scholarly journals Exact and approximate symmetries for light propagation equations with higher order nonlinearity

2010 ◽  
Vol 31 (2) ◽  
pp. 123-140 ◽  
Author(s):  
M. E. Garcia ◽  
V. F. Kovalev ◽  
L. L. Tatarinova
Keyword(s):  
Light Propagation ◽  
Higher Order ◽  
Approximate Symmetries

scholarly journals The effect of higher-order dispersion on slow light propagation in photonic crystal waveguides

2006 ◽  
Vol 14 (4) ◽  
pp. 1658 ◽  
Author(s):  
R.J.P. Engelen ◽  
Y. Sugimoto ◽  
Y. Watanabe ◽  
J.P. Korterik ◽  
N. Ikeda ◽  
...  
Keyword(s):  
Photonic Crystal ◽  
Light Propagation ◽  
Slow Light ◽  
Higher Order ◽  
Photonic Crystal Waveguides ◽  
Higher Order Dispersion ◽  
Order Dispersion

scholarly journals Symmetry at the Cellular Mesoscale

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1170 ◽  
Author(s):  
David S. Goodsell
Keyword(s):  
Functional Role ◽  
Point Group ◽  
Living Cells ◽  
Higher Order ◽  
Group Symmetry ◽  
Point Group Symmetry ◽  
Natural Consequence ◽  
Evolutionary Mechanisms ◽  
Approximate Symmetries ◽  
Mesoscale Structure

Symmetry plays a functional role in the structure and action of biomolecules and their associations and interactions in living cells. This symmetry is a natural consequence of the evolutionary mechanisms that lead to the development of life, and it ranges from perfect point-group symmetry in protein oligomers to more approximate symmetries in the higher-order mesoscale structure of cellular environments.

scholarly journals Relationship between Unstable Point Symmetries and Higher-Order Approximate Symmetries of Differential Equations with a Small Parameter

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1612
Author(s):  
Mahmood R. Tarayrah ◽  
Alexei F. Cheviakov
Keyword(s):  
Differential Equations ◽  
Approximate Solutions ◽  
Higher Order ◽  
Point Symmetry ◽  
Approximate Symmetries ◽  
Symmetries Of Differential Equations ◽  
Exact Symmetry ◽  
Local Symmetries ◽  
Perturbed Model ◽  
Unperturbed Equation

The framework of Baikov–Gazizov–Ibragimov approximate symmetries has proven useful for many examples where a small perturbation of an ordinary or partial differential equation (ODE, PDE) destroys its local exact symmetry group. For the perturbed model, some of the local symmetries of the unperturbed equation may (or may not) re-appear as approximate symmetries. Approximate symmetries are useful as a tool for systematic construction of approximate solutions. For algebraic and first-order differential equations, to every point symmetry of the unperturbed equation, there corresponds an approximate point symmetry of the perturbed equation. For second and higher-order ODEs, this is not the case: a point symmetry of the original ODE may be unstable, that is, not have an analogue in the approximate point symmetry classification of the perturbed ODE. We show that such unstable point symmetries correspond to higher-order approximate symmetries of the perturbed ODE and can be systematically computed. Multiple examples of computations of exact and approximate point and local symmetries are presented, with two detailed examples that include a fourth-order nonlinear Boussinesq equation reduction. Examples of the use of higher-order approximate symmetries and approximate integrating factors to obtain approximate solutions of higher-order ODEs are provided.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Quantitative EPMA of nitrogen : A tricky element in the electron-probe microanalyzer

1992 ◽  
Vol 50 (2) ◽  
pp. 1622-1623
Author(s):  
G.F. Bastin ◽  
H.J.M. Heijligers
Keyword(s):  
Background Subtraction ◽  
Electron Probe ◽  
Detection System ◽  
Higher Order ◽  
Light Elements ◽  
Strong Suppression ◽  
Electron Probe Microanalyzer ◽  
Quantitative Epma ◽  
Peak Count ◽  
Lead Stearate

Among the ultra-light elements B, C, N, and O nitrogen is the most difficult element to deal with in the electron probe microanalyzer. This is mainly caused by the severe absorption that N-Kα radiation suffers in carbon which is abundantly present in the detection system (lead-stearate crystal, carbonaceous counter window). As a result the peak-to-background ratios for N-Kα measured with a conventional lead-stearate crystal can attain values well below unity in many binary nitrides . An additional complication can be caused by the presence of interfering higher-order reflections from the metal partner in the nitride specimen; notorious examples are elements such as Zr and Nb. In nitrides containing these elements is is virtually impossible to carry out an accurate background subtraction which becomes increasingly important with lower and lower peak-to-background ratios. The use of a synthetic multilayer crystal such as W/Si (2d-spacing 59.8 Å) can bring significant improvements in terms of both higher peak count rates as well as a strong suppression of higher-order reflections.

Effects of Higher-Order Laue Zone reflections on structure images

1993 ◽  
Vol 51 ◽  
pp. 450-451
Author(s):  
H. S. Kim ◽  
S. S. Sheinin
Keyword(s):  
Wave Vector ◽  
Theoretical Calculations ◽  
Reciprocal Lattice ◽  
Image Plane ◽  
Bloch Wave ◽  
Dynamical Theory ◽  
Higher Order ◽  
Lattice Image ◽  
Lattice Vector ◽  
Image Position

The importance of image simulation in interpreting experimental lattice images is well established. Normally, in carrying out the required theoretical calculations, only zero order Laue zone reflections are taken into account. In this paper we assess the conditions for which this procedure is valid and indicate circumstances in which higher order Laue zone reflections may be important. Our work is based on an analysis of the requirements for obtaining structure images i.e. images directly related to the projected potential. In the considerations to follow, the Bloch wave formulation of the dynamical theory has been used.The intensity in a lattice image can be obtained from the total wave function at the image plane is given by: where ϕg(z) is the diffracted beam amplitide given by In these equations,the z direction is perpendicular to the entrance surface, g is a reciprocal lattice vector, the Cg(i) are Fourier coefficients in the expression for a Bloch wave, b(i), X(i) is the Bloch wave excitation coefficient, ϒ(i)=k(i)-K, k(i) is a Bloch wave vector, K is the electron wave vector after correction for the mean inner potential of the crystal, T(q) and D(q) are the transfer function and damping function respectively, q is a scattering vector and the summation is over i=l,N where N is the number of beams taken into account.

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