This paper proposes a new matrix product, namely, semi-tensor product. It is a general-ization of the conventional matrix product. Meanwhile, it is also closely related to Kronecker (tensor) product of matrices. The p...This paper proposes a new matrix product, namely, semi-tensor product. It is a general-ization of the conventional matrix product. Meanwhile, it is also closely related to Kronecker (tensor) product of matrices. The purpose of introducing this product is twofold: (i) treat multi-dimensional da-ta; (ii) treat nonlinear problems in a linear way. Then the computer and numerical methods can be easily used for solving nonlinear problems. Properties and formulas are deduced. As an application, the Morgan's problem for control systems is formulated as a numerically solvable problem.展开更多
We introduce the notion of the contraction integrated semigroups and give the Lumber-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their appl...We introduce the notion of the contraction integrated semigroups and give the Lumber-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their application, a necessary and sufficient condition for q-matrices Q generating a contraction integrated semigroup is given, and a necessary and sufficient condition for a transition function to be a Feller-Reuter-Riley transition function is also given in terms of its q-matrix.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 this paper a comprehensive introduction for modeling and control of networked evolutionary games （NEGs） via semi-tensor product （STP） approach is presented. First, we review the mathematical model of an NEG, wh...In this paper a comprehensive introduction for modeling and control of networked evolutionary games （NEGs） via semi-tensor product （STP） approach is presented. First, we review the mathematical model of an NEG, which consists of three ingredients： network graph, fundamental network game, and strategy updating rule. Three kinds of network graphs are considered, which are i） undirected graph for symmetric games; ii） directed graph for asymmetric games, and iii） d-directed graph for symmetric games with partial neighborhood information. Three kinds of fundamental evolutionary games （FEGs） are discussed, which are i） two strategies and symmetric （S-2）; ii） two strategies and asymmetric （A-2）; and iii） three strategies and symmetric （S-3）. Three strategy updating rules （SUR） are introduced, which are i） Unconditional Imitation （UI）; ii） Fermi Rule（FR）; iii） Myopic Best Response Adjustment Rule （MBRA）. First, we review the fundamental evolutionary equation （FEE） and use it to construct network profile dynamics （NPD）of NEGs. To show how the dynamics of an NEG can be modeled as a discrete time dynamics within an algebraic state space, the fundamental evolutionary equation （FEE） of each player is discussed. Using FEEs, the network strategy profile dynamics （NSPD） is built by providing efficient algorithms. Finally, we consider three more complicated NEGs： i） NEG with different length historical information, ii） NEG with multi-species, and iii） NEG with time-varying payoffs. In all the cases, formulas are provided to construct the corresponding NSPDs. Using these NSPDs, certain properties are explored. Examples are presented to demonstrate the model constructing method, analysis and control design technique, and to reveal certain dynamic behaviors of NEGs.展开更多
Collagen materials were crosslinked by 1-ethyl-3-(3-dimethyl aminopropyl) carbodiimide (EDC) in the presence of chondroitin sulfate (CS), one of glycosaminoglycans (GAGS). PVA and chitosan were also blended with colla...Collagen materials were crosslinked by 1-ethyl-3-(3-dimethyl aminopropyl) carbodiimide (EDC) in the presence of chondroitin sulfate (CS), one of glycosaminoglycans (GAGS). PVA and chitosan were also blended with collagen. The physical and chemical properties of the matrices were characterized by SEM, DSC, and ESCA. L929 cells were implanted on the matrices to show the cytotoxic and the biological characters of the materials. The results indicate that EDC is an effective and non-cytotoxic cross-link reagent, which can replace the common dialdehyde reagent. The attachment of CS can improve the stability of collagen and accelerate cell growth. The addition of PVA can prepare porous matrices with smaller bore size. There are reactions between the chitosan and collagen, and the composite has good biological character. The presence of chitosan can also increase the amount of incorporated CS.展开更多
Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction for many mixed orthogonal arrays. But t...Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction for many mixed orthogonal arrays. But there are also orthogonal arrays which cannot be obtained by the usual difference matrices, such as mixed orthogonal arrays of run size 60. In order to construct these mixed orthogonal arrays, a class of special so-called generalized difference matrices were discovered by Zhang (1989,1990,1993,2006) from the orthogonal decompositions of projection matrices. In this article, an interesting equivalent relationship between orthogonal arrays and the generalized difference matrices is presented and proved. As an application, a lot of new orthogonal arrays of run size 60 have been constructed.展开更多
基金This work was supported by the National Natural Science Foundation of China ( Grant Nos. G69774008, G59837270) National 973 Project (Grant No. G1998020308) National Key Project of China.
