共查询到20条相似文献,搜索用时 31 毫秒
1.
Mikhail Perepelitsa 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2010,114(1):267-276
We consider the Navier–Stokes equations for the motion of a compressible, viscous, pressureless fluid in the domain
W = \mathbbR3+{\Omega = \mathbb{R}^3_+} with the no-slip boundary conditions. We construct a global in time, regular weak solution, provided that initial density
ρ
0 is bounded and the magnitude of the initial velocity u
0 is suitably restricted in the norm ||?{r0(·)}u0(·)||L2(W) + ||?u0(·)||L2(W){\|\sqrt{\rho_0(\cdot)}{\bf u}_0(\cdot)\|_{L^2(\Omega)} + \|\nabla{\bf u}_0(\cdot)\|_{L^2(\Omega)}}. 相似文献
2.
QIU ZhiJian School of Economic Mathematics Southwestern University of Finance Economics Chengdu China 《中国科学A辑(英文版)》2008,51(1):131-142
Let G be a bounded open subset in the complex plane and let H~2(G) denote the Hardy space on G. We call a bounded simply connected domain W perfectly connected if the boundary value function of the inverse of the Riemann map from W onto the unit disk D is almost 1-1 with respect to the Lebesgue measure on D and if the Riemann map belongs to the weak-star closure of the polynomials in H~∞(W). Our main theorem states: in order that for each M∈Lat (M_z), there exist u∈H~∞(G) such that M=∨{uH~2(G)}, it is necessary and sufficient that the following hold: (1) each component of G is a perfectly connected domain; (2) the harmonic measures of the components of G are mutually singular; (3) the set of polynomials is weak-star dense in H~∞(G). Moreover, if G satisfies these conditions, then every M∈Lat (M_z) is of the form uH~2(G), where u∈H~∞(G) and the restriction of u to each of the components of G is either an inner function or zero. 相似文献
3.
In this article we study the exponential behavior of the continuous stochastic Anderson model, i.e. the solution of the stochastic
partial differential equation u(t,x)=1+∫0tκΔxu (s,x) ds+∫0t W(ds,x) u (s,x), when the spatial parameter x is continuous, specifically x∈R, and W is a Gaussian field on R+×R that is Brownian in time, but whose spatial distribution is widely unrestricted. We give a partial existence result of the
Lyapunov exponent defined as limt→∞t−1 log u(t,x). Furthermore, we find upper and lower bounds for lim supt→∞t−1 log u(t,x) and lim inft→∞t−1 log u(t,x) respectively, as functions of the diffusion constant κ which depend on the regularity of W in x. Our bounds are sharper, work for a wider range of regularity scales, and are significantly easier to prove than all previously
known results. When the uniform modulus of continuity of the process W is in the logarithmic scale, our bounds are optimal.
This author's research partially supported by NSF grant no. : 0204999 相似文献
4.
Jack D. Koronel 《Israel Journal of Mathematics》1976,24(2):119-138
The paper gives a necessary and sufficient condition for the embedding of the Orlicz-Sobolev spaceW
kLA (Ω) inC(Ω). The same condition is also found to be necessary and sufficient so that a continuous function inW
kLA (Ω) be differentiable of orderk almost everywhere in Ω. 相似文献
5.
E. V. Derets 《Ukrainian Mathematical Journal》2000,52(3):368-378
We establish lower bounds for the Kolmogorov widths d
2n-1(W
r
H
1ω.L
p
) and Gel’fand widths d
2n-1(W
r
H
1ω.L
p
) of the classes of functions W
r
H
1ω with a convex integral modulus of continuity ω(t). 相似文献
6.
LetW be an algebraically closed filed of characteristic zero, letK be an algebraically closed field of characteristic zero, complete for an ultrametric absolute value, and letA(K) (resp. ℳ(K)) be the set of entire (resp. meromorphic) functions inK. For everyn≥7, we show that the setS
n(b) of zeros of the polynomialx
n−b (b≠0) is such that, iff, g ∈W[x] or iff, g ∈A(K), satisfyf
−1(S
n(b))=g
−1(S
n(b)), thenf
n=g
n. For everyn≥14, we show thatS
n(b) is such that iff, g ∈W({tx}) or iff, g ∈ ℳ(K) satisfyf
−1(S
n(b))=g
−1(S
n(b)), then eitherf
n=g
n, orfg is a constant. Analogous properties are true for complex entire and meromorphic functions withn≥8 andn≥15, respectively.
For everyn≥9, we show that the setY
n(c) of zeros of the polynomial
, (withc≠0 and 1) is an ursim ofn points forW[x], and forA(K). For everyn≥16, we show thatY
n(c) is an ursim ofn points forW(x), and for ℳ(K). We follow a method based on thep-adic Nevanlinna Theory and use certain improvement of a lemma obtained by Frank and Reinders. 相似文献
7.
