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非线性算子方程变号解及其对Hammerstein积分方程的应用
锥 不动点指数 变号解
2012/3/23
本文利用锥理论讨论了在[WTBX]E[WTBZ]空间非线性算子方程变号解的存在性，并将抽象结果应用于Hammerstein积分方程。
Homogenizations of integro-differential equations with L{é}vy operators with asymmetric and degenerate densities
Homogenizations of integro-differential equations L{é}vy operators asymmetric degenerate densities
2011/1/21
We consider periodic homogenization problems for the L´evy operators with asymmetric L´evy densities. The formal asymptotic expansion used for the -stable (symmetric) L´evy operator...
介绍了加权弱Hardy空间的相关概念,在其原子分解的基础上,研究了Marcinkiewicz积分在弱Hardy空间的加权有界性,借助于权函数的性质及不等式估计,得到了Ω满足Lipα(0<α≤1)条件时,Marcinkiewicz积分在加权弱Hardy空间WHΩ1(Rn)上是有界的结果.
Systematic method of generating new integrable systems via inverse Miura maps
modified integrable systems Lax representation (inverse) Miura transformation
2010/12/28
We provide a new natural interpretation of the Lax representation for an integrable system; that is,
本文将正则方法与积分迭代法相结合，提出波数域正则—积分迭代法用于位场向下延拓。该迭代法以位场正则向下延拓值为迭代初值，并用正则向下延拓算子处理迭代过程中的剩余谱，使得在加快迭代收敛的同时，压制噪声谱，以提高延拓的稳定性；计算了改进迭代法的最优步长，对比分析了改进迭代法的收敛性和滤波特性，同时提出采用犔曲线准则计算正则向下延拓的正则参数，并将其扩展到波数域以提高计算速度和适应波数域迭代法。基于理论...
Celebrating Cercignani's conjecture for the Boltzmann equation
Cercignani’s conjecture spectral gap Boltzmann equation relative entropy
2010/12/9
Cercignani’s conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann’s nonlinear integral operator in rarefied gas dynamics. Related to the field of...
DGH方程的尖峰孤立子的稳定性
稳定性 DGH方程 孤立子
2014/1/11
尖峰孤立子是一个非线性色散方程的尖峰孤立波解, 是浅水波理论中的一个模型. 本文通过构造一个泛函和守恒律来证明DGH方程的尖峰孤立子在H^1中的轨道稳定性. 该稳定性定理表明, 如果一个波在开始时与尖锋孤立子接近,则在之后的任何时间仍然与它接近.
A pseudospectral quadrature method for Navier-Stokes equations on rotating spheres
Navier-Stokes equations unit sphere vector spherical harmonics
2010/12/8
In this work, we describe, analyze, and implement a pseudospec-tral quadrature method for a global computer modeling of the incompressible surface Navier-Stokes equations on the rotating unit sphere. ...
Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time
Darboux polynomials rational first integrals bounded degree
2010/12/7
In this paper we study planar polynomial differential systems of this form: dX dt = ˙X = A(X, Y ),dY dt = ˙Y = B(X, Y ),where A,B ∈ Z[X, Y ] and deg A ≤ d, degB ≤ d, kAk1 ≤ H and kBk1 ≤H. A lot of pro...
The Evaluation of a Quartic Integral via Schwinger, Schur and Bessel
integrals hypergeomteric functions Bessel functions Schur functions
2010/12/6
We provide additional methods for the evaluation of the integral N0,4(a;m) := Z 1 0 dx (x4 + 2ax2 + 1)m+1 where m 2 N and a 2 (−1,1) in the form N0,4(a;m) = 2m+3/2(a + 1)m+1/2 Pm(a)
where Pm(a...
On integral equations related to weighted Toepitz operators
Toeplitz operators Lipschitz spaces holomorphic Besov spaces Hardy spaces
2010/12/7
For weighted Toeplitz operators T N ' defined on spaces of holomorphic functions in the unit ball, we derive regularity prop-erties of the solutions f to the integral equation T N ' (f) = h in terms o...
Lax equations and Knizhnik-Zamolodchikov connection
Current algebra Lax operator algebra Lax integrable system
2010/12/10
Given a Lax system of equations with the spectral parameter on a Riemann surface we construct a projective unitary representation of the Lie algebra of Hamiltonian vector fields by Knizhnik-Zamolodchi...
Double Series Involving Binomial Coefficients and the Sine Integral
Double Series Involving Binomial Coefficients Sine Integral
2010/11/26
By dividing hypergeometric series representations of the inverse sine by sin-1(x) and ntegrating, new double series representations of integers and constants arise. Binomial coefficients and the sine ...
A class of Gaussian processes with fractional spectral measures
Gaussian processe fractional spectral measures
2010/11/26
We study a family of stationary increment Gaussian processes, indexed by time. These processes are determined by certain measures (generalized spectral measures), and our focus here is on the case w...
On Weyl calculus in infinitely many variables
Weyl calculus infinite-dimensional Heisenberg group coadjoint orbit
2010/11/30
We outline an abstract approach to the pseudo-differential Weyl calculus for operators in function spaces in infinitely many variables. Our earlier approach to the Weyl calculus for Lie group represen...