• 호남수학학술지
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• 제36권1호
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• pp.199-215
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• 2014

Owing to the development of the notion of normal adjacency of a digital product [9], product properties of digital topological properties were studied efficiently. To equivalently represent a normal adjacency of a digital product, the present paper proposes an S-compatible adjacency of a digital product. This approach can be helpful to understand a normal adjacency of a digital product. Finally, using an S-compatible adjacency of a digital product, we can study product properties of digital topological properties, which improves the presentations of the normal adjacency of a digital product in [9] and [5, 6].

• 호남수학학술지
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• 제37권1호
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• pp.135-147
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• 2015

Owing to the notion of a normal adjacency for a digital product in [8], the study of product properties of digital topological properties has been substantially done. To explain a normal adjacency of a digital product more efficiently, the recent paper [22] proposed an S-compatible adjacency of a digital product. Using an S-compatible adjacency of a digital product, we also study product properties of digital topological properties, which improves the presentations of a normal adjacency of a digital product in [8]. Besides, the paper [16] studied the product property of two digital covering maps in terms of the $L_S$- and the $L_C$-property of a digital product which plays an important role in studying digital covering and digital homotopy theory. Further, by using HS- and HC-properties of digital products, the paper [18] studied multiplicative properties of a digital fundamental group. The present paper compares among several kinds of adjacency relations for digital products and proposes their own merits and further, deals with the problem: consider a Cartesian product of two simple closed $k_i$-curves with $l_i$ elements in $Z^{n_i}$, $i{\in}\{1,2\}$ denoted by $SC^{n_1,l_1}_{k_1}{\times}SC^{n_2,l_2}_{k_2}$. Since a normal adjacency for this product and the $L_C$-property are different from each other, the present paper address the problem: for the digital product does it have both a normal k-adjacency of $Z^{n_1+n_2}$ and another adjacency satisfying the $L_C$-property? This research plays an important role in studying product properties of digital topological properties.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.526-530
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• 1998

In this note by considering the notions of F-polygroups, the product of F-polygroups, F-subpolygroups and (weak) normal F-subpolygroups two questions are given. Then by an example it is shown that the answer of one of the questions (posed in the paper [12]) is in general negative. In other words, the product of two normal F-subpolygroups need not be normal.

• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.545-557
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• 2015

A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we define two new operation on vague graphs namely normal product and tensor product and study about the degree of a vertex in vague graphs which are obtained from two given vague graphs G₁ and G₂ using the operations cartesian product, composition, tensor product and normal product. These operations are highly utilized by computer science, geometry, algebra, number theory and operation research. In addition to the existing operations these properties will also be helpful to study large vague graph as a combination of small, vague graphs and to derive its properties from those of the smaller ones.

• 한국수학교육학회지시리즈A:수학교육
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• 제13권3호
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• pp.17-18
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• 1975

거리공간과 Normal countable compact의 위상적이 Normal이라는 것은 A.H. Stone에 의하여 이미 밝혀졌고, V.I. Malyhin은 space expX의 Cardrmal invariant와 공간 X 사이의 관계를 논하였다. 본 논문에서는 V.I. Malyin이 밝힌 tightness의 개념을 도입하여 countable tightness의 pracompact와 normal strongly countable compact 공간의 topological product가 Normal이라는 것을 증명하였다.

• 호남수학학술지
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• 제35권3호
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• pp.515-524
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• 2013

To study product properties of digital spaces, we strongly need to formulate meaningful adjacency relations on digital products. Thus the paper [7] firstly developed a normal adjacency relation on a digital product which can play an important role in studying the multiplicative property of a digital fundamental group, and product properties of digital coverings and digitally continuous maps. The present paper mainly surveys the normal adjacency relation on a digital product, improves the assertion of Boxer and Karaca in the paper [4] and restates Theorem 6.4 of the paper [19].

• Kyungpook Mathematical Journal
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• 제57권3호
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• pp.457-471
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• 2017

A necessary and sufficient condition for the product AB of a selfadjoint operator A and a bounded selfadjoint operator B to be normal is given. Various properties of the factors of the unitary polar decompositions of A and B are obtained in the case when the product AB is normal. A block operator model for pairs (A, B) of selfadjoint operators such that B is bounded and AB is normal is established. The case when both operators A and B are bounded is discussed. In addition, the example due to Rehder is reexamined from this point of view.

• 대한수학회지
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• 제46권6호
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• pp.1165-1178
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• 2009

In this paper we classify finite groups whose nonnormal subgroups are of order p or pq, where p, q are primes. As a by-product, we also classify the finite groups in which all nonnormal subgroups are cyclic.

• 대한수학회논문집
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• 제17권2호
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• pp.253-260
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• 2002

For an outer action $\alpha$ of a finite group G on a factor M, it was proved that H is a, normal subgroup of G if and only if there exists a finite group F and an outer action $\beta$ of F on the crossed product algebra M $\times$$_{\alpha}$ G = (M $\times$$_{\alpha}$ F. We generalize this to infinite group actions. For an outer action $\alpha$ of a discrete group, we obtain a Galois correspondence for crossed product algebras related to normal subgroups. When $\alpha$ satisfies a certain condition, we also obtain a Galois correspondence for fixed point algebras. Furthermore, for a minimal action $\alpha$ of a compact group G and a closed normal subgroup H, we prove $M^{G}$ = ( $M^{H}$)$^{{beta}(G/H)}$for a minimal action $\beta$ of G/H on $M^{H}$.f G/H on $M^{H}$.TEX> H/.

• 대한수학회지
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• 제61권5호
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• pp.899-922
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• 2024

Let f(z) be a primitive holomorphic cusp form and g(z) be a Maass cusp form. In this paper, we give quantitative results for the sign changes of coefficients of triple product L-functions L(f × f × f, s) and L(f × f × g, s).