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1.
J. Sunklodas 《Lithuanian Mathematical Journal》2007,47(3):327-335
We estimate the difference
for bounded functions h: ℝ → ℝ satisfying the Lipschitz condition, where Z
v
= B
v
−1
∑
i=0
∞
v
i
X
i
and
with discount factor ν such that 0 < ν < 1. Here {X
n
, n ≥ 0} is a sequence of strongly mixing random variables with
, and N is a standard normal random variable. In a particular case, the obtained upper bounds are of order O((1 − ν)1/2).
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 3, pp. 399–409, July–September, 2007.
The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-15/07. 相似文献
2.
For any positive real numbers A, B, and d satisfying the conditions
, d>2, we construct a Gabor orthonormal basis for L2(ℝ), such that the generating function g∈L2(ℝ) satisfies the condition:∫ℝ|g(x)|2(1+|x|
A
)/log
d
(2+|x|)dx < ∞ and
. 相似文献
3.
In this paper, we show that if the sum ∑r=1∞
Ψ(r) diverges, then the set of points (x, z, w) ∈ ℝ × ℂ × ℚp satisfying the inequalities , and for infinitely many integer polynomials P has full measure. With a special choice of parameters v
i
and λ
i
, i = 1, 2, 3, we can obtain all the theorems in the metric theory of transcendental numbers which were known in the real, complex,
or p-adic fields separately. 相似文献
4.
Nonexistence of invariant graphs in all supercritical energy levels of mechanical Lagrangians in T
2
Rafael O. Ruggiero 《Bulletin of the Brazilian Mathematical Society》2006,37(3):419-449
Let (T2, g) be a smooth Riemannian structure in the torus T2. We show that given ε > 0 and any C∞ function U : T2 → ℝ there exists a C1 function Uε with Lipschitz derivatives that is ε-C0 close to U for which there are no continuous invariant graphs in any supercritical energy level of the mechanical Lagrangian Lε : TT2 → ℝ given by
. We also show that given n ∈ ℕ, the set of C∞ potentials U : T2 → ℝ for which there are no continuous invariant graphs in any supercritical energy level E ≤ n of
is C0 dense in the set of C∞ functions.
Partially supported by CNPq, FAPERJ-Cientistas do nosso estado. 相似文献
5.
We consider the weighted Hardy integral operatorT:L
2(a, b) →L
2(a, b), −∞≤a<b≤∞, defined by
. In [EEH1] and [EEH2], under certain conditions onu andv, upper and lower estimates and asymptotic results were obtained for the approximation numbersa
n(T) ofT. In this paper, we show that under suitable conditions onu andv,
where ∥w∥p=(∫
a
b
|w(t)|p
dt)1/p.
Research supported by NSERC, grant A4021.
Research supported by grant No. 201/98/P017 of the Grant Agency of the Czech Republic. 相似文献
6.
Considering the positive d-dimensional lattice point Z
+
d
(d ≥ 2) with partial ordering ≤, let {X
k: k ∈ Z
+
d
} be i.i.d. random variables taking values in a real separable Hilbert space (H, ‖ · ‖) with mean zero and covariance operator Σ, and set $
S_n = \sum\limits_{k \leqslant n} {X_k }
$
S_n = \sum\limits_{k \leqslant n} {X_k }
, n ∈ Z
+
d
. Let σ
i
2, i ≥ 1, be the eigenvalues of Σ arranged in the non-increasing order and taking into account the multiplicities. Let l be the dimension of the corresponding eigenspace, and denote the largest eigenvalue of Σ by σ
2. Let logx = ln(x ∨ e), x ≥ 0. This paper studies the convergence rates for $
\sum\limits_n {\frac{{\left( {\log \log \left| n \right|} \right)^b }}
{{\left| n \right|\log \left| n \right|}}} P\left( {\left\| {S_n } \right\| \geqslant \sigma \varepsilon \sqrt {2\left| n \right|\log \log \left| n \right|} } \right)
