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中国矿业大学数学学院硕士研究生在Riemann-Hilbert方法与可积系统问题方面取得进展（图）
中国矿业大学数学学院 硕士研究生 Riemann-Hilbert方法 可积系统问题
2019/12/10
近日，我校数学学院硕士研究生彭卫琪与导师田守富特聘研究员等在数学物理学领域的著名期刊 Journal of Geometry and Physics上发表题为“Riemann-Hilbert method and multi-soliton solutions for three-component coupled nonlinear Schrödinger equations”的论文。
A spectral theory of linear operators on rigged Hilbert spaces under certain analyticity conditions
generalized eigenvalue resonance pole rigged Hilbert space Gelfand triplet generalized function
2011/9/22
Abstract: A spectral theory of linear operators on rigged Hilbert spaces (Gelfand triplets) is developed under the assumptions that a linear operator $T$ on a Hilbert space $\mathcal{H}$ is a perturba...
Inverse scattering transform for the Degasperis-Procesi equation: a Riemann-Hilbert approach
Degasperis–Procesi equation Camassa–Holm equation inverse scattering trans-form Riemann–Hilbert problem asymptotics
2011/10/10
Abstract: We present the inverse scattering transform approach to the Cauchy problem on the line for the Degasperis-Procesi equation $u_{txx}-2u_x+2u_xu_{xx}+uu_{xxx}=0$ in the form of an associated R...
Relativistic Quantum and Classical Mechanics in the Hilbert Space
Relativistic Quantum Classical Mechanics the Hilbert Space
2011/8/18
Abstract: We present a formulation of relativistic classical and quantum mechanics in the Hilbert space with a linkage through the Ehrenfest quantization. We start with the covariant form of the Loren...
Arbitrary-order Hilbert spectral analysis for time series possessing scaling statistics: a comparison study with detrended fluctuation analysis and wavelet leaders
Arbitrary-order Hilbert spectral analysis time series wavelet leaders
2011/8/5
Abstract: In this paper we present an extended version of Hilbert-Huang transform, namely arbitrary-order Hilbert spectral analysis, to characterize the scale-invariant properties of a time series dir...
Riemann--Hilbert problems, matrix orthogonal polynomials and discrete matrix equations with singularity confinement
Riemann--Hilbert problems matrix orthogonal polynomials discrete matrix equations singularity confinement
2011/7/27
Abstract: In this paper matrix orthogonal polynomials in the real line are described in terms of a Riemann--Hilbert problem. This approach provides an easy derivation of discrete equations for the cor...
Riemann-Hilbert Problem and Quantum Field Theory: Integrable Renormalization, Dyson-Schwinger Equations
Riemann-Hilbert Problem Quantum Field Theory
2010/11/19
In the first purpose, we concentrate on the theory of quantum integrable systems underlying the Connes-Kreimer approach. We introduce a new family of Hamiltonian systems depended on the perturbative ...
Radial and Azimuthal Profiles of Two-Qubit/Rebit Hilbert-Schmidt Separability Probabilities
Radial Azimuthal Profiles Two-Qubit/Rebit Hilbert-Schmidt Separability Probabilities
2010/11/8
We reduce the long-standing problem of ascertaining the Hilbert-Schmidt probability that a generic pair of qubits is separable to that of determining the specific nature of a one-dimensional (separabi...
Pauli graphs when the Hilbert space dimension contains a square: why the Dedekind psi function ?
Pauli graphs Hilbert space dimension Dedekind psi function
2010/10/27
We study the commutation relations within the Pauli groups built on all decompositions of a given Hilbert space dimension q, containing a square, into its factors.
本文反Rieman-Hilbert变换应用到四维反自对偶方程, 并由此导出了'tHooft的瞬子解.
引入基于Hilbert变换的相空间重建手段, 对合肥光源(HLS)逐束团测量系统采集的数据进行了全面的分析, 其中包括单个束流位置监测器(BPM)数据的相空间重建, 逐圈逐束团振荡相位信息、束团振荡模式信息、逐束团横向工作点(tune值)变换. 提出了新的分析束团tune值的手段, 提供传统方法无可比拟的更高的时间和频率分辨率. 还对不同模式的阻尼率进行了计算, 这为衡量逐束团反馈系统的效果提供了...
我们在超主手征场模型中找到了一种新的对变换——C变换,发现在这种变换下体系具有一个与没有中心项的Virasoro代数相关的无穷维李代数,利用Riemann-Hilbert变换,我们探讨了C变换的物理根源.
Full-Field Optical Coherence Tomography Based on Hilbert Transform
Full-field optical coherence tomography (FF-OCT) Phase shifting interferometry (PSI) Hilbert transform
2009/6/2
Novel image restoration technique suitable for parallel detection in full-field optical coherence tomography (FF-OCT) is introduced. An en-face information of a sample can be demodulated from only two...
On the Contractivity of Hilbert-Schmidt distance under open system dynamics
Hilbert-Schmidt distance system dynamics
2010/4/12
We show that the Hilbert-Schmidt distance, unlike the trace distance, between quantum states is generally not monotonic for open quantum systems subject to Lindblad semigroup dynamics. Sufficient cond...
Three-Hilbert-Space Formulation of Quantum Mechanics
Three-Hilbert-Space Formulation Quantum Mechanics
2010/4/7
In paper [Znojil M., Phys. Rev. D 78 (2008), 085003, 5 pages, arXiv:0809.2874] the two-Hilbert-space (2HS, a.k.a. cryptohermitian) formulation of Quantum Mechanics has been revisited. In the present c...