Search results for "VECTOR"
showing 10 items of 2660 documents
Dual attachment pairs in categorically-algebraic topology
2011
[EN] The paper is a continuation of our study on developing a new approach to (lattice-valued) topological structures, which relies on category theory and universal algebra, and which is called categorically-algebraic (catalg) topology. The new framework is used to build a topological setting, based in a catalg extension of the set-theoretic membership relation "e" called dual attachment, thereby dualizing the notion of attachment introduced by the authors earlier. Following the recent interest of the fuzzy community in topological systems of S. Vickers, we clarify completely relationships between these structures and (dual) attachment, showing that unlike the former, the latter have no inh…
Vacancy-like Dressed States in Topological Waveguide QED
2020
We identify a class of dressed atom-photon states formingat the same energy of the atom at any coupling strength. As a hallmark, their photonic component is an eigenstate of the bare photonic bath with a vacancy in place of the atom. The picture accommodates waveguide-QED phenomena where atoms behave as perfect mirrors, connecting in particular dressed bound states (BS) in the continuum or BIC with geometrically-confined photonic modes. When applied to photonic lattices, the framework provides a general criterion to predict dressed BS in lattices with topological properties by putting them in one-to-one correspondence with photonic BS. New classes of dressed BS are thus predicted in the pho…
The convective eigenvalues of the one–dimensional p–Laplacian as p → 1
2020
Abstract This paper studies the limit behavior as p → 1 of the eigenvalue problem { − ( | u x | p − 2 u x ) x − c | u x | p − 2 u x = λ | u | p − 2 u , 0 x 1 , u ( 0 ) = u ( 1 ) = 0 . We point out that explicit expressions for both the eigenvalues λ n and associated eigenfunctions are not available (see [16] ). In spite of this hindrance, we obtain the precise values of the limits lim p → 1 + λ n . In addition, a complete description of the limit profiles of the eigenfunctions is accomplished. Moreover, the formal limit problem as p → 1 is also addressed. The results extend known features for the special case c = 0 ( [6] , [28] ).
Random Tensor Theory: Extending Random Matrix Theory to Mixtures of Random Product States
2012
We consider a problem in random matrix theory that is inspired by quantum information theory: determining the largest eigenvalue of a sum of p random product states in $${(\mathbb {C}^d)^{\otimes k}}$$ , where k and p/d k are fixed while d → ∞. When k = 1, the Marcenko-Pastur law determines (up to small corrections) not only the largest eigenvalue ( $${(1+\sqrt{p/d^k})^2}$$ ) but the smallest eigenvalue $${(\min(0,1-\sqrt{p/d^k})^2)}$$ and the spectral density in between. We use the method of moments to show that for k > 1 the largest eigenvalue is still approximately $${(1+\sqrt{p/d^k})^2}$$ and the spectral density approaches that of the Marcenko-Pastur law, generalizing the random matrix…
Removing the saturation assumption in Bank-Weiser error estimator analysis in dimension three
2020
International audience; We provide a new argument proving the reliability of the Bank-Weiser estimator for Lagrange piecewise linear finite elements in both dimension two and three. The extension to dimension three constitutes the main novelty of our study. In addition, we present a numerical comparison of the Bank-Weiser and residual estimators for a three-dimensional test case.
The filter and calibration wheel for the ATHENA wide field imager
2016
The planned filter and calibration wheel for the Wide Field Imager (WFI) instrument on Athena is presented. With four selectable positions it provides the necessary functions, in particular an UV/VIS blocking filter for the WFI detectors and a calibration source. Challenges for the filter wheel design are the large volume and mass of the subsystem, the implementation of a robust mechanism and the protection of the ultra-thin filter with an area of 160 mm square. This paper describes performed trade-offs based on simulation results and describes the baseline design in detail. Reliable solutions are envisaged for the conceptual design of the filter and calibration wheel. Four different varian…
Early detection and classification of bearing faults using support vector machine algorithm
2017
Bearings are one of the most critical elements in rotating machinery systems. Bearing faults are the main reason for failures in electrical motors and generators. Therefore, early bearing fault detection is very important to prevent critical system failures in the industry. In this paper, the support vector machine algorithm is used for early detection and classification of bearing faults. Both time and frequency domain features are used for training the support vector machine learning algorithm. The trained classier can be employed for real-time bearing fault detection and classification. By using the proposed method, the bearing faults can be detected at early stages, and the machine oper…
Sensorless control of induction motors using an extended Kalman filter and linear quadratic tracking
2017
Induction motors are the most commonly used prime-movers in industrial applications. Many induction motors supplied by frequency converters are coupled with a physical angular rotor position/velocity sensor which makes the drive complex and require maintenance. This paper presents a sensorless control structure to avoid using a physical angular rotor position/velocity sensor. The proposed method estimates and control the angular rotor velocity using optimal control theory. The optimal controller used in this paper is based on linear quadratic tracking and the states of the machine are estimated using an extended Kalman filter. Both the controller and the estimator utilize the same internal …
Theoretical insights on the importance of anchoring vs molecular geometry in magnetic molecules acting as junctions
2019
The anchoring of the molecule to an electrode is known to be a key factor in single-molecule spintronics experiments. Likewise, a relaxation down to the most stable geometry is a critical step in theoretical simulations of transport through single-molecule junctions. Herein we present a set of calculations designed to analyze and compare the effect of different anchoring points and the effect of perturbations in the molecular geometry and interelectrode distance. As model system we chose the [V($\alpha$-C$_3$S$_5$)$_3$]$^{2-}$ complex connecting two Au(111) electrodes in a slightly compressed geometry. In our calculations, the attachment happens through an S-Au bond, a common anchoring stra…
B-Scan image analysis for position and shape defect definition in plates
2016
Definition of size, shape and location of defects into a mechanical component is of extreme importance in the manufacturing industry in general and particularly in high-tech applications, and in applications that can become dangerous due to the structural failure of mechanical components. In this paper, a laser-UT system has been used to define position and shape of internal defects in aluminum plates. An infrared pulsed laser is used to generate ultrasonic waves in a point of the plate and a CW laser interferometer is used as receiver to acquire the out-of-plane displacements due to the ultrasonic waves in another point of the plate. The method consists of acquiring a B-Scan map on which s…