• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.149-160
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• 1995

We consider the problem of optimal adaptive estiamtion of the euclidean parameter vector $\theta$ of the univariate non-linerar autogressive time series model ${X_t}$ which is defined by the following system of stochastic difference equations ; $X_t = \sum^p_{i=1} \theta_i \cdot T_i(X_{t-1})+e_t, t=1, \cdots, n$, where $\theta$ is the unknown parameter vector which descrives the deterministic dynamics of the stochastic process ${X_t}$ and ${e_t}$ is the sequence of white noises with unknown density $f(\cdot)$. Under some general growth conditions on $T_i(\cdot)$ which guarantee ergodicity of the process, we construct a sequence of adaptive estimatros which is locally asymptotic minimax (LAM) efficient and also attains the least possible covariance matrix among all regular estimators for arbitrary symmetric density.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.115-126
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• 2016

Let $E{\subset}{\mathbb{F}}^d_q$, the d-dimensional vector space over the finite field with q elements. Construct a graph, called the distance graph of E, by letting the vertices be the elements of E and connect a pair of vertices corresponding to vectors x, y 2 E by an edge if ${\parallel}x-y{\parallel}:=(x_1-y_1)^2+{\cdots}+(x_d-y_d)^2=1$. We shall prove that the non-overlapping chains of length k, with k in an appropriate range, are uniformly distributed in the sense that the number of these chains equals the statistically correct number, $1{\cdot}{\mid}E{\mid}^{k+1}q^{-k}$ plus a much smaller remainder.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.193-200
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• 1994

Let x : $M^{n}$ .rarw. $E^{m}$ be an isometric immersion of a manifold $M^{n}$ into the Euclidean space $E^{m}$ and .DELTA. the Laplacian of $M^{n}$ defined by -div.omicron.grad. The family of such immersions satisfying the condition .DELTA.x = .lambda.x, .lambda..mem.R, is characterized by a well known result ot Takahashi (8]): they are either minimal in $E^{m}$ or minimal in some Euclidean hypersphere. As a generalization of Takahashi's result, many authors ([3,6,7]) studied the hypersurfaces $M^{n}$ in $E^{n+1}$ satisfying .DELTA.x = Ax + b, where A is a square matrix and b is a vector in $E^{n+1}$, and they proved independently that such hypersurfaces are either minimal in $E^{n+1}$ or hyperspheres or spherical cylinders. Since .DELTA.x = -nH, the submanifolds mentioned above satisfy .DELTA.H = .lambda.H or .DELTA.H = AH, where H is the mean curvature vector field of M. And the family of hypersurfaces satisfying .DELTA.H = .lambda.H was explored for some cases in [4]. In this paper, we classify space curves x : R .rarw. $E^{3}$ satisfying .DELTA.x = Ax + b or .DELTA.H = AH, and find conditions for such curves to be equivalent.alent.alent.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.235-244
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• 1999

We will derive some identities related to p-scalars, p-vectors, and non-holonomic frames in a generalized 2-dimensional Riemannian manifold $X_2$.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.1
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• pp.23-29
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• 2007

Let X and Y be vector spaces. In this paper we prove that a mapping $f:X{\rightarrow}Y$ satisfies the following functional equation $${\large}\sum_{1{\leq}k<l{\leq}n}\;(f(x_k+x_l)+f(x_k-x_l))-2(n-1){\large}\sum_{i=1}^{n}f(x_i)=0$$ if and only if the mapping f is quadratic. In addition we investigate the generalized Hyers-Ulam-Rassias stability problem for the functional equation.

• The Journal of Korean Society for Radiation Therapy
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• v.28 no.1
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• pp.27-34
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• 2016

Purpose : Retrospective evaluation of setup changes using the corrected position during helical tomotherapy Materials and Methods : Head and neck cancer patients were randomly sampled and summarized into 3 groups: Group 1(32) Brain, Group 2 2(28)Maxillar, Nasal cavity, Group 3 (35) Nasopharynx(NPX), Tongue, Tonsil, and Oropharynx(OPX). In 3 groups, the statistical tests based on repeated measurements among 30 times of the duration of treatment by applying X, Y, Z axis errors, roll, weight changes, and vectors as variables. Results : The statistical test results showed that there was no difference between x-axis (p = 0.458) and y-axis (p=0.986) and in roll (p = 0.037), weight change (p <0.001), and the vector (p <0.001). In addition, the pattern between the three groups based on the fraction revealed no difference in x-axis (p = 0.430) and roll (p = 0.299) but a difference in y-axis (.023), weight change (p = 0.001), and vector (p = 0.028). Conclusion : The results of the retrospective evaluation found the change in the group 3 with respect Y, Z, weight, and vector and a larger random error during the treatment including low neck.

