Higher‐order special self‐adjoint equations and particle dynamics

1983 ◽  
Vol 24 (10) ◽  
pp. 2433-2437 ◽  
Author(s):  
James L. Reid ◽  
John R. Ray
Keyword(s):  
Particle Dynamics ◽  
Higher Order ◽  
Adjoint Equations

Higher order volume-preserving schemes for charged particle dynamics

2016 ◽  
Vol 305 ◽  
pp. 172-184 ◽  
Author(s):  
Yang He ◽  
Yajuan Sun ◽  
Jian Liu ◽  
Hong Qin
Keyword(s):  
Charged Particle ◽  
Particle Dynamics ◽  
Higher Order ◽  
Volume Preserving

scholarly journals Related oscillation criteria for higher order self-adjoint differential and integro-differential equations

1978 ◽  
Vol 80 (3-4) ◽  
pp. 333-345
Author(s):  
William T. Reid
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Comparison Theorems ◽  
Adjoint Equations ◽  
Limited Attention ◽  
Adjoint Systems ◽  
Comparison Criteria ◽  
Real Linear ◽  
Detailed Application ◽  
Scalar Equations

Within recent years considerable attention has been devoted to extensions of the classical Sturmian theory of real linear homogeneous differential equations of the second order. In particular, such extensions have included not only self-adjoint systems of differential equations, but also higher order self-adjoint differential and integro-differential equations. For problems in these latter categories, however, only limited attention has been given to detailed application of the general oscillation and comparison criteria. The present paper is devoted to this area, and, in particular, it is shown how existing criteria may be exploited to obtain comparison theorems between equations of different orders. Although the presented results have ready extensions to vector differential and integro-differential equations of higher order, [see, for example, 5,6,7], for simplicity attention is restricted to scalar equations. Section 2 is devoted to the statement of known general criteria of oscillation for self-adjoint equations of higher order, with special applications of these criteria presented in Section 3. Finally, Section 4 sketches the framework of corresponding applications for self-adjoint higher order integro-differential equations.

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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