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1.
Let
be a nondecreasing sequence of positive numbers and let l
1,α be the space of real sequences
for which
. We associate every sequence ξ from l
1,α with a sequence
, where ϕ(·) is a permutation of the natural series such that
, j ∈ ℕ. If p is a bounded seminorm on l
1,α and
, then
Using this equality, we obtain several known statements.
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 7, pp. 1002–1006, July, 2005. 相似文献
2.
3.
Characterization of Compact Support of Fourier Transform for Orthonormal Wavelets of L^2(R^d) 总被引:1,自引:0,他引:1
Zhi Hua Zhang 《数学学报(英文版)》2005,21(4):855-864
Let{ψμ} be an orthonormal wavelet of L^2(R^d) and the support of a whole of its Fourier transform be Uμsupp{ψμ}=Пi=1^d[Ai, Di]-Пi=1^d(Bi, Ci), Ai≤Bi≤Ci≤Di. Under the weakest condition that each │ψμ│, is continuous for ω ∈ δ(Пi=1^d[Ai, Di]), a characterization of the above support of a whole is given. 相似文献
4.
We establish necessary and sufficient conditions for the logarithms of the maximum terms of the entire Dirichlet series
and
to be asymptotically equivalent as Re z → +∞ outside a certain set of finite measure.
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 4, pp. 571–576, April, 2005. 相似文献
5.
I. E. Chyzhykov 《Ukrainian Mathematical Journal》2007,59(7):1088-1109
For arbitrary 0 ≤ σ ≤ ρ ≤ σ + 1, we describe the class A
σ
ρ
of functions g(z) analytic in the unit disk
= {z : ∣z∣ < 1} and such that g(z) ≠ 0, ρT[g] = σ, and ρM[g] = ρ, where
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 7, pp. 979–995, July, 2007. 相似文献
6.
Teresa D'Aprile Juncheng Wei 《Calculus of Variations and Partial Differential Equations》2006,25(1):105-137
We study the following system of Maxwell-Schrödinger equations $ \Delta u - u - \delta u \psi+ f(u)=0, \quad \Delta \psi + u^2 = 0 \mbox{in} {\mathbb R}^N , u, \;\psi > 0, \quad u, \;\psi \to 0 \ \mbox{as} \ |x| \to + \infty, $ where δ > 0, u, ψ : $\psi: {\mathbb R}^N \to {\mathbb R}We study the following system of Maxwell-Schr?dinger equations
where δ > 0, u, ψ :
, f :
, N ≥ 3. We prove that the set of solutions has a rich structure: more precisely for any integer K there exists δK > 0 such that, for 0 < δ < δK, the system has a solution (uδ, ψδ) with the property that uδ has K spikes centered at the points
. Furthermore, setting
, then, as δ → 0,
approaches an optimal configuration for the following maximization problem:
Subject class: Primary 35B40, 35B45; Secondary 35J55, 92C15, 92C40 相似文献
7.
Yah SUN Gen Xiang CHAI 《数学学报(英文版)》2007,23(4):685-696
In this article the following random intercept mixed effects model will be considered: yij = vi =v^τijβ+ εij,i=1,…,m;j=1,2,…,ni, where {vi} are i.i.d, random effects with mean α 2. 2 and finite variance σ^2 v, {εij} are i.i.d, random errors with finite variance ε^2 ε. Here we will estimate α,σ^2 v,σ^2 ε,β and study their large sample properties, such as strong consistency, strong convergence rates and asymptotic normality. 相似文献
8.
We investigate the correlation between the constants K(ℝn) and
, where
is the exact constant in a Kolmogorov-type inequality, ℝ is the real straight line,
, L
l
p, p
(G
n) is the set of functions ƒ ∈ L
p
(G
n
) such that the partial derivative
belongs to L
p
(G
n
),
, 1 ≤ p ≤ ∞, l ∈ ℕn, α ∈ ℕ
0
n
= (ℕ ∪ 〈0〉)n, D
α
f is the mixed derivative of a function ƒ, 0 < μi < 1,
, and ∑
i=0
n
. If G
n
= ℝ, then μ0=1−∑
i=0
n
(α
i
/l
i
), μi = αi/l
i
,
if
, then μ0=1−∑
i=0
n
(α
i
/l
i
) − ∑
i=0
n
(λ/l
i
), μi = αi/ l
i
+ λ/l
i
,
, λ ≥ 0. We prove that, for λ = 0, the equality
is true.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 5, pp. 597–606, May, 2006. 相似文献
9.
We discuss purely singular finite-rank perturbations of a self-adjoint operator A in a Hilbert space . The perturbed operators
are defined by the Krein resolvent formula
, Im z 0, where B
z are finite-rank operators such that dom B
z dom A = |0}. For an arbitrary system of orthonormal vectors
satisfying the condition span |
i
} dom A = |0} and an arbitrary collection of real numbers
, we construct an operator
that solves the eigenvalue problem
. We prove the uniqueness of
under the condition that rank B
z = n. 相似文献
10.
For an arbitrary self-adjoint operator B in a Hilbert space
, we present direct and inverse theorems establishing the relationship between the degree of smoothness of a vector
with respect to the operator B, the rate of convergence to zero of its best approximation by exponential-type entire vectors of the operator B, and the k-modulus of continuity of the vector x with respect to the operator B. The results are used for finding a priori estimates for the Ritz approximate solutions of operator equations in a Hilbert space.
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 5, pp. 633–643, May, 2005. 相似文献
11.
