• Korean Journal of Mathematics
• /
• v.3 no.1
• /
• pp.71-79
• /
• 1995

• Communications of the Korean Mathematical Society
• /
• v.10 no.3
• /
• pp.681-688
• /
• 1995

Fixed-point theory has an extension to coincidences. For a pair of maps $f,g:X_1 \to X_2$, a coincidence of f and g is a point $x \in X_1$ such that $f(x) = g(x)$, and $Coin(f,g) = {x \in X_1 $\mid$ f(x) = g(x)}$ is the coincidence set of f and g. The Nielsen coincidence number N(f,g) and the Lefschetz coincidence number L(f,g) are used to estimate the cardinality of Coin(f,g). The aspherical manifolds whose fundamental group has a normal solvable subgroup of finite index is called infrasolvmanifolds. We show that if $M_1,M_2$ are compact connected orientable infrasolvmanifolds, then $N(f,g) \geq $\mid$L(f,g)$\mid$$ for every $f,g : M_1 \to M_2$.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.5
• /
• pp.1353-1362
• /
• 2016

Using the notion of complete nonabelian exterior square $G\hat{\wedge}G$ of a pro-p-group G (p prime), we develop the theory of the exterior degree $\hat{d}(G)$ in the infinite case, focusing on its relations with the probability of commuting pairs d(G). Among the main results of this paper, we describe upper and lower bounds for $\hat{d}(G)$ with respect to d(G). Here the size of the second homology group $H_2(G,\mathbb{Z}_p)$ (over the p-adic integers $\mathbb{Z}_p$) plays a fundamental role. A further result of homological nature is placed at the end, in order to emphasize the influence of $H_2(G,\mathbb{Z}_p)$ both on G and $\hat{d}(G)$.

• Kyungpook Mathematical Journal
• /
• v.62 no.1
• /
• pp.193-204
• /
• 2022

A subset S of V(G), where G is a simple undirected graph, is a hop dominating set if for each v ∈ V(G)＼S, there exists w ∈ S such that d_G(v, w) = 2 and it is a locating-hop set if N_G(v, 2) ∩ S ≠ N_G(v, 2) ∩ S for any two distinct vertices u, v ∈ V(G)＼S. A set S ⊆ V(G) is a locating-hop dominating set if it is both a locating-hop and a hop dominating set of G. The minimum cardinality of a locating-hop dominating set of G, denoted by 𝛄_lh(G), is called the locating-hop domination number of G. In this paper, we investigate some properties of this newly defined parameter. In particular, we characterize the locating-hop dominating sets in graphs under some binary operations.

• Korean Journal of Community Nutrition
• /
• v.21 no.4
• /
• pp.332-343
• /
• 2016

Objectives: Study purpose was to investigate perception on diet, diet problems and related factors among young adult women using focus group interviews (FGI) based on the Social Cognitive Theory (SCT). Methods: Eight groups of FGI were conducted with 47 female undergraduate or graduate students. Guide for FGI included questions regarding perception on optimal diet, diet problems and cognitive, behavioral, and environmental factors of SCT. FGI were video, audio-taped, transcribed and analyzed by themes and sub-themes. Results: Subjects showed irregular eating habits (skipping breakfast, irregular meal time) and selection of unhealthy foods as the main diet problems. Regarding cognitive factors related to optimal diet, subjects mentioned positive outcome expectations (e.g., health promotion, skin health, improvement in eating habits, etc.) and negative outcome expectations (e.g., annoying, hungry, expensive, taste). Factors that promoted optimal diet were mainly received from information from mobile or internet and access to menu or recipes. Factors that prevented optimal diet included influence from friends, lack of time and cooking skills. Behavioral factors for optimal diet included behavioral capability regarding snacks, healthy eating and smart food selection. Subjects mentioned mass media (mobile, internet, TV) as the influential physical environment, and significant others (parents, friends, grandparents) as the influential social environment in optimal diet. For education topics, subjects wanted to learn about healthy meals, basic nutrition, disease and nutrition, and weight control. They wanted to learn those aspects by using mobile or internet, lectures (cooking classes), campaign and events. Conclusions: Study results might be used for planning education regarding optimal diet for young adult women. Education programs need to focus on increasing positive outcome expectations (e.g., health) and behavioral capability for healthy eating and food selection, reducing negative outcome expectations (e.g., cost, taste) and barriers, making supportive environments for optimal diet, and incorporating topics and methods found in this study.

