• Journal of applied mathematics & informatics
• /
• v.39 no.5_6
• /
• pp.689-701
• /
• 2021

The purpose of this paper is to optimize the number of source places required for the unique representation of the destination using the tools of graph theory. A subset S of vertices of a graph G is called a rational resolving set of G if for each pair u, v ∈ V - S, there is a vertex s ∈ S such that d(u/s) ≠ d(v/s), where d(x/s) denotes the mean of the distances from the vertex s to all those y ∈ N[x]. A rational resolving set is called minimal rational resolving set if no proper subset of it is a rational resolving set. In this paper we study varieties of minimal rational resolving sets defined on the basis of its complements and compute the minimum and maximum cardinality of such sets, respectively called as lower and upper rational metric dimensions for power of a path P_n analysing various possibilities.

• International journal of advanced smart convergence
• /
• v.7 no.4
• /
• pp.128-137
• /
• 2018

In the programming education, there is a great need of a teaching support system that can support the learner in the programming process regardless of the computer language due to instructor's difficulty of checking the progress of learners in real-time. Its importance is especially important in lower grade coding classes such as in K-12 education because they are not used to coding and so simple problems can be regarded as complex problems. For this, a pilot coding education support system based on Levenshtein distance algorithm which shows learners' progress to given solution in real-time was developed in order to help learners to solve complex problems easily, and the learners' motivation and self-efficacy was measured for estimating the usefulness of developed system targeting elementary school students. When the learners use the developed system, it was found that a statistically significant difference appears in the sub-factors of learning motivation compared with traditional class teaching environments. Among the sub-factors of self-efficacy, the efficacy dimension showed statistically significant difference too.

• Korean Journal of Mathematics
• /
• v.29 no.1
• /
• pp.25-40
• /
• 2021

In this article we introduce tribonacci sequence spaces c0(T) and c(T) derived by the domain of a newly defined regular tribonacci matrix T. We give some topological properties, inclusion relations, obtain the Schauder basis and determine ��-, ��- and ��- duals of the spaces c0(T) and c(T). We characterize certain matrix classes (c0(T), Y) and (c(T), Y), where Y is any of the spaces c0, c or ℓ∞. Finally, using Hausdorff measure of non-compactness we characterize certain class of compact operators on the space c0(T).

• Communications of the Korean Mathematical Society
• /
• v.37 no.1
• /
• pp.137-161
• /
• 2022

In this article, we study the existence and multiplicity of homoclinic solutions for the following fourth-order differential equation (1) u⁽⁴⁾(x) + ωu''(x) + a(x)u(x) = f(x, u(x)), ∀x ∈ ℝ where a(x) is not required to be either positive or coercive, and F(x, u) = ∫^u₀ f(x, v)dv is of subquadratic or superquadratic growth as |u| → ∞, or satisfies only local conditions near the origin (i.e., it can be subquadratic, superquadratic or asymptotically quadratic as |u| → ∞). To the best of our knowledge, there is no result published concerning the existence and multiplicity of homoclinic solutions for (1) with our conditions. The proof is based on variational methods and critical point theory.

• Journal of Applied and Pure Mathematics
• /
• v.4 no.1_2
• /
• pp.27-36
• /
• 2022

An innovation diffusion model is proposed model consists of three classes, namely, a non-adopter class, adopter class innovation-I, and adopter class innovation-II in a partially competitive and cooperative market. The proposed model is analyzed with the help of the qualitative theory of a system of ordinary differential equations. Basic influence numbers associated with first and second innovation $R_{0_1}$ and $R_{0_2}$ respectively in the absence of each other are quantified. Then the overall basic influence number (R₀) of the system is assessed for analyzing stability in the market in different situations. Sensitivity analysis of basic influence numbers associated with first and second innovation in the absence of each other is carried out. Numerical simulation supports our analytical findings.

• Communications of the Korean Mathematical Society
• /
• v.39 no.1
• /
• pp.259-266
• /
• 2024

The purpose of this note is a wide generalization of the topological results of various classes of ideals of rings, semirings, and modules, endowed with Zariski topologies, to r-strongly irreducible r-ideals (endowed with Zariski topologies) of monoids, called terminal spaces. We show that terminal spaces are T₀, quasi-compact, and every nonempty irreducible closed subset has a unique generic point. We characterize rarithmetic monoids in terms of terminal spaces. Finally, we provide necessary and sufficient conditions for the subspaces of r-maximal r-ideals and r-prime r-ideals to be dense in the corresponding terminal spaces.

• The Korean Journal of Applied Statistics
• /
• v.22 no.2
• /
• pp.387-402
• /
• 2009

In this paper we have considered the problem of estimating the population mean $\bar{Y}$ of the study variable y using auxiliary information in presence of non-response. Classes of estimators for $\bar{Y}$ in the presence of non-response on the study variable y only and complete response on the auxiliary variable x is available, have been proposed in different situations viz., (i) population mean $\bar{X}$ is known, (ii) when population mean $\bar{X}$ and variance $S^2_x$ are known; (iii) when population mean $\bar{X}$ is not known: and (iv) when both population mean $\bar{X}$ and variance $S^2_x$ are not known: single and two-phase (or double) sampling. It has been shown that various estimators including usual unbiased estimator and the estimators reported by Rao (1986), Khare and Srivastava (1993, 1995) and Tabasum and Khan (2006) are members of the proposed classes of estimators. The optimum values of the first phase sample size n', second phase sample size n and the sub sampling fraction 1/k have been obtained for the fixed cost and the fixed precision. To illustrate foregoing, we have carried out an empirical investigation to reflect the relative performance of all the potentially competing estimators including the one due to Hansen and Hurwitz (1946) estimator, Rao (1986) estimator, Khare and Srivastava (1993, 1995) and Tabasum and Khan (2006) estimator.

