Search results for "linear"
showing 10 items of 7165 documents
Hold-in, Pull-in and Lock-in Ranges for Phase-locked Loop with Tangential Characteristic of the Phase Detector
2019
In the present paper the phase-locked loop (PLL), an electric circuit widely used in telecommunications and computer architectures is considered. A new modification of the PLL with tangential phase detector characteristic and active proportionally-integrating (PI) filter is introduced. Hold-in, pull-in and lock-in ranges for given circuit are studied rigorously. It is shown that lock-in range of the new PLL model is infinite, compared to the finite lock-in range of the classical PLL. peerReviewed
Whispering Gallery Modes: Advanced Photonic Applications
2019
Los micro-resonadores basados en Whispering Gallery Modes (WGMs) han atraido un gran interés en las últimas décadas debido a su fuerte confinamiento de la luz. Tales micro-resonadores pueden ser fabricados con diferentes geometrías y materiales. Estos micro-resonadores exhiben factores de calidad Q altos y volúmenes modales pequeños, lo que permite realizar un gran número de estudios y aplicaciones, como por ejemplo el estudio de efectos no-lineales ópticos. La delgada anchura spectral que presentan las resonancias WGM permite la medida de pequeñas perturbaciones de los parámetros de los micro-resonadores, con un límite de detección bajo. Esta tesis proporciona la caracterización experiment…
Generalized frame operator, lower semiframes, and sequences of translates
2023
Given an arbitrary sequence of elements $\xi =\lbrace \xi _n\rbrace _{n\in \mathbb {N}}$ of a Hilbert space $(\mathcal {H},\langle \cdot ,\cdot \rangle )$, the operator $T_\xi$ is defined as the operator associated to the sesquilinear form $\Omega _\xi (f,g)=\sum _{n\in \mathbb {N}} \langle f , \xi _n\rangle \langle \xi _n , g\rangle$, for $f,g\in \lbrace h\in \mathcal {H}: \sum _{n\in \mathbb {N}}|\langle h , \xi _n\rangle |<^>2<\infty \rbrace$. This operator is in general different from the classical frame operator but possesses some remarkable properties. For instance, $T_\xi$ is always self-adjoint with regard to a particular space, unconditionally defined, and, when xi is a lo…
An Inverse Problem for the Relativistic Boltzmann Equation
2020
We consider an inverse problem for the Boltzmann equation on a globally hyperbolic Lorentzian spacetime $(M,g)$ with an unknown metric $g$. We consider measurements done in a neighbourhood $V\subset M$ of a timelike path $\mu$ that connects a point $x^-$ to a point $x^+$. The measurements are modelled by a source-to-solution map, which maps a source supported in $V$ to the restriction of the solution to the Boltzmann equation to the set $V$. We show that the source-to-solution map uniquely determines the Lorentzian spacetime, up to an isometry, in the set $I^+(x^-)\cap I^-(x^+)\subset M$. The set $I^+(x^-)\cap I^-(x^+)$ is the intersection of the future of the point $x^-$ and the past of th…
Triacylglycerol Analysis in Human Milk and Other Mammalian Species: Small-Scale Sample Preparation, Characterization, and Statistical Classification …
2015
In this work, a method for the separation of triacylglycerols (TAGs) present in human milk and from other mammalian species by reversed-phase high-performance liquid chromatography using a core–shell particle packed column with UV and evaporative light-scattering detectors is described. Under optimal conditions, a mobile phase containing acetonitrile/n-pentanol at 10 °C gave an excellent resolution among more than 50 TAG peaks. A small-scale method for fat extraction in these milks (particularly of interest for human milk samples) using minimal amounts of sample and reagents was also developed. The proposed extraction protocol and the traditional method were compared, giving similar results…
A blow-up result for a nonlinear wave equation on manifolds: the critical case
2021
We consider a inhomogeneous semilinear wave equation on a noncompact complete Riemannian manifold (Formula presented.) of dimension (Formula presented.), without boundary. The reaction exhibits the combined effects of a critical term and of a forcing term. Using a rescaled test function argument together with appropriate estimates, we show that the equation admits no global solution. Moreover, in the special case when (Formula presented.), our result improves the existing literature. Namely, our main result is valid without assuming that the initial values are compactly supported.
Modelling of rotations by using matrix solutions of nonlinear wave equations
2007
A family of matrix solutions of nonlinear wave equations is extended and its application to modelling is given. It is shown that a similarity transformation, induced by the matrix solution, is equivalent to the rotation. Matrix solutions are used for modelling helical motions and vortex rings, simultaneous rotations and particles collision, mapping contraction and pulsating spheres. Geometrical interpretation of the doubling of rotation angle in each step of sequential mapping contraction is given. First Published Online: 14 Oct 2010
The role of physical activity in the link between menopausal status and mental well-being
2020
OBJECTIVE To examine the relationship between menopausal status and mental well-being, and whether this relationship varies as a function of physical activity (PA). METHODS Based on a hormonal analysis and bleeding diary, women aged 47 to 55 were categorized as pre (n = 304), early peri (n = 198), late peri (n = 209), or postmenopausal (n = 387). Mental well-being was assessed using the Centre for Epidemiologic Studies Depression Scale, the International Positive and Negative Affect Schedule Short Form, and the Satisfaction with Life Scale. PA was self-reported and categorized as low, medium, and high. Associations between variables were analyzed using multivariate linear regression adjuste…
The Potentials of Tangible Technologies for Learning Linear Equations
2020
Tangible technologies provide interactive links between the physical and digital worlds, thereby merging the benefits of physical and virtual manipulatives. To explore the potentials of tangible technologies for learning linear equations, a tangible manipulative (TM) was designed and developed. A prototype of the initial TM was implemented and evaluated using mixed methods (i.e., classroom interventions, paper-based tests, thinking aloud sessions, questionnaires, and interviews) in real classroom settings. Six teachers, 24 primary school students, and 65 lower secondary school students participated in the exploratory study. The quantitative and qualitative analysis revealed that the initial…
All-Possible-Couplings Approach to Measuring Probabilistic Context
2013
From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may ‘‘directly’’ influence them, but (iii) other inputs provide a ‘‘context’’ for this response by influencing its probabilistic relations to other responses. These contextual influences are very different, say, in classical kinetic theory and in the entanglement paradigm of quantum mechanics, which are traditionally interpreted as representing different forms of physical determinism. One can mathematically construct systems with other types of contextuality, whether or …