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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...
Simplicial Differerential Calculus, Divided Differences, and Construction of Weil Functors
divided differences differential calculus jet functor scalar extension
2010/12/6
We define a simplicial differential calculus by generalizing divided differences from the case of curves to the case of general maps, defined on general topological vector spaces, or even on modules o...
Operational methods and Lorentz-type equations of motion
Operational methods Lorentz-type equations of motion
2010/12/9
We propose an operational method for the solution of di erential equations involv-ing vector products. The technique we propose is based on the use of the evolution operator, de ned in such a way that...
Berry-Esséen Bounds for Long Memory Moving Averages via Stein's Method and Malliavin Calculus
limit theorems long memory moving average multiple stochastic integrals Malliavin calculus weak convergence
2010/12/1
Using the Stein method on Wiener chaos introduced in [10] we prove Berry-Ess´een bounds for long memory moving averages.
对$n$维多重非齐次调和方程${\it \Delta}^{(k)}u=f(x),x\in\mbox{\boldmath $R$}^{n}$, 给出了基本解的递推公式以及多重调和函数的积分关系式.在非齐次项$f(x)$为$m$次调和的情形下将域上的积分转化为沿边界的积分,进而应用直接法给出了基本边界积分方程.对$f(x)$为一般光滑函数的情形,给出了用泰勒多项式逼近时相应的误差估计并证明了含误差项的...
Recursive Generation of Isochronous Hamiltonian Systems
Isochronous Hamiltonian Systems collective coordinate $Q$ isochronous oscillators
2010/4/2
We propose a simple procedure to identify the collective coordinate $Q$ which is used to generate the isochronous Hamiltonian. The new isochronous Hamiltonian generates more and more isochronous oscil...
Intrinsic Equations for a Relaxed Elastic Line on an Oriented Hypersurface in the Minkowski Space Rn1
Elastic line Minkowski space
2010/3/1
We gived the intrinsic equations for a relaxed elastic line on an oriented surface in {\Bbb {R}}13 ([1],[2]). In this paper, we derived the intrinsic equations for a relaxed elastic line on an oriente...
New Exact Solutions of a Generalized Shallow Water Wave Equation
Exact Solutions Generalized Shallow Water Wave Equation
2010/4/2
In this work an extended Jacobian elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate to classify new exact travelling wave s...