共查询到20条相似文献,搜索用时 15 毫秒
1.
Aleksandar Ivić 《The Ramanujan Journal》2009,19(2):207-224
We obtain, for T
ε
≤U=U(T)≤T
1/2−ε
, asymptotic formulas for
where Δ(x) is the error term in the classical divisor problem, and E(T) is the error term in the mean square formula for
. Upper bounds of the form O
ε
(T
1+ε
U
2) for the above integrals with biquadrates instead of square are shown to hold for T
3/8≤U=U(T)≪
T
1/2. The connection between the moments of E(t+U)−E(t) and
is also given. Generalizations to some other number-theoretic error terms are discussed.
相似文献
2.
A. V. Ustinov 《Journal of Mathematical Sciences》2006,137(2):4722-4738
Statistical properties of continued fractions for numbers a/b, where a and b lie in the sector a, b ≥ 1, a2 + b2 ≤ R2, are studied. The main result is an asymptotic formula with two meaning terms for the quantity
where sx(a/b) = |{j ε {1, …, s}: [0; tj, …, ts] ≤ x}| is the Gaussian statistic for the fraction a/b = [t0; t1, …, ts]. Bibliography: 12 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 322, 2005, pp. 186–211. 相似文献
3.
M. N. Mishra B. L. S. Prakasa Rao 《Statistical Inference for Stochastic Processes》2011,14(2):101-109
Consider a stochastic process {X
t
, 0 ≤ t ≤ T} governed by a stochastic differential equation given by
dXt = S(Xt) dt + e dWtH, X0=x0, 0 £ t £ T dX_t= S(X_t) \;dt + \epsilon \; dW_t^H,\quad X_0=x_0,\quad 0 \leq t \leq T 相似文献
4.
Let T(t), t ≥ 0, be a C
0-semigroup of linear operators acting in a Hilbert space H with norm ‖·‖. We prove that T(t) is uniformly bounded, i.e., ‖T(t)‖ ≤ M, t ≥ 0, if and only if the following condition is satisfied:
5.
TAOYOUSHAN GAOGUOZHU 《高校应用数学学报(英文版)》1998,13(3):271-280
In this paper the forced neutral difterential equation with positive and negative coefficients d/dt [x(t)-R(t)x(t-r)] P(t)x(t-x)-Q(t)x(t-σ)=f(t),t≥t0,is considered,where f∈L^1(t0,∞)交集C([t0,∞],R^ )and r,x,σ∈(0,∞),The sufficient conditions to oscillate for all solutions of this equation are studied. 相似文献
6.
In this work we prove a new strong convergence result of the regularized successive approximation method given by yn+1 = qnz0 + (1 - qn)T^nyn, n = 1, 2,…,where lim n→∞ qn = 0 and ∞∑n=1 qn=∞ for T a total asymptotically nonexpansive mapping, i.e., T is such that
││T^n x - T^n y││ ≤ x - y ││ + kn^(1)φ(││x - y││) + kn^(2),where kn^1 and kn^2 are real null convergent sequences and φ:R^+→R^+ is continuous such that φ(0)=0 and limt→∞φ(t)/t≤ C for a certain constant C 〉 0. Among other features, our results essentially generalize existing results on strong convergence for T nonexpansive and asymptotically nonexpansive. The convergence and stability analysis is given for both self- and nonself-mappings. 相似文献 7.
LetA be the class of normalized analytic functions in the unit disk Δ and define the class
8.
Song Bo Hou 《数学学报(英文版)》2011,27(10):1935-1940
Let (M,g(t)), 0 ≤ t ≤ T, be an n-dimensional closed manifold with nonnegative Ricci curvature, |Rc| ≤ C/t for some constant C > 0 and g(t) evolving by the Ricci flow
|
设为首页 | 免责声明 | 关于勤云 | 加入收藏 |
Copyright©北京勤云科技发展有限公司 京ICP备09084417号 |