Convergence to Diffusion Waves for Nonlinear Evolution Equations with Ellipticity and Damping, and with Different End States 总被引:1,自引:0,他引:1
Chang Jiang ZHU Zhi Yong ZHANG Hui YIN 《数学学报(英文版)》2006,22(5):1357-1370
In this paper, we consider the global existence and the asymptotic behavior of solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects: {ψt=-(1-α)ψ-θx+αψxx, θt=-(1-α)θ+νψx+(ψθ)x+αθxx(E) with initial data (ψ,θ)(x,0)=(ψ0(x),θ0(x))→(ψ±,θ±)as x→±∞ where α and ν are positive constants such that α 〈 1, ν 〈 4α(1 - α). Under the assumption that |ψ+ - ψ-| + |θ+ - θ-| is sufficiently small, we show the global existence of the solutions to Cauchy problem (E) and (I) if the initial data is a small perturbation. And the decay rates of the solutions with exponential rates also are obtained. The analysis is based on the energy method. 相似文献
12.
We study the set of infinitely differentiable periodic functions in terms of generalized -derivatives defined by a pair of sequences ψ
1 and ψ
2. It is shown that every function ƒ from the set has at least one derivative whose parameters ψ
1 and ψ
2 decrease faster than any power function and, at the same time, for any function ƒ ∈ different from a trigonometric polynomial, there exists a pair ψ whose parameters ψ
1 and ψ
2 have the same rate of decrease and for which the -derivative no longer exists.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1399–1409, October, 2007. 相似文献
13.
A. M. Arkhipov 《Journal of Mathematical Sciences》2006,139(6):7013-7024
In this paper, we consider the Kuramoto-Sivashinskii equation on the multidimensional torus with a Riemannian metric:
where
. For this equation the theorem on energy transfer holds. It is formulated in the following way. Let
be the Fourier expansion of the function u. Denote by P
N
and P
N
⊥
the operators of rejection of the “leading” and, respectively, “lowest” terms of the Fourier expansion (harmonics), i.e.,
.
For any ρ > 0,N ∈ ℕ, s ≥ n/2+5, and λ ∈ (0, 1), there exists R such that for any function. ϕ ∈
lying outside the ball
in the ball
, there exists an instant of time t ∈ (0, 1) such that g
KS
t
ϕ=ψ and
. Here, R is a constant depending on the metric (g), n
s
is the sth Sobolev norm, and
is the C
1-norm.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 24, Dynamical
Systems and Optimization, 2005. 相似文献
14.
D. V. Husak 《Ukrainian Mathematical Journal》2005,57(9):1413-1423
We consider a random walk
for which the characteristic function of jumps ξ
k
satisfies the condition of almost semicontinuity. The problem of the exit of random walks S
n
of this type from a finite interval is studied.
__________
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 9, pp. 1209–1217, September, 2005. 相似文献
15.
The set of infinitely differentiable periodic functions is studied in terms of generalized -derivatives defined by a pair of sequences ψ
1 and ψ
2. In particular, we establish that every function f from the set has at least one derivative whose parameters ψ
1 and ψ
2 decrease faster than any power function. At the same time, for an arbitrary function f ∈ different from a trigonometric polynomial, there exists a pair ψ whose parameters ψ
1 and ψ
2 have the same rate of decrease and for which the -derivative no longer exists. We also obtain new criteria for 2π-periodic functions real-valued on the real axis to belong
to the set of functions analytic on the axis and to the set of entire functions.
Deceased. (A. I. Stepanets)
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1686–1708, December, 2008. 相似文献
16.
Precise asymptotics in the Baum-Katz and davis law of large numbers for positively associated sequences 总被引:6,自引:1,他引:5
§ 1 Introduction and resultsL et { X,Xi;i≥ 1} be a sequence of i.i.d.random variables,and set Sn= ni=1 Xi,n≥1.Hsu and Robbins[1 ] introduced the conceptof complete convergence.They together withErdos[2 ] proved n≥ 1 P(|Sn|≥εn) <∞ ,ε>0 (1)if and only if EX=0 and EX2 <∞ .L ater,Spitzer[3] proved n≥ 11n P(|Sn|≥εn) <∞ ,ε>0if and only if EX =0 and E|X|<∞ .More generally,it was shown by Baum and Katz[4 ]that,for 0
0 (… 相似文献
17.
Bin Heng SONG Huai Yu JIAN 《数学学报(英文版)》2005,21(5):1183-1190
We establish the existence of fundamental solutions for the anisotropic porous medium equation, ut = ∑n i=1(u^mi)xixi in R^n × (O,∞), where m1,m2,..., and mn, are positive constants satisfying min1≤i≤n{mi}≤ 1, ∑i^n=1 mi 〉 n - 2, and max1≤i≤n{mi} ≤1/n(2 + ∑i^n=1 mi). 相似文献
18.
I. V. Kal’chuk 《Ukrainian Mathematical Journal》2007,59(9):1342-1363
We obtain asymptotic equalities for the upper bounds of approximations by Weierstrass operators on the functional classes
and
in the metrics of the spaces Ĉ and
respectively.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 9, pp. 1201–1220, September, 2007. 相似文献
19.
Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes 总被引:1,自引:0,他引:1
Yun Xia LI Li Xin ZHANG 《数学学报(英文版)》2006,22(1):143-156
In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai+kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞) is an absolutely solutely summable sequence of real numbers. 相似文献
20.
Let Γ be the set of all permutations of the natural series and let α = {α j}
j∈ℕ, ν = {νj}
j∈ℕ, and η = {ηj}
j∈ℕ be nonnegative number sequences for which
is defined for all γ:= {γ(j)}
j∈ℕ ∈ Γ and η ∈ l
p. We find
in the case where 1 < p < ∞.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 10, pp. 1430–1434, October, 2005. 相似文献