness, convexity are also under user's control.
文摘In today's aircraft,the hardware redundancy is driven by the critical surfaces resulting in single point-failures.Reconfiguration technology remoVes the single surface criticality by employing control surfaces with aerodynamic redundancy.This paper studies a control reconfiguration scheme based on Control Mixer Concept.A technique for the design of a control mixer for an aircraft with damaged surfaces/actuators using the pseudo-inverse is developed and applied.This paper discusses its applications and limitations based on linear analysis and computer simulation.
文摘The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability of the problem is given. A numerical algorithm for solving the problem is provided and a numerical example is presented.
文摘Melanocytic matricoma is a very rare adnexal tumor that recapitulates the anagen hair follicle bulb. Few cases of malignant melanocytic matricoma have been reported, thus criteria for malignant potential have not been previously reviewed. We report a case of an 81 year old male that was originally diagnosed as atypical melanocytic matricoma. The site was re-excised with a small focus of residual tumor, but all margins were negative. The re-excision site healed without complication. However, two years after the original biopsy, a new 8 mm firm nodule appeared at the re-excision site, which was subsequently diagnosed as malignant melanocytic matricoma (MMM). In the following paper we will report a new case of MMM and review potential criteria that could be used in the future to establish malignant potential.
基金National Natural Science Foundation of China!(No.6 97740 33)
文摘As it is well known,it is difficult to identify a nonlinear time varying system using traditional identification approaches,especially under unknown nonlinear function.Neural networks have recently emerged as a successful tool in the area of identification and control of time invariant nonlinear systems.However,it is still difficult to apply them to complicated time varying system identification.In this paper we present a learning algorithm for identification of the nonlinear time varying system using feedforward neural networks.The main idea of this approach is that we regard the weights of the network as a state of a time varying system,then use a Kalman filter to estimate the state.Thus the network implements nonlinear and time varying mapping.We derived both the global and local learning algorithms.Simulation results demonstrate the effectiveness of this approach.
文摘A systematic geometric model has been presented for calibration of a newly designed 5-axis turbine blade grinding machine. This machine is designed to serve a specific purpose to attain high accuracy and high efficiency grinding of turbine blades by eliminating the hand grinding process. Although its topology is RPPPR （P： prismatic; R： rotary）, its design is quite distinct from the competitive machine tools. As error quantification is the only way to investigate, maintain and improve its accuracy, calibra- tion is recommended for its performance assessment and acceptance testing. Systematic geometric error modeling technique is implemented and 52 position dependent and position independent errors are identified while considering the machine as five rigid bodies by eliminating the set-up errors of workpiece and cutting tool. 39 of them are found to have influential errors and are accommodated for finding the resultant effect between the cutting tool and the workpiece in workspace volume. Rigid body kinematics techniques and homogenous transformation matrices are used for error synthesis.
基金Supported by the German Research Foundation(DFG)(No.Forschergruppe 536)the Hundred Talents Program of the Chinese Academy of Sciences
文摘In the past few decades, the increase in grazing intensity has led to soil degradation and desertification in Inner Mongolia grassland, China, due to population growth and shift in the socio-economic system. Two sites with different grazing intensities, continuous grazing site （CG） with 1.2 sheep ha-1 year-1 and heavy grazing site （HG） with 2.0 sheep ha-1 year-1, were investigated at the Inner Mongolia Grassland Ecosystem Research Station （43° 37′ 50″ N, 116° 42′ 18″ E） situated in the northern China to i） characterize the temporal distribution of soil water content along soil profile; and ii） quantify the water fluxes as affected by grazing intensity. Soil water content was monitored by time domain refiectometry （TDR） probes. Soil water retention curves were determined by pressure membrane extractor, furthermore processed by RETC （RETention Curve） software. Soil matric potential, plant available water and water flux were calculated using these data. Both sites showed an identical seasonal soil water dynamics within four defined hydraulic periods： i） wetting transition coincided with a dramatic water increase due to snow and frozen soil thawing from March to April; 2） wet summer, rainfall in accordance with plant growth from May to September; 3） drying transition, a decrease of soil water from October to November due to rainfall limit; and 4） dry winter, freezing from December to next February. Heavy grazing largely reduced soil water content by 43%-48% and plant available water by 46%-61% as compared to the CG site. During growing season net water flux was nearly similar between HG （242 mm） and CG （223 mm） sites between 5 and 20 cm depths. However, between 20 and 40 cm depths, the upward flux was more pronounced at HG site than at CG site, indicating that water was depleted by root uptake at HG site but stored at CG site. In semi-arid grassland ecosystem, grazing intensity can affect soil water regime and flux, particularly in the growing season.
基金supported by the National Natural Science Foundation of China(61174094)the Tianjin Natural Science Foundation of China(13JCYBJC1740014JCYBJC18700)
文摘Using semi-tensor product of matrices, the controllability and stabilizability of finite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions are represented in matrix forms.Based on this algebraic description, a necessary and sufficient condition is proposed for checking whether a state is controllable to another one. By this condition, an algorithm is established to find all the control sequences of an arbitrary length. Moreover, the stabilizability of finite automata is considered, and a necessary and sufficient condition is presented to examine whether some states can be stabilized. Finally, the study of illustrative examples verifies the correctness of the presented results/algorithms.
