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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。
HIGGS BUNDLES AND LOCAL SYSTEMS ON RIEMANN SURFACES
HIGGS BUNDLES LOCAL SYSTEMS RIEMANN SURFACES
2015/12/17
These notes are based on lectures given at the Third International School on Geometry and Physics at the Centre de Recerca Matem`atica in Barcelona, March 26–30, 2012. The aim ofthe School’s four lect...
Rank One Higgs Bundles and Representations of Fundamental Groups of Riemann Surfaces
Higgs Bundles Fundamental Groups
2015/9/29
Goldman gratefully acknowledges partial support by NSF grants
DMS-9504764, DMS-9803518, DMS-0103889 and a Semester Research
Award from the General Research Board of the University of
Maryland in Fa...
On the Complete Integrability of a One Generalized Riemann Type Hydrodynamic System
Lax type integrability Riemann type hydrodynamic system symplectic method differential-algebraic approach
2012/4/26
The complete integrability of a generalized Riemann type hydrodynamic system is studied by means of symplectic and differential-algebraic tools. A compatible pair of polynomial Poissonian structures, ...
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...
Series representations of the Riemann and Hurwitz zeta functions and series and integral representations of the first Stieltjes constant
Hurwitz zeta function Riemann zeta function Dirichlet L function generalized Bernoulli number
2011/7/26
Series representations of the Riemann and Hurwitz zeta functions and series and integral representations of the first Stieltjes constant.
Sums of alternating products of Riemann zeta values and solution of a Monthly problem
first Stieltjes constant Euler constant Riemann zeta function digamma function
2011/7/26
Abstract: We solve problem 11585 proposed by B. Burdick, AMM June-July 2011 {bf 118} (6), p. 558 for the sum of certain products of Riemann zeta function values. We further point out an alternating su...
Sharp asymptotics for Toeplitz determinants, fluctuations and the gaussian free field on a Riemann surface
Sharp asymptotics fluctuations the gaussian free Riemann surface
2011/7/26
Abstract: We consider canonical determinantal point processes with N particles on a compact Riemann surface X defined with respect to the constant curvature metric and show that in the large N-limit t...
Uniform asymptotics for the full moment conjecture of the Riemann zeta function
full moment conjecture the Riemann zeta function $L$-functions Number Theory
2011/7/28
Abstract: Conrey, Farmer, Keating, Rubinstein, and Snaith recently conjectured formulas for the full asymptotics of the moments of $L$-functions. In the case of the Riemann zeta function, their conjec...
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 ...
Distribution of the Riemann zeros represented by the Fermi gas
Distribution the Riemann zeros represented Fermi gas
2010/11/8
The multiparticle density matrices for degenerate, ideal Fermi gas system in any dimension are calculated. The results are expressed as a determinant form, in which a correlation kernel plays a vital ...
Classical Particle in Presence of Magnetic Field, Hyperbolic Lobachevsky and Spherical Riemann Models
Magnetic Field Spherical Riemann Models Hyperbolic Lobachevsky
2010/4/1
Motion of a classical particle in 3-dimensional Lobachevsky and Riemann spaces is studied in the presence of an external magnetic field which is analogous to a constant uniform magnetic field in Eucli...
On a Nonlocal Ostrovsky-Whitham Type Dynamical System, Its Riemann Type Inhomogeneous Regularizations and Their Integrability
Dynamical System Short-wave perturbations
2010/4/1
Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability...
本文通过实例证明了Schwarzchild解与Booth解是任意空间维Riemann时空中的解的一个亏格