scholarly journals Variational principles for conformal geodesics

2021 ◽  
Vol 111 (5) ◽  
Author(s):  
Maciej Dunajski ◽  
Wojciech Kryński
Keyword(s):  
Fourth Order ◽  
Variational Formulation ◽  
Variational Principles ◽  
Lagrangian Formulation ◽  
Invariant System ◽  
Third Order ◽  
Conformally Invariant ◽  
Integral Curves

AbstractConformal geodesics are solutions to a system of third-order equations, which makes a Lagrangian formulation problematic. We show how enlarging the class of allowed variations leads to a variational formulation for this system with a third-order conformally invariant Lagrangian. We also discuss the conformally invariant system of fourth-order ODEs arising from this Lagrangian and show that some of its integral curves are spirals.

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

scholarly journals Perturbative linearization of super-Yang-Mills theories in general gauges

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Hannes Malcha ◽  
Hermann Nicolai
Keyword(s):  
Large Class ◽  
Fourth Order ◽  
Landau Gauge ◽  
Third Order ◽  
Yang Mills ◽  
Free Theory ◽  
Non Linear ◽  
Functional Measure ◽  
Non Local ◽  
Jacobi Determinant

Abstract Supersymmetric Yang-Mills theories can be characterized by a non-local and non-linear transformation of the bosonic fields (Nicolai map) mapping the interacting functional measure to that of a free theory, such that the Jacobi determinant of the transformation equals the product of the fermionic determinants obtained by integrating out the gauginos and ghosts at least on the gauge hypersurface. While this transformation has been known so far only for the Landau gauge and to third order in the Yang-Mills coupling, we here extend the construction to a large class of (possibly non-linear and non-local) gauges, and exhibit the conditions for all statements to remain valid off the gauge hypersurface. Finally, we present explicit results to second order in the axial gauge and to fourth order in the Landau gauge.

Construction of dipole type singular solutions for a biharmonic equation with critical Sobolev exponent

2002 ◽  
Vol 2 (4) ◽  
Author(s):  
Sarni Baraket
Keyword(s):  
Fourth Order ◽  
Weak Solutions ◽  
Biharmonic Equation ◽  
Critical Sobolev Exponent ◽  
Singular Solutions ◽  
Invariant Equation ◽  
Conformally Invariant ◽  
Sobolev Exponent

AbstractIn this paper, we construct positive weak solutions of a fourth order conformally invariant equation on S

Incommensurately modulated structure of TaGe0.354Te2: application of crenel functions

1996 ◽  
Vol 52 (1) ◽  
pp. 100-109 ◽  
Author(s):  
F. Boucher ◽  
M. Evain ◽  
V. Petříček
Keyword(s):  
Detailed Analysis ◽  
Fourth Order ◽  
X Ray Diffraction ◽  
Third Order ◽  
Modulated Structure ◽  
X Ray ◽  
First Order ◽  
Germanium Telluride ◽  
Orthorhombic Cell ◽  
Orthogonalization Procedure

The incommensurately modulated structure of tantalum germanium telluride, TaGe0.354Te2, was determined by single-crystal X-ray diffraction. The dimensions of the basic orthorhombic cell are a = 6.4394 (5), b = 14.025 (2), c = 3.8456 (5) Å, V = 347.3 (1) Å3 and Z = 4. The (3 + 1)-dimensional superspace group is Pnma(00γ)s00, γ = 0.3544 (3). Refinements on 1641 reflections with I ≥ 3σ(I) converged to R = 0.065 and 0.044 for 526 main reflections and R = 0.061, 0.12, 0.28 and 0.32 for 782 first-order, 237 second-order, 37 third-order and 59 fourth-order satellites, respectively. Since the structure exhibits a strong occupational modulation of both Ta and Ge atoms, along with important displacive modulation waves, crenel functions were used in the refinement in combination with an orthogonalization procedure. Such an approach is shown to be the most convenient and to give reliable coordinations and distances. A detailed analysis of some Te...Te distances is performed, in connection with already known commensurately and incommensurately modulated MAx Te2 structures.

An Accelerated Iterative Method with Third-Order Convergence

2012 ◽  
Vol 220-223 ◽  
pp. 2658-2661
Author(s):  
Zhong Yong Hu ◽  
Liang Fang ◽  
Lian Zhong Li
Keyword(s):  
Iterative Method ◽  
Fourth Order ◽  
Newton’S Method ◽  
Newton's Method ◽  
New Method ◽  
Order Convergence ◽  
Third Order ◽  
Numerical Examples ◽  
Modified Newton’S Method ◽  
Jarratt Method

We present a new modified Newton's method with third-order convergence and compare it with the Jarratt method, which is of fourth-order. Based on this new method, we obtain a family of Newton-type methods, which converge cubically. Numerical examples show that the presented method can compete with Newton's method and other known third-order modifications of Newton's method.