$
\sum\limits_n {\frac{{\left( {\log \log \left| n \right|} \right)^b }}
{{\left| n \right|\log \left| n \right|}}} P\left( {\left\| {S_n } \right\| \geqslant \sigma \varepsilon \sqrt {2\left| n \right|\log \log \left| n \right|} } \right)
. We show that when l ≥ 2 and b > −l/2, E[‖X‖2(log ‖X‖)
d−2(log log ‖X‖)
b+4] < ∞ implies $
\begin{gathered}
\mathop {\lim }\limits_{\varepsilon \searrow \sqrt {d - 1} } (\varepsilon ^2 - d + 1)^{b + l/2} \sum\limits_n {\frac{{\left( {\log \log \left| n \right|} \right)^b }}
{{\left| n \right|\log \left| n \right|}}P\left( {\left\| {S_n } \right\| \geqslant \sigma \varepsilon \sqrt 2 \left| n \right|\log \log \left| n \right|} \right)} \hfill \\
= \frac{{K(\Sigma )(d - 1)^{\frac{{l - 2}}
{2}} \Gamma (b + l/2)}}
{{\Gamma (l/2)(d - 1)!}} \hfill \\
\end{gathered}
$
\begin{gathered}
\mathop {\lim }\limits_{\varepsilon \searrow \sqrt {d - 1} } (\varepsilon ^2 - d + 1)^{b + l/2} \sum\limits_n {\frac{{\left( {\log \log \left| n \right|} \right)^b }}
{{\left| n \right|\log \left| n \right|}}P\left( {\left\| {S_n } \right\| \geqslant \sigma \varepsilon \sqrt 2 \left| n \right|\log \log \left| n \right|} \right)} \hfill \\
= \frac{{K(\Sigma )(d - 1)^{\frac{{l - 2}}
{2}} \Gamma (b + l/2)}}
{{\Gamma (l/2)(d - 1)!}} \hfill \\
\end{gathered}
, where Γ(·) is the Gamma function and $
\prod\limits_{i = l + 1}^\infty {((\sigma ^2 - \sigma _i^2 )/\sigma ^2 )^{ - {1 \mathord{\left/
{\vphantom {1 2}} \right.
\kern-\nulldelimiterspace} 2}} }
$
\prod\limits_{i = l + 1}^\infty {((\sigma ^2 - \sigma _i^2 )/\sigma ^2 )^{ - {1 \mathord{\left/
{\vphantom {1 2}} \right.
\kern-\nulldelimiterspace} 2}} }
. 相似文献
7.
S. V. Kislyakov 《Journal of Mathematical Sciences》2009,156(5):824-833
Let 1 < r < 2 and let b is a weight on ℝ such that satisfies the Muckenhoupt condition Ar′/2 (r′ is the exponent conjugate to r). If fj are functions whose Fourier transforms are supported on mutually disjoint intervals, then
for 0 < p ≤ r. Bibliography: 9 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 355, 2008, pp. 180–198. 相似文献
8.
This article is concerned with the decay property in theL 1 norm ast»∞ of the nonnegative solutions of the initial value problem in ? n $\left\{ {\begin{array}{*{20}c} {u_t = \Delta u + \mu |\nabla \upsilon |^q } \\ {\upsilon _t = \Delta \upsilon + \upsilon |\nabla \upsilon |^p } \\ \end{array} } \right.$ for different values of the parametersp, q≥1 and when μ, ν<0. If $pq > \frac{{\inf \left( {p,q} \right)}}{{n + 1}} + \left( {n + 2} \right)/\left( {n + 1} \right)$ then lim t→∞∥u(t)+v(t)∥1>0 and when $pq< \frac{{\inf \left( {p,q} \right)}}{{n + 1}} + \left( {n + 2} \right)/\left( {n + 1} \right)$ then lim t→∞∥u(t)+v(t)∥1>0. 相似文献
9.
Martin Fuchs 《Mathematical Methods in the Applied Sciences》1996,19(15):1225-1232
We discuss certain classes of quasi-static non-Newtonian fluids for which a power-law of the form σD=∇ϕ(ℰv) holds. Here σD is the stress deviator, v the velocity field, ℰv its symmetric derivative and ϕ is the function \[ \phi ({\cal E}v)=\frac 12\mu _\infty \left| {\cal E}v\right| ⁁2+\frac 1p\mu _0\left\{ \begin{array}{c} \left( 1+\left| {\cal E}v\right| ⁁2\right) ⁁{p/2} \\ \text{or} \\ \left| {\cal E}v\right| ⁁p \end{array} \right\}, \] ϕ(ℰv)=1 2 μ∞∣ℰv∣2+1 p μ0 (1+∣ℰv∣2)p/2 or ∣ℰv∣p, μ∞⩾0, μ0⩾0, μ∞+μ0>0, 1<p<∞. We then prove various regularity results for the velocity field v, for example differentiability almost everywhere and local boundedness of the tensor ℰv. 相似文献
10.
