• Korean Journal of Mathematics
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• v.29 no.3
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• pp.483-492
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• 2021

This article concerns the property that for any element a in a ring, if a²ⁿ = aⁿ for some n ≥ 2 then a² = a. The class of rings with this property is large, but there also exist many kinds of rings without that, for example, rings of characteristic ≠2 and finite fields of characteristic ≥ 3. Rings with such a property is called reduced-over-idempotent. The study of reduced-over-idempotent rings is based on the fact that the characteristic is 2 and every nonzero non-identity element generates an infinite multiplicative semigroup without identity. It is proved that the reduced-over-idempotent property pass to polynomial rings, and we provide power series rings with a partial affirmative argument. It is also proved that every finitely generated subring of a locally finite reduced-over-idempotent ring is isomorphic to a finite direct product of copies of the prime field {0, 1}. A method to construct reduced-over-idempotent fields is also provided.

• Communications for Statistical Applications and Methods
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• v.29 no.1
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• pp.127-150
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• 2022

We discuss multiple change-point estimation as edge detection in piecewise smooth functions with finitely many jump discontinuities. In this paper we propose change-point estimators using concentration kernels with Fourier coefficients. The change-points can be located via the signal based on Fourier transformation system. This method yields location and amplitude of the change-points with refinement via concentration kernels. We prove that, in an appropriate asymptotic framework, this method provides consistent estimators of change-points with an almost optimal rate. In a simulation study the proposed change-point estimators are compared and discussed. Applications of the proposed methods are provided with Nile flow data and daily won-dollar exchange rate data.

• Honam Mathematical Journal
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• v.26 no.3
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• pp.247-256
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• 2004

Buchmann and Williams[1] proposed a key exchange system making use of the properties of the maximal order of an imaginary quadratic field. $H{\ddot{u}}hnlein$ et al. [6,7] also introduced a cryptosystem with trapdoor decryption in the class group of the non-maximal imaginary quadratic order with prime conductor q. Their common techniques are based on the properties of the invertible ideals of the maximal or non-maximal orders respectively. Kim and Moon [8], however, proposed a key-exchange system and a public-key encryption scheme, based on the class semigroups of imaginary quadratic non-maximal orders. In Kim and Moon[8]'s cryptosystem, a non-invertible ideal is chosen as a generator of key-exchange ststem and their secret key is some characteristic value of the ideal on the basis of Zanardo et al.[9]'s quantity for ideal equivalence. In this paper we propose the methods for finding the non-invertible ideals corresponding to non-primitive quadratic forms and clarify the structure of the class semigroup of non-maximal order as finitely disjoint union of groups with some quantities correctly. And then we correct the misconceptions of Zanardo et al.[9] and analyze Kim and Moon[8]'s cryptosystem.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.8
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• pp.659-665
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• 2000

In this paper a platoon merging control system is considered as a remotely located system with state represented by a stochastic process. in the system it is common to encounter situations where a single decision maker controls a large number of subsystems and observation and control signals are sent over a communication channel with finite capacity and significant transmission delays. Unlike a classical estimation problem where the observation is a continuous process corrupted by additive noise there is a constraint that the observation must be coded and transmitted over a digital communication channel with fintie capacity. A recursive coder-estimator sequence is a state estimation scheme based on observations transmitted with finite communication capacity constraint. in this paper we introduce a stochastic model for the lead vehicle in a platoon of vehicles in a lane considering the angle between the road surface and a horizontal plane as a stochastic process. In order to merge two platoons the lead vehicle of the following platoon is controlled by a remote control station. Using the observation transmitted over communication channel the remote control station designs the feedback controller. The simulation results show that the intervehicle spacings and the deviations from the desired intervehicle spacing are well regulated.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.227-245
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• 2011

In this paper, we introduce a new iterative method for finding a common element of the set of solutions for mixed equilibrium problem, the set of solutions of the variational inequality for a ${\beta}$inverse-strongly monotone mapping and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Ces$\`{a}$ro mean approximation method. We prove that the sequence converges strongly to a common element of the above three sets under some mind conditions. Our results improve and extend the corresponding results of Kumam and Katchang [A viscosity of extragradient approximation method for finding equilibrium problems, variational inequalities and fixed point problems for nonexpansive mapping, Nonlinear Analysis: Hybrid Systems, 3(2009), 475-86], Peng and Yao [Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems, Mathematical and Computer Modelling, 49(2009), 1816-828], Shimizu and Takahashi [Strong convergence to common fixed points of families of nonexpansive mappings, Journal of Mathematical Analysis and Applications, 211(1) (1997), 71-83] and some authors.

• Journal of KIISE:Software and Applications
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• v.26 no.8
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• pp.1028-1038
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• 1999

