scholarly journals General Variation Theory: A Perspective of Generalized Science

2020 ◽  
pp. 1-20
Author(s):  
Shunqing Cao ◽  
Jinzheng Li ◽  
Qing Yang
Keyword(s):  
Variation Theory ◽  
General Variation

Rosen-Chambers Variation Theory of Linearly-Damped Classic and Quantum Oscillator

2014 ◽  
Vol 4 (1) ◽  
pp. 404-426
Author(s):  
Vincze Gy. Szasz A.
Keyword(s):  
Harmonic Oscillator ◽  
Classical Mechanics ◽  
Universal Time ◽  
Variation Theory ◽  
Quantum Oscillator ◽  
Variation Principle ◽  
Poisson Brackets ◽  
Mathematical Meaning ◽  
Damped Harmonic Oscillator ◽  
Damped Oscillator

Phenomena of damped harmonic oscillator is important in the description of the elementary dissipative processes of linear responses in our physical world. Its classical description is clear and understood, however it is not so in the quantum physics, where it also has a basic role. Starting from the Rosen-Chambers restricted variation principle a Hamilton like variation approach to the damped harmonic oscillator will be given. The usual formalisms of classical mechanics, as Lagrangian, Hamiltonian, Poisson brackets, will be covered too. We shall introduce two Poisson brackets. The first one has only mathematical meaning and for the second, the so-called constitutive Poisson brackets, a physical interpretation will be presented. We shall show that only the fundamental constitutive Poisson brackets are not invariant throughout the motion of the damped oscillator, but these show a kind of universal time dependence in the universal time scale of the damped oscillator. The quantum mechanical Poisson brackets and commutation relations belonging to these fundamental time dependent classical brackets will be described. Our objective in this work is giving clearer view to the challenge of the dissipative quantum oscillator.

Does high-variation training facilitate transfer of training in paediatric transthoracic echocardiography?

2020 ◽  
pp. 1-7
Author(s):  
Colin J. McMahon ◽  
Sarah Gallagher ◽  
Adam James ◽  
Aoife Deery ◽  
Mark Rhodes ◽  
...  
Keyword(s):  
Transfer Of Training ◽  
Assessment Tool ◽  
Qualitative Interviews ◽  
Training Group ◽  
Variation Theory ◽  
Cardiac Lesion ◽  
Cumulative Score ◽  
Hands On ◽  
Performance Report ◽  
Technical Proficiency

Abstract Background: Factors that facilitate transfer of training in paediatric echocardiography remain poorly understood. This study assessed whether high-variation training facilitated successful transfer in paediatric echocardiography. Methods: A mixed-methods study of transfer of technical and interpretive skill application amongst postgraduate trainees. Trainees were randomised to a low or high-variation training group. After a period of 8 weeks intensive echocardiography training, we video-recorded how trainees completed an echocardiogram in a complex cardiac lesion not previously encountered. Blinded quantitative analysis and scoring of trainee performance (echocardiogram performance, report, and technical proficiency) were performed using a validated assessment tool by a blinded cardiologist and senior cardiac physiologist. Qualitative interviews of the trainees were recorded to ascertain trainee experiences during the training and transfer process. Results: Sixteen trainees were enrolled in the study. For the cumulative score for all three components tested (echocardiogram performance, report, and technical proficiency), χ2 = 8.223, p = .016, which showed the high-variation group outperformed the low-variation group. Two common themes which assisted in the transfer emerged from interviews are as follows: (1) use of strategies described in variation theory to describe abnormal hearts, (2) the use of formative live feedback from trainers during hands-on training. Conclusion: Training strategies exposing trainees to high-variation training may aid transfer of paediatric echocardiography skills.

scholarly journals Designing Tasks for a Dynamic Online Environment: Applying Research into Students’ Difficulties with Linear Equations

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 557
Author(s):  
Morten Elkjær ◽  
Uffe Thomas Jankvist
Keyword(s):  
Design Theory ◽  
Teaching And Learning ◽  
Linear Equations ◽  
Task Design ◽  
Tree Structure ◽  
Learning Trajectory ◽  
Variation Theory ◽  
Online Environment ◽  
School Students ◽  
Personalised Learning

Despite almost half a century of research into students’ difficulties with solving linear equations, these difficulties persist in everyday mathematics classes around the world. Furthermore, the difficulties reported decades ago are the same ones that persist today. With the immense number of dynamic online environments for mathematics teaching and learning that are emerging today, we are presented with a perhaps unique opportunity to do something about this. This study sets out to apply the research on lower secondary school students’ difficulties with equation solving, in order to eventually inform students’ personalised learning through a specific task design in a particular dynamic online environment (matematikfessor.dk). In doing so, task design theory is applied, particularly variation theory. The final design we present consists of eleven general equation types—ten types of arithmetical equations and one type of algebraic equation—and a broad range of variations of these, embedded in a potential learning-trajectory-tree structure. Besides establishing this tree structure, the main theoretical contribution of the study and the task design we present is the detailed treatment of the category of arithmetical equations, which also involves a new distinction between simplified and non-simplified arithmetical equations.