• Kyungpook Mathematical Journal
• /
• v.13 no.2
• /
• pp.235-240
• /
• 1973

A k-dimensional vector bundle is a bundle ${\xi}=(E,P,B,F^k)$ with fibre $F^k$ satisfying the local triviality, where F is the field of real numbers R or complex numbers C ([1], [2] and [3]). Let $Vect_k(X)$ be the set consisting of all isomorphism classes of k-dimensional vector bundles over the topological space X. Then $Vect_F(X)=\{Vect_k(X)\}_{k=0,1,{\cdots}}$ is a semigroup with Whitney sum (${\S}1$). For a pair (X, A) of topological spaces, a difference isomorphism over (X, A) is a vector bundle morphism ([2], [3]) ${\alpha}:{\xi}_0{\rightarrow}{\xi}_1$ such that the restriction ${\alpha}:{\xi}_0{\mid}A{\longrightarrow}{\xi}_1{\mid}A$ is an isomorphism. Let $S_k(X,A)$ be the set of all difference isomorphism classes over (X, A) of k-dimensional vector bundles over X with fibre $F^k$. Then $S_F(X,A)=\{S_k(X,A)\}_{k=0,1,{\cdots}}$, is a semigroup with Whitney Sum (${\S}2$). In this paper, we shall prove a relation between $Vect_F(X)$ and $S_F(X,A)$ under some conditions (Theorem 2, which is the main theorem of this paper). We shall use the following theorem in the paper. THEOREM 1. Let ${\xi}=(E,P,B)$ be a locally trivial bundle with fibre F, where (B, A) is a relative CW-complex. Then all cross sections S of ${\xi}{\mid}A$ prolong to a cross section $S^*$ of ${\xi}$ under either of the following hypothesis: (H1) The space F is (m-1)-connected for each $m{\leq}dim$ B. (H2) There is a relative CW-complex (Y, X) such that $B=Y{\times}I$ and $A=(X{\times}I)$ ${\cap}(Y{\times}O)$, where I=[0, 1]. (For proof see p.21 [2]).

• Journal of The Korean Society of Agricultural Engineers
• /
• v.49 no.6
• /
• pp.77-84
• /
• 2007

This study aims to analyze temporal variation of rural tourist potential in village level. In order to analyze the temporal variation, this study applied a green-tourism potential evaluation model(GPEM) to a study area, Namilmyun with 18 villages, which located on county of Kumsan, province of Chungnam. GPEM consists of two factors about human resources, which is quantified by resident population of the village who will be participated in village management for green-tourism, and amenity resources, which is calculated by an evaluation table with 31 criteria and their weighting values. Data surveying for the study area was performed at August 2003 and 2006, respectively, in order to quantity the 31 evaluation criteria of GPEM. From the analysis results, the amenity resources with three sub-classes of industrial, natural, and social resources showed that the evaluation values of 2006 were increased in more than those of 2003, displaying the increase rate of ranging from 108% to 112% in the three sub-classes, except of one village in social resources and three village in natural resources with reduction. In human resources, the evaluation values of 2006 were highly increased more than those of 2003, showing the rate of 556% in the gradient of linear regression line. In green tourism potential in each village, the evaluation results for two time series showed that the potential is increased by time, which the increase rate of the potential is 114%. Ultimately, the results of this study enable us to realize that the green-tourism potential in each village over time is increased, for example, due to developing new facilities in the village by investment of government and participating in rural tourism by resident people over time. From the analysis and results, the methodology of this study can be applied to analyze the temporal variation of the potential for villages having investment from government.

• Journal of Families and Better Life
• /
• v.29 no.2
• /
• pp.73-87
• /
• 2011

The purpose of this study is to investigate the influence of children's socia-demographic variables(i.e., gender, birth order, and the amount of time staying in kindergarten) on, leadership, self-regulation and children's peer play behaviors. The participants of this study are 336 children aged between five and seven in four classes in a private kindergarten and eight classes in a private preschool located in the capital region. The results revealed that, girls showed more leadership, self-regulation, and play interaction section than boys: whereas, boys showed higher response in play disruption and the lack of play disconnection. However, birth order, did not have a significant effect on the sub-domain of leadership, self-regulation competence, and peer play behaviors. As for the duration children stay in preschool or in preschool or kindergarten, children who spend half-day showed higher reaction in behavioral self-control and emotional taking abilities than children who stay in the preschool or kindergarten full day. On the other hand, self-esteem of full-time children was higher than half-time children. Children who were emotionally sensitive, knew how to lead their peer group, and those who were sociable and self-regulated presented to be more active in peer-interaction than others. Second, as the result of the correlation analysis reveals, children's leadership, self-regulation competence, peer play behaviors, and play interaction had a meaningful effect on the sub-variations of children's leadership and self-regulation and they showed significant influence upon play disruption and play disconnection. In addition, girls who were not able to manage or to inspect their behavior and had insensitive emotion demonstrated higher tendency to play disconnected. Children, who participated in full-day program with having difficulties in self-regulation or inspecting their behavior properly but had a strong leadership and insensitive showed play disruption highly.