• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1435-1445
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• 2019

We consider a checkpointing model for silent errors, where a checkpoint is taken every fixed number of verifications. Assuming generally distributed i.i.d. inter-occurrence times of errors, we derive the reliability of the model as a function of the number of verifications between two checkpoints and the duration of work interval between two verifications.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.447-454
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• 2008

In this short note, we will point out and modify some logical errors in literatures about the theory of cellular automata.

• Journal of the Korean School Mathematics Society
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• v.15 no.1
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• pp.53-80
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• 2012

This study was designed to find the characteristics of mathematical errors and discourse in simultaneous equations and inequalities for migrant students from North Korea. 5 sample students participated, who attended in an alternative school for the migrant students from North Korea at the study in Seoul, Korea. A total of 8 lesson units were performed as an extra curriculum activity once a week during the 1st semester, 2011. The results indicated that students showed technical errors, encoding errors, misunderstood symbols, misinterpreted language, and misunderstood Chines characters of Koreans and the discourse levels improved from the zero level to the third level, but the scenes of the third level did not constantly happen. Nevertheless, the components of discourse, explanation & justification, were activated and as a result, evaluation & elaboration increased in ERE pattern on communication.

• Journal of the Korean Mathematical Society
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• v.40 no.1
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• pp.29-40
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• 2003

Let K be a nonempty closed bounded convex subset of an arbitrary smooth Banach space X and T : KlongrightarrowK be a strictly hemi-contractive operator. Under some conditions we obtain that the Mann iteration method with errors both converges strongly to a unique fixed point of T and is almost T-stable on K. The results presented in this paper generalize the corresponding results in [l]-[7], [20] and others.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.251-261
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• 2003

The purpose of this paper is to establish the necessary and sufficient conditions which ensure the strong convergence of the Ishikawa iterative schemes with errors to the unique fixed point of a $\Phi$-hemicontractive mapping defined on a nonempty convex subset of a normed linear space. The results of this paper extend substantially most of the recent results.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1323-1339
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• 2008

In this paper, a new class of $(h,{\eta})$-proximal for proper functionals in Hilbert spaces is introduced. The existence and Lip-schitz continuity of the $(h,{\eta})$-proximal mappings for proper functionals are proved. A class of generalized nonlinear quasi-variational-like inclusions in Hilbert spaces is introduced. A perturbed three-step iterative algorithm with errors for the generalized nonlinear quasi-variational-like inclusion is suggested. The existence and uniqueness theorems of solution for the generalized nonlinear quasi-variational-like inclusion are established. The convergence and stability results of iterative sequence generated by the perturbed three-step iterative algorithm with errors are discussed.

• East Asian mathematical journal
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• v.28 no.1
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• pp.63-71
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• 2012

The aim of this article is to study an implicit iteration process with errors for a finite family of non-Lipschitzian asymptotically non expansive mappings in the intermediate sense in Banach spaces. Also we establish some strong convergence theorems and a weak convergence theorem for said scheme to converge to a common fixed point for non Lipschitzian asymptotically nonexpansive mappings in the intermediate sense. The results presented in this paper extend and improve the corresponding results of [1], [3]-[8], [10]-[11], [13]-[14], [16] and many others.

• Journal for History of Mathematics
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• v.15 no.3
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• pp.35-48
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• 2002

In this paper, we explore development of mathematical knowledge, especially calculus, non-Euclidean geometry, Euler's theorem, and the comparison of the number of elements in two infinite sets. And we analyze kinds of errors and the roles for errors with respect to increasing knowledge in mathematics.

• Journal of Korean Society for Atmospheric Environment
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• v.17 no.1
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• pp.51-56
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• 2001

This study was carried out to interpret mathematically hydraulic behaviour in packing tower which packed 50 mm plastic Hiflow-ring with a dimension of 300 mm wide and 1,400 mm high. In view of energy saving, the recent packing. 50 mm plastic Higlow-ring was superior to conventional packings because of low pressure drop in high loads. As relative error between numerically predicted and experimentally obtained values was less then 6% in the loading and flooding point, it found that therir results appeared to be adequate. Comparison of hose two values in both dry and wet packing conditions. relative errors amount to 3.96 and 5.6%, respectively. In order to evaluate the operating characteristics of packing, the type, size, and material for packings must be estimated in various system and loads. This study is able to calculated pressure drop, hold-up, gas and liquid loads using mathematical interpretation. For these calculation, the specific constants of each packings must be calculated first all. The method of mathematical interpretation in this study turned out to be superior to the existing methods because of reduced errors at loading and flooding point.

• School Mathematics
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• v.5 no.2
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• pp.209-221
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• 2003

This study focuses on the necessity of developing the material for teachers who are involved in diagnosing and prescribing students' mathematical errors. And it also intends to stimulate the related research of this area. For this, it tries to suggest the fundamental components-(1)types and frequencies of errors, (2) diagnostic test kit, (3)causes of errors, (4)ideas for prevention, (5)ideas for correction, (6)practice for settlement, and (7) performance test kit and frame of the teaching guide book for the teachers according to the general procedure of diagnosis and prescription. Finally it provides the concrete research areas for the future study.