• Honam Mathematical Journal
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• v.44 no.4
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• pp.521-534
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• 2022

In this paper, we introduce a new class 𝓡^k_λ(λ ≥ 1, k is any positive real number) of univalent complex functions, which consists of functions f of the form f(z) = z + Σ^∞_n=2 a_nzⁿ (|z| < 1) satisfying the subordination condition $$(1-{\lambda}){\frac{f(z)}{z}}+{\lambda}f^{\prime}(z){\prec}{\frac{1+r^2_kz^2}{1-k{\tau}_kz-{\tau}^2_kz^2}},\;{\tau}_k={\frac{k-{\sqrt{k^2+4}}}{2}$$, and investigate the Fekete-Szegö problem for the coefficients of f ∈ 𝓡^k_λ which are connected with k-Fibonacci numbers $F_{k,n}={\frac{(k-{\tau}_k)^n-{\tau}^n_k}{\sqrt{k^2+4}}}$ (n ∈ ℕ ∪ {0}). We obtain sharp upper bound for the Fekete-Szegö functional |a₃-𝜇a²₂| when 𝜇 ∈ ℝ. We also generalize our result for 𝜇 ∈ ℂ.

• Journal of Korea Soil Environment Society
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• v.1 no.1
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• pp.55-65
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• 1996

Soil quality of most of Soil Network area was estimated healthy by employing Soil Pollution Indices (Soil Pollution Score and Soil Pollution Class). However, 1.5∼3.7% of the total Soil Network area was determined Soil Pollution Class (SPC) 4 which may need cleanup process due to slight or heavy pollution with arsenics and heavy metals. Numbers of the SPC 4 sites were 9, 47, 19, 17, and 17 in 1987, 1989, 1991, 1993, and 1994, respectively During 1987 and 1994, all of SPC 4 sites were identified agricultural land except one in 1994. Soil Pollution Scores (SPSs) was determined high around smelters, metalliferous mines, and industrial sites among the 16 major soil pollution sources of the Soil Network. Also, most area of SPC 4 sites were densely populated in these area of the Soil Network. SPSs of Inchon and Taegu were high among the other major cities and provinces in Korea. Numbers of SPC 4 were high in the province of Kangwon, Kyongbuk, Kyongnam amongst. Cumulative numbers of SPC 4 multiplied by a weighting value 0.3 during 1987 and 1994 of the Soil Network were regressed to develop a model equation for prospecting the soil quality. The model equation was Y= 1.16+0.23x, where as Y is the number of Class 4 and x is the year. Resulting the area of SPC 4 were 4.8%, 6.0%, 6.6% of the Soil Network in the year of 2001, 2006, 2011, respectively Based on this results, the area of SPC 4 would increase 5, 7, and 10 times comparing the area polluted with heavy metals in 1987.

• Journal of Preventive Medicine and Public Health
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• v.38 no.4
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• pp.443-448
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• 2005

Objectives : This study was done to evaluate the reliability of education and occupational class between using the health survey and the death certificate data. Methods : The 1998 National Health and Nutrition Examination Survey (NHANES) was conducted on a cross-sectional probability sample of South Korean households, and it contained unique 13-digit personal identification numbers that were linked to the data on mortality from the Korean National Statistical Office. The data from 263 deaths were used to estimate the agreement rates and the Kappa indices of the education and occupational class between using the NHANES data and the death certificate data. Results : The simple and weighted Kappa indices for education were 0.60 (95% CI=0.53-0.68) and 0.73 (95% CI=0.67-0.79) respectively, if the educational level was grouped into five categories: no-formal-education, elementary-school, middle-school, high-school and college or over. The overall agreement rate was 71.9% for these educational groups. The magnitude of reliability, as measured by the overall agreement rates and Kappa indices, tended to increase with a decrease in the educational class. The number of non-educated people with using the death certificate data was smaller than that with using the NHANES data. For the occupational class (manual workers, non-manual workers and others), the Kappa index was 0.40 (95% CI=0.30-0.51), which was relatively lower than that for the educational class. Compared with the NHANES, the number of non-manual workers for the deceased who were aged 30-64 tended to be increased (8 to 12) when using the death certificate data, whereas the number of manual workers tended to be decreased (59 to 41). Conclusions : The socioeconomic inequalities in the mortality rates that were based on the previous unlinked studies in South Korea were not due to a numerator/denominator bias. The mortality rates for the manual workers and the no-education groups might have been underestimated.

