Search results for "equation"
showing 10 items of 4219 documents
Musical pitch quantization as an eigenvalue problem
2020
How can discrete pitches and chords emerge from the continuum of sound? Using a quantum cognition model of tonal music, we prove that the associated Schrödinger equation in Fourier space is invariant under continuous pitch transpositions. However, this symmetry is broken in the case of transpositions of chords, entailing a discrete cyclic group as transposition symmetry. Our research relates quantum mechanics with music and is consistent with music theory and seminal insights by Hermann von Helmholtz.
The dependence of circular dichroism in photoemission on the optical properties of Cs monolayers on Pt(111)
1997
We report on the dependence of dichroic photoemission excited by circularly polarised light on the angle of photon incidence. We measured the difference in the angle-resolved photoemission intensities from Cs 5p semi-core levels excited by photons of opposite helicity, which is known as CDAD. We found that the dependence of the measured differences on the angle of light incidence deviates strongly from the model of CDAD for free atoms, as expected. Using the Fresnel equations and a complex index of refraction, one finds that not only the third component but also the second component of the Stokes vector is responsible for the excitation process. Both Stokes components change sign if the ini…
Identification of stiffness, dissipation and input parameters of multi degree of freedom civil systems under unmeasured base excitations
2009
A time domain dynamic identification technique based on a statistical moment approach has been formulated for civil systems under base random excitations in the linear state. This technique is based on the use of classically damped models characterized by a mass proportional damping. By applying the Itô stochastic calculus, special algebraic equations that depend on the statistical moments of the response can be obtained. These equations can be used for the dynamic identification of the mechanical parameters that define the structural model, in the case of unmeasured input as well, and the identification of the input itself. Furthermore, the above equations demonstrate the possibility of id…
An output-only stochastic parametric approach for the identification of linear and nonlinear structures under random base excitations: Advances and c…
2014
In this paper a time domain output-only Dynamic Identification approach for Civil Structures (DICS) first formulated some years ago is reviewed and presented in a more generalized form. The approach in question, suitable for multi- and single-degrees-of-freedom systems, is based on the statistical moments and on the correlation functions of the response to base random excitations. The solving equations are obtained by applying the Itô differential stochastic calculus to some functions of the response. In the previous version ([21] Cavaleri, 2006; [22] Benfratello et al., 2009), the DICS method was based on the use of two classes of models (Restricted Potential Models and Linear Mass Proport…
The development of school well-being in secondary school: High academic buoyancy and supportive class- and school climate as buffers
2021
Abstract Students experience increasing pressure to perform well and worry about their academic performance before critical school transitions. These challenges may compromise students' school well-being. Drawing on the Model of Personality and Affect for Education (Matthews et al., 2005) as well as on the Conservation of Resources Theory (Hobfoll, 1989), we investigated the buffering role of high academic buoyancy and supportive class- and school climate against decreases in school well-being (i.e., school-related stress, anti-school attitude, and satisfaction with school) among Finnish lower secondary school students (N = 1024) from grades seven to nine. Controlling for gender, fluid inte…
Oscillatory Behavior of Second-Order Nonlinear Neutral Differential Equations
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/143614 Open Access We study oscillatory behavior of solutions to a class of second-order nonlinear neutral differential equations under the assumptions that allow applications to differential equations with delayed and advanced arguments. New theorems do not need several restrictive assumptions required in related results reported in the literature. Several examples are provided to show that the results obtained are sharp even for second-order ordinary differential equations and improve related contributions to the subject.
Asymptotic Behavior of Higher-Order Quasilinear Neutral Differential Equations
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/395368 Open Access We study asymptotic behavior of solutions to a class of higher-order quasilinear neutral differential equations under the assumptions that allow applications to even- and odd-order differential equations with delayed and advanced arguments, as well as to functional differential equations with more complex arguments that may, for instance, alternate indefinitely between delayed and advanced types. New theorems extend a number of results reported in the literature. Illustrative examples are presented.
Systematisation of Systems Solving Physics Boundary Value Problems
2020
A general conservation law that defines a class of physical field theories is constructed. First, the notion of a general field is introduced as a formal sum of differential forms on a Minkowski manifold. By the action principle the conservation law is defined for such a general field. By construction, particular field notions of physics, e.g., magnetic flux, electric field strength, stress, strain etc. become instances of the general field. Hence, the differential equations that constitute physical field theories become also instances of the general conservation law. The general field and the general conservation law together correspond to a large class of relativistic hyperbolic physical …
Oscillation of fourth-order quasilinear differential equations
2015
We study oscillatory behavior of a class of fourth-order quasilinear differential equations without imposing restrictive conditions on the deviated argument. This allows applications to functional differential equations with delayed and advanced arguments, and not only these. New theorems are based on a thorough analysis of possible behavior of nonoscillatory solutions; they complement and improve a number of results reported in the literature. Three illustrative examples are presented.
Integrability of the one dimensional Schrödinger equation
2018
We present a definition of integrability for the one dimensional Schroedinger equation, which encompasses all known integrable systems, i.e. systems for which the spectrum can be explicitly computed. For this, we introduce the class of rigid functions, built as Liouvillian functions, but containing all solutions of rigid differential operators in the sense of Katz, and a notion of natural boundary conditions. We then make a complete classification of rational integrable potentials. Many new integrable cases are found, some of them physically interesting.