In this paper, we provide a separation theorem for the singular linear quadratic （LQ） control problem of ItS-type linear systems in the case of the state being partially observable. Above all, the Kalmam Bucy filter...In this paper, we provide a separation theorem for the singular linear quadratic （LQ） control problem of ItS-type linear systems in the case of the state being partially observable. Above all, the Kalmam Bucy filtering of the dynamics is given by means of Girsanov transformation, by which the suboptimal feedback control of the LQ problem is determined. Furthermore, it is shown that the well-posedness of the LQ problem is equivalent to the solvability of a generalized differential Riccati equation （GDRE）.展开更多
We show a method to separate the sound field radiated by a signal source from the sound field radiated by noise sources and to reconstruct the sound field radiated by the signal source. The proposed method is based on...We show a method to separate the sound field radiated by a signal source from the sound field radiated by noise sources and to reconstruct the sound field radiated by the signal source. The proposed method is based on reciprocity theorem and the Fourier transform. Both the sound field and its gradient on a measurement surface are needed in the method. Evanescent waves are considered in the method, which ensures a high resolution reconstruction in the near field region of the signal source when evanescent waves can be measured. A simulation is given to verify the method and the influence of measurement noise on the method is discussed.展开更多
A kind of cone separation theorems is established, by which the extension theorems for cone linear continuous operators are developed. As an application, the extension theorem for positive linear continuous operators ...A kind of cone separation theorems is established, by which the extension theorems for cone linear continuous operators are developed. As an application, the extension theorem for positive linear continuous operators is given.展开更多
By using function S-rough sets（function singular rough sets）, this paper gives rough law generation and the theorem of rough law generation.Based on these results above, the paper proposes rough law separation, the ...By using function S-rough sets（function singular rough sets）, this paper gives rough law generation and the theorem of rough law generation.Based on these results above, the paper proposes rough law separation, the theorem of rough law separation, the compound generation theorem of rough law bands, and the principle of rough law bands.In the end, an application of rough law separation in recognizing the risk law of profit is presented.展开更多
In this paper, by virtue of separation theorems of convex sets and scalarization functions, some minimax inequalities are first considered. As applications, some existence theorems of vector equilibrium problems with ...In this paper, by virtue of separation theorems of convex sets and scalarization functions, some minimax inequalities are first considered. As applications, some existence theorems of vector equilibrium problems with different order structures were also obtained.展开更多
This paper extends Farkas Minkowski’s Lemma and Stiemke’s Lemma from the Euclidean space to (l 1,l ∞). The extensions of Farkas Minkowski’s Lemma and Stiemke’s Lemma are the Basic Valuation Theore...This paper extends Farkas Minkowski’s Lemma and Stiemke’s Lemma from the Euclidean space to (l 1,l ∞). The extensions of Farkas Minkowski’s Lemma and Stiemke’s Lemma are the Basic Valuation Theorem in the case (l 1,l ∞). The security price is weakly arbitrage free if and only if there exists a positive state vector; the security price is strictly arbitrage free if and only if there exists a strictly positive state vector. The present value of the securities prices at date 0 is the value of their returns over all countably infinite possible states of nature at date 1.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 61174078)the Mathematical Tianyuan Youth Foundation of China (Grant No. 11126094)+1 种基金the Key Project of Natural Science Foundation of Shandong Province (Grant No. ZR2009GZ001)the research project of "SDUST Spring Bud" (Grant No.2009AZZ074)
文摘In this paper, we provide a separation theorem for the singular linear quadratic （LQ） control problem of ItS-type linear systems in the case of the state being partially observable. Above all, the Kalmam Bucy filtering of the dynamics is given by means of Girsanov transformation, by which the suboptimal feedback control of the LQ problem is determined. Furthermore, it is shown that the well-posedness of the LQ problem is equivalent to the solvability of a generalized differential Riccati equation （GDRE）.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11374270 and 11674294
文摘We show a method to separate the sound field radiated by a signal source from the sound field radiated by noise sources and to reconstruct the sound field radiated by the signal source. The proposed method is based on reciprocity theorem and the Fourier transform. Both the sound field and its gradient on a measurement surface are needed in the method. Evanescent waves are considered in the method, which ensures a high resolution reconstruction in the near field region of the signal source when evanescent waves can be measured. A simulation is given to verify the method and the influence of measurement noise on the method is discussed.
文摘A kind of cone separation theorems is established, by which the extension theorems for cone linear continuous operators are developed. As an application, the extension theorem for positive linear continuous operators is given.
基金supported partly by the Natural Science Foundation of Shandong Province of China (Y2007Ho2)the Elementary and Advanced Technology Foundation of Henan Province of China (082300410040)
文摘By using function S-rough sets（function singular rough sets）, this paper gives rough law generation and the theorem of rough law generation.Based on these results above, the paper proposes rough law separation, the theorem of rough law separation, the compound generation theorem of rough law bands, and the principle of rough law bands.In the end, an application of rough law separation in recognizing the risk law of profit is presented.
文摘In this paper, by virtue of separation theorems of convex sets and scalarization functions, some minimax inequalities are first considered. As applications, some existence theorems of vector equilibrium problems with different order structures were also obtained.
文摘This paper extends Farkas Minkowski’s Lemma and Stiemke’s Lemma from the Euclidean space to (l 1,l ∞). The extensions of Farkas Minkowski’s Lemma and Stiemke’s Lemma are the Basic Valuation Theorem in the case (l 1,l ∞). The security price is weakly arbitrage free if and only if there exists a positive state vector; the security price is strictly arbitrage free if and only if there exists a strictly positive state vector. The present value of the securities prices at date 0 is the value of their returns over all countably infinite possible states of nature at date 1.