• Restorative Dentistry and Endodontics
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• v.42 no.1
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• pp.48-53
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• 2017

Objectives: The aim of this study was to investigate the ability of the fluorescence-aided caries excavation (FACE) device to detect residual caries by comparing conventional methods in vivo. Materials and Methods: A total of 301 females and 202 males with carious teeth participated in this study. The cavity preparations were done by grade 4 (Group 1, 154 teeth), grade 5 (Group 2, 176 teeth), and postgraduate (Group 3, 173 teeth) students. After caries excavation using a handpiece and hand instruments, the presence of residual caries was evaluated by 2 investigators who were previously calibrated for visual-tactile assessment with and without magnifying glasses and trained in the use of a FACE device. The tooth number, cavity type, and presence or absence of residual caries were recorded. The data were analyzed using the Chi-square test, the Fisher's Exact test, or the McNemar test as appropriate. Kappa statistics was used for calibration. In all tests, the level of significance was set at p = 0.05. Results: Almost half of the cavities prepared were Class II (Class I, 20.9%; Class II, 48.9%; Class III, 20.1%; Class IV, 3.4%; Class V, 6.8%). Higher numbers of cavities left with caries were observed in Groups 1 and 2 than in Group 3 for all examination methods. Significant differences were found between visual inspection with or without magnifying glasses and inspection with a FACE device for all groups (p < 0.001). More residual caries were detected through inspection with a FACE device (46.5%) than through either visual inspection (31.8%) or inspection with a magnifying glass (37.6%). Conclusions: Within the limitations of this study, the FACE device may be an effective method for the detection of residual caries.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.843-849
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• 2012

Let G = (V, E) be a graph with chromatic number ${\chi}(G)$. dominating set D of G is called a chromatic transversal dominating set (ctd-set) if D intersects every color class of every ${\chi}$-partition of G. The minimum cardinality of a ctd-set of G is called the chromatic transversal domination number of G and is denoted by ${\gamma}_{ct}$(G). In this paper we characterize the class of trees, unicyclic graphs and cubic graphs for which the chromatic transversal domination number is equal to the connected domination number.

• Journal of Korean Institute of Industrial Engineers
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• v.20 no.4
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• pp.65-72
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• 1994

An independent set of nodes is a set of nodes no two of which are joined by an edge. An independent set is called maximal if no more nodes can be added to the set without destroying its independence. The greatest number of maximal independent set is the maximum possible number of maximal independent set of a graph. We consider the greatest number of maximal independent set in connected graphs with fixed numbers of edges and nodes. For arbitrary number of nodes with a certain class of number of edges, we present the connected graphs with the greatest number of maximal independent set. For a given class of number of edges, the structure of graphs with the greatest number of maximal independent set is that the two components are completely joined; one consists of disjoint triangles as many as possible and the other is the complete graph with remaining nodes.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.479-491
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• 2017

We investigate the zeros of Epstein zeta functions associated with positive definite quadratic forms with rational coefficients in the vertical strip ${\sigma}_1$ < ${\Re}s$ < ${\sigma}_2$, where 1/2 < ${\sigma}_1$ < ${\sigma}_2$ < 1. When the class number h of the quadratic form is bigger than 1, Voronin gave a lower bound and Lee gave an asymptotic formula for the number of zeros. Recently Gonek and Lee improved their results by providing a new upper bound for the error term when h > 3. In this paper, we consider the cases h = 2, 3 and provide an upper bound for the error term, smaller than the one for the case h > 3.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.279-287
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• 2012

Let $k$ be a field containing the field $\mathbb{Q}$ of rational numbers and let $R=k[x_{ij}{\mid}1{\leq}i{