A Geometrical Solution for the Inverse Kinematics of Three Revolute Manipulators

1993 ◽  
Author(s):  
Eugene F. Fichter
Keyword(s):  
Fourth Order ◽  
Inverse Kinematics ◽  
Solution Procedure ◽  
Order Equation ◽  
Algebraic Solution ◽  
Computer Implementation ◽  
Third Order ◽  
Fourth Order Equation ◽  
Inverse Kinematics Problem

Abstract Points of intersection of a circle and a torus are used to find a solution to the inverse kinematics problem for a three revolute manipulator. Both geometrical and algebraic solution procedures are discussed. The algebraic procedure begins with a third order equation instead of the usual fourth order equation. Since the procedure is basically geometrical it lends itself to a computer implementation which graphically displays each steps in the solution procedure. The potential of this approach for both design and pedagogy is discussed.

scholarly journals An optimal fourth-order family of modified Cauchy methods for finding solutions of nonlinear equations and their dynamical behavior

2019 ◽  
Vol 17 (1) ◽  
pp. 1567-1598
Author(s):  
Tianbao Liu ◽  
Xiwen Qin ◽  
Qiuyue Li
Keyword(s):  
Nonlinear Equations ◽  
Fourth Order ◽  
Dynamical Behavior ◽  
Basins Of Attraction ◽  
Second Derivative ◽  
Third Order ◽  
Numerical Tests ◽  
The Family ◽  
Theoretical Results ◽  
High Computational Efficiency

Abstract In this paper, we derive and analyze a new one-parameter family of modified Cauchy method free from second derivative for obtaining simple roots of nonlinear equations by using Padé approximant. The convergence analysis of the family is also considered, and the methods have convergence order three. Based on the family of third-order method, in order to increase the order of the convergence, a new optimal fourth-order family of modified Cauchy methods is obtained by using weight function. We also perform some numerical tests and the comparison with existing optimal fourth-order methods to show the high computational efficiency of the proposed scheme, which confirm our theoretical results. The basins of attraction of this optimal fourth-order family and existing fourth-order methods are presented and compared to illustrate some elements of the proposed family have equal or better stable behavior in many aspects. Furthermore, from the fractal graphics, with the increase of the value m of the series in iterative methods, the chaotic behaviors of the methods become more and more complex, which also reflected in some existing fourth-order methods.

Attenuated microvascular alterations in coarctation hypertension

1989 ◽  
Vol 256 (1) ◽  
pp. H213-H221 ◽  
Author(s):  
D. L. Stacy ◽  
R. L. Prewitt
Keyword(s):  
Fourth Order ◽  
Vascular Tone ◽  
Structural Parameters ◽  
Renal Hypertension ◽  
Second Order ◽  
Hypertensive Rats ◽  
Third Order ◽  
Flow Dependence ◽  
Vascular Beds ◽  
Microvascular Alterations

Arteriolar vasoconstriction, structural reductions in dilated diameter, and rarefaction have been observed in vascular beds with chronic renal hypertension. To determine their pressure or flow dependence, these functional and structural parameters were studied in the developing and chronic stages of coarctation hypertension in the cremaster muscle, a normotensive skeletal muscle bed that is protected from the effects of elevated microvascular pressures. Hypertension was produced in rats by placing a silver clip around the abdominal aorta above the branches of the renal arteries. In hypertensive rats, resting diameters were reduced in second-order arterioles after 4 and 8 wk, in third-order arterioles after 2, 4, and 8 wk, and in fourth-order arterioles after 4 and 8 wk, vs. controls. Vascular tone was elevated in second-order arterioles after 2, 4, and 8 wk and in third- and fourth-order arterioles after 8 wk in hypertensive rats. No increases in medial-intimal area were found at any stage of hypertension in any arteriolar order. The density of small arterioles (3rd-5th orders) was reduced by 20% in hypertensive rats at 8 wk but was unchanged at the other time periods. These arteriolar alterations, especially the absence of structural reductions in diameter, are attenuated compared with those observed in one-kidney, one-clip hypertension and suggest that most of the arteriolar alterations that occur in renal hypertension are pressure or flow dependent.

scholarly journals Asymptotic formulae for linear equations

1972 ◽  
Vol 13 (2) ◽  
pp. 147-152 ◽  
Author(s):  
Don B. Hinton
Keyword(s):  
Asymptotic Behaviour ◽  
Fourth Order ◽  
Linear Equations ◽  
Order Equation ◽  
Third Order ◽  
Fourth Order Equation ◽  
The Third ◽  
Asymptotic Formulae ◽  
Image Position

Numerous formulae have been given which exhibit the asymptotic behaviour as t → ∞solutions ofwhere F(t) is essentially positive and Several of these results have been unified by a theorem of F. V. Atkinson [1]. It is the purpose of this paper to establish results, analogous to the theorem of Atkinson, for the third order equationand for the fourth order equation

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