• Communications for Statistical Applications and Methods
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• v.16 no.5
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• pp.841-849
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• 2009

Let {$X_n$, n ${\ge}$ 1} be a negatively associated sequence of identically distributed random variables with mean zeros and positive finite variances. Set $S_n$ = ${\Sigma}^n_{i=1}\;X_i$. Suppose that 0 < ${\sigma}^2=EX^2_1+2{\Sigma}^{\infty}_{i=2}\;Cov(X_1,\;X_i)$ < ${\infty}$. We prove that, if $EX^2_1(log^+{\mid}X_1{\mid})^{\delta}$ < ${\infty}$ for any 0< ${\delta}{\le}1$, then $\lim_{{\epsilon}\downarrow0}{\epsilon}^{2{\delta}}\sum_{{n=2}}^{\infty}\frac{(logn)^{\delta-1}}{n^2}ES^2_nI({\mid}S_n{\mid}\geq{\epsilon}{\sigma}\sqrt{nlogn}=\frac{E{\mid}N{\mid}^{2\delta+2}}{\delta}$, where N is the standard normal random variable. We also prove that if $S_n$ is replaced by $M_n=max_{1{\le}k{\le}n}{\mid}S_k{\mid}$ then the precise rate still holds. Some results in Fu and Zhang (2007) are improved to the complete moment case.

• Journal of the Institute of Convergence Signal Processing
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• v.8 no.3
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• pp.222-226
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• 2007

In this paper we composed the dual fuzzy rules using each region of specific points and $e-{\Delta}e$ phase plane In order to make dual fuzzy rule base. We composed the fuzzy control rules which can decrease rise time, delay time, maximum overshoot than basic fuzzy control rules. proposed method is alternately use at specific points of $e-{\Delta}e$ phase plane with two fuzzy control rules that is one control rule occruing the steady state error in transient region and another fuzzy control rule use to decrease the steady state error and rapidly converge at the convergence region. Also, two fuzzy control rules in the $e-{\Delta}e$ phase plane decide the change time according to response characteristics of plants. In order to confirm thef proposed algorithm. As the results of experiments through the hydraulic servo motor control system with a DSP processor, We verified that proposed dual fuzzy control rules get the good response compare with the basic fuzzy control rule.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.305-317
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• 2004

We construct the empirical Bayes (EB)estimation of the parameter in two-side truncated distribution families with asymmetric Linex loss using negatively associated (NA) samples. The asymptotical optimality and convergence rate of the EB estimation is obtained. We will show that the convergence rate can be arbitrarily close to $O(n^{-q}),\;q\;=\;{\lambda}s(\delta\;-\;2)/\delta(s\;+\;2)$.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.1009-1024
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• 2017

In this paper, we consider the new faster iterative scheme due to Sintunavarat and Pitea ([32]) for further investigation and we prove its strong and ${\Delta}$-convergence theorems, data dependence and stability results in hyperbolic space. Our results extend, improve and generalize several recent results in CAT(0) space and uniformly convex Banach space.

• Journal of the Korean Statistical Society
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• v.31 no.1
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• pp.33-43
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• 2002

The empirical Bayes linear loss two-action problem is studied. An empirical Bayes test $\delta$$_{n}$ $^{*}$ is proposed. It is shown that $\delta$$_{n}$ $^{*}$ is asymptotically optimal in the sense that its regret converges to zero at a rate $n^{-1}$ over a class of priors and the rate $n^{-1}$ is the optimal rate of convergence of empirical Bayes tests.sts.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.713-727
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• 2016

In this paper, we introduce two general iteration schemes with bounded error terms and prove some theorems related to the strong and ${\Delta}$-convergence of these iteration schemes for multi-valued maps in a hyperbolic space. The results which are presented here extend and improve some well-known results in the current literature.

