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71.
Pascal Noble 《Archive for Rational Mechanics and Analysis》2007,186(1):53-76
The phenomenon of roll-waves occurs when shallow water flows down open inclined channels. This flow is described by the Saint
Venant’s equations with a friction term due to Chezy. In the case of a flat bottom, their existence (as entropic and periodic
travelling waves) follows from a classical work due to DRESSLER [6].
The aim of this paper is to prove the existence of roll-waves when the bottom is modulated by a small periodic perturbation.
Following JIN and KATSOULAKIS [15], we first compute a Burgers-type equation which possesses “pulsating” roll-waves (the wave
speed oscillates around an average velocity). We prove, in a mathematically rigorous fashion, the existence of these solutions. 相似文献
72.
Michael Struwe 《Calculus of Variations and Partial Differential Equations》2003,16(4):431-437
Extending our previous work [5] on this subject we show global existence of smooth solutions to the Cauchy problem for wave
maps from the (1 + 2)-dimensional Minkowski space to an arbitrary smooth, compact Riemannian manifold without boundary, for
arbitrary smooth, radially symmetric data.
Received: 14 December 2001 / Accepted: 1 March 2002 / Published online: 6 August 2002 相似文献
73.
We consider the differential operators Ψ
k
, defined by Ψ1(y) =y and Ψ
k+1(y)=yΨ
k
y+d/dz(Ψ
k
(y)) fork ∈ ℕ fork∈ ℕ. We show that ifF is meromorphic in ℂ and Ψ
k
F has no zeros for somek≥3, and if the residues at the simple poles ofF are not positive integers, thenF has the formF(z)=((k-1)z+a)/(z
2+β
z+γ) orF(z)=1/(az+β) where α, β, γ ∈ ℂ. If the residues at the simple poles ofF are bounded away from zero, then this also holds fork=2. We further show that, under suitable additional conditions, a family of meromorphic functionsF is normal if each Ψ
k
(F) has no zeros. These conditions are satisfied, in particular, if there exists δ>0 such that Re (Res(F, a)) <−δ for all polea of eachF in the family. Using the fact that Ψ
k
(f
′/f) =f
(k)/f, we deduce in particular that iff andf
(k) have no zeros for allf in some familyF of meromorphic functions, wherek≥2, then {f
′/f :f ∈F} is normal.
The first author is supported by the German-Israeli Foundation for Scientific Research and Development G.I.F., G-643-117.6/1999,
and INTAS-99-00089. The second author thanks the DAAD for supporting a visit to Kiel in June–July 2002. Both authors thank
Günter Frank for helpful discussions. 相似文献
74.
For ϕ a δ-subharmonic function, sharp results are obtained that connectA(r, ϕ), B(r, ϕ) andT(r, ϕ), whereA(r, ϕ)=inf|z|=r
ϕ(z),B(r, ϕ)=sup|z|=r
ϕ(z), andT(r, ϕ) is the Nevanlinna characteristics. 相似文献
75.
Lihong Wang 《Annals of the Institute of Statistical Mathematics》2004,56(2):251-264
The purpose of this paper is to investigate the asymptotic properties of the least squares estimates (L
2-estimates) and the least absolute deviation estimates (L
1-estimates) of the parameters of a nonlinear regression model subject to a set of equality and inequality restrictions, which
has a long-range dependent stationary process as its stochastic errors. Then we will compare the asymptotic relative efficiencies
of the above estimators. 相似文献
76.
77.
78.
79.
Yang Dai Faquan Li Xuewu Cheng Zhiling Jiang Shunsheng Gong 《Optics & Laser Technology》2007,39(7):1374-1379
In Shack–Hartmann wavefront sensor (SHWS), the behavior of the irradiance pattern produced by the micro-lens array is important for an accurate centroid estimation. In this paper, the behavior of a micro-lens array in SHWS is analyzed using Fourier optics, and reveals that in addition to the main, expected spots, secondary spots with smaller intensities also appeared as a result of diffraction by the small dimensions of the micro-lens and interference from the different micro-lenses. This result is confirmed by comparing with a irradiance pattern taken from an actual SHWS. The additional error in centroid estimation caused by these secondary spots is discussed and relationship to the parameters of the micro-lens of SHWS is analyzed. 相似文献
80.
The vibrational dynamics of protein folding is analyzed in the framework of Tsallis statistics. We employ exact expressions
for classical harmonic oscillators by considering the unnormalized constraints. As q→1, we show that these approximations agree with the result of Gaussian network model. 相似文献