文摘This paper proposes a new matrix product, namely, semi-tensor product. It is a general-ization of the conventional matrix product. Meanwhile, it is also closely related to Kronecker (tensor) product of matrices. The purpose of introducing this product is twofold: (i) treat multi-dimensional da-ta; (ii) treat nonlinear problems in a linear way. Then the computer and numerical methods can be easily used for solving nonlinear problems. Properties and formulas are deduced. As an application, the Morgan's problem for control systems is formulated as a numerically solvable problem.
文摘We introduce the notion of the contraction integrated semigroups and give the Lumber-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their application, a necessary and sufficient condition for q-matrices Q generating a contraction integrated semigroup is given, and a necessary and sufficient condition for a transition function to be a Feller-Reuter-Riley transition function is also given in terms of its q-matrix.
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This work was partially supported by National Natural Science Foundation of China （Nos. 61273013, 61333001, 61104065, 61322307）.
文摘In this paper a comprehensive introduction for modeling and control of networked evolutionary games （NEGs） via semi-tensor product （STP） approach is presented. First, we review the mathematical model of an NEG, which consists of three ingredients： network graph, fundamental network game, and strategy updating rule. Three kinds of network graphs are considered, which are i） undirected graph for symmetric games; ii） directed graph for asymmetric games, and iii） d-directed graph for symmetric games with partial neighborhood information. Three kinds of fundamental evolutionary games （FEGs） are discussed, which are i） two strategies and symmetric （S-2）; ii） two strategies and asymmetric （A-2）; and iii） three strategies and symmetric （S-3）. Three strategy updating rules （SUR） are introduced, which are i） Unconditional Imitation （UI）; ii） Fermi Rule（FR）; iii） Myopic Best Response Adjustment Rule （MBRA）. First, we review the fundamental evolutionary equation （FEE） and use it to construct network profile dynamics （NPD）of NEGs. To show how the dynamics of an NEG can be modeled as a discrete time dynamics within an algebraic state space, the fundamental evolutionary equation （FEE） of each player is discussed. Using FEEs, the network strategy profile dynamics （NSPD） is built by providing efficient algorithms. Finally, we consider three more complicated NEGs： i） NEG with different length historical information, ii） NEG with multi-species, and iii） NEG with time-varying payoffs. In all the cases, formulas are provided to construct the corresponding NSPDs. Using these NSPDs, certain properties are explored. Examples are presented to demonstrate the model constructing method, analysis and control design technique, and to reveal certain dynamic behaviors of NEGs.
基金This work is supported by the National Natural Science Foundation of China for Prominent Younth(No.59625306)National Emphasis Basis Subject(973.Programn)G1999054309-4.
文摘Collagen materials were crosslinked by 1-ethyl-3-(3-dimethyl aminopropyl) carbodiimide (EDC) in the presence of chondroitin sulfate (CS), one of glycosaminoglycans (GAGS). PVA and chitosan were also blended with collagen. The physical and chemical properties of the matrices were characterized by SEM, DSC, and ESCA. L929 cells were implanted on the matrices to show the cytotoxic and the biological characters of the materials. The results indicate that EDC is an effective and non-cytotoxic cross-link reagent, which can replace the common dialdehyde reagent. The attachment of CS can improve the stability of collagen and accelerate cell growth. The addition of PVA can prepare porous matrices with smaller bore size. There are reactions between the chitosan and collagen, and the composite has good biological character. The presence of chitosan can also increase the amount of incorporated CS.
基金supported by the National Natural Science Foundation of China(1127105011371183+2 种基金61403036)the Science and Technology Development Foundation of CAEP(2013A04030202013B0403068)
基金supported by Visiting Scholar Foundation of Key Lab in University and by National Natural Science Foundation of China (Grant No. 10571045)Specialized Research Fund for the Doctoral Program of Higher Education of Ministry of Education of China (Grant No. 44k55050)
文摘Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction for many mixed orthogonal arrays. But there are also orthogonal arrays which cannot be obtained by the usual difference matrices, such as mixed orthogonal arrays of run size 60. In order to construct these mixed orthogonal arrays, a class of special so-called generalized difference matrices were discovered by Zhang (1989,1990,1993,2006) from the orthogonal decompositions of projection matrices. In this article, an interesting equivalent relationship between orthogonal arrays and the generalized difference matrices is presented and proved. As an application, a lot of new orthogonal arrays of run size 60 have been constructed.
