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showing 10 items of 4526 documents
Numerical study of blow-up and stability of line solitons for the Novikov-Veselov equation
2017
International audience; We study numerically the evolution of perturbed Korteweg-de Vries solitons and of well localized initial data by the Novikov-Veselov (NV) equation at different levels of the 'energy' parameter E. We show that as |E| -> infinity, NV behaves, as expected, similarly to its formal limit, the Kadomtsev-Petviashvili equation. However at intermediate regimes, i.e. when |E| is not very large, more varied scenarios are possible, in particular, blow-ups are observed. The mechanism of the blow-up is studied.
ON THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION WITH A QUASI-PERIODIC POTENTIAL
1980
Modified Landau levels, damped harmonic oscillator and two-dimensional pseudo-bosons
2010
In a series of recent papers one of us has analyzed in some details a class of elementary excitations called {\em pseudo-bosons}. They arise from a special deformation of the canonical commutation relation $[a,a^\dagger]=\1$, which is replaced by $[a,b]=\1$, with $b$ not necessarily equal to $a^\dagger$. Here, after a two-dimensional extension of the general framework, we apply the theory to a generalized version of the two-dimensional Hamiltonian describing Landau levels. Moreover, for this system, we discuss coherent states and we deduce a resolution of the identity. We also consider a different class of examples arising from a classical system, i.e. a damped harmonic oscillator.
Bill2d - a software package for classical two-dimensional Hamiltonian systems
2015
Abstract We present Bill2d , a modern and efficient C++ package for classical simulations of two-dimensional Hamiltonian systems. Bill2d can be used for various billiard and diffusion problems with one or more charged particles with interactions, different external potentials, an external magnetic field, periodic and open boundaries, etc. The software package can also calculate many key quantities in complex systems such as Poincare sections, survival probabilities, and diffusion coefficients. While aiming at a large class of applicable systems, the code also strives for ease-of-use, efficiency, and modularity for the implementation of additional features. The package comes along with a use…
Optical implementation of the weighted sliced orthogonal nonlinear generalized correlation for nonuniform illumination conditions.
2002
Optical pattern recognition under variations of illumination is an important issue. The sliced orthogonal nonlinear generalized (SONG) correlation has been proposed as an optical pattern recognition tool to discriminate with high efficiency between objects. But, at the same time, the SONG correlation is very sensitive to gray-scale image variations. In a previous work, we expanded the definition of the SONG correlation to the Weighted SONG (WSONG) correlation to modify the discrimination capability in a controlled way. Here, we propose to use the WSONG when pattern recognition is obtained by means of optical correlation under nonuniform illumination. The calculation of the WSONG correlation…
Comparing technology acceptance of K‐12 teachers with and without prior experience of learning management systems : A Covid‐19 pandemic study
2021
Covid-19 pandemic has caused a massive transformation in K-12 settings towards online education. It is important to explore the factors that facilitate online teaching technology adoption of teachers during the pandemic. The aim of this study was to compare Learning Management System (LMS) acceptance of Finnish K-12 teachers who have been using a specific LMS as part of their regular teaching before the Covid-19 pandemic (experienced group) and teachers who started using it for emergency remote teaching during the pandemic (inexperienced group). Based on the Unified Theory of Acceptance and Use of Technology framework, a self-report questionnaire was administered to 196 teachers (nexperienc…
Special factors and the combinatorics of suffix and factor automata
2011
AbstractThe suffix automaton (resp. factor automaton) of a finite word w is the minimal deterministic automaton recognizing the set of suffixes (resp. factors) of w. We study the relationships between the structure of the suffix and factor automata and classical combinatorial parameters related to the special factors of w. We derive formulae for the number of states of these automata. We also characterize the languages LSA and LFA of words having respectively suffix automaton and factor automaton with the minimal possible number of states.
Covariant Operator Formalism for Quantized Superfields
1988
The Takahashi-Umezawa method of deriving the free covariant quantization relations from the linear equations of motion is extended to superfields. The Cauchy problem for free superfields is solved, and an expression for the time independent scalar product is given. For the case of interacting fields, we give the general Kallen-Lehmann spectral representation for the two-point superfield Green functions and, after the introduction of the asymptotic condition for superfields, we give the superfield extension of the Yang-Feldman equation. The case of the D = 2 real scalar superfield and the case of the D = 4 chiral superfield are discussed in detail.
The Tan 2Θ Theorem in fluid dynamics
2017
We show that the generalized Reynolds number (in fluid dynamics) introduced by Ladyzhenskaya is closely related to the rotation of the positive spectral subspace of the Stokes block-operator in the underlying Hilbert space. We also explicitly evaluate the bottom of the negative spectrum of the Stokes operator and prove a sharp inequality relating the distance from the bottom of its spectrum to the origin and the length of the first positive gap.