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Analysis and nomograph development for a leaky pipeline carrying plug flow based on numerical modeling and experimental validation. [PDF]

Sci Rep
Ferroudji H, Barooah A, Hassan I, Sleiti AK, Gomari SR, Hamilton M, Rahman MA.   +6 more
europepmc   +1 more source

Amplitude-Frequency Response Characteristics and Parameter Optimization of a Bistable Nonlinear Energy Sink Under Wide-Frequency Harmonic Excitation. [PDF]

Materials (Basel)
Bao X, Lou J, Yang Q, Wang J, Yang M, Tan M.   +5 more
europepmc   +1 more source

Flexible ultrasound array for subcortical brain stimulation in humans: a simulation study. [PDF]

NPJ Acoust
Huo H, DiSpirito A, Wang N, Li C, Moon S, Qiu C, Yin K, Wu H, Sun B, Horstmeyer R, Feng W, Jiang X, Ni X, Yao J.   +13 more
europepmc   +1 more source

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The numerical range and decomposable numerical range of matrices

Linear and Multilinear Algebra, 1991
Let m and n be positive integers such that 1≤m≤n. Denote by the set of all n×m complex matrices. For a matrix , the mth decomposable numerical range of A is the set When m=1, it reduces to the classical numerical range of A which is denoted by W(A). It is known that is contaned in W(Cm (A)), where Cm (A) is the mth compound of A. In this paper we study
Natália Bebiano, Chi-Kwong Li, Jo[etilde]o Da Providência   +2 more
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Numerical range submultiplicity

Linear and Multilinear Algebra, 2015
Let and be elements of a complex unital Banach algebra. The numerical range submultiplicity is investigated. As a consequence of the inclusions established, we confirm a conjecture that if and are self-adjoint operators such that is positive then the product is self-adjoint whenever it is normal.
Mohamed Barraa, Mohamed Boumazgour
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Ratio Numerical Ranges of Operators

Integral Equations and Operator Theory, 2011
Let \(H\) be a Hilbert space and \(L(H)\) the algebra of bounded linear operators on \(H\). For \(A\in L(H)\), the numerical range of \(A\) is given by \(W(A)= \{\langle Ax,x\rangle:x\in H,\;\langle x,x\rangle=1\}\). For \(A,B\in L(H)\), \(B\neq 0\), define the ratio numerical range \[ W(A/B)=\left\{\frac{\langle Ax,x\rangle}{\langle Bx,x\rangle}:x\in ...
Rodman, Leiba, Spitkovsky, Ilya M.
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Numerical Ranges II

1973
Numerical Ranges II is a sequel to Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras written by the same authors and published in this series in 1971. The present volume reflects the progress made in the subject, expanding and discussing topics under the general headings of spatial and algebra numerical ranges and ...
F. F. Bonsall, J. Duncan
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Numerical Range of Matrix Polynomials

SIAM Journal on Matrix Analysis and Applications, 1994
Let \(A_ i\), \(i = 1, \dots, m\) be \(n \times n\) matrices with complex coefficients and consider the matrix polynomial \(P(\lambda) = \sum_{i=0}^ m A_ i \lambda^ i\). The numerical range of \(P(\lambda)\) is defined through \[ W \bigl( P(\lambda) \bigr) : = \{\mu \in \mathbb{C} \mid x^* P(\mu)x = 0 \quad \text{for some nonzero} \quad x \in \mathbb{C}
Li, Chi-Kwong, Rodman, Leiba
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