Results 41 to 50 of about 6,682,316 (219)
Maximization of the Spectral Gap for Chemical Graphs by means of a Solution to a Mixed Integer Semidefinite Program [PDF]
Computer Methods in Materials Science, 2016 In this paper we analyze the spectral gap of a weighted graph which is the difference between the smallest positive and largest negative eigenvalue of its adjacency matrix. Such a graph can represent e.g. a chemical organic molecule.
Soňa Pavlíková, Daniel Ševčovič
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Real factorization of positive semidefinite matrix polynomials
Linear Algebra and its ApplicationsSuppose $Q(x)$ is a real $n\times n$ regular symmetric positive semidefinite matrix polynomial. Then it can be factored as $$Q(x) = G(x)^TG(x),$$ where $G(x)$ is a real $n\times n$ matrix polynomial with degree half that of $Q(x)$ if and only if $\det(Q(x))$ is the square of a nonzero real polynomial.
Sarah Gift, Hugo J. Woerdeman
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Laser &Photonics Reviews, EarlyView.Coherence variation is ubiquitous in nature, yet determining how it constrains physical observables remains challenging for multimode waves. To address this challenge, this work establishes a majorization‐based theory that identifies the supremum and infimum in the set of input coherence spectra, which provide optimal universal bounds for any linear ...
Shiyu Li, Cheng Guo
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Data‐driven emulation of flow‐dependent background‐error variance in variational data assimilation
Quarterly Journal of the Royal Meteorological Society, EarlyView.A machine‐learning approach is developed to emulate flow‐dependent background‐error variance within a variational data assimilation framework. The method reproduces uncertainty information that would normally require a 50‐member ensemble using only five members, while maintaining comparable observation fit and forecast performance.
Wei Pan +3 more
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On the Perturbation of Schur Complements in Positive Semidefinite Matrices [PDF]
, 1998 This note gives perturbation bounds for the Schur complement of a positive definite matrix in a positive semidefinite matrix.
Stewart, G. W.
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有关矩阵广义逆的惯性指数及其应用(Inertia formulae related to the generalized inverse with applications)
Zhejiang Daxue xuebao. Lixue ban, 2019 In this paper, firstly, we establish the inertia formulae for some matrix expressions related to the generalized inverse . Then, as applications, based on the derived inertia formulae, we study the definiteness of some matrices.
WUZhongcheng(吴中成) +1 more
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Neural Network‐Based Runtime Monitoring and Control for Unknown Nonlinear Systems
International Journal of Robust and Nonlinear Control, EarlyView.ABSTRACT Real‐time system monitoring and stabilization become especially challenging when the system dynamics are unknown. This article introduces a novel design for monitoring and stabilizing unknown nonlinear systems with measurement noise. The design utilizes a generic modelling framework by decomposing the system into a known tunable linear ...
Jianglin Lan, Xianxian Zhao, Ron Patton
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Purifications of multipartite states: limitations and constructive methods
New Journal of Physics, 2013 We analyze the description of quantum many-body mixed states using matrix product states and operators. We consider two such descriptions: (i) as a matrix product density operator of bond dimension D ; and (ii) as a purification that is written as a ...
Gemma De las Cuevas +3 more
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Marginally Strictly Negative Imaginary Systems
International Journal of Robust and Nonlinear Control, EarlyView.ABSTRACT This article revisits a fundamental question in negative imaginary (NI) systems theory: what is the weakest viable notion of strictness that still preserves the classical feedback stability picture? To address this question, we introduce the notion of marginally strictly negative imaginary (MSNI) systems to accommodate simple nonzero imaginary‐
Tianzhe Zhang +3 more
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On the range of a Hadamard power of a positive semidefinite matrix
Linear Algebra and its Applications, 2006 For a polynomial mapping \(F:\mathbb{C}^n\to\mathbb{C}^n\) the Jacobian conjecture asserts that \(F\) is invertible if \(JF\in\mathbb{C}^*\), where \(JF\) denotes the Jacobian matrix of \(F\). \textit{L. M. Druzkowski} [Math. Ann. 264, 303--313 (1983; Zbl 0504.13006)] showed that it suffices to prove the Jacobian conjecture for all cubic-linear ...
Sun, Xiaosong, Du, Xiankun, Liu, Dayan
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