Results 261 to 270 of about 607,065 (288)

The Dynamics of Vector Fields with Singularities

Acta Mathematica Sinica, English Series, 2022
The article is a survey of recent results on dynamics of vector fields exhibiting singularities that are accumulated by recurrent regular points robustly. The author considers the notion of singular hyperbolicity as introduced in [\textit{C. A. Morales} et al., Ann. Math. (2) 160, No. 2, 375--432 (2004; Zbl 1071.37022)].
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On the Singular “Vectors” of the Lyapunov Operator

SIAM Journal on Algebraic Discrete Methods, 1987
For a matrix \(A\in R^{n\times n}\), the separation of \(A^ T\) and A is defined as \(sep(A^ T,-A)=\min_{X}\| A^ TX+XA\| /\| X\|,\) \(X\neq 0\), where \(\|.\|\) denotes the Frobenius matrix norm. The conjecture that the minimizer X is a real symmetric matrix is discussed.
Byers, Ralph, Nash, Stephen
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Genericity and Singularities in Vector Optimization

1978
Let C∞ be the set of smooth maps u from X to Y, where X and Y are open smooth manifolds of dimension n and m respectively (for our purposes we shall take Y = Rm). Let Λ be an open convex cone in Rm with non empty interior, \(\bar \Lambda \) its closure, ∂Λ its boundary.
MARZOLLO A, PASCOLETTI A, SERAFINI, Paolo   +2 more
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Understanding Singular Vectors

The College Mathematics Journal, 2013
SummaryA certain weighted average of the rows (and columns) of a non-negative matrix yields a surprisingly simple, heuristical approximation to its singular vectors. There are correspondingly good approximations to the singular values. Such rules of thumb provide an intuitive interpretation of the singular vectors that helps explain why the SVD is so ...
David James, Cynthia Botteron
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Singularities in vectoral fields

SPIE Proceedings, 1999
Novel approach for the analysis of singularities in vector fields has been proposed. The essence of this approach is scalar consideration of the phase vortices at the orthogonal field components. The new type of vortices are introduced, namely the phase-difference vortices. The sign principle for the phase-difference vortices is formulated.
Oleg V. Angelsky, R. N. Besaha, Alexey I. Mokhun, Igor I. Mokhun, M. O. Sopin, Marat S. Soskin, Mikhail V. Vasnetsov   +6 more
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Vector optimization: Singularities, regularizations

Mathematical Methods of Operations Research, 1998
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Singularities of vector fields on

Nonlinearity, 1998
In his well known paper `Singularities of vector fields', Takens made a topological classification of vector fields up to codimension 2 and introduced a semialgebraic stratification to distinguish the different cases; from dimensions he had to use the notion of `weak--equivalence'.
F Dumortier, S Ibáñez
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Nonlinear singular vectors and nonlinear singular values

Science in China Series D: Earth Sciences, 2000
A novel concept of nonlinear singular vector and nonlinear singular value is introduced, which is a natural generalization of the classical linear singular vector and linear singular value to the nonlinear category. The optimization problem related to the determination of nonlinear singular vectors and singular values is formulated. The general idea of
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Zero-One Rounding of Singular Vectors

2012
We propose a generic and simple technique called dyadic rounding for rounding real vectors to zero-one vectors, and show its several applications in approximating singular vectors of matrices by zero-one vectors, cut decompositions of matrices, and norm optimization problems. Our rounding technique leads to the following consequences.
Amit Deshpande 0001, Ravindran Kannan, Nikhil Srivastava   +2 more
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Singularities of Analytic Vector Functions

American Journal of Mathematics, 1935
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