Multiconfigurational second-order perturbative methods: Overview and comparison of basic properties

1995 ◽  
Vol 90 (2-3) ◽  
pp. 167-187 ◽  
Author(s):  
Jean-Paul Malrieu ◽  
Jean-Louis Heully ◽  
Andr�i Zaitsevskii
Keyword(s):  
Second Order ◽  
Basic Properties ◽  
Perturbative Methods

Multiconfigurational second-order perturbative methods: Overview and comparison of basic properties

1995 ◽  
Vol 90 (2) ◽  
pp. 167 ◽  
Author(s):  
Jean-Paul Malrieu ◽  
Jean-Louis Heully ◽  
Andréi Zaitsevskii
Keyword(s):  
Second Order ◽  
Basic Properties ◽  
Perturbative Methods

Properties of Cyclide Dyupen and Their Application. Part 2

2015 ◽  
Vol 3 (2) ◽  
pp. 9-22 ◽  
Author(s):  
Сальков ◽  
Nikolay Sal'kov
Keyword(s):  
Coordinate System ◽  
Classical Solution ◽  
Graphical Representation ◽  
Second Order ◽  
Minor Axis ◽  
Center Line ◽  
Focal Line ◽  
Basic Properties ◽  
Primary Focus ◽  
Rotating Coordinates

In the first part of this paper has discussed about the basic properties of cyclide Dupin, and has gave some examples of their applications: three ways of solving the problem of Apollonius exclusively by means of compass and ruler, using identified properties cyclide Dupin, that is, given a classical solution of the problem. In the second of part of the work continued consideration of the properties of cyclide Dupin. Proposed and proved the possibility ask cyclide Dupin arbitrary ellipse as the center line of the forming a plurality of spheres and a sphere with the center belong - ing to the ellipse. Proved the adequacy of this information is used to build the cyclide Dupin. Geometrically proved that the focal line of cychlid are not that other, as curves of the second order. Given the graphical representation of the focal lines of cychlid. Shown polyconic compliance focal lines of cichlid of Dupin, which is considered in all four cases. The proposed formation of the hyperbolic surfaces of the fourth order with one or two primary curves of the second order, in this case ellipses. Apply sofocus this ellipse the hyperbola. Although the primary focus of the ellipse lying in the plane of the hoe, with the center coinciding with the origin of coordinates, is stationary, and the coordinate system rotates around the z axis. Then the points of intersection of the rotating coordinates x and y with a fixed ellipse specify new values for the major and minor axis of the ellipse with resultant changes in the form defocuses of the hyperbola. Although this modeling is not directly connected with Cychlidae Dupin, but clearly follows from the properties of its focal curves – curves of the second order. Withdrawn Equations of the surface and its throat.

scholarly journals Orthogonal-Based Second Order Hybrid Initial Value Problem Solver

2016 ◽  
Vol 5 (2) ◽  
Author(s):  
E O Adeyefa
Keyword(s):  
Orthogonal Polynomial ◽  
Basis Function ◽  
Initial Value Problem ◽  
Recursive Formula ◽  
Second Order ◽  
Problem Solver ◽  
Initial Value ◽  
Basic Properties ◽  
New Class ◽  
Collocation Technique

This work focuses on development of an initial value problem solver by employing a new class of orthogonal polynomial, the basis function. We present the recursive formula of the class of polynomials constructed and adopt collocation technique to develop the method. The method was analyzed for its basic properties and findings show that the method is accurate and convergent.

scholarly journals Overview and comparative analysis of the properties of the Hodge-de Rham and Tachibana operators

Filomat ◽  
2015 ◽  
Vol 29 (10) ◽  
pp. 2429-2436
Author(s):  
S.E. Stepanov ◽  
I.I. Tsyganok ◽  
J. Mikes
Keyword(s):  
Comparative Analysis ◽  
Riemannian Manifolds ◽  
Differential Forms ◽  
Second Order ◽  
Exterior Differential ◽  
Basic Properties ◽  
De Rham

In the present paper we consider two natural, elliptic, self-adjoint second order di_erential operators acting on exterior differential forms on Riemannian manifolds. These operators are the wellknown Hodge-de Rham and little-known Tachibana operators. Basic properties of these operators are very similar, or vice versa are dual with respect to each other. We review the results (partly obtained by the authors) on the geometry of these operators and demonstrate the comparative analysis of their properties.

scholarly journals On q-Difference Riccati Equations and Second-Order Linear q-Difference Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Zhi-Bo Huang
Keyword(s):  
Complex Plane ◽  
Difference Equations ◽  
Gamma Function ◽  
Riccati Equations ◽  
Second Order ◽  
Value Distribution ◽  
Meromorphic Solutions ◽  
Order Linear ◽  
Basic Properties ◽  
Casorati Determinant

We consider q-difference Riccati equations and second-order linear q-difference equations in the complex plane. We present some basic properties, such as the transformations between these two equations, the representations and the value distribution of meromorphic solutions of q-difference Riccati equations, and the q-Casorati determinant of meromorphic solutions of second-order linear q-difference equations. In particular, we find that the meromorphic solutions of these two equations are concerned with the q-Gamma function when q∈ℂ such that 0<|q|<1. Some examples are also listed to illustrate our results.

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

Sign in / Sign up

Export Citation Format

Share Document