• 대한한의학회지
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• 제27권3호
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• pp.132-144
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• 2006

Objectives: In order to improve our understanding of the meridian, it is necessary to analyze how meridian theory formed. In this regard, the primitive form of meridians requires further study. Methods: Data from the pre-Han and Han dynasties were used, as such data document primitive forms of the meridian. Results: 1. Some of the terminology of the primitive meridians did not include symmetrical terms such as hand, foot, yin and yang; instead, terms of travel area were used. 2. In the primitive meridians, most travel from the bottom to the top. 3. The twelve meridian system had not yet been introduced into the primitive system. 4. In the primitive meridians, only a few had branches. 5. In the primitive meridians, they did not have obvious connections with the five vital organs and the six viscera. Conclusions: Although the primitive meridian system differs from the modem, studying the primitive meridians may improve our understanding of the modem meridians.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.403-410
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• 2006

For a finite group G, #Cent(G) denotes the number of centralizers of its elements. A group G is called n-centralizer if #Cent(G) = n, and primitive n-centralizer if #Cent(G) = #Cent($\frac{G}{Z(G)}$) = n. The first author in [1], characterized the primitive 6-centralizer finite groups. In this paper we continue this problem and characterize the primitive 7-centralizer finite groups. We prove that a finite group G is primitive 7-centralizer if and only if $\frac{G}{Z(G)}{\simeq}D_{10}$ or R, where R is the semidirect product of a cyclic group of order 5 by a cyclic group of order 4 acting faithfully. Also, we compute #Cent(G) for some finite groups, using the structure of G modulu its center.

• 대한수학회보
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• 제35권4호
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• pp.719-726
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• 1998

In this paper, we consider conjugacy of subgroups of some split metacyclic groups of odd prime power order to determine the numbers of conjugacy classes of subgroups of those groups. The study was motivated by the linear isomorphism problem of metacyclic primitive linear groups.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.25-43
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• 2005

Let F be a finite field of prime power order q(odd) and the multiplicative order of q modulo $2^{n}\;(n>1)\;be\; {\phi}(2^{n})/2$. If n > 3, then q is odd number(prime or prime power) of the form $8m{\pm}3$. If q = 8m - 3, then the ring $R_{2^n} = F[x]/ < x^{2^n}-1 >$ has 2n primitive idempotents. The explicit expressions for these primitive idempotents are obtained and the minimal QR cyclic codes of length $2^{n}$ generated by these idempotents are completely described. If q = 8m + 3 then the expressions for the 2n - 1 primitive idempotents of $R_{2^n}$ are obtained. The generating polynomials and the upper bounds of the minimum distance of minimal QR cyclic codes generated by these 2n-1 idempotents are also obtained. The case n = 2,3 is dealt separately.

• 대한수학회지
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• 제34권4호
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• pp.791-807
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• 1997

There are several kinds of orders in a quaternion algebra. In this article, the relation between the orders is studied.

• 대한수학회논문집
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• 제28권1호
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• pp.71-77
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• 2013

Consider a multiplicative group of integers modulo $n$, denoted by $\mathbb{Z}_n^*$. Any element $a{\in}\mathbb{Z}_n^*$ is said to be a semi-primitive root if the order of $a$ modulo $n$ is ${\phi}(n)/2$, where ${\phi}(n)$ is the Euler phi-function. In this paper, we discuss some interesting properties of the multiplicative groups of integers possessing semi-primitive roots and give its applications to solving certain congruences.

• 호남수학학술지
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• 제33권2호
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• pp.181-186
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• 2011

Consider a multiplicative group of integers modulo n, denoted by $\mathbb{Z}_n^*$. Any element $a{\in}\mathbb{Z}_n^*$ n is said to be a semi-primitive root if the order of a modulo n is $\phi$(n)/2, where $\phi$(n) is the Euler phi-function. In this paper, we classify the multiplicative groups of integers having semi-primitive roots and give interesting properties of such groups.

• 대한수학회보
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• 제55권3호
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• pp.971-997
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• 2018

The parity of cyclotomic numbers of order 2, 4 and 6 associated with 4-cyclotomic cosets modulo an odd prime p are obtained. Hence the explicit expressions of primitive idempotents of minimal cyclic codes of length $p^n$, $n{\geq}1$ over the quaternary field $F_4$ are obtained. These codes are observed to be subcodes of Q codes of length $p^n$. Some orthogonal properties of these subcodes are discussed. The minimal cyclic codes of length 17 and 43 are also discussed and it is observed that the minimal cyclic codes of length 17 are two weight codes. Further, it is shown that a Q code of prime length is always cyclotomic like a binary duadic code and it seems that there are infinitely many prime lengths for which cyclotomic Q codes of order 6 exist.

• Korean Journal of Mathematics
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• 제20권4호
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• pp.395-402
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• 2012

A digraph D is primitive if there is a positive integer $k$ such that there is a walk of length $k$ between arbitrary two vertices of D. The exponent of a primitive digraph is the least such $k$. Wielandt graph $W_n$ of order $n$ is known as the digraph whose exponent is $n^2-2n+2$, which is the maximum of all the exponents of the primitive digraphs of order n. It is known that the diameter of the multiple direct product of a digraph $W_n$ strictly increases according to the multiplicity of the product. And it stops when it attains to the exponent of $W_n$. In this paper, we find the diameter of the direct product of Wielandt graphs.

• 한국산업융합학회 논문집
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• 제4권2호
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• pp.149-155
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• 2001

The use of primitive cell volume and zero order Laue (ZOLZ) pattern is proposed to identify phase in a complex microstructure. Single convergent beam electron pattern containing higher order Laue zone ring from a nanosized region is sufficient to calculate the primitive cell volume of the phase, while ZOLZ pattern is used to determine the zone axis of the crystal. A computer program is used to screen out possible phases from the value of measured cell volume from convergent beam electron diffraction (CBED) pattern. Indexing of ZOLZ pattern follows in the program to find the zone axis of the identification from a single CBED pattern. An example of the analysis is given from the rapidly solidified $Al-Al_3Ti$ system.