Results 1 to 10 of about 524,744 (263)
Generalized oscillatory matrices [PDF]
Linear Algebra and Its Applications, 2003 The paper is a continuation of the recent series of the authors' works [see for example \textit{M. Fiedler} and \textit{T. L. Markham}, Linear Algebra Appl. 345, 9-28 (2002; Zbl 0995.15016) and references therein] on the theory of totally nonnegative matrices over noncommutative rings. Let \(R\) be a noncommutative ring with the identity 1 and positive
Miroslav Fiedler, Shaun M Fallat
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Two results on basic oscillatory matrices [PDF]
Linear Algebra and Its Applications, 2004 Denote by \(L_k\) (resp. \(U_k\)), \(k=1,\ldots, n-1\), the class of all \(n\times n\) matrices of the form \(D+aE_{n-k+1,n-k}\) (resp. \(D+aE_{n-k,n-k+1}\)) with a positive diagonal matrix \(D\) and a positive \(a\), where \(E_{i,j}\) is the matrix with \(1\) at the position \((i,j)\) and zeros elsewhere.
Miroslav Fiedler
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A remark on oscillatory matrices [PDF]
Linear Algebra and Its Applications, 2004 The class of oscillatory matrices introduced by \textit{F. P. Gantmacher} and \textit{M. G. Krein} [Oscillation matrices and kernels and small vibrations of mechanical systems (2002; Zbl 1002.74002)] is considered. An \(n\times n\) matrix \(A\) is called totally nonnegative (resp. totally positive) if any minor of \(A\) is nonnegative (resp. positive).
Shaun M Fallat
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On the schur and singular value decompositions of oscillatory matrices [PDF]
Linear Algebra and Its Applications, 1997 The author describes the Schur, singular value, and polar decomposition of oscillatory matrices. A class of rectangular matrices is introduced, which generalizes oscillatory matrices, and the existence and uniqueness of a solution of the corresponding total least squares problem, is proved.
J M Pena
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A class of oscillatory matrices with exponent n−1 [PDF]
Linear Algebra and Its Applications, 2007 The authors describe the class of \(n\times n\) oscillatory matrices which have maximal exponent equal to \(n-1\). \textit{F. P. Gantmacher} and \textit{M. G. Krein} [Oscillation matrices and kernels and small vibrations of mechanical systems. (2002; Zbl 1002.74002)] laid the groundwork for the theory of oscillatory matrices.
Shaun Fallat
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Bidiagonal factorizations and quasi-oscillatory rectangular matrices [PDF]
Linear Algebra and Its Applications, 2008 An \(m\times n\) real matrix \(A\) is called totally nonnegative if all its minors are nonnegative, and totally positive if all its minors are positive. The authors define a totally nonnegative matrix \(A\) to be quasi-oscillatory if some positive integral power of \(AA^{\top}\) is totally positive.
Juan R Torregrosa
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The eigenvalue distribution of oscillatory and strictly sign-regular matrices [PDF]
Linear Algebra and Its Applications, 1996 A formula is derived for the ratio of two successive eigenvalues of an oscillatory matrix \(A\), the formulae for the eigenvalues being \(\lambda_{p+1} = \lambda_p \lim_{j \to\infty} N(A^j_p)^{1/j} = \lambda_p \inf_{j \in \mathbb{N}} N(A^j_p)^{1/j}\), where \(N\) is the Hopf oscillation ratio. Related formulae are also derived for strictly sign-related
Eveson, S.P.
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On the exponent of several classes of oscillatory matrices [PDF]
Linear Algebra and Its Applications, 2021 Oscillatory matrices were introduced in the seminal work of Gantmacher and Krein. An $n\times n$ matrix $A$ is called oscillatory if all its minors are nonnegative and there exists a positive integer $k$ such that all minors of $A^k$ are positive. The smallest $k$ for which this holds is called the exponent of the oscillatory matrix $A$. Gantmacher and
Michael Margaliot, Yoram Zarai
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Soliton management in a variable-coefficient coupled dispersionless system via Darboux transformation [PDF]
Scientific ReportsWe study a coupled dispersionless system in $$(1+1)$$ dimensions with a time-dependent coefficient in the nonlinear coupling. The model consists of a real field u(x, t) and a complex field $$\psi (x,t)$$ , driven by a prescribed modulation function ...
H. W. A. Riaz +2 more
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A dynamical systems model of emotional contagion: Oscillatory coupling in the circumplex of affect. [PDF]
PLoS ONEBackgroundEmotional contagion plays a crucial role in shaping group dynamics, interpersonal relationships, and affective regulation. Mathematical models of affect and agent-based models of emotional contagion are well established, but fewer formulations ...
Diego Alexander Garzón-Alvarado +3 more
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