• Journal of the Korean Statistical Society
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• v.26 no.2
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• pp.231-243
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• 1997

In this paper we investigate weak convergence of the intergral processes whose index set is the non-compact infinite time interval. Our first goal is to develop the empirical central limit theorem as random elements of [0, .infty.) for an integral process which is constructed from iid variables. In developing the weak convergence as random elements of D[0, .infty.), we will use a result of Ossiander(4) whose proof heavily depends on the total boundedness of the index set. Our next goal is to establish the empirical central limit theorem for the Kaplan-Meier integral process as random elements of D[0, .infty.). In achieving the the goal, we will use the above iid result, a representation of State(6) on the Kaplan-Meier integral, and a lemma on the uniform order of convergence. The first result, in some sense, generalizes the result of empirical central limit therem of Pollard(5) where the process is regarded as random elements of D[-.infty., .infty.] and the sample paths of limiting Gaussian process may jump. The second result generalizes the first result to random censorship model. The later also generalizes one dimensional central limit theorem of Stute(6) to a process version. These results may be used in the nonparametric statistical inference.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.29 no.1
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• pp.31-38
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• 1984

The length of anthers, filaments and glumes (Palea and lemma) of leading rice cultivars was measured before and after anthesis. A few cultivars which have long anthers and filaments after anthesis were identified. Correlation coefficients between measurements were calculated.

• International Journal of Aeronautical and Space Sciences
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• v.14 no.3
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• pp.256-263
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• 2013

The saturation of the actuator impairs the response performance of the near space interceptor control system. A control system based on the properties of linear tracking system is designed for this problem. The properties are that the maximum value of the pseudo-Lyapunov function of the linear tracking control system do not present at the initial state but at the steady state, based on which the bounded stability problem is converted into linear tracking problem. The pseudo-Lyapunov function of the linear tracking system contain the input variables; the amplitude and frequency of the input variables affect the stability of the nonlinear control system. Designate expected closed-loop poles area for different input commands and obtain a controller which is function of input variables. The coupling between variables and linear matrices make the control system design problem non-convex. The non-convex problem is converted into a convex LMI according to the Shur complement lemma and iterative algorithm. Finally the simulation shows that the designed optimal control system is quick and accurate; the rationality of the presented design techniques is validated.

• School Mathematics
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• v.7 no.4
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• pp.353-373
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• 2005

The purpose of this paper is to analysis the basic network problem which can be applied to the mathematically gifted students in elementary school. Mainly, we discuss didactic transpositions of the double counting principle, the game of sprouts, Eulerian graph problem, and the minimum connector problem. Here the double counting principle is related to the handshaking lemma; in any graph, the sum of all the vertex-degree is equal to the number of edges. The selection of these subjects are based on the viewpoint; to familiar to graph theory, to raise algorithmic thinking, to apply to the real-world problem. The theoretical background of didactic transpositions of these subjects are based on the Polya's mathematical heuristics and Lakatos's philosophy of mathematics; quasi-empirical, proofs and refutations as a logic of mathematical discovery.

• Proceedings of the KIEE Conference
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• 1988.07a
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• pp.898-901
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• 1988

Up to now, using adaptive control method, Identification deals with system whose entire state variables and prameters are accessible for measurement. In practical situations, all the state variables cannot be measured and it is impossible to directly apply since the parameters of the system are unknown. Therefore, in this paper, using only input-output data, such a model of the system is not available since the parameters of the system are unknown. this leads to the concept of an adptive observer in which both the parameters and the state variable of the system are identified simultaniously. Lyapunov's direct method and Kalman-Yakubovich (K-Y) lemma are employed to ensure the stability of this schemes. The feature is that the signal and adaptive gain which is generated from filter is imposed upon feedback vector and then state variables and the unknown parameters can be identified. To show the usefulness of the proposed schemes, computer simulation result of unknown second-order system shows the effectiveness of the proposed schems.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.7
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• pp.483-490
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• 2004

