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1.
Numerical schemes for systems with multiple spatio-temporal scales are investigated. The multiscale schemes use asymptotic results for this type of systems which guarantee the existence of an effective dynamics for some suitably defined modes varying slowly on the largest scales. The multiscale schemes are analyzed in general, then illustrated on a specific example of a moderately large deterministic system displaying chaotic behavior due to Lorenz. Issues like consistency, accuracy, and efficiency are discussed in detail. The role of possible hidden slow variables as well as additional effects arising on the diffusive time-scale are also investigated. As a byproduct we obtain a rather complete characterization of the effective dynamics in Lorenz model. 相似文献
2.
We study a class of random variational inequalities on random sets and give measurability, existence, and uniqueness results in a Hilbert space setting. In the special case where the random and the deterministic variables are separated, we present a discretization technique based on averaging and truncation, prove a Mosco convergence result for the feasible random set, and establish norm convergence of the approximation procedure. 相似文献
3.
Limit cycles for two classes of planar polynomial differential systems with uniform isochronous centers 下载免费PDF全文
In this article, we study the maximum number of limit cycles for two classes of planar polynomial differential systems with uniform isochronous centers. Using the first-order averaging method, we analyze how many limit cycles can bifurcate from the period solutions surrounding the centers of the considered systems when they are perturbed inside the class of homogeneous polynomial differential systems of the same degree. We show that the maximum number of limit cycles, $m$ and $m+1$, that can bifurcate from the period solutions surrounding the centers for the two classes of differential systems of degree $2m$ and degree $2m+1$, respectively. Both of the bounds can be reached for all $m$. 相似文献
4.
We study subgradient methods for computing the saddle points of a convex-concave function. Our motivation comes from networking
applications where dual and primal-dual subgradient methods have attracted much attention in the design of decentralized network
protocols. We first present a subgradient algorithm for generating approximate saddle points and provide per-iteration convergence
rate estimates on the constructed solutions. We then focus on Lagrangian duality, where we consider a convex primal optimization
problem and its Lagrangian dual problem, and generate approximate primal-dual optimal solutions as approximate saddle points
of the Lagrangian function. We present a variation of our subgradient method under the Slater constraint qualification and
provide stronger estimates on the convergence rate of the generated primal sequences. In particular, we provide bounds on
the amount of feasibility violation and on the primal objective function values at the approximate solutions. Our algorithm
is particularly well-suited for problems where the subgradient of the dual function cannot be evaluated easily (equivalently,
the minimum of the Lagrangian function at a dual solution cannot be computed efficiently), thus impeding the use of dual subgradient
methods. 相似文献
5.
6.
利用Riccati变换及积分平均技巧,建立一类具有非线性中立项及分布偏差变元的二阶中立型方程的振动准则,我们的结果推广并改进了一些已有的结果. 相似文献
7.
考虑二阶非线性椭圆型微分方程∑^n_{i,j}∂/∂x_i{A_{i,j}(x,y)∂/∂x_j}+q(x)f(y)=0 (E),其中q(x)在外区域 Ω∈R\+n上变号. 利用偏Riccati变换和积分平均技巧, 建立了方程(E)所有解振动的充分准则. 相似文献
8.
Jaume Llibre Marco Antonio Teixeira Joan Torregrosa 《Mathematical Physics, Analysis and Geometry》2007,10(3):237-249
The goal of this paper is double. First, we illustrate a method for studying the bifurcation of limit cycles from the continuum
periodic orbits of a k-dimensional isochronous center contained in ℝ
n
with n ⩾ k, when we perturb it in a class of differential systems. The method is based in the averaging theory. Second, we consider a particular polynomial differential
system in the plane having a center and a non-rational first integral. Then we study the bifurcation of limit cycles from
the periodic orbits of this center when we perturb it in the class of all polynomial differential systems of a given degree.
As far as we know this is one of the first examples that this study can be made for a polynomial differential system having
a center and a non-rational first integral.
The first and third authors are partially supported by a MCYT/FEDER grant MTM2005-06098-C01, and by a CIRIT grant number 2005SGR-00550.
The second author is partially supported by a FAPESP–BRAZIL grant 10246-2. The first two authors are also supported by the
joint project CAPES–MECD grant HBP2003-0017. 相似文献
9.
In this paper we consider random perturbations of dynamical systems and diffusion processes with a first integral. We calculate, under some assumptions, the limiting behavior of the slow component of the perturbed system in an appropriate time scale for a general class of perturbations. The phase space of the slow motion is a graph defined by the first integral. This is a natural generalization of the results concerning random perturbations of Hamiltonian systems. Considering diffusion processes as the unperturbed system allows to study the multidimensional case and leads to a new effect: the limiting slow motion can spend non-zero time at some points of the graph. In particular, such delay at the vertices leads to more general gluing conditions. Our approach allows one to obtain new results on singular perturbations of PDEs.
Mathematics Subject Classification (2001): 60H10; 34C29; 35B20 相似文献
10.
Keeyoon Sung 《Journal of Quantitative Spectroscopy & Radiative Transfer》2007,107(3):385-406
Ground-based solar absorption infrared spectra were recorded in the Canadian Arctic during the early spring of 2004 using a moderate-resolution Fourier transform spectrometer, the Portable Atmospheric Research Interferometric Spectrometer for the Infrared (PARIS-IR). As part of the Canadian Arctic Atmospheric Chemistry Experiment (ACE) validation campaign, the PARIS-IR instrument recorded solar absorption spectra of the atmosphere from February to March 2004 as the Sun returned to the Arctic Stratospheric Ozone Observatory (AStrO) near Eureka, Nunavut, Canada (80.05°N, 86.42°W). In this paper, we briefly outline the PARIS-IR instrument configuration and data acquisition in the high Arctic. We discuss the retrieval methodology, characterization and error analysis associated with total and partial column retrievals. We compare the PARIS-IR measurements of N2O and O3 column amounts with those from the Fourier transform spectrometer (ACE-FTS) onboard the Canadian SCISAT-1 satellite and the ozonesonde data obtained at Eureka during the validation campaign. 相似文献