Population Subdivision and Molecular Sequence Variation: Theory and Analysis of Drosophila ananassae Data

Genetics ◽  
2003 ◽  
Vol 165 (3) ◽  
pp. 1385-1395
Author(s):  
Claus Vogl ◽  
Aparup Das ◽  
Mark Beaumont ◽  
Sujata Mohanty ◽  
Wolfgang Stephan
Keyword(s):  
Sequence Data ◽  
Isolation By Distance ◽  
Allele Frequencies ◽  
Drosophila Ananassae ◽  
Population Subdivision ◽  
Variation Theory ◽  
Peripheral Populations ◽  
Molecular Variation ◽  
Data Set ◽  
Evolutionary Forces

Abstract Population subdivision complicates analysis of molecular variation. Even if neutrality is assumed, three evolutionary forces need to be considered: migration, mutation, and drift. Simplification can be achieved by assuming that the process of migration among and drift within subpopulations is occurring fast compared to mutation and drift in the entire population. This allows a two-step approach in the analysis: (i) analysis of population subdivision and (ii) analysis of molecular variation in the migrant pool. We model population subdivision using an infinite island model, where we allow the migration/drift parameter 0398; to vary among populations. Thus, central and peripheral populations can be differentiated. For inference of 0398;, we use a coalescence approach, implemented via a Markov chain Monte Carlo (MCMC) integration method that allows estimation of allele frequencies in the migrant pool. The second step of this approach (analysis of molecular variation in the migrant pool) uses the estimated allele frequencies in the migrant pool for the study of molecular variation. We apply this method to a Drosophila ananassae sequence data set. We find little indication of isolation by distance, but large differences in the migration parameter among populations. The population as a whole seems to be expanding. A population from Bogor (Java, Indonesia) shows the highest variation and seems closest to the species center.

The determination of energies and wavefunctions with full electronic correlation

1969 ◽  
Vol 310 (1500) ◽  
pp. 43-61 ◽  
Keyword(s):  
Correlation Function ◽  
Wave Equation ◽  
Variational Problems ◽  
Variation Theory ◽  
Electronic Correlation ◽  
Convergence Properties

It has been widely thought that the use of wavefunctions with full electronic correlation would involve integrals of 3 N dimensions, where N is the number of electrons. Here it is shown that by a method similar to that of variation theory a set of equations which determine the orbitals and correlation function can be derived so that they only involve integrals of up to nine dimensions. Even these nine-dimensional integrals have some special characteristics which make them equivalent to six-dimensional integrals in some methods of integration. The method is formulated for the particular canonical choice of correlation function that has been previously investigated by the authors and is based on a particular trans-correlated kind of wave equation and on some particular convergence properties recently shown for bi-variational problems. This appears to provide a solution to the problem of including all r ij - quantities in wavefunctions: a problem which has been variously discussed for the last thirty years.

scholarly journals Exploring learners’ Acceptance and Attitude towards Mobile Assisted Language Learning (MALL)

2021 ◽  
Vol 6 (16) ◽  
pp. 49-54
Author(s):  
Tengku Nazatul Shima Tengku Paris ◽  
Nurma Abdul Manap ◽  
Hafiza Abas ◽  
Lo Mun Ling
Keyword(s):  
Language Learning ◽  
Publishing House ◽  
Variation Theory ◽  
Board Game ◽  
English Grammar ◽  
Mobile Assisted Language Learning ◽  
International Publishing ◽  
The Subject ◽  
Theory Of Variation ◽  
Open Access Article

Two main reasons contributing to the lack of mastery in English grammar by students are their apprehension towards the subject and their difficulty understanding tenses. To alleviate the fear and trigger learners' interest in learning grammar, an interactive digital board game was designed via MALL targeted at TESL students. This paper aims to explore these students' perceptions of the game. The game uses the Theory of Variation as a theoretical basis that acknowledges that discernment is a function of variation.  A questionnaire and interviews were administered to the students. The findings show that the game helps enhance grammar learning.   Keywords: Digital board game, Grammar, Mobile Assisted Language Learning, Variation theory eISSN: 2398-4287© 2021. The Authors. Published for AMER ABRA cE-Bs by e-International Publishing House, Ltd., UK. This is an open access article under the CC BYNC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer–review under responsibility of AMER (Association of Malaysian Environment-Behaviour Researchers), ABRA (Association of Behavioural Researchers on Asians/Africans/Arabians) and cE-Bs (Centre for Environment-Behaviour Studies), Faculty of Architecture, Planning & Surveying, Universiti Teknologi MARA, Malaysia. DOI: https://doi.org/10.21834/ebpj.v6i16.2734

scholarly journals Variational Histogram Equalization for Single Color Image Defogging

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Li Zhou ◽  
Du Yan Bi ◽  
Lin Yuan He
Keyword(s):  
Color Image ◽  
State Of The Art ◽  
Color Space ◽  
Histogram Equalization ◽  
Degradation Model ◽  
Image Defogging ◽  
Hsi Color Space ◽  
General Variation ◽  
Bad Weather ◽  
Physical Degradation

Foggy images taken in the bad weather inevitably suffer from contrast loss and color distortion. Existing defogging methods merely resort to digging out an accurate scene transmission in ignorance of their unpleasing distortion and high complexity. Different from previous works, we propose a simple but powerful method based on histogram equalization and the physical degradation model. By revising two constraints in a variational histogram equalization framework, the intensity component of a fog-free image can be estimated in HSI color space, since the airlight is inferred through a color attenuation prior in advance. To cut down the time consumption, a general variation filter is proposed to obtain a numerical solution from the revised framework. After getting the estimated intensity component, it is easy to infer the saturation component from the physical degradation model in saturation channel. Accordingly, the fog-free image can be restored with the estimated intensity and saturation components. In the end, the proposed method is tested on several foggy images and assessed by two no-reference indexes. Experimental results reveal that our method is relatively superior to three groups of relevant and state-of-the-art defogging methods.

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