A. A. Kovalevskii 《Ukrainian Mathematical Journal》1996,48(9):1402-1422
By using special local characteristics of domains Ω
s
⊂Ω,s=12,..., we establish necessary and sufficient conditions for the γ-convergence of sequences of integral functionalsI
λs
:W
k,m
(Ω
s
)→ℝ, λ⊂Ω to interal functionals defined on W
k,m
(Ω).
Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk. Translated from Ukrainskii Matematicheskii
Zhurnal, Vol. 48, No. 9, pp. 1236–1254, September, 1996. 相似文献
8.
Let Ω and Π be two finitely connected hyperbolic domains in the complex plane
\Bbb C{\Bbb C}
and let R(z, Ω) denote the hyperbolic radius of Ω at z and R(w, Π) the hyperbolic radius of Π at w. We consider functions f that are analytic in Ω and such that all values f(z) lie in the domain Π. This set of analytic functions is denoted by A(Ω, Π). We prove among other things that the quantities
Cn(W,P) := supf ? A(W,P)supz ? W\frac|f(n)(z)| R(f(z),P)n! (R(z,W))nC_n(\Omega,\Pi)\,:=\,\sup_{f\in A(\Omega,\Pi)}\sup_{z\in \Omega}\frac{\vert f^{(n)}(z)\vert\,R(f(z),\Pi)}{n!\,(R(z,\Omega))^n}
are finite for all
n ? \Bbb N{n \in {\Bbb N}}
if and only if ∂Ω and ∂Π do not contain isolated points. 相似文献
9.
James R. Holub 《Israel Journal of Mathematics》1985,52(3):231-238
LetW(D) denote the set of functionsf(z)=Σ
n=0
∞
A
n
Z
n
a
nzn for which Σn=0
∞|a
n
|<+∞. Given any finite set lcub;f
i
(z)rcub;
i=1
n
inW(D) the following are equivalent: (i) The generalized shift sequence lcub;f
1(z)z
kn
,f
2(z)z
kn+1, …,f
n
(z)z
(k+1)n−1rcub;
k=0
∞
is a basis forW(D) which is equivalent to the basis lcub;z
m
rcub;
m=0
∞
. (ii) The generalized shift sequence is complete inW(D), (iii) The function
has no zero in |z|≦1, wherew=e
2πiti
/n. 相似文献
10.
《复变函数与椭圆型方程》2012,57(12):837-843
Let W be a nonnegative summable function whose logarithm is also summable with respect to the Lebesgue measure on the unit circle. For 0?<?p?<?∞ , Hp (W) denotes a weighted Hardy space on the unit circle. When W?≡?1, H p(W) is the usual Hardy space Hp . We are interested in Hp ( W)+ the set of all nonnegative functions in Hp ( W). If p?≥?1/2, Hp + consists of constant functions. However Hp ( W)+ contains a nonconstant nonnegative function for some weight W. In this paper, if p?≥?1/2 we determine W and describe Hp ( W)+ when the linear span of Hp ( W)+ is of finite dimension. Moreover we show that the linear span of Hp (W)+ is of infinite dimension for arbitrary weight W when 0?<?p?<?1/2. 相似文献
11.
Suppose W is a Weyl group with Φ = Φ(W) a root system of W. The set D of root differences is given by D = {α − β : α, β, ∈ Φ}. We define t(Φ) to be the maximum exponent of the torsion subgroup of
for any
In this article we show that if W is of type An, then t(Φ) = 2n.
Received: 25 November 2004 相似文献
12.
We consider finite element methods applied to a class of Sobolev equations inR d(d ≥ 1). Global strong superconvergence, which only requires that partitions are quais-uniform, is investigated for the error between the approximate solution and the Ritz-Sobolev projection of the exact solution. Two order superconvergence results are demonstrated inW 1,p (Ω) andL p(Ω) for 2 ≤p < ∞. 相似文献
13.
Aissa Guesmia 《Israel Journal of Mathematics》2001,125(1):83-92
We consider in this paper the evolution systemy″−Ay=0, whereA =∂
i(aij∂j) anda
ij ∈C
1 (ℝ+;W
1,∞ (Ω)) ∩W
1,∞ (Ω × ℝ+), with initial data given by (y
0,y
1) ∈L
2(Ω) ×H
−1 (Ω) and the nonhomogeneous conditiony=v on Γ ×]0,T[. Exact controllability means that there exist a timeT>0 and a controlv such thaty(T, v)=y′(T, v)=0. The main result of this paper is to prove that the above system is exactly controllable whenT is “sufficiently large”. Moreover, we obtain sharper estimates onT. 相似文献
14.
