Smooth Curve Approximation to the Energy‐Level Distribution for Quantum Harmonic Oscillators

1963 ◽  
Vol 39 (12) ◽  
pp. 3258-3262 ◽  
Author(s):  
Everett Thiele
Keyword(s):  
Energy Level ◽  
Smooth Curve ◽  
Harmonic Oscillators ◽  
Curve Approximation

scholarly journals Bethe Ansatz for XXX chain with negative spin

2019 ◽  
Vol 34 (31) ◽  
pp. 1950197
Author(s):  
Kun Hao ◽  
Dmitri Kharzeev ◽  
Vladimir Korepin
Keyword(s):  
Energy Level ◽  
Quantum Chromodynamics ◽  
Bethe Ansatz ◽  
Thermodynamic Limit ◽  
Spin Chain ◽  
Degrees Of Freedom ◽  
Harmonic Oscillators ◽  
Effective Theory ◽  
Scattering State ◽  
Topological Excitation

[Formula: see text] spin chain with spin [Formula: see text] appears as an effective theory of Quantum Chromodynamics. It is equivalent to lattice nonlinear Schroediger’s equation: interacting chain of harmonic oscillators [bosonic]. In thermodynamic limit each energy level is a scattering state of several elementary excitations [lipatons]. Lipaton is a fermion: it can be represented as a topological excitation [soliton] of original [bosonic] degrees of freedom, described by the group [Formula: see text]. We also provide the CFT description (including local quenches) and Yang–Yang thermodynamics of the model.

B-Spline Curve Approximation with Nearly Arc-Length Parameterization

2014 ◽  
Vol 513-517 ◽  
pp. 3372-3376 ◽  
Author(s):  
Si Hui Shu ◽  
Zi Zhi Lin ◽  
Yun Ding
Keyword(s):  
Three Dimensional ◽  
Smooth Curve ◽  
Least Square ◽  
Arc Length ◽  
Key Factors ◽  
B Spline ◽  
Spline Curve ◽  
Curve Approximation ◽  
Fitting Algorithm ◽  
Data Points

An algorithm of B-spline curve approximation with the three-dimensional data is presented in this paper. In this algorithm, we will get a smooth curve which is nearly arc-length parameterization. The smoothness and uniform parameterization are key factors of the approximating curve, specifically in skinning surface and surface approximation. Firstly, the data points are fitted using local interpolation, this local fitting algorithm yields n Bezier segments, each segment having speed equal to 1 at their end and midpoints. Then segments are composed of a C1 continuous cubic B-spline curve which named controlling curve. But the controlling curves control points are redundancy, so we find another curve to approximate the controlling curve using least square approximation with smoothness

Number of Steps Walked Predicts Energy Level, and Mood

2013 ◽  
Author(s):  
Robert E. Thayer ◽  
Olga Godes ◽  
Nicole E. Lobato ◽  
Marcelino Serrano ◽  
Jorge Hernandez ◽  
...  
Keyword(s):  
Energy Level
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