• Journal for History of Mathematics
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• v.22 no.2
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• pp.99-116
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• 2009

In this paper we study errors related with constructing regular polygons in the book 'Method of Ruler and Compass' written three hundreds years ago. It is well known that regular heptagon and regular nonagon are not constructible using compass and ruler. But in this book construction methods of these regular polygons is suggested. We show that the construction methods are incorrect, it include some errors.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.853-868
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• 2022

We study the structure of right regular commutators, and call a ring R strongly C-regular if ab - ba ∈ (ab - ba)²R for any a, b ∈ R. We first prove that a noncommutative strongly C-regular domain is a division algebra generated by all commutators; and that a ring (possibly without identity) is strongly C-regular if and only if it is Abelian C-regular (from which we infer that strong C-regularity is left-right symmetric). It is proved that for a strongly C-regular ring R, (i) if R/W(R) is commutative, then R is commutative; and (ii) every prime factor ring of R is either a commutative domain or a noncommutative division ring, where W(R) is the Wedderburn radical of R.

• Journal of Computing Science and Engineering
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• v.8 no.2
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• pp.78-86
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• 2014

Aiming to solve the problems of high memory access and big storage space and long matching time in the regular expression matching of extended finite automaton (XFA), a new regular expression matching algorithm based on high-efficient finite automaton is presented in this paper. The basic idea of the new algorithm is that some extra judging instruments are added at the starting state in order to reduce any unnecessary transition paths as well as to eliminate any unnecessary state transitions. Consequently, the problems of high memory access consumption and big storage space and long matching time during the regular expression matching process of XFA can be efficiently improved. The simulation results convey that our proposed scheme can lower approximately 40% memory access, save about 45% storage space consumption, and reduce about 12% matching time during the same regular expression matching process compared with XFA, but without degrading the matching quality.

• Kyungpook Mathematical Journal
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• v.64 no.3
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• pp.499-504
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• 2024

Let Γ be a distance-regular graph with valency k and diameter D ≥ 3. It has been shown that for a fixed real number α > 2, if Γ has at most αk vertices, then there are only finitely many such graphs, except for the cases where (D = 3 and Γ is imprimitive) and (D = 4 and Γ is antipodal and bipartite). And there is a classification for α ≤ 3. In this paper, we further study such distance-regular graphs for α > 3. Let 𝛽 ≥ 3 be an integer, and let Γ be a distance-regular graph with valency k, diameter D ≥ 3 and at most 𝛽k + 1 vertices. Note that if D ≥ 𝛽 + 1, then Γ must have at least 𝛽k + 2 vertices. Thus, the assumption that Γ has at most 𝛽k + 1 vertices implies that D ≤ 𝛽. We focus on the case where D = β and provide a classification of distance-regular graphs having at most Dk + 1 vertices.

• KIISE Transactions on Computing Practices
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• v.23 no.2
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• pp.97-103
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• 2017

Many hardware-based regular expression matching architectures have been proposed for high-performance matching. In particular, regular expression processors, which perform pattern matching by treating the regular expressions as the instruction sequence like general purpose processors, have been proposed. After instruction sequence and data are provided in the instruction memory and data memory, respectively, a regular expression processor can perform pattern matching. To use a regular expression processor as a coprocessor, we need the host interface to transfer the instruction and data into the memory of a regular expression processor. In this paper, we design and implement the host interface between a host and a regular expression processor in the DE1-SoC board and the application program interface. We verify the operations of the host interface and a regular expression processor by executing the application programs which perform pattern matching using the application program interface.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.261-271
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• 2007

The symbol C($m_1^{n_1}m_2^{n_2}{\cdots}m_s^{n_s}$) denotes a 2-regular graph consisting of $n_i$ cycles of length $m_i,\;i=1,\;2,\;{\cdots},\;s$. In this paper, we give some construction methods of cyclic($K_v$, G)-designs, and prove that there exists a cyclic($K_v$, G)-design when $G=C((4m_1)^{n_1}(4m_2)^{n_2}{\cdots}(4m_s)^{n_s}\;and\;v{\equiv}1(mod\;2|G|)$.

• Journal of Korean Elementary Science Education
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• v.23 no.3
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• pp.219-227
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• 2004

This study aims to investigate science teaching and learning for the gifted in comparison with regular classrooms in elementary schools. A questionnaire was developed to survey gifted and general students＇ perceptions to elementary science teaching and teaming with employing a teaching and learning model for the gifted by Maker and Neilson (1995, 1996). The 28 item questionnaire consisted of four categories of content, teaching and teaming process, student product, and learning environment, and each category included six to nine items. Randomly selected 114 students from gifted classes and 99 students for regular classes responded to the questionnaire through the use of five-point Likert scale. It was found that there are significant differences between gifted and regular classes of science at all four categories of the teaching and learning model for the gifted. Therefore, science teaching and teaming for the gifted seemed to be differentiated from regular classes and emphasized students＇ creativity. However, no differences were appeared in a few items: study of gifted people and research methods (gifted=3.0; regular=.21 F=2.54), students＇ freedom of choice for topics of lessons, tasks, etc., (gifted=3.1; regular=3.0, F=0.31), student product addressed to real audience (gifted=2.8, regular=2.6, F=0.96), and students＇ high mobility to seek for data in library, etc. during class periods (gifted=2.3, regular= 2.3, F=0.01). It was concluded that science education for the gifted in Korea calls for quality improvement in terms of teaching and teaming in various aspects.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.601-610
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• 2018

In the present paper, we construct an ordered regular equivalence relation on an ordered semihyperring by 2-hyperideals such that the corresponding quotient structure is also an ordered semihyperring.

• Korean Journal of Mathematics
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• v.17 no.1
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• pp.25-36
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• 2009

We compute spectrums of left regular isometries and weighted left regular isometries of a strongly perforated semigroup $P=\{0,2,3,4,{\cdots}\}$.

• East Asian mathematical journal
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• v.31 no.1
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• pp.119-126
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• 2015

The aim of this paper is to research certain properties of conic regular functions of conic quaternion variables in $\mathbb{C}^2$. We generalize the properties of conic regular functions and the Cauchy theorem of conic regular functions in conic quaternion analysis.