The descriptor system model has a high ability in representing dynamical systems. It can preserve physical parameters in the coefficient matrices, and describe the dynamic part, static part, and even the improper part of the system in the same form. The design of mixed $H_{2}/H_{\infty}$ controllers for linear time-invariant descriptor systems is considered in this paper. Firstly, an $H_2$ and $H_{\infty}$ synthesis problems fur a descriptor system are presented separately in terms of linear matrix inequalities (LMIs) based on the bounded real lemma. Then, we show that the existence of a mixed $H_2/H_{\infty}$ controller by which the $H_2$ norm of the second channel is minimized while keeping the $H_2$ norm bound of the first channel less than ${\gamma}$, is reduced to the linear objective minimization problem. The class of desired controllers that are assumed to have the same structure as the plant is parameterized by using the linearizing change of variables.

• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.5
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• pp.817-832
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• 2015

This paper presents a state feedback based backstepping control algorithm to address the trajectory tracking problem of an underactuated Unmanned Surface Vessel (USV) in the horizontal plane. A nonlinear three Degree of Freedom (DOF) underactuated dynamic model for USV is considered, and trajectory tracking controller that can track both curve trajectory and straight line trajectory with high accuracy is designed as the well known Persistent Exciting (PE) conditions of yaw velocity is completely relaxed in our study. The proposed controller has further been enriched by incorporating an integral action additionally for enhancing the steady state performance and control precision of the USV trajectory tracking control system. Global stability of the overall system is proved by Lyapunov theory and Barbalat's Lemma, and then simulation experiments are carried out to demonstrate the effectiveness of the controller designed.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.51 no.8
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• pp.409-416
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• 2002

This paper presents a fault location algorithm using direct 3-phase circuit analysis for distribution power networks. The unbalanced feature of distribution networks due to single phase loads or asymmetric operation prohibits us from using the conventional symmetrical component transformation. Even though the symmetrical component transformation provides us with a very easy tool in three phase network analysis, it is limited to balanced systems in utilizing its strong point, which is not suitable for distribution networks. In this paper, a fault location algorithm using direct 3-phase circuit analysis is developed. The algorithm is derived and it Is shown that the proposed method if we use matrix inverse lemma, is not more difficult then the conventional methods using symmetrical component transformation. Since the symmetrical component transformation is not used in the suggested method, unbalanced networks also can be handled with the same difficulty as balanced networks. The case study results show the correctness and effectiveness of the proposed algorithm.

• Genomics & Informatics
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• v.12 no.4
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• pp.254-260
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• 2014

Best linear unbiased prediction (BLUP) has been used to estimate the fixed effects and random effects of complex traits. Traditionally, genomic relationship matrix-based (GRM) and random marker-based BLUP analyses are prevalent to estimate the genetic values of complex traits. We used three methods: GRM-based prediction (G-BLUP), random marker-based prediction using an identity matrix (so-called single-nucleotide polymorphism [SNP]-BLUP), and SNP-SNP variance-covariance matrix (so-called SNP-GBLUP). We used 35,675 SNPs and R package "rrBLUP" for the BLUP analysis. The SNP-SNP relationship matrix was calculated using the GRM and Sherman-Morrison-Woodbury lemma. The SNP-GBLUP result was very similar to G-BLUP in the prediction of genetic values. However, there were many discrepancies between SNP-BLUP and the other two BLUPs. SNP-GBLUP has the merit to be able to predict genetic values through SNP effects.

• Journal of Plant Biology
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• v.37 no.1
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• pp.53-67
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• 1994

The opal phytolith types in Oryza sativa L. were examined with light and scanning electron microscope, and we suggested the standard tenninoligies based on original cells of the phytoliths in situ. The distinctive fonus of opal phytoliths were observed in all plant parts such as leaf blade, leaf sheath, culm, root, glume, lemma, and palea. The phytolith fonus originated from long cell, short cell, and dennal appendages were different from part to part. The opal phytoliths derived from the long cells showed the most various form: twelve types were identified based on side wall shape. The results showed that the leaf blade did include almost all types of opal phytolith observed in the other parts of rice.f rice.