共查询到20条相似文献,搜索用时 31 毫秒
1.
E. G. Emel'yanov 《Journal of Mathematical Sciences》1998,89(1):976-987
We solve the problems on the maximum of the conformal radius R(D,1) in the family D(R0) of all simply connected domains D ⊃ ℂ containing the points 0 and 1 and having a fixed value of the conformal radius R(D,0)=R0, and in the family D(R0, ρ) of domains from D(R0) with given hyperbolic distance ρ=ρD(0,1) between 0 and 1. Analogs of the mentioned problems for doubly-connected domains with given conformal module are considered.
Solution of the above problems is based on results of general character in the theory of problems of extremal decomposition
and related module problems. Bibliography: 7 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 93–108. 相似文献
2.
Vladimir Semenovich Korolyuk 《Journal of Mathematical Sciences》2011,179(2):273-289
Three main schemes of limit theorems for random evolutions are discussed: averaging, diffusion approximation, and the asymptotics
of large deviations. Markov stochastic evolutions with locally independent increments on increasing time intervals T
ε
= t/ε → ∞, ε → 0, are considered. The asymptotic behavior of random evolutions is investigated with the use of solutions of the singular perturbation
problems for reducibly invertible operators. 相似文献
3.
Summary Let Lεu and L
0
v be the elliptic and “backward” heat operators defined by(1.1) and(1.2), respectively. The following question is considered for a pair of “non-well posed” initial-boundary value problems for Lε and L
0
: if u and v are the respective solutions, under what restrictions on the classes of admissible solutions and in what sense,
if any, does u converge to v as ɛ →0?
This research was supported in part by the National Science Foundation Grant No. GP 5882 with Cornell University. 相似文献
4.
E. V. Frolova 《Journal of Mathematical Sciences》2009,159(4):580-595
The unique solvability of the two-phase Stefan problem with a small parameter ε ∈ [0; ε
0] at the time derivative in the heat equations is proved. The solution is obtained on a certain time interval [0; t
0] independent of ε. The solution of the Stefan problem is compared with the solution to the Hele–Shaw problem corresponding to the case ε = 0. The solutions of both problems are not assumed to coincide at the initial moment of time. Bibliography: 18 titles.
Dedicated to Vsevolod Alekseevich Solonnikov on the occasion of his jubilee
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 362, 2008, pp. 337–363. 相似文献
5.
Ranjan Kumar Mohanty 《Numerical Algorithms》2010,54(3):379-393
In this paper, the use of N-AGE and Newton-N-AGE iterative methods on a variable mesh for the solution of one dimensional
parabolic initial boundary value problems is considered. Using three spatial grid points, a two level implicit formula based
on Numerov type discretization is discussed. The local truncation error of the method is of O(k2hl-1 +khl +hl3)O({k^2h_l^{-1} +kh_l +h_l^3}), where h
l
> 0 and k > 0 are the step lengths in space and time directions, respectively. We use a special technique to handle singular parabolic
equations. The advantage of using these algorithms is highlighted computationally. 相似文献
6.
The problem of estimation of a distribution function is considered in the case where the observer has access only to a part
of the indicator random values. Some basic asymptotic properties of the constructed estimates are studied. The limit theorems
are proved for continuous functionals related to the estimation of [^(F)]n(x) {\hat{F}_n}(x) in the space C[a, 1 - a], 0 < a < 1/2. 相似文献
7.
A variational method is developed within the class of functions of boundary rotation not exceedingkπ which is based on the fact that the set of representing measuresμ is convex. It shows that an extremal problem related to a functional with Gateaux derivative and some constraints leads to
extremal measuresμ
0 with finite support. The positive and negative part of aμ
0 is located at points where a functionJ (depending onμ
0) reaches its maximum and minimum respectively. The method is tested successfully on various problems. 相似文献
8.
In previous papers [MS 1, 2], we considered stationary critical points of solutions of the initial-boundary value problems
for the heat equation on bounded domains in ℝN,N ≧ 2. In [MS 1], we showed that a solutionu has a stationary critical pointO if and only ifu satisfies a certain balance law with respect toO for any time. Furthermore, we proved necessary and sufficient conditions relating the symmetry of the domain to the initial
datau
0; in this way, we gave a characterization of the ball in ℝN([MS 1]) and of centrosymmetric domains ([MS 2]). In the present paper, we consider a rotationA
dby an angle 2π/d,d ≧ 2 for planar domains and give some necessary and some sufficient conditions onu
0 which relate to domains invariant underA
d. We also establish some conjectures.
