scholarly journals Third order integrability conditions for homogeneous potentials of degree −1

2012 ◽  
Vol 53 (8) ◽  
pp. 082704 ◽  
Author(s):  
Thierry Combot ◽  
Christoph Koutschan
Keyword(s):  
Third Order ◽  
Integrability Conditions ◽  
Homogeneous Potentials

scholarly journals LIFTS OF GOLDEN STRUCTURES ON THE TANGENT BUNDLE

2021 ◽  
pp. 643
Author(s):  
Geeta Verma
Keyword(s):  
Tangent Bundle ◽  
Third Order ◽  
Integrability Conditions ◽  
Complete Lift ◽  
Tangent Bundles ◽  
Order Tangent

The present paper aims to study the complete lift of golden structure on tangent bundles. Integrability conditions for complete lift and third-order tangent bundle are established.

Integrability conditions of geodesic flow on homogeneous Monge manifolds

2013 ◽  
Vol 35 (1) ◽  
pp. 111-127 ◽  
Author(s):  
THIERRY COMBOT ◽  
THOMAS WATERS
Keyword(s):  
Rational Function ◽  
Geodesic Flow ◽  
Algebraic Manifold ◽  
Integrability Conditions ◽  
Homogeneous Potentials ◽  
Algebraic Manifolds ◽  
Integrability Criterion

AbstractWe prove a meromorphic integrability criterion for the geodesic flow of an algebraic manifold of the form ${z}^{p} - f({x}_{1} , \ldots , {x}_{n} )= 0$ with the induced metric of ${ \mathbb{C} }^{n+ 1} $ and $f$ a homogeneous rational function, using a parallel between the properties of such algebraic manifolds and homogeneous potentials. We then apply this criterion to the manifolds of the form $z= {\lambda }_{1} { x}_{1}^{k} + \cdots + {\lambda }_{n} { x}_{n}^{k} $, $k\in { \mathbb{Z} }^{+ } $, and ${x}^{n} {y}^{m} {z}^{l} = 1, n, m, l\in \mathbb{Z} $, and prove that their geodesic flow is not integrable except for some given exceptional cases.

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

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.

The influence of third-order interactions on the density profile of associating hard spheres

1997 ◽  
Vol 91 (4) ◽  
pp. 761-767 ◽  
Author(s):  
D. HENDERSON ◽  
S. SOKOŁOWSKI ◽  
R. ZAGORSKI ◽  
A. TROKHYMCHUK
Keyword(s):  
Density Profile ◽  
Hard Spheres ◽  
Third Order

Electro-Optic Modulator for Compensation of Third-Order Intermodulation Distortion Using Frequency Chirp Modulation

2020 ◽  
Vol E103.C (11) ◽  
pp. 653-660
Author(s):  
Daichi FURUBAYASHI ◽  
Yuta KASHIWAGI ◽  
Takanori SATO ◽  
Tadashi KAWAI ◽  
Akira ENOKIHARA ◽  
...  
Keyword(s):  
Intermodulation Distortion ◽  
Frequency Chirp ◽  
Third Order ◽  
Chirp Modulation ◽  
Electro Optic ◽  
Electro Optic Modulator
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