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【期刊论文】Oscillation of Self-Adjoint Second-Order Vector Difference Equations to the Parameter
史玉明, YUMING SHI
PERGAMON Computers and Mathematics with Applications 45(2003)1591-1600,-0001,():
-1年11月30日
This paper is concerned with oscillation of self-adjoint second-order vector difference equations with respect to a parameter. Properties of zeros and monotonicity of matrix-valued so-lutions are studied. The oscillation of two consecutive polynomials for vector-valued solutions is discussed. A separation theorem for matrix-valued solutions is also obtained.
Second-order vector difference equation, Oscillation with respect to a parameter
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【期刊论文】Spectral Theory of Second-Order Vector Difference Equations*
史玉明, Yuming Shi and Shaozhu Chcn
Journal of Mathematical Analysis and Applications 239, 195-212 (1999),-0001,():
-1年11月30日
This paper is concerned with spectral problems of second-order vector difference equation with two-point boundary value conditions, where the matrix-valued coneffcient of the leading term may be singular. A concept of self-adjointness of the boundary value conditions is introduced. The self-adjointness of the corresponding difference operator is discussed on a suitable admissible function space, and fundamental spcetal results are obtained. The dual orthogonality of eigenfunc-tions is shown in a special case. Reyleigh's principles and the minimax theorems in two linear spaces are given. As an application, a comparison theorem for eigenval-ues of two Sturm-Liouville problems is presented.
second-order difference equation, boundary value problem, spectral theory, self-adjoint operator
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【期刊论文】Introduction to anti-control of discrete chaos: theory and applications
史玉明, BY GUANRONG CHEN, * AND YUMING SHI
Phil. Trans. R. Soc. A(2006)364, 2433-2447,-0001,():
-1年11月30日
In this paper, the notion of anti-control of chaos (or chaotification) is introduced, which means to make an originally non-chaotic dynamical system chaotic or enhance the existing chaos of a chaotic system. The main interest in this paper is to employ the classical feedback control techniques. Only the discrete case is discussed in detail, including both finite-dimensional and infinite-dimensional settings.
chaos, chaotification, finite-and infinite-dimensional discrete chaos
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