This research was partially supported by a Grant-in-Aid for Scientific Research (C) (# 10640175) and (B) (# 12440042) of the
Japan Society for the Promotion of Science. The first author was supported also by the Italian MURST. 相似文献
9.
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
10.
G. V. Shevchenko 《Computational Mathematics and Mathematical Physics》2011,51(4):537-549
Nonlinear systems with a stationary (i.e., explicitly time independent) right-hand side are considered. For time-optimal control
problems with such systems, an iterative method is proposed that is a generalization of one used to solve nonlinear time-optimal
control problems for systems divided by phase states and controls. The method is based on constructing finite sequences of
simplices with their vertices lying on the boundaries of attainability domains. Assuming that the system is controllable,
it is proved that the minimizing sequence converges to an ɛ-optimal solution after a finite number of iterations. A pair {T, u(·)} is called an ɛ-optimal solution if |T − T
opt| − ɛ, where T
opt is the optimal time required for moving the system from the initial state to the origin and u is an admissible control that moves the system to an ɛ-neighborhood of the origin over the time T. 相似文献
11.
Khursheed Alam 《Annals of the Institute of Statistical Mathematics》1971,23(1):411-418
Summary There are givenk Poisson processes with mean arrival times 1/λ1,...1/λ
k
. Let λ[1]≦λ[2]≦...≦λ[k] denote the ordered set of values λ1...,λ[k]. We consider three procedures for selecting the process corresponding to λ[k]. The processes are observed until there areN arrivals from any of the given processes, when the processes are observed continuously, or until there are at leastN arrivals, when the processes are observed at successive intervals of time whereN is a pre-determined positive integer. In the continuous case, the process for which theNth arrival time is shortest, is selected. In the discrete case, the selection involves certain randomization.
Given (λ[k]/λ[k-1])≧0>1, it is shown that the probability of a correct selection (Pcs) is minimized whenθλ[1]=θλ[2]=...=θλ[k-1]=θλ[k]=θλ, say. The Pcs for this configuration is independent of λ for two of the given procedures, and monotone increasing in λ for
the third. The value ofN is determined by a lower bound placed on the value of the Pcs.
The problem of selecting from given Poisson processes for the discrete case is related to the problem of selecting from given
Poisson populations. An application of the given procedures to a problem of selecting the “most probable event” from a multinomial
population, is considered. 相似文献
12.
S. S. Sinelnikov 《Moscow University Mathematics Bulletin》2011,66(4):158-162
For a Lévy process X = (X
t
)0≤t<∞ we consider the time θ = inf{t ≥ 0: sup
s≤t
X
s
= sup
s≥0
X
s
}. We study an optimal approximation of the time θ using the information available at the current instant. A Lévy process being a combination of a Brownian motion with a drift
and a Poisson process is considered as an example. 相似文献
13.
Adam Bobrowski 《Journal of Evolution Equations》2010,10(3):663-675
We show that generation theorems for cosine families related to one-dimensional Laplacians in C[0, ∞] may be obtained by Lord Kelvin’s method of images, linking them with existence of invariant subspaces of the basic
cosine family. This allows us to deal with boundary conditions more general than those considered before (Bátkal and Engel
in J Differ Equ 207:1–20, 2004; Chill et al. in Functional analysis and evolution equations. The Günter Lumer volume, Birkhauser,
Basel, pp 113–130, 2007; Xiao and Liang in J Funct Anal 254:1467–1486, 2008) and to give explicit formulae for transition
kernels of related Brownian motions on [0, ∞). As another application we exhibit an example of a family of equibounded cosine
operator functions in C[0, ∞] that converge merely on C
0(0, ∞] while the corresponding semigroups converge on the whole of C[0, ∞]. 相似文献
14.
Wolfgang Wasow 《Commentarii Mathematici Helvetici》1971,46(1):65-86
A system of linear differential equations of the vectorial form εdy/dx=A (x, ε) y is considered, where ε is a positive parameter, and the matrixA (x, ε) is holomorphic in |x|⩽x
0, 0 < ε ⩽ ε0 , with an asymptotic expansionsA (x, ε) ∼ ∑
r=0
∞
A
r
(x) ε
r
, as ε→0. The eigenvalues ofA
0(x) are supposed to coalesce atx=0 so as to make this point a simple turning point. With the help of refinements of the representations for the inner and
outer asymptotic solutions, as ε→0, that were introduced in the articles [9] and [10] by the author (see the references at
the end of the paper), explicit connection formulas between these solutions are calculated. As part of this derivation it
is shown that only the diagonal entries of the connection matrix are asymptotically relevant. 相似文献
15.