• Journal of the Korean Chemical Society
• /
• v.54 no.4
• /
• pp.363-373
• /
• 2010

Computational studies were carried out on the opiates morphine, heroin, codeine, pentazocine, and buprenorphine, under the density functional theory. The geometric parameters of the pharmacophore and substituents were evaluated at the B3LYP/6-31+G(d) level of theory. The electronic structure calculations were performed using the same hybrid functional at the B3LYP/6-311++G (d,p) level of theory. The atomic charges were obtained by Mulliken population analysis. Given the reported biological activity, calculated partition coefficients, and electronic and geometric analysis, pentazocine and buprenorphine were chosen as models for proposed analogues. These analogues were then studied and compared with the model molecules. The study reveals that the geometry and electronic structure of the pharmacophore remains consistent in the presence of different substituents. Because the proposed analogues preserve the studied properties of the model molecules, it is likely that these analogues display biological activity.

• Bulletin of the Korean Chemical Society
• /
• v.33 no.9
• /
• pp.2861-2866
• /
• 2012

Results of the comparisons of various density functional theory (DFT) methods with different basis sets for predicting the molecular geometry of TPOP24N-Oxide macrocycle, an oxoporphyrin N-oxide, are reported in this paper. DFT methods, including M06-2X, B3LYP, LSDA, B3PW91, PBEPBE, and BPV86, are examined. Different basis sets, such as 6-$31G^*$, 6-31+G (d, p), 6-311+G (d, p), and 6-311++G (d, p), are also considered. The M06-2X/6-$31G^*$ level is superior to all other density functional methods used in predicting the geometry of TPOP24N-Oxide. The geometries of regioisomeric chlorin N-oxide and oxoporphyrin N-oxide are reported using M06-2X/6-$31G^*$ method. The geometry effects of oxoporphyrin and chlorin N-oxide regioisomers are increased ${\beta}-{\beta}$ bond lengths by N-oxidation because the bond overlap index due to charge transfers is decreased. In N-oxidation ring (II, III), angles that include ${\beta}-{\beta}$ bond length increase as the bond overlap index of ${\beta}-{\beta}$ bond is decreased by N-oxidation. The potential energy surfaces of chlorin N-oxide and oxoporphyrin N-oxide are explored by M06-2X/6-$31G^*$, and single-point calculations are performed at levels up to M06-2X/6-311++G (d, p). Total and relative energies are then calculated. The results indicate that chlorin 24 N-oxides are more stable than chlorin 22 N-oxides in chlorin N-oxide regioisomers. Moreover, TPOP24N-Oxide is less stable than TPOP22N-Oxide.

• Journal of the Korean Chemical Society
• /
• v.22 no.2
• /
• pp.67-77
• /
• 1978

MO's of a complex are expanded in terms of the set of Shull-Lowdin functions based on a single point, the nucleus of central metal ion, and the result was interpreted from the viewpoint of perturbation theory. We find that even in the case of $[NiF_6]^{4-}$, which has relatively small covalency, excited configurations with high orbital angular momentum are considerably mixed into $e_g$ and $t_{2g}$, orbitals of central metal ion, and that the distortions in these orbitals differ from each other. Therefore it is concluded that the energy difference between $e^*_g$ and $t^*_{2g}$, orbitals evaluated in the MO scheme has little meaning of the unique parameter 10Dq in the crystal field theory, and that such a unique parameter cannot be defined in a rigorous sense in the MO scheme.

• Journal of the Korean Society of Safety
• /
• v.11 no.1
• /
• pp.16-26
• /
• 1996

In a series of original papers, [1-17] efficient methods and algorithms have been presented, for the exact solution of many reliability problems represented by binary networks. A starting point of these methods was the concept of domination, firstly introduced in ,elation with reliability problems in [2]. It's application to directed networks resulted in the development of a topological formula for the classical problem of the two terminal reliability. This result was extended later to the all-terminal and the k-terminal reliability problems. All papers mentioned above use a path oriented representation for the network topology. In practical applications, however, it is common and often advantageous to work with cut sets. This article considers the Domination theory for reliability problem of a network. Some topological formula are derived and the power and the application of this formula are shown through the alternative proof of topological formula of A. Satyanarayana [2].

• Journal of the Korean Mathematical Society
• /
• v.44 no.1
• /
• pp.199-210
• /
• 2007

Given a field K and a finite group G, it is a very interesting problem, although very difficult, to find all Galois extensions over K whose Galois group is isomorphic to G. In this paper, we prepare a theoretical background to study this type of problem when G is the Mathieu group $M_{24}$ and K is a field of characteristic two.