• Korean Journal of Mathematics
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• v.25 no.4
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• pp.563-577
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• 2017

We define a weak fuzzy equivalence relation and a weak fuzzy congruence and develop some properties of the weak fuzzy equivalence relations and the weak fuzzy congruences on semigroups.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.229-234
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• 2009

We find congruences for the t-expansion coefficients of a Drinfeld modular form for ${\Gamma}^+_0$(Q), where Q is a monic irreducible polynomial. As an application we obtain new congruence relations for the t-expansion coefficients of Drinfeld modular forms for ${GL_2}(\mathbb{F}_q[T])$.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.565-566
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• 2017

An error in the proof of Theorem 1 of "On partition congruences for overcubic partition pairs" [Commun. Korean Math. Soc. 27 (2012), no. 3, 477-482] is corrected.

• 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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.4
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• pp.276-283
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• 2008

We investigate the images and preimages of intuitionistic fuzzy G-equivalence relations and G-congruences under product mappings.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.405-417
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• 2021

The aim of this paper is to provide the residues of Euler polynomials modulo p² in terms of alternating sums of like powers of numbers in arithmetical progression. Also, we establish the analogue of a classical congruence of Lehmer.

• Journal of the Korean Mathematical Society
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• v.59 no.4
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• pp.685-697
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• 2022

Recently, Gireesh, Shivashankar, and Naika [11] found some infinite classes of congruences for the 3- and the 9-regular cubic partitions modulo powers of 3. We extend their study to all the 3^k-regular cubic partitions. We also find new families of congruences.

• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.155-166
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• 2023

In 2018, Andrews introduced the partition functions ${\mathfrak{EO}}$(n) and ${\bar{\mathfrak{EO}}}$(n). The first of these denotes the number of partitions of n in which every even part is less than each odd part, and the second counts the number of partitions enumerated by the first in which only the largest even part appears an odd number of times. In 2021, Pore and Fathima introduced a new partition function ${\mathfrak{EO}}_e$(n) which counts the number of partitions of n which are enumerated by ${\bar{\mathfrak{EO}}}$(n) together with the partitions enumerated by ${\bar{\mathfrak{EO}}}$(n) where all parts are odd and the number of parts is even. They also proved some particular congruences for ${\bar{\mathfrak{EO}}}$(n) and ${\mathfrak{EO}}_e$(n). In this paper, we establish infinitely many families of congruences modulo 2, 4, 5 and 8 for ${\bar{\mathfrak{EO}}}$(n) and modulo 4 for ${\mathfrak{EO}}_e$(n). For example, if p ≥ 5 is a prime with Legendre symbol $({\frac{-3}{p}})=-1$, then for all integers n ≥ 0 and α ≥ 0, we have ${\bar{\mathfrak{EO}}}(8{\cdot}p^{2{\alpha}+1}(pn+j)+{\frac{19{\cdot}p^{2{\alpha}+2}-1}{3}}){\equiv}0$ (mod 8); 1 ≤ j ≤ (p - 1).

• Honam Mathematical Journal
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• v.38 no.2
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• pp.403-423
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• 2016

We introduce the concepts of interval-valued fuzzy complete inner-unitary subsemigroups and interval-valued fuzzy group congruences on a semigroup. And we investigate some of their properties. Also, we prove that there is a one to one correspondence between the interval-valued fuzzy complete inner-unitary subsemigroups and the interval-valued fuzzy group congruences on a regular semigroups.

• Journal of the Korean Home Economics Association
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• v.25 no.3
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• pp.95-106
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• 1987

The purpose of this study is to investigate educational and occupational value orientations and transmissions between parents and college-aged children. The specific objectives are as follows; 1. To investigate parents and children's value orientations. 2. To estimate value congruence and transmissions between parents and children. 3. To find out the effects of three kinds of variables (demographic, family life, and expectation) on children's value orientations. To study the generational congruences and transmissions, four kinds of questionnarie and matched samples of mother-daughter and father-son were used. The data were obtained through 110 pairs and analyzed by t-test, Pearson's correlation, and multiple regression. The resluts are summerized as follows; 1. Significant value differences are found between parents group and children group. 2. Mother-daughter congruences are more than father-son congruences, but the correlation coefficients are low. 3. The variables selectively influence on children's value orientations.