M. Vanninathan 《Proceedings Mathematical Sciences》1981,90(3):239-271
In this paper, we treat some eigenvalue problems in periodically perforated domains and study the asymptotic behaviour of
the eigenvalues and the eigenvectors when the number of holes in the domain increases to infinity Using the method of asymptotic
expansion, we give explicit formula for the homogenized coefficients and expansion for eigenvalues and eigenvectors. If we
denote by ε the size of each hole in the domain, then we obtain the following aysmptotic expansion for the eigenvalues: Dirichlet:
λε = ε−2 λ + λ0 +O (ε), Stekloff: λε = ελ1 +O (ε2), Neumann: λε = λ0 + ελ1 +O (ε2).
Using the method of energy, we prove a theorem of convergence in each case considered here. We briefly study correctors in
the case of Neumann eigenvalue problem. 相似文献
16.
We show the relative consistency of ℵ1 satisfying a combinatorial property considered by David Fremlin (in the question DU from his list) in certain choiceless
inner models. This is demonstrated by first proving the property is true for Ramsey cardinals. In contrast, we show that in
ZFC, no cardinal of uncountable cofinality can satisfy a similar, stronger property. The questions considered by D. H. Fremlin
are if families of finite subsets of ω1 satisfying a certain density condition necessarily contain all finite subsets of an infinite subset of ω1, and specifically if this and a stronger property hold under MA + ?CH. Towards this we show that if MA + ?CH holds, then for every family ? of ℵ1 many infinite subsets of ω1, one can find a family ? of finite subsets of ω1 which is dense in Fremlins sense, and does not contain all finite subsets of any set in ?.
We then pose some open problems related to the question.
Received: 2 June 1999 / Revised version: 2 February 2000 / Published online: 18 July 2001 相似文献
17.
The Dirichlet and Neumann problems for the Laplace operator in a bounded domain in Euclidean space are considered. Some estimates
of the difference N
N(λ) - N
D(λ) of counting functions are discussed. 相似文献
18.
In this paper the Cauchy problem for the following nonhomogeneous Burgers’ equation is considered : (1)u
t
+uu
x
=μu
xx
−kx,x ∈R,t > 0, where μ and k are positive constants. Since the nonhomogeneous term kx does not belong to any Lp(R) space, this type of equation is beyond usual Sobolev framework in some sense. By Hopf-Cole transformation, (1) takes the
form (2)ϕ
t
−ϕ
xx
= −x
2
ϕ. With the help of the Hermite polynomials and their properties, (1) and (2) are solved exactly. Moreover, the large time
behavior of the solutions is also considered, similar to the discussion in Hopf’s paper. Especially, we observe that the nonhomogeneous
Burgers’ equation (1) is nonlinearly unstable. 相似文献
19.
Two inverse problems for the Sturm-Liouville operator Ly = s-y″ + q(x)y on the interval [0, fy] are studied. For θ ⩾ 0, there is a mapping F:W
2θ → l
B
θ, F(σ) = {s
k
}1∞, related to the first of these problems, where W
2∞ = W
2∞[0, π] is the Sobolev space, σ = ∫ q is a primitive of the potential q, and l
B
θ is a specially constructed finite-dimensional extension of the weighted space l
2θ, where we place the regularized spectral data s = {s
k
}1∞ in the problem of reconstruction from two spectra. The main result is uniform lower and upper bounds for ∥σ - σ1∥θ via the l
B
θ-norm ∥s − s1∥θ of the difference of regularized spectral data. A similar result is obtained for the second inverse problem, that is, the
problem of reconstructing the potential from the spectral function of the operator L generated by the Dirichlet boundary conditions. The result is new even for the classical case q ∈ L
2, which corresponds to θ = 1. 相似文献
20.
I. B. Bokolishvily S. A. Kaschenko G. G. Malinetskii A. B. Potapov 《Journal of Nonlinear Science》1994,4(1):545-562
Summary We consider four models of partial differential equations obtained by applying a generalization of the method of normal forms
to two-component reaction-diffusion systems with small diffusionu
t=εDu
xx+(A+εA
1)u+F(u),u ∈ ℝ2. These equations (quasinormal forms) describe the behaviour of solutions of the original equation forε → 0.
One of the quasinormal forms is the well-known complex Ginzburg-Landau equation. The properties of attractors of the other
three equations are considered. Two of these equations have an interesting feature that may be called asensitivity to small parameters: they contain a new parameterϑ(ε)=−(aε
−1/2 mod 1) that influences the behaviour of solutions, but changes infinitely many times whenε → 0. This does not create problems in numerical analysis of quasinormal forms, but makes numerical study of the original
problem involvingε almost impossible. 相似文献