• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.191-201
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• 2007

In this paper we introduce the notion of congruence on a ternary semigroup and study some interesting properties. We also introduce the notions of cancellative congruence, group congruence and Rees congruence and characterize these congruences in ternary semigroups.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.937-941
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• 2023

For each positive integer n, a square congruence graph S(n) is the graph with vertex set H = {1, 2, 3,...., n} and two vertices a, b are adjacent if they are distinct and a² ≡ b² (mod n). In this paper we investigate some structural properties of square congruence graph and we obtain the relationship between clique number, chromatic number and maximum degree of square congruence graph. Also we study square congruence graph with p vertices or 2p vertices for any prime number p.

• Asia Marketing Journal
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• v.14 no.4
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• pp.167-188
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• 2013

In today's society with its emphasis on unlimited information access, control of available information about high-technology products is often vital to their success. When a product is released, consumers may initially be attracted through information about its remarkable internal and external features. They may also perceive a degree of congruence between their own personalities and the product image as more information becomes available over time. Consumers' changing impressions of the product may influence personality congruence negatively or positively. These changes and their effects on preference for high-technology products are the focus of this paper. A survey was given to a sample of 206 students at K University to investigate the degree to which consumer behavior can be influenced by personality congruence. The need for clear and definite product knowledge in this process and the effect of product information on preference were also investigated. Three analyses were conducted. The results of Analysis 1 showed the influence of personality congruence on preference for high-technology products. Judgments about personality congruence were based on non-compensatory rather than compensatory information processing. The respondents considered certain aspects of a product's personality rather than the product as a whole when making preference decisions. The results of Analysis 2 indicated that when less information was available about a product, consumers who perceived high personality congruence with the product tended to have higher preference for it compared to those who perceived low personality congruence with the product. On the other hand, when consumers were given more information, no difference was observed in the impact of personality on preference between perceived high and low personality congruence. Lastly, the results of Analysis 3 showed that when consumers with high need for closure (NFC) perceived high congruence between their own personalities and a product, objective information regarding the product was not used in decision-making: instead, judgments about the product were based on perceived personality congruence. On the other hand, high-NFC consumers who perceived low personality congruence between themselves and the product tended to require more information about the product in order to give it a positive evaluation. In contrast, low-NFC consumers who perceived high personality congruence felt comfortable with large amounts of information. For low-NFC consumers who perceived low congruence, the level of information had no influence on preference.

• Journal for History of Mathematics
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• v.20 no.2
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• pp.109-126
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• 2007

This paper is to study theorems related with congruence of triangles in Lobachevskii's and Hadamard's geometry textbooks, and to compare their proof methods. We find out that Lobachevskii's geometry textbook contains 5 theorems of triangles' congruence, but doesn't explain congruence of right triangles. In Hadamard's geometry textbook description system of the theorems of triangles' congruence is similar with our mathematics textbook. Hadamard's geometry textbook treat 3 theorems of triangles' congruence, and 2 theorems of right triangles' congruence. But in Hadamard's geometry textbook all theorems are proved.

• Journal of the East Asian Society of Dietary Life
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• v.22 no.1
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• pp.120-132
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• 2012

The purpose of this study was to investigate thet 5 dimensions of brand personality that could affect brand attachment, and actual and ideal self-congruence in the family restaurant. Also, this study investigated the effects of actual and ideal self-congruence on brand attachment. Questionnaires were given to a sample of customers who visited one of the 4 famous national brands of family restaurants in Daegu. A total of 332 questionnaires were analyzed with SPSS/$PC^+$and LISREL. There were four major empirical research findings. First, sincerity, competence, sophistication and ruggedness affected brand attachment. And second, sincerity, competence and sophistication affected actual self-congruence. Third, sincerity and sophistication affected ideal self-congruence. And fourth, actual self-congruence affected brand attachment. However, the excitement dimension of brand personality did not affect brand attachment,; dimensions of excitement and ruggedness did not affect actual self-congruence,; dimensions of excitement, competence and ruggedness did not affect ideal self-congruence. Also, ideal self-congruence did not affect brand attachment. Based on these findings, marketers of family restaurants were recommended to strengthen the dimensions of sincerity, competence, and sophistication, and to weaken the ruggedness dimension.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.307-316
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• 2008

Real life problems can be expressed as a congruence modulus n and split into a system of congruence equations in modulus factors of n. A system of congruence equations can be combined into a congruence equation under certain conditions. This paper uniquely presents and critically reviews the generalized Chinese Remainder Theorem (CRT) for combining systems of congruence equations into single congruence equations. Sequential and parallel implementation strategies of the generic CRT are outlined. A variety of unique applications of the CRT are discussed.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.177-182
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• 2005

If a semigroup S has no nontrivial congruences then S is either simple or 0-simple.([2]) By contrast with ring theory, not every congruence on a semigroup is associated with an ideal, hence some simple(or 0-simple) semigroup may have a nontrivial congruence. Thus it is a short note for the characterization of a simple(or 0-simple) semigroup that is congruence-free. A semigroup that has no nontrivial congruences is said to be congruence-free.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.241-248
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• 2006

We define a G-fuzzy congruence, which is a generalized fuzzy congruence, and characterize the G-fuzzy congruence generated by a left and right compatible fuzzy relation on a semigroup.

• Journal of Distribution Research
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• v.8 no.1
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• pp.21-46
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• 2003

Despite importance of private brands in the retail industry, not many studies have been performed on factors affecting consumers' attitude formation toward private brands. This study tries to understand attitude formation toward private brands from the perspective of image congruence. Focusing on three types of image congruence-image congruence between a private brand and a consumer's self, image congruence between a store and a product category used for a private brand, and image congruence between a store and a consumer's self - this study explores relationships and effects of these three types of image congruence on attitudes toward private brands. According to results, image congruence between a private brand and a consumer's self has the strongest effect among three types of image congruence. Image congruence between a store and a product category also has a significant positive effect on attitudes toward private brands. Effects of image congruence between a store and a consumer's self on attitudes toward private brands were opposite to the hypothesized direction, and explanations about the unexpected result are provided.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.6
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• pp.771-779
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• 2005

We introduce two concepts of intuitionistic fuzzy Rees congruence on a semigroup and intuitionistic fuzzy Rees con-gruence semigroup. As an important result, we prove that for a intuitionistic fuzzy Rees congruence semigroup S, the set of all intuitionistic fuzzy ideals of S and the set of all intuitionistic fuzzy congruences on S are lattice isomorphic. Moreover, we show that a homomorphic image of an intuitionistic fuzzy Rees congruence semigroup is an intuitionistic fuzzy Rees congruence semigroup.