• Journal for History of Mathematics
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• v.11 no.1
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• pp.19-26
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• 1998

We investigate "Church's Thesis" and "Turing's Thesis", which are commonly considered as equivalent foundations of computability theory or recursion theory in mathematical logic and computer science. A careful historical and logical analysis of Godel's recursiveness, Church's ${\lambda}$-definability and Turing computability should distinguish between Church's Thesis and Turing's Thesis.and Turing's Thesis.

• East Asian mathematical journal
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• v.39 no.3
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• pp.331-347
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• 2023

We present an identity on moments of a compound random variable by using an auxiliary counting random variable. Based on this identity, we develop a new recurrence formula for obtaining the raw and central moments of any order for a given compound random variable.

• The Transactions of the Korea Information Processing Society
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• v.4 no.12
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• pp.3069-3077
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• 1997

This paper is concerned with a new paradigm for parallel evaluation of linear recursion rules which contain transitive dependency in a shared-nothing parallel architecture. For parallel evaluation of rules, we consider a shared-nothing parallel architecture that consists of a set of nodes and a message passing network to these nodes. An evaluation of normalized rules is a computation of the proof theoretic meaning of a collection of rules. We shall here define normalized recursion rules which contain transitive dependency, present an equivalent expression for the rule, propose a paradigm for Parallel evaluation of normalized rule based on the equivalent expression using join, partition, and transitive closure operations, and analyze response-time complexity.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.973-978
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• 2005

In this paper, we investigate an improved mobile robot localization method using Kalman filter. The highlight of the paper lies in the formulation of combined Kalman filter and its application to mobile robot experiment. The combined Kalman filter is a kind of extended Kalman filter which has an extra degree of freedom in Kalman filtering recursion. It consists of the standard Kalman filter, i.e., the predictor-corrector and the perturbation estimator which reconstructs unknown dynamics in the state transition equation of mobile robot. The combined Kalman filter (CKF) enables to achieve robust localization performance of mobile robot in spite of heavy perturbation such as wheel slip and doorsill crossover which results in large odometric errors. Intrinsically, it has the property of integrating the innovation in Kalman filtering, i.e., the difference between measurement and predicted measurement and thus it is so much advantageous in compensating uncertainties which has not been reflected in the state transition model of mobile robot. After formulation of the CKF recursion equation, we show how the design parameters can be determined and how much beneficial it is through simulation and experiment for a two-wheeled mobile robot under indoor GPS measurement system composed of four ultrasonic satellites. In addition, we discuss what should be considered and what prerequisites are needed to successfully apply the proposed CKF in mobile robot localization.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.23-48
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• 2007

This study begins from posing a problem, 'formal introduction of mathematical induction in school mathematics'. Most students may learn the mathematical induction at the level of instrumental understanding without meaningful understanding about its meaning and structure. To improve this didactical situation, we research on the historical progress of mathematical induction from implicit use in greek mathematics to formalization by Pascal and Fermat. And we identify various types of thinking included in the developmental process: recursion, regression, analytic thinking, synthetic thinking. In special, we focused on the role of regression in mathematical induction, and then from that role we induce the implications for teaching mathematical induction in school mathematics.

• Journal of Fashion Business
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• v.7 no.4
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• pp.105-120
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• 2003

Culture and society exist in the present, but they came from the past. So did clothing. As dressing is deeply based on culture pattern of the times, it is affected by various culture patterns and still keeps developing in modern times. This study is intended to examine the features of retro fashion on culture and dressing of the 19th century. The features of retro fashion on Neoclassical and Romantic culture and dressing are objection to the existing pattern, recursion to the past, and creativity characteristic of pattern of those days. Neoclassicism arose as it rejected Baroque and Rococo style, and imitated culture and artistic pattern of Greece and Rome. Romanticism objected to formal and universal pattern of Neoclassicism, and imitated Gothic style while recognizing historical facts and studying medieval times. Dressing in Neoclassicism did not accept exaggerated and luxurious Rococo pattern, and imitated simple, soft and straight silhouette of Greece and Rome and created its unique Empire Style. Romanticism imitated luxurious style of Renaissance, the Middle Ages, Baroque, and Rococo, different from simple and straight neoclassical style during the Bourbon restoration, and created its unique style. Thus, it is shown that retro fashion on Neoclassical and Romantic culture and dressing reflect the style of those days.

• The Journal of Natural Sciences
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• v.8 no.2
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• pp.63-67
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• 1996

Adaptive algorithms based on the higher order error criterion such as the LVCMS and the LMF show performance degradation if input signal contains additive noise with a heavier-tailed density. Conventional analysis often neglects higher order terms in the recursion and my not suit for prediction exact behavior of these higher order algorithms. This paper presents a new convergence analysis which contains all the higher order term in the recursion. The analysis shows that the higher order terms, which are often neglected, dose not affect the upper bound on the step size but the misadjustment. However, the effect decreases sharply proportional to the square of the step size.

• Journal of Information Processing Systems
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• v.16 no.4
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• pp.832-844
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• 2020

The degree of dispersion of a random variable can be described by the variance, which reflects the distance of the random variable from its mean. However, the time complexity of the traditional variance calculation algorithm is O(n), which results from full calculation of all samples. When the number of samples increases or on the occasion of high speed signal processing, algorithms with O(n) time complexity will cost huge amount of time and that may results in performance degradation of the whole system. A novel multi-step recursive algorithm for variance calculation of the time-varying data series with O(1) time complexity (constant time) is proposed in this paper. Numerical simulation and experiments of the algorithm is presented and the results demonstrate that the proposed multi-step recursive algorithm can effectively decrease computing time and hence significantly improve the variance calculation efficiency for time-varying data, which demonstrates the potential value for time-consumption data analysis or high speed signal processing.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.11a
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• pp.53-56
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• 2007

Symmerge is a stable minimum storage algorithm for merging that needs $O(mlog\frac{n}{m})$ element comparisons, where m and n are the sizes of the input sequences with m ${\leqq}$ n. According to the lower bound for merging, the algorithm is asymptotically optimal regarding the number of comparisons. The objective of this paper is to consider the relationship between m and n for the spanning case with the recursion level m-1.

• East Asian mathematical journal
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• v.34 no.1
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• pp.59-67
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• 2018

We present new recurrence formulas for the raw and central moments of a compound binomial random variable. Our approach involves relating two compound binomial random variables that have parameters with a difference of 1 for the number of trials, but which have the same parameters for the success probability for each trial. As a consequence of our recursions, the raw and central moments of a binomial random variable are obtained in a recursive manner without the use of Stirling numbers.