Search results for "Abstract algebra"

Minimum Time Control of the Restricted Three-Body Problem

2012

The minimum time control of the circular restricted three-body problem is considered. Controllability is proved on an adequate submanifold. Singularities of the extremal flow are studied by means of a stratification of the switching surface. Properties of homotopy maps in optimal control are framed in a simple case. The analysis is used to perform continuations on the two parameters of the problem: The ratio of the masses, and the magnitude of the control.

Scaling behavior of Tan's contact for trapped Lieb-Liniger bosons: From two to many

2018

We show that the contact parameter of N harmonically trapped interacting one-dimensional bosons at zero temperature can be analytically and accurately obtained by a simple rescaling of the exact two-boson solution, and that N-body effects can be almost factorized. The small deviations observed between our analytical results and density matrix renormalization group (DMRG) calculations are more pronounced when the interaction energy is maximal (i.e., at intermediate interaction strengths) but they remain bounded by the large-N local-density approximation obtained from the Lieb-Liniger equation of state stemming from the Bethe ansatz. The rescaled two-body solution is so close to the exact one…

Delineating Aspects of Understanding Eigentheory through Assessment Development

2018

International audience; In this report, we share insights we have gained from developing an assessment for documenting students' understanding of eigentheory. We explain the literature and theory that influenced the assessment's development and share question examples. We frame our results in terms of three eigentheory settings (Ax = λx, (A - λI)x = 0, and eigenspaces) and four interpretations (numeric, algebraic, geometric, and verbal). Results from our analysis include students' reasoning being influenced by setting, insights into students' struggle with understanding eigenspaces, and the importance of making connections between and across various interpretations.

Accelerometry - Simple, but challenging

2017

Influence of the type of illumination on the measurement of the modulation transfer function in the living human eye: A theoretical study

1999

Abstract Applications such as refractive surgery demand an objective appraisal of the retinal image quality. The modulation transfer function (MTF) provides that information when measured directly. Moreover, the MTF obtained using a simple and objective method such as that described in this paper allows the neural contrast sensitivity function (CSF) to be obtained from the global CSF and the MTF. When calculating the MTF it must be borne in mind whether the applicable theory is coherent or incoherent. In the literature, the developed theory presents some approximations and incongruities. Also, it is interesting to note that the method of recording the MTF (short or long time of integration,…

High Order Textural Classification of Two SAR ERS Images on Mount Cameroon

2006

Abstract Many researchers have demonstrated that textural data increase the precision of a classification when they are combined with level of grey information. However, the calculation of textural parameters of order two is often too long in a computer. The problem is more complex when one must compute higher order textural parameters, which however can considerably improve the precision of a classification. This work is based on statistical methods of order two and three for the calculation of textural parameters [Akono et al., 2003]. In this work, we suggest a new method of calculation of textural parameters, which is more general, not limiting itself only on order two or three, but whic…

Cross-Linked Polyamine from Imidazolium-Based Materials: A Simple Route to Useful Catalytic Materials

2018

Anodic Dehydrogenative Cyanamidation of Thioethers: Simple and Sustainable Synthesis of N‐Cyanosulfilimines

2021

Abstract A novel and very simple to perform electrochemical approach for the synthesis of several N‐cyanosulfilimines in good to excellent yields was established. This method provides access to biologically relevant sulfoximines by consecutive oxidation using electro‐generated periodate. This route can be easily scaled‐up to gram quantities. The S,N coupling is carried out at an inexpensive carbon anode by direct oxidation of sulfide. Therefore, the designed process is atom economic and represents a new “green route” for the synthesis of sulfilimines and sulfoximines.

Simulation of Dense Polymer Systems in Two and Three Dimensions

1991

Dense polymer systems are modeled by self- and mutually avoiding walks on lattices. Both simple models where the step length is one lattice spacing and more complicated models where the step length is distinctly longer and may fluctuate (“bond fluctuation model”) are discussed, and it is shown that the computer simulation of such models gives useful insight to understand the thermodynamic phase behavior and the relaxational dynamics of dense polymer solutions and polymer melts. The huge demands in computing power needed for a successful simulation of such systems can be covered by parallel computers such as the multitransputer facility of the University of Mainz.

Ferrochirality: A simple theoretical model of interacting dynamically invertible helical polymers, 1. The basic effects

1994

The effect of interaction between reversible helical polymers of the poly(hexyl isocyanate) type is investigated by using a molecular field model. It is shown that for interacting helices a critical temperature exists below which they must adopt a common helix-sense spontaneously, even in the absence of any external or intrinsic chiral force