• The Plant Pathology Journal
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• v.38 no.6
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• pp.551-571
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• 2022

Xylella fastidiosa is xylem-limited bacterium capable of infecting a wide range of host plants, resulting in Pierce's disease in grapevine, citrus variegated chlorosis, olive quick decline syndrome, peach phony disease, plum leaf scald, alfalfa dwarf, margin necrosis and leaf scorch affecting oleander, coffee, almond, pecan, mulberry, red maple, oak, and other types of cultivated and ornamental plants and forest trees. In the European Union, X. fastidiosa is listed as a quarantine organism. Since its first outbreak in the Apulia region of southern Italy in 2013 where it caused devastating disease on Olea europaea (called olive leaf scorch and quick decline), X. fastidiosa continued to spread and successfully established in some European countries (Corsica and PACA in France, Balearic Islands, Madrid and Comunitat Valenciana in Spain, and Porto in Portugal). The most recent data for Europe indicates that X. fastidiosa is present on 174 hosts, 25 of which were newly identified in 2021 (with further five hosts discovered in other parts of the world in the same year). From the six reported subspecies of X. fastidiosa worldwide, four have been recorded in European countries (fastidiosa, multiplex, pauca, and sandyi). Currently confirmed X. fastidiosa vector species are Philaenus spumarius, Neophilaenus campestris, and Philaenus italosignus, whereby only P. spumarius (which has been identified as the key vector in Apulia, Italy) is also present in Americas. X. fastidiosa control is currently based on pathogen-free propagation plant material, eradication, territory demarcation, and vector control, as well as use of resistant plant cultivars and bactericidal treatments.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.161-174
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• 2018

The aim of this article is to study the k-almost Ricci soliton and k-almost gradient Ricci soliton on contact metric manifold. First, we prove that if a compact K-contact metric is a k-almost gradient Ricci soliton, then it is isometric to a unit sphere $S^{2n+1}$. Next, we extend this result on a compact k-almost Ricci soliton when the flow vector field X is contact. Finally, we study some special types of k-almost Ricci solitons where the potential vector field X is point wise collinear with the Reeb vector field ${\xi}$ of the contact metric structure.

• Journal of the Korean Data and Information Science Society
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• v.11 no.1
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• pp.37-45
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• 2000

Consider the problem of estimating a $p{\times}1$ mean vector ${\underline{\theta}}(p{\geq}4)$ under the quadratic loss, based on a sample ${\underline{x}_{1}},\;{\cdots}{\underline{x}_{n}}$. We find an optimal decision rule within the class of Lindley type decision rules which shrink the usual one toward the mean of observations when the underlying distribution is that of a variance mixture of normals and when the norm ${\parallel}\;{\underline{\theta}}\;-\;{\bar{\theta}}{\underline{1}}\;{\parallel}$ is known, where ${\bar{\theta}}=(1/p){\sum_{i=1}^p}{\theta}_i$ and $\underline{1}$ is the column vector of ones.

• Honam Mathematical Journal
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• v.25 no.1
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• pp.95-115
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• 2003

Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}(p{\geq}4)$ under the quadratic loss, based on a sample $X_1,\;{\cdots}X_n$. We find an optimal decision rule within the class of Lindley type decision rules which shrink the usual one toward the mean of observations when the underlying distribution is that of a variance mixture of normals and when the norm $||{\theta}-{\bar{\theta}}1||$ is known, where ${\bar{\theta}}=(1/p)\sum_{i=1}^p{\theta}_i$ and 1 is the column vector of ones. When the norm is restricted to a known interval, typically no optimal Lindley type rule exists but we characterize a minimal complete class within the class of Lindley type decision rules. We also characterize the subclass of Lindley type decision rules that dominate the sample mean.