• Journal of Korean Ophthalmic Optics Society
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• v.8 no.2
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• pp.47-52
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• 2003

117 undergraduate ophthalmic optics students volunteered to participate in this study. They ranged in age from 19 to 26 years. Subject, had best corrected visual acuity of at least 1.0 in both eyes, no strabismus, no amblyopia, and no history of ocular surgery. 37 subjects are esphoria and 25 subjects are $3{\Delta}$ and less, and the rest of 12 subjects show more $4{\Delta}$. Average phoria amount is $2.96{\Delta}$ at far distance and $1.08{\Delta}$ at near distance, respectively. The variation of phoria amount in far and near distance, unchanging subjects are 3, 8 subjects are increase esophoria amount, and 26 subjects are phoria amount decreasing or appear exophoria. The reason of esophoria amount is decreasing in near distance, and the results are convergence burden decreases. At positive relative convergence, the expected value in far distance, blurred point is 7, break point is 16, and recovery point is 12. And negative relative convergence, break point is 7 and recovery point is 13, respectively. Moreover, at positive relative convergence, the expected value in near distance is blurred point is 8, break point is 7 and recovery point is 22. And negative relative convergence, blurred point is 2, break point is 8 and recovery point is 12, respectively.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.633-641
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• 2004

In this paper we deal with functions in higher dimension. We provide several convergence theorem for approximation by convolution type delta sequence. We also give sufficient and necessary condition for Gibbs phenomenon to exist.

• Journal of Environmental Analysis, Health and Toxicology
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• v.21 no.4
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• pp.229-236
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• 2018

In this study, inter-laboratory comparison was done using elemental analyzer-isotope ratio mass spectrometers (EA-IRMSs) to determine carbon and nitrogen contents as well as stable carbon and nitrogen isotopic compositions (${\delta}^{13}C$ and ${\delta}^{15}N$) of five environmental samples containing lake and marine sediments, higher plant leaves, and fish muscle, and one organic analytical standard (Protein (Casein) Standard OAS). Five national laboratories participated in this comparison study, and each laboratory analyzed all five samples and the analytical standard. Results showed that variations in total organic carbon (TOC) and total nitrogen (TN) contents as well as ${\delta}^{13}C_{TOC}$ and ${\delta}^{15}N_{TN}$ values among the laboratories were large compared to the analytical uncertainties. The results highlighted the inhomogeneity of the test samples and thus, the need to select suitable standard reference materials for future inter-laboratory studies. Further inter-laboratory comparison exercises could promote good measurement practices in the acquisition of stable carbon and nitrogen isotopic composition data.

• East Asian mathematical journal
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• v.24 no.1
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• pp.35-43
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• 2008

Let E be a uniformly convex Banach space and K be a nonempty closed convex subset of E. Let ${\{T_i\}}^N_{i=1}$ be N nonexpansive self-mappings of K with $F\;=\;{\cap}^N_{i=1}F(T_i)\;{\neq}\;{\theta}$ (here $F(T_i)$ denotes the set of fixed points of $T_i$). Suppose that one of the mappings in ${\{T_i\}}^N_{i=1}$ is semi-compact. Let $\{{\alpha}_n\}\;{\subset}\;[{\delta},\;1-{\delta}]$ for some ${\delta}\;{\in}\;(0,\;1)$ and $\{{\beta}_n\}\;{\subset}\;[\tau,\;1]$ for some ${\tau}\;{\in}\;(0,\;1]$. For arbitrary $x_0\;{\in}\;K$, let the sequence {$x_n$} be defined iteratively by $\{{x_n\;=\;{\alpha}_nx_{n-1}\;+\;(1-{\alpha}_n)T_ny_n,\;\;\;\;\;\;\;\;\; \atop {y_n\;=\;{\beta}nx_{n-1}\;+\;(1-{\beta}_n)T_nx_n},\;{\forall}_n{\geq}1,}$, where $T_n\;=\;T_{n(modN)}$. Then {$x_n$} convergence strongly to a common fixed point of the mappings family ${\{T_i\}}^N_{i=1}$. The result presented in this paper generalized and improve the corresponding results of Chidume and Shahzad [C. E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62(2005), 1149-1156] even in the case of ${\beta}_n\;{\equiv}\;1$ or N=1 are also new.