• Honam Mathematical Journal
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• v.42 no.2
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• pp.213-218
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• 2020

Assume that K is a number field and K_ur is the maximal unramified extension of it. When Gal(K_ur/K) is an infinite group. It is known that Gal(K_ur/K) is generated by finitely many Frobenius classes of Gal(K_ur/K) by Y. Ihara. In this paper, we will give the explicit number of Frobenius classes which generate whole group Gal(K_ur/K).

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1025-1039
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• 2022

For given non-negative real numbers 𝛼_k with ∑^m_k=1 𝛼_k = 1 and normalized analytic functions f_k, k = 1, …, m, defined on the open unit disc, let the functions F and Fn be defined by F(z) := ∑^m_k=1 𝛼_kf_k(z), and F_n(z) := n^-1 ∑^n-1_j=0 e^-2j𝜋i/nF(e^2j𝜋i/nz). This paper studies the functions f_k satisfying the subordination zf'_k(z)/F_n(z) ≺ h(z), where the function h is a convex univalent function with positive real part. We also consider the analogues of the classes of starlike functions with respect to symmetric, conjugate, and symmetric conjugate points. Inclusion and convolution results are proved for these and related classes. Our classes generalize several well-known classes and the connections with the previous works are indicated.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.797-811
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• 2024

In this paper, we define the torsion graph determined by equivalence classes of torsion elements and denote it by A_E(M). The vertex set of A_E(M) is the set of equivalence classes {[x] | x ∈ T(M)^*}, where two torsion elements x, y ∈ T(M)^* are equivalent if ann(x) = ann(y). Also, two distinct classes [x] and [y] are adjacent in A_E(M), provided that ann(x)ann(y)M = 0. We shall prove that for every torsion finitely generated module M over a Dedekind domain R, a vertex of A_E(M) has degree two if and only if it is an associated prime of M.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.949-968
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• 2019

In this work, we characterize some matrix classes concerning the Binomial sequence spaces b^r,s_∞ and b^r,s_p, where 1 ≤ p < ∞. Moreover, by using the notion of Hausdorff measure of noncompactness, we characterize the class of compact matrix operators from b^r,s₀, b^r,s_c and b^r,s_∞ into c₀, c and ℓ_∞, respectively.

• The Pure and Applied Mathematics
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• v.22 no.4
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• pp.359-364
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• 2015

We present smooth simply connected closed 4k-dimensional manifolds N := N_k, for each k ∈ {2, 3, ⋯}, with distinct symplectic deformation equivalence classes [[ω_i]], i = 1, 2. To distinguish [[ω_i]]’s, we used the symplectic Z invariant in [4] which depends only on the symplectic deformation equivalence class. We have computed that Z(N, [[ω₁]]) = ∞ and Z(N, [[ω₂]]) < 0.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.147-160
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• 2024

In this paper, we define two new classes of monomial ideals I_𝑙,d and J_k,d. When d ≥ 2k + 1 and 𝑙 ≤ d - k - 1, we give the exact formulas to compute the depth and Stanley depth of quotient rings S/I^t_𝑙,d for all t ≥ 1. When d = 2k = 2𝑙, we compute the depth and Stanley depth of quotient ring S/I_𝑙,d. When d ≥ 2k, we also compute the depth and Stanley depth of quotient ring S/J_k,d.

• Journal of Korea Entertainment Industry Association
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• v.13 no.6
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• pp.187-202
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• 2019

The main goal of this study is to investigate influence of trust in physical education (PE) teachers and immersion experience in PE classes on attitude and satisfaction during PE classes. Total 863 middle school students in Gwang-ju metropolitan area were recruited by utilizing a convenience sampling method. All data were analyzed by using SPSS statistic program ver. 25.0 (frequency analysis, exploratory factor analysis, reliability analysis, correlation analysis, multiple regression analysis). Alpha was set at 0.05. The results of this study is summarized as in the following. First, all sub-factors of trust in the PE teachers partially positively or negatively influence sub-factors of attitude during PE classes. Second, sub-factors of satisfaction during PE classes were partially positively affected to trust in the PE teachers. Third, Attitude during PE Classes were found to have partial positive influence on immersion experience in PE classes. Fourth, sub-factors of immersion experience in PE classes have partial positive effect on the sub-factors of satisfaction during PE classes. Thus, in order to the positive attitude and greater satisfaction during PE classes, it is important to establish the trust of PE teachers through maintaining interaction with students, constructing better systemic class, and creating the class conditions based on considering students' ability. In addition, in order to enhance immersion experiences of students during PE classes, it is necessary to set up learning goals and tasks based on ability of students, to study various teaching method, and to make only focusing on the performance based PE classes without grading.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.2
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• pp.1-12
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• 2003

L. H. Encinas, A. J. Menezes, and J. M. Masque in [2] proposed a classification of isomorphism classes of hyperelliptic curve of genus 2 over finite fields with characteristic different from 2 and 5. Y. Choie and D. Yun in [1] obtained for the number of isomorphic classes of hyperelliptic curves of genus 2 over $F_q$ using direct counting method. In this paper we will classify the isomorphism classes of hyperelliptic curves of genus 2 over $F_{2^n}$ for odd n, represented by an equation of the form $y^2+a_5y=x^5+a_8x+a_{10}(a_5{\neq}0)$.

• International Journal of Contents
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• v.15 no.2
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• pp.59-74
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• 2019

The objective of this study was to analyze the influence of physical education classes based on Flipped Learning on self-directed learning abilities and learning attitude towards these classes, for middle school students. The study selected 90 students as an experimental group (3 classes) and 97 students as a control group (3 classes), among 240 students of the first-year students attending a middle school located at Jeonju City of South Korea, applying convenience sampling, one of the non-probability sampling methods. For the experimental group, 36 sessions of physical education classes were held for 14 weeks, while the control group received teacher-centered classes. Comparing the results with the control group, the experimental group showed significant differences in terms of all sub factors of self-directed learning abilities, namely; desire for learning, learning objective establishment, basic self-management abilities, selection of learning strategy and self-reflection. Moreover, the experimental group manifested significant differences in terms of all sub factors of attitude towards the physical education subjects, namely; positive emotions, negative emotions, health & physical strength, interpersonal relations, physical activities & movements, and active participation & positive performance. From the findings, it can be considered that physical education classes based on Flipped Learning contributed to improving self-directed learning abilities and attitude towards physical education classes. This result can serve as a significant basic material for designing and performing classes in raising the understanding of Flipped Learning and effectively applying Flipped Learning in physical education classes.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1387-1400
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• 2021

Suppose that $T=\(\array{A&0\\U&B}\)$ is a formal triangular matrix ring, where A and B are rings and U is a (B, A)-bimodule. Let ℭ₁ and ℭ₂ be two classes of left A-modules, 𝔇₁ and 𝔇₂ be two classes of left B-modules. We prove that (ℭ₁, ℭ₂) and (𝔇₁, 𝔇₂) are admissible balanced pairs if and only if (p(ℭ₁, 𝔇₁), h(ℭ₂, 𝔇₂) is an admissible balanced pair in T-Mod. Furthermore, we describe when ($P^{C_1}_{D_1}$, $I^{C_2}_{D_2}$) is an admissible balanced pair in T-Mod. As a consequence, we characterize when T is a left virtually Gorenstein ring.