Search results for "Linear Algebra"
showing 10 items of 552 documents
Comparison of non-Markovianity criteria in a qubit system under random external fields
2013
We give the map representing the evolution of a qubit under the action of non-dissipative random external fields. From this map we construct the corresponding master equation that in turn allows us to phenomenologically introduce population damping of the qubit system. We then compare, in this system, the time-regions when non-Markovianity is present on the basis of different criteria both for the non-dissipative and dissipative case. We show that the adopted criteria agree both in the non-dissipative case and in the presence of population damping.
Financial Stress and Basis in Energy Markets
2021
We investigate the relationship between energy commodities bases, inventory and financial stress from 1994 to 2018. We find that, from the 1998 Asian crisis the effect of financial stress on energy commodities bases gradually increased and from the 2008 crisis became positive, while the effect of inventory showed a gradual decline over time. The reactions of bases to changes in financial stress is nonlinear, as they are higher in the high financial stress periods. This is more profound in crude oil market than heating oil and natural gas. Moreover, the reactions of bases to the changes in inventory is nonlinear, as the reactions are lower when the inventory level is high confirming the theo…
Estimation of the mechanical properties of the eye through the study of its vibrational modes.
2017
Measuring the eye's mechanical properties in vivo and with minimally invasive techniques can be the key for individualized solutions to a number of eye pathologies. The development of such techniques largely relies on a computational modelling of the eyeball and, it optimally requires the synergic interplay between experimentation and numerical simulation. In Astrophysics and Geophysics the remote measurement of structural properties of the systems of their realm is performed on the basis of (helio-)seismic techniques. As a biomechanical system, the eyeball possesses normal vibrational modes encompassing rich information about its structure and mechanical properties. However, the integral a…
Comparison of different theory models and basis sets in the calculation of 13C NMR chemical shifts of natural products.
2004
The influence of the calculation method in mimicking experimental 13C NMR chemical shifts of 15 low-polarity natural products singularly containing 10–20 carbon atoms was investigated by employing different quantum chemistry approaches and basis sets, both in the preliminary geometry optimizations and in the following single-point 13C GIAO calculations of the NMR chemical shifts. The geometries of the involved species were optimized at the PM3, HF, B3LYP and mPW1PW91 levels whereas the 13C NMR parameters were determined at the HF, B3LYP and mPW1PW91 levels. Different combinations of basis sets were also tested. The consistency and efficiency of the considered combinations of geometry optimi…
Vibrational Spectrum of HXeSH revisited : Combined computational and experimental study
2020
Vibrational spectrum of HXeSH embedded in low-temperature matrix is experimentally studied. To support the spectrum interpretation, anharmonic vibrational analysis is performed using different models and basis sets and the data is compared with previous experimental and theoretical analyses. Computations of overtones and combination modes allowed for new band assignments. The HXeSH molecule exhibits high anharmonicity similarly as other molecules from the noble-gas hydride family. Comparison of the employed computational methods shows once again that the modelling of the noble-gas compounds faces theoretical challenges to yield quantitatively reliable results. peerReviewed
Two positive solutions for a nonlinear parameter-depending algebraic system
2021
The existence of two positive solutions for a nonlinear parameter-depending algebraic system is investigated. The main tools are a finite dimensional version of a two critical point theorem and a recent weak-strong discrete maximum principle.
Two positive solutions for a nonlinear parameter-depending algebraic system
2021
The existence of two positive solutions for a nonlinear parameter-depending algebraic system is investigated. The main tools are a finite dimensional version of a two critical point theorem and a recent weak-strong discrete maximum principle.
Correspondence between generalized binomial field states and coherent atomic states
2008
We show that the N-photon generalized binomial states of electromagnetic field may be put in a bijective mapping with the coherent atomic states of N two-level atoms. We exploit this correspondence to simply obtain both known and new properties of the N-photon generalized binomial states. In particular, an over-complete basis of these binomial states and an orthonormal basis are obtained. Finally, the squeezing properties of generalized binomial state are analyzed.
Fostering Heuristic Strategies in Mathematics Teacher Education
2018
International audience; The “double discontinuity” stated by Felix Klein 1908 is still relevant in the mathematics teacher education at German universities. We are developing a course approach, which is intended to bridge the double discontinuity in a didactic dimension. We offer additional learning opportunities for teacher students, which are characterized by clarifications of mathematical methods that are fundamental to the regular lecture contents. We focus especially on reflections on heuristic strategies, which are the core part of mathematical methods according to George Pólya. Feedback shows that students consider our approach as helpful in the transition from school to university.
Students' problems in the identification of subspaces in Linear Algebra
2018
International audience; The goal of the study presented in this paper is the investigation of students' problems with exercises concerning central topics of linear algebra courses at university level. We present the results of our analysis of students' work on an exercise about subspaces of . We evaluated the written solutions of the task as well as transcripts based on videos taken of student groups working on the problem. We identified and classified descriptions of vector spaces and subspaces that varied widely and demonstrated highly different skills in working with geometric or formal algebraic objects. We analyzed how far students could progress in a complex reasoning process, and ide…