You Ming Liu 《数学学报(英文版)》2001,17(3):501-506
Let g(x) ∈L
2(R) and ğ(ω) be the Fourier transform of g(x). Define g
mn
(x) = e
imx
g(x−2πn). In this paper we shall give a sufficient and necessary condition under which {g
mn
(x)} constitutes an orthonormal basis of L
2(R) for compactly supported g(ω) or ˘(ω).
Received March 25, 1999, Revised November 5, 1999, Accepted September 6, 2000 相似文献
15.
We consider an algebra of operator sequences containing, among others, the approximation sequences to convolution type operators
on cones acting on
Lp(\mathbb R2)L^{p}(\mathbb {R}^2), with 1 < p < ∞. To each operator sequence (An) we associate a family of operators
Wx(An) ? L(Lp(\mathbb R2))W_{x}(A_{n}) \in \mathcal {L}(L^{p}(\mathbb {R}^2)) parametrized by x in some index set. When all Wx(An) are Fredholm, the so-called approximation numbers of An have the α-splitting property with α being the sum of the kernel dimensions of Wx(An). Moreover, the sum of the indices of Wx(An) is zero. We also show that the index of some composed convolution-like operators is zero. Results on the convergence of
the e\epsilon-pseudospectrum, norms of inverses and condition numbers are also obtained. 相似文献
16.
We consider generalized Morrey type spaces Mp( ·),q( ·),w( ·)( W) {\mathcal{M}^{p\left( \cdot \right),\theta \left( \cdot \right),\omega \left( \cdot \right)}}\left( \Omega \right) with variable exponents p(x), θ(r) and a general function ω(x, r) defining a Morrey type norm. In the case of bounded sets
W ì \mathbbRn \Omega \subset {\mathbb{R}^n} , we prove the boundedness of the Hardy–Littlewood maximal operator and Calderón–Zygmund singular integral operators with
standard kernel. We prove a Sobolev–Adams type embedding theorem Mp( ·),q1( ·),w1( ·)( W) ? Mq( ·),q2( ·),w2( ·)( W) {\mathcal{M}^{p\left( \cdot \right),{\theta_1}\left( \cdot \right),{\omega_1}\left( \cdot \right)}}\left( \Omega \right) \to {\mathcal{M}^{q\left( \cdot \right),{\theta_2}\left( \cdot \right),{\omega_2}\left( \cdot \right)}}\left( \Omega \right) for the potential type operator I
α(·) of variable order. In all the cases, we do not impose any monotonicity type conditions on ω(x, r) with respect to r. Bibliography: 40 titles. 相似文献
17.
Vito Lampret 《Central European Journal of Mathematics》2012,10(2):775-787
An asymptotic approximation of Wallis’ sequence W(n) = Π
k=1
n
4k
2/(4k
2 − 1) obtained on the base of Stirling’s factorial formula is presented. As a consequence, several accurate new estimates
of Wallis’ ratios w(n) = Π
k=1
n
(2k−1)/(2k) are given. Also, an asymptotic approximation of π in terms of Wallis’ sequence W(n) is obtained, together with several double inequalities such as, for example,
W(n) ·(an + bn ) < p < W(n) ·(an + b¢n )W(n) \cdot (a_n + b_n ) < \pi < W(n) \cdot (a_n + b'_n ) 相似文献
18.
Etsuko Bannai 《Graphs and Combinatorics》2001,17(4):589-598
It is known that for each matrix W
i
and it's transpose
t
W
i
in any four-weight spin model (X, W
1, W
2, W
3, W
4; D), there is attached the Bose-Mesner algebra of an association scheme, which we call Nomura algebra. They are denoted by N(W
i
) and N(
t
W
i
) = N′(W
i
) respectively. H. Guo and T. Huang showed that some of them coincide with a self-dual Bose-Mesner algebra, that is, N(W
1) = N′(W
1) = N(W
3) = N′(W
3) holds. In this paper we show that all of them coincide, that is, N(W
i
), N′(W
i
), i=1, 2, 3, 4, are the same self-dual Bose-Mesner algebra.
Received: June 17, 1999 Final version received: Januray 17, 2000 相似文献
19.
Violeta Petkova 《Archiv der Mathematik》2009,93(4):357-368
We study the spectrum σ(M) of the multipliers M which commute with the translations on weighted spaces ${L_{\omega}^{2}(\mathbb{R})}
20.
Ferenc Weisz 《数学学报(英文版)》2010,26(9):1627-1640
A general summability method, the so-called θ-summability is considered for multi-dimensional Fourier transforms. Under some conditions on θ, it is proved that the maximal operator of the θ-means defined in a cone is bounded from the amalgam Hardy space W(hp, e∞) to W(Lp,e∞). This implies the almost everywhere convergence of the θ-means in a cone for all f ∈ W(L1, e∞) velong to L1. 相似文献
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