본 논문에선 LR 문법의 부분 클래스를 동치인 LL 문법으로 변환하는 방법을 제시한다. 이 변환이 적용 가능한 문법을 확장된k`-transformable 문법이라 정의한다. 변환된 문법은 left-to-right 커버의 성질을 만족한다. 기존 연구에서 제시한 변환 방법은 LR 문법의 부분 클래스인 {{{{k`-transformable 클래스와 PLR 클래스를 LL 문법으로 바꾼다. 이 논문에서 제시하는 새로운 변환 방법의 적용 가능한 문법의 범위는 k`-transformable 클래스와 PLR 클래스를 포함한다. 기존의 커버링 성질을 만족하는 LL로의 문법 변환은 보편적인 LR 파서의 행동을 시뮬레이션하여 얻어진다. 이 과정에서 쉬프트, 리듀스 행동 이외에 무한의 가능성을 가진 스택 스트링의 유한 표현을 위해 리덕션 심볼에 대한 예상 행동이 추가된다. 본 논문에서는 파싱 문맥을 나타내는 LR 아이템들을 기존의 스택 스트링 표현 형태에 추가하여 스택 스트링 표현법을 정제하고, 리덕션 심볼에 대한 예상 방법을 확장하는 정형식을 제시한다. 이에 근거하여 LL 커버링 문법이 존재하는 클래스를 확장된 {{{{k`-transformable 문법으로 확장시킨다.Abstract A new transformation of a subclass of LR(k`) grammars into equivalent LL(k`) grammars is studied. The subclass of LR(k`) grammars is called extended k`-transformable. The transformed LL(k`) grammars left-to-right cover the original LR(k`) grammars. Previous transformations transform k`-transformable and PLR(k`) into LL(k`). The new transformation is more powerful in that it handles the extended k`-transformable subclass of LR(k`), which strictly includes k`-transformable and PLR(k`) classes. The previous covering transformations into LL grammars are obtained by simulating the actions of the conventional LR parser. Specially, a predict action of reduction goals is added to the action set in order to finitely represent stack string. In this paper, the stack string representation is refined by adding LR items to represent a parsing context, and the prediction of reduction goal is extended by generalizing the prediction formalism. Based on them, the previous grammar classes with LL({{{{k`) covering grammars are extended to extended k`-transformable grammars.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.1
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• pp.19-28
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• 2007

Discrete topology optimization processes of structures start from an initial design domain which is described by the topology of constant material densities. During optimization procedures, the structural topology changes in order to satisfy optimization problems in the fixed design domain, and finally, the optimization produces material density distributions with optimal topology. An introduction of initial holes in a design domain presented by Eschenauer et at. has been utilized in order to improve the optimization convergence of boundary-based shape optimization methods by generating finite changes of design variables. This means that an optimal topology depends on an initial topology with respect to topology optimization problems. In this study, it is investigated that various optimal topologies can be yielded under constraints of usable material, when partial solid phases are deposited in an initial design domain and thus initial topology is finitely changed. As a numerical application, structural topology optimization of a simple MBB-Beam is carried out, applying partial circular solid phases with varying sizes to an initial design domain.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.34 no.8
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• pp.799-807
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• 2010

Direct numerical simulations (DNS) of turbulent channel flow for which the drag is reduced by using polymer additives have been performed by a pseudo-spectral method. The Reynolds number based on the friction velocity and half-channel height is 395, and the polymeric stresses due to the polymer additives are evaluated using the FENE-P (finitely extensible nonlinear elastic-Peterlin) model. The numerical results show that the drag reduction rate is significantly affected by the parameters used in the FENE-P model, such as the maximum extensibility and relaxation time of the polymer molecules. The turbulence data for both low- and high-drag reduction regimes are analyzed. In addition, the effects of FENE-P model parameters on the flow characteristics have been investigated for the same drag reduction rate due to the polymer additives. Finally, the present DNS results have been used to verify the correlation between rheological parameters and the extent of drag reduction, which was suggested by Li et al. (2006).

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.3
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• pp.253-261
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• 2004

Game theory is mathematical analysis developed to study involved in making decisions. In 1928, Von Neumann proved that every two-person, zero-sum game with finitely many pure strategies for each player is deterministic. As well, in the early 50's, Nash presented another concept as the basis for a generalization of Von Neumann's theorem. Another central achievement of game theory is the introduction of evolutionary game theory, by which agents can play optimal strategies in the absence of rationality. Not the rationality but through the process of Darwinian selection, a population of agents can evolve to an Evolutionary Stable Strategy (ESS) introduced by Maynard Smith. Keeping pace with these game theoretical studies, the first computer simulation of co-evolution was tried out by Hillis in 1991. Moreover, Kauffman proposed NK model to analyze co-evolutionary dynamics between different species. He showed how co-evolutionary phenomenon reaches static states and that these states are Nash equilibrium or ESS introduced in game theory. Since the studies about co-evolutionary phenomenon were started, however many other researchers have developed co-evolutionary algorithms, in this paper we propose Game theory based Co-Evolutionary Algorithm (GCEA) and confirm that this algorithm can be a solution of evolutionary problems by searching the ESS.To evaluate newly designed GCEA approach, we solve several test Multi-objective Optimization Problems (MOPs). From the results of these evaluations, we confirm that evolutionary game can be embodied by co-evolutionary algorithm and analyze optimization performance of GCEA by comparing experimental results using GCEA with the results using other evolutionary optimization algorithms.

• The KIPS Transactions:PartD
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• v.14D no.7
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• pp.733-742
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• 2007

A data stream is a massive unbounded sequence of data elements continuously generated at a rapid rate. Due to this reason, memory usage for data stream analysis should be confined finitely although new data elements are continuously generated in a data stream. To satisfy this requirement, data stream processing sacrifices the correctness of its analysis result by allowing some errors. The old distribution statistics are diminished by a predefined decay rate as time goes by, so that the effect of the obsolete information on the current result of clustering can be eliminated without maintaining any data element physically. This paper proposes a grid based clustering algorithm for a data stream. Given a set of initial grid cells, the dense range of a grid cell is recursively partitioned into a smaller cell based on the distribution statistics of data elements by a top down manner until the smallest cell, called a unit cell, is identified. Since only the distribution statistics of data elements are maintained by dynamically partitioned grid cells, the clusters of a data stream can be effectively found without maintaining the data elements physically. Furthermore, the memory usage of the proposed algorithm is adjusted adaptively to the size of confined memory space by flexibly resizing the size of a unit cell. As a result, the confined memory space can be fully utilized to generate the result of clustering as accurately as possible. The proposed algorithm is analyzed by a series of experiments to identify its various characteristics