共查询到20条相似文献,搜索用时 15 毫秒
1.
Tachen Liang 《Journal of Applied Mathematics and Computing》2007,23(1-2):153-165
This paper deals with the empirical Bayes two-action problem of testingH 0 : θ ≤ θo versusH 1 : θ > θo using a linear error loss for some discrete nonexponential families having probability function either $\begin{gathered} f_1 (x|\theta ) = (x\alpha + 1 - \theta )\theta ^x /\prod\limits_{j = 0}^x {(j\alpha + 1)} \\ or \\ f_1 (x|\theta ) = \left[ {\theta \prod\limits_{j = 0}^{x - 1} {(j\alpha + 1 - \theta )} } \right]/\left[ {\prod\limits_{j = 0}^x {(j\alpha + 1)} } \right] \\ \end{gathered} $ Two empirical Bayes tests δn* and δn** are constructed. We have shown that both δn* and δn** are asymptotically optimal, and their regrets converge to zero at an exponential decay rate O(exp( -cn)) for some c > 0, wheren is the number of historical data available when the present decision problem is considered. 相似文献
2.
Based on the coincidence degree theory of Mawhin, we get a new general existence result for the following higher-order multi-point
boundary value problem at resonance
$\begin{gathered}
x^{(n)} (t) = f(t,x(t),x'(t),...,x^{(n - 1)} (t)),t \in (0,1), \hfill \\
x(0) = \sum\limits_{i = 1}^m {a_i x(\xi _i ),x'(0) = ... = x^{(n - 2)} (0) = 0,x^{(n - 1)} (1) = } \sum\limits_{j = 1}^l {\beta _j x^{(n - 1)} (\eta _j )} , \hfill \\
\end{gathered}
$\begin{gathered}
x^{(n)} (t) = f(t,x(t),x'(t),...,x^{(n - 1)} (t)),t \in (0,1), \hfill \\
x(0) = \sum\limits_{i = 1}^m {a_i x(\xi _i ),x'(0) = ... = x^{(n - 2)} (0) = 0,x^{(n - 1)} (1) = } \sum\limits_{j = 1}^l {\beta _j x^{(n - 1)} (\eta _j )} , \hfill \\
\end{gathered}
相似文献
3.
Yuji Liu 《Journal of Applied Mathematics and Computing》2007,23(1-2):167-182
The existence of solutions of the following multi-point boundary value problem $\left\{ \begin{gathered} x^{(n)} (t) = f(t,x(t),x^\prime (t),...,x^{(n - 2)} (t)) + r(t),0 < t < 1, \\ x^{(i)} (\xi _i ) = 0 for i = 0,1,... ,n - 3, ( * ) \\ \alpha x^{(n - 2)} (0) = \beta x^{(n - 1)} (0) = \gamma x^{(n - 1)} (1) + \tau x^{(n - 1)} (1) = 0 \\ \end{gathered} \right.$ is studied. Sufficient conditions for the existence of at least one solution of BVP(*) are established. It is of interest that the growth conditions imposed on f are allowed to be super-linear (the degrees of phases variables are allowed to be greater than 1 if it is a polynomial). The results are different from known ones since we don’t apply the Green’s functions of the corresponding problem and the method to obtain a priori bounds of solutions are different enough from known ones. Examples that can not be solved by known results are given to illustrate our theorems. 相似文献
4.
The modified Bernstein-Durrmeyer operators discussed in this paper are given byM_nf≡M_n(f,x)=(n+2)P_(n,k)∫_0~1p_n+1.k(t)f(t)dt,whereWe will show,for 0<α<1 and 1≤p≤∞ 相似文献
5.
N. E. Lushpai 《Mathematical Notes》1974,16(2):701-708
For the classes of periodic functions with r-th derivative integrable in the mean,we obtain a best quadrature formula of the form $$\begin{gathered} \int_0^1 {f(x)dx = \sum\nolimits_{k = 0}^{m - 1} {\sum\nolimits_{l = 0}^\rho {p_{k,l} } } } f^{(l)} (x_k ) + R(f),0 \leqslant \rho \leqslant r - 1, \hfill \\ 0 \leqslant x_0< x_1< ...< x_{m - 1} \leqslant 1, \hfill \\ \end{gathered}$$ where ρ=r?2 and r?3, r=3, 5, 7, ..., and we determine an exact bound for the error of this formula. 相似文献
6.
BOUNDARYVALUEPROBLEMSOFSINGULARLYPERTURBEDINTEGRO-DIFFERENTIALEQUATIONSZHOUQINDEMIAOSHUMEI(DepartmentofMathematics,JilinUnive... 相似文献
7.
For the functional differential equationu (n) (t)=f(u)(t) we have established the sufficient conditions for solvability and unique solvability of the boundary value problems $$u^{(i)} (0) = c_i (i = 0,...,m - 1), \smallint _0^{ + \infty } |u^{(m)} (t)|^2 dt< + \infty $$ and $$\begin{gathered} u^{(i)} (0) = c_i (i = 0),...,m - 1, \hfill \\ \smallint _0^{ + \infty } t^{2j} |u^{(j)} (t)|^2 dt< + \infty (j = 0,...,m), \hfill \\ \end{gathered} $$ wheren≥2,m is the integer part of $\tfrac{n}{2}$ ,c i ∈R, andf is the continuous operator acting from the space of (n?1)-times continuously differentiable functions given on an interval [0,+∞] into the space of locally Lebesgue integrable functions. 相似文献
8.
A. A. Abilov 《Mathematical Notes》1992,52(1):631-635
Let
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