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71.
72.
Alexander G. Ramm Alexandra B. Smirnova Angelo Favini 《Annali di Matematica Pura ed Applicata》2003,182(1):37-52
A nonlinear operator equation F(x)=0, F:H→H, in a Hilbert space is considered. Continuous Newton’s-type procedures based on a construction of a dynamical system with
the trajectory starting at some initial point x
0 and becoming asymptotically close to a solution of F(x)=0 as t→+∞ are discussed. Well-posed and ill-posed problems are investigated.
Received: June 29, 2001; in final form: February 26, 2002?Published online: February 20, 2003
This paper was finished when AGR was visiting Institute for Theoretical Physics, University of Giessen. The author thanks
DAAD for support 相似文献
73.
Runge–Kutta based convolution quadrature methods for abstract, well-posed, linear, and homogeneous Volterra equations, non
necessarily of sectorial type, are developed. A general representation of the numerical solution in terms of the continuous
one is given. The error and stability analysis is based on this representation, which, for the particular case of the backward
Euler method, also shows that the numerical solution inherits some interesting qualitative properties, such as positivity,
of the exact solution. Numerical illustrations are provided. 相似文献
74.
Joseph Majdalani Sjoerd W. Rienstra 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(2):289-308
The bidirectional vortex refers to the bipolar, coaxial swirling motion that can be triggered, for example, in cyclone separators
and some liquid rocket engines with tangential aft-end injectors. In this study, we present an exact solution to describe
the corresponding bulk motion in spherical coordinates. To do so, we examine both linear and nonlinear solutions of the momentum
and vorticity transport equations in spherical coordinates. The assumption will be that of steady, incompressible, inviscid,
rotational, and axisymmetric flow. We further relate the vorticity to some power of the stream function. At the outset, three
possible types of similarity solutions are shown to fulfill the momentum equation. While the first type is incapable of satisfying
the conditions for the bidirectional vortex, it can be used to accommodate other physical settings such as Hill’s vortex.
This case is illustrated in the context of inviscid flow over a sphere. The second leads to a closed-form analytical expression
that satisfies the boundary conditions for the bidirectional vortex in a straight cylinder. The third type is more general
and provides multiple solutions. The spherical bidirectional vortex is derived using separation of variables and the method
of variation of parameters. The three-pronged analysis presented here increases our repertoire of general mean flow solutions
that rarely appear in spherical geometry. It is hoped that these special forms will permit extending the current approach
to other complex fluid motions that are easier to capture using spherical coordinates. 相似文献
75.
A fictitious domain approach to the numerical solution of PDEs in stochastic domains 总被引:1,自引:0,他引:1
We present an efficient method for the numerical realization of elliptic PDEs in domains depending on random variables. Domains
are bounded, and have finite fluctuations. The key feature is the combination of a fictitious domain approach and a polynomial
chaos expansion. The PDE is solved in a larger, fixed domain (the fictitious domain), with the original boundary condition
enforced via a Lagrange multiplier acting on a random manifold inside the new domain. A (generalized) Wiener expansion is
invoked to convert such a stochastic problem into a deterministic one, depending on an extra set of real variables (the stochastic
variables). Discretization is accomplished by standard mixed finite elements in the physical variables and a Galerkin projection
method with numerical integration (which coincides with a collocation scheme) in the stochastic variables. A stability and
convergence analysis of the method, as well as numerical results, are provided. The convergence is “spectral” in the polynomial
chaos order, in any subdomain which does not contain the random boundaries. 相似文献
76.
For a general K3 surface S of genus g, with 2 ≤ g ≤ 10, we prove that the intermediate Jacobians of the family of prime Fano threefolds of genus g containing S as a hyperplane section, form generically an algebraic completely integrable Hamiltonian system.
The first author is partially supported by grant MI1503/2005 of the Bulgarian Foundation for Scientific Research. 相似文献
77.
We study the connection between universal central extensions in the categories of precrossed and crossed modules. They are compared with several kinds of universal central extensions in the categories of groups, epimorphisms of groups, groups with operators and modules over a group. We study the relationship between the homologies defined in these categories. Applications to relative algebraic K-theory are also obtained. 相似文献
78.
Tokuzo Shiga 《Probability Theory and Related Fields》1997,108(3):417-439
Summary. We study the exponential decay rate of the survival probability up to time t>0 of a random walker moving in Zopf;
d
in a temporally and spatially fluctuating random environment. When the random walker has a speed parameter κ>0, we investigate
the influence of κ on the exponential decay rate λ(d,κ). In particular we prove that for any fixed d≥1, λ(d,κ) behaves like as logκ as κ↘0.
Received: 21 May 1996 / In revised form: 2 February 1997 相似文献
79.
80.
R. M. Dudley 《Probability Theory and Related Fields》1994,100(2):175-189
Summary In a separable metric space, if two Borel probability measures (laws) are nearby in a suitable metric, then there exist random variables with those laws which are nearby in probability. Specifically, by a well-known theorem of Strassen, the Prohorov distance between two laws is the infimum of Ky Fan distances of random variables with those laws. The present paper considers possible extensions of Strassen's theorem to two random elements one of which may be (compact) set-valued and/or non-measurable. There are positive results in finite-dimensional spaces, but with factors depending on the dimension. Examples show that such factors cannot entirely be avoided, so that the extension of Strassen's theorem to the present situation fails in infinite dimensions.This research was partially supported by a Guggenheim Fellowship, by National Science Foundation grant DMS 8505550 at MSRI-Berkeley, and other NSF grants 相似文献