For given 2n×2n matricesS
13,S
24 with rank(S
13,S
24)=2n
we consider the eigenvalue problem:u′=A(x)u+B(x)v,v′=C
1(x;λ)u-A
T(x)v with
相似文献
11.
E. I. Berezhnoi 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2009,44(3):163-171
Under the assumptions that Δ(f, h)(t) = |f(t + h) − f(t)|, X is a symmetric space of functions in [0, 1], α ∈ (0, 1) and p ∈ [1, ∞) are any fixed number, by the triple (X, α, p) a Besov type space Λ
X,p
α
is constructed, where the norm is given by the equality
12.
13.
K. J. Wirths 《分析论及其应用》1996,12(3):98-100
Let
be such that |p(eiq)|≤1 for ϕ∈R and |p(1)|=a∈[0,1]. An inequality of Dewan and Govil for the sum |av|+|an|, 0≤u<v≤n is sharpened. 相似文献
14.
The asymptotic expansions are studied for the vorticity
to 2D incompressible Euler equations with-initial vorticity
, where ϕ0(x) satisfies |d ϕ0(x)|≠0 on the support of
and
is sufficiently smooth and with compact support in ℝ2 (resp. ℝ2×T) The limit,v(t,x), of the corresponding velocity fields {v
ɛ(t,x)} is obtained, which is the unique solution of (E) with initial vorticity ω0(x). Moreover,
(ℤ2)) for all 1≽p∞, where
and ϕ(t,x) satisfy some modulation equation and eikonal equation, respectively. 相似文献
15.
T. A. Suslina 《Functional Analysis and Its Applications》2012,46(3):234-238
In a bounded domain O ⊂ ℝd with C 1,1 boundary a matrix elliptic second-order operator A D,ɛ with Dirichlet boundary condition is studied. The coefficients of this operator are periodic and depend on x/ɛ, where ɛ s 0 is a small parameter. The sharp-order error estimate $
\left\| {A_{D,\varepsilon }^{ - 1} - \left( {A_D^0 } \right)^{ - 1} } \right\|\left. {L_2 \to L_2 \leqslant C\varepsilon } \right|
$
\left\| {A_{D,\varepsilon }^{ - 1} - \left( {A_D^0 } \right)^{ - 1} } \right\|\left. {L_2 \to L_2 \leqslant C\varepsilon } \right|
相似文献
16.
Let
be a polynomial degreen and let
. Then according to Bernstein’s inequality ‖p’‖≤n‖p‖. It is a well known open problem to obtain inequality analogous to Bernstein’s
inequality for the class IIn of polynomials satisfying p(z)≡znp(1/z). Here we obtain an inequality analogous to Bernstein’s inequality for a subclass of IIn. Our results include several of the known results as special cases. 相似文献
17.
Dr. Erhard Braune 《Monatshefte für Mathematik》1978,85(1):1-3
The following theorem is proved, based on an irrationality measure fore a (a∈0, rational) ofP. Bundschuh: Letp, q, u, v∈0 be rational integers withq≥1,v≥1,a=u/v, 0<δ≤2. If $$\begin{gathered} q > \exp \{ u^2 ((ea)^2 /8) (1 + u^2 (a e/2)^2 ) + |u|^{8/\delta } e^{2/\delta } + (4/\delta )\log \upsilon + \hfill \\ + (2/\delta )\log 12 + |a| + \log (3 + 20|a|e^{|a|} )) + \log ((3/2)e^{|a|} ) + e/2\} , \hfill \\ then |e^a - p/q| > q^{ - (2 + \delta )} . \hfill \\ \end{gathered} $$ 相似文献
18.
Let ( Y,d,dl )\left( {\mathcal{Y},d,d\lambda } \right) be (ℝ
n
, |·|, μ), where |·| is the Euclidean distance, μ is a nonnegative Radon measure on ℝ
n
satisfying the polynomial growth condition, or the Gauss measure metric space (ℝ
n
, |·|, d
λ
), or the space (S, d, ρ), where S ≡ ℝ
n
⋉ ℝ+ is the (ax + b)-group, d is the left-invariant Riemannian metric and ρ is the right Haar measure on S with exponential growth. In this paper, the authors introduce and establish some properties of the atomic Hardy-type spaces
{ Xs ( Y ) }0 < s \leqslant ¥\left\{ {X_s \left( \mathcal{Y} \right)} \right\}_{0 < s \leqslant \infty } and the BMO-type spaces
{ BMO( Y, s ) }0 < s \leqslant ¥\left\{ {BMO\left( {\mathcal{Y}, s} \right)} \right\}_{0 < s \leqslant \infty }. Let H
1
( Y )\left( \mathcal{Y} \right) be the known atomic Hardy space and L
01
( Y )\left( \mathcal{Y} \right) the subspace of f ∈ L
1
( Y )\left( \mathcal{Y} \right) with integral 0. The authors prove that the dual space of X
s
( Y )\left( \mathcal{Y} \right) is BMO( Y,s )BMO\left( {\mathcal{Y},s} \right) when s ∈ (0,∞), X
s
( Y )\left( \mathcal{Y} \right) = H
1
( Y )\left( \mathcal{Y} \right) when s ∈ (0, 1], and X
∞
( Y )\left( \mathcal{Y} \right) = L
01
( Y )\left( \mathcal{Y} \right) (or L
1
( Y )\left( \mathcal{Y} \right)). As applications, the authors show that if T is a linear operator bounded from H
1
( Y )\left( \mathcal{Y} \right) to L
1
( Y )\left( \mathcal{Y} \right) and from L
1
( Y )\left( \mathcal{Y} \right) to L
1,∞
( Y )\left( \mathcal{Y} \right), then for all r ∈ (1,∞) and s ∈ (r,∞], T is bounded from X
r
( Y )\left( \mathcal{Y} \right) to the Lorentz space L
1,s
( Y )\left( \mathcal{Y} \right), which applies to the Calderón-Zygmund operator on (ℝ
n
, |·|, μ), the imaginary powers of the Ornstein-Uhlenbeck operator on (ℝ
n
, |·|, d
γ
) and the spectral operator associated with the spectral multiplier on (S, d, ρ). All these results generalize the corresponding results of Sweezy, Abu-Shammala and Torchinsky on Euclidean spaces. 相似文献
19.
This paper deals with a coupled system of fourth-order parabolic inequalities |u|t ≥ 2u + |v|q,|v|t ≥ 2v + |u|p in S = Rn × R+ with p,q > 1,n ≥ 1.A FujitaLiouville type theorem is established that the inequality system does not admit nontrivial nonnegative global solutions on S whenever n4 ≤ max(ppq+11,pqq+11).Since the general maximum-comparison principle does not hold for the fourth-order problem,the authors use the test function method to get the global non-existence of nontrivial solutions. 相似文献
20.
Bao Yongguang 《分析论及其应用》1995,11(4):15-23
Let ξn −1 < ξn −2 < ξn − 2 < ... < ξ1 be the zeros of the the (n−1)-th Legendre polynomial Pn−1(x) and −1=xn<xn−1<...<x1=1, the zeros of the polynomial
. By the theory of the inverse Pal-Type interpolation, for a function f(x)∈C
[−1,1]
1
, there exists a unique polynomial Rn(x) of degree 2n−2 (if n is even) satisfying conditions Rn(f, ξk) = f (εk) (1 ⩽ k ⩽ n −1); R1
n(f,xk)=f1(xk)(1≤k≤n). This paper discusses the simultaneous approximation to a differentiable function f by inverse Pal-Type interpolation
polynomial {Rn(f, x)} (n is even) and the main result of this paper is that if f∈C
[1,1]
r
, r≥2, n≥r+2, and n is even then |R1
n(f,x)−f1(x)|=0(1)|Wn(x)|h(x)·n3−r·E2n−r−3(f(r)) holds uniformly for all x∈[−1,1], where
. 相似文献
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