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1,853 results on '"Liu, Yuan-Yuan"'

7. Duality family of KdV equation

Author

Gu, Xin, Liu, Yuan-Yuan, Li, Wen-Du, and Dai, Wu-Sheng

Subjects
Mathematical Physics, Nonlinear Sciences - Exactly Solvable and Integrable Systems
Abstract

It is revealed that there exist duality families of the KdV type equation. A duality family consists of an infinite number of generalized KdV (GKdV) equations. A duality transformation relates the GKdV equations in a duality family. Once a family member is solved, the duality transformation presents the solutions of all other family members. We show some dualities as examples, such as the soliton solution-soliton solution duality and the periodic solution-soliton solution duality.

Published
2022

8. Irregular License Plate Recognition via Global Information Integration

Author

Liu, Yuan-Yuan, Liu, Qi, Chen, Song-Lu, Chen, Feng, Yin, Xu-Cheng, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Rudinac, Stevan, editor, Hanjalic, Alan, editor, Liem, Cynthia, editor, Worring, Marcel, editor, Jónsson, Björn Þór, editor, Liu, Bei, editor, and Yamakata, Yoko, editor

Published
2024
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16. Scattering approach for calculating one-loop effective action and vacuum energy

Author

Liu, Yuan-Yuan, Li, Shi-Lin, Chen, Yu-Jie, Li, Wen-Du, and Dai, Wu-Sheng

Subjects
High Energy Physics - Theory
Abstract

We propose an approach for calculating one-loop effective actions and vacuum energies in quantum field theory. Spectral functions are functions defined by the eigenvalues of an operator. One-loop effective actions and vacuum energies in quantum field theory, as well as scattering phase shifts and scattering amplitudes in quantum mechanics, are all spectral functions. If a transformation between different spectral functions is identified, we can obtain a spectral function from another through the transformation. In this paper, we convert quantum mechanical methods for calculating scattering phase shifts and scattering amplitudes into quantum field theory methods for calculating one-loop effective actions and vacuum energies. As examples, the Born approximation and the WKB approximation in quantum mechanics are converted into quantum field theory methods. We also calculate the one-loop effective action and vacuum energy of scalar fields in the Schwarzschild spacetime and the Reissner-Nordstr\"{o}m spacetime as examples. Some integral representations of the Bessel function are given in appendices.

Published
2022
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19. Eliminating oscillation in partial sum approximation of periodic function

Author

Li, Shi-Lin, Liu, Yuan-Yuan, Li, Wen-Du, and Dai, Wu-Sheng

Subjects
Mathematics - General Mathematics
Abstract

If we cannot obtain all terms of a series, or if we cannot sum up a series, we have to turn to the partial sum approximation which approximate a function by the first several terms of the series. However, the partial sum approximation often does not work well for periodic functions. In the partial sum approximation of a periodic function, there exists an incorrect oscillation which cannot be eliminated by keeping more terms, especially at the domain endpoints. A famous example is the Gibbs phenomenon in the Fourier expansion. In the paper, we suggest an approach for eliminating such oscillations in the partial sum approximation of periodic functions.

Published
2021

27. Detected Cases of Bribery in China: The Analysis of Court Records

Author

Liu, Yuan Yuan, Pohlmann, Markus, Series Editor, Bär, Stefan, Series Editor, Elias, Friederike, Series Editor, Klinkhammer, Julian, Series Editor, Valarini, Elizangela, Series Editor, Dannecker, Gerhard, editor, Dölling, Dieter, editor, Hermann, Dieter, editor, Höly, Kristina, editor, Trombini, Maria Eugenia, editor, and Mitra, Subrata K., editor

Published
2023
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28. New Laws and Law Enforcement to Fight Against Bribery in China

Author

Liu, Yuan Yuan, Pohlmann, Markus, Series Editor, Bär, Stefan, Series Editor, Elias, Friederike, Series Editor, Klinkhammer, Julian, Series Editor, Valarini, Elizangela, Series Editor, Dannecker, Gerhard, editor, Dölling, Dieter, editor, Hermann, Dieter, editor, Höly, Kristina, editor, Trombini, Maria Eugenia, editor, and Mitra, Subrata K., editor

Published
2023
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33. Exactly solvable Gross-Pitaevskii type equations

Author

Liu, Yuan-Yuan, Li, Wen-Du, and Dai, Wu-Sheng

Subjects
Condensed Matter - Quantum Gases
Abstract

TWe suggest a method to construct exactly solvable Gross-Pitaevskii type equations, especially the variable-coefficient high-order Gross-Pitaevskii type equations. We show that there exists a relation between the Gross-Pitaevskii type equations. The Gross-Pitaevskii equations connected by the relation form a family. In the family one only needs to solve one equation and other equations in the family can be solved by a transform. That is, one can construct a series of exactly solvable Gross-Pitaevskii type equations from one exactly solvable Gross-Pitaevskii type equation. As examples, we consider the family of some special Gross-Pitaevskii type equations: the nonlinear Schr\"odinger equation, the quintic Gross-Pitaevskii equation, and cubic-quintic Gross-Pitaevskii equation. We also construct the family of a kind of generalized Gross-Pitaevskii type equation.

Published
2020
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37. Scalar field in Reissner-Nordstr\'om spacetime: Bound state and scattering state

Author

Li, Shi-Lin, Liu, Yuan-Yuan, Li, Wen-Du, and Dai, Wu-Sheng

Subjects
General Relativity and Quantum Cosmology
Abstract

In this paper, we solve the massive scalar field in the Reissner-Nordstr\"om spacetime. The scalar field in the Reissner-Nordstr\"om spacetime has both bound states and scattering states. For bound states, we solve the bound-state wave function and the eigenvalue spectrum. For scattering states, we solve the scattering wave function and give an explicit expression for scattering phase shift by the integral equation method. Especially, we introduce the tortoise coordinate for the Reissner-Nordstr\"om spacetime.

Published
2019
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45. Accelerating T1ρ Dispersion Imaging with Multiple Relaxation Signal Compensation

Author

LIU Yuan-yuan, YANG Yu-xin, ZHU Qing-yong, CUI Zhuo-xu, CHENG Jing, LIU Cong-cong, LIANG Dong, and ZHU Yan-jie

Subjects
magnetic resonance quantitative imaging, t1ρ dispersion, signal compensation, low-rank plus sparse, Electricity and magnetism, QC501-766
Abstract

Magnetic resonance imaging (MRI) can quantify characteristic values of tissues, serving as an important tool for scientific and clinical research. Magnetic resonance T1ρ relaxation time reflects the low-frequency motional processes between water and macromolecules. At high fields of 3 T and above, T1ρ is greatly affected by the chemical exchange between water and exchangeable protons, and T1ρ dispersion measured with varying spin-lock fields can be utilized to analyze and quantify the proton exchange process. However, it is time-consuming to obtain T1ρ-weighted images with different spin-lock fields, which limits its application. To solve this problem, a fast T1ρ dispersion imaging method based on multiple relaxation signal compensation strategy is proposed in this work, which compensates the T1ρ-weighted images at different locking frequencies to the same signal strength level, and combines the low-rank plus sparse model in the reconstruction. Experimental results show that the proposed method achieves good reconstruction results even when the acceleration factor is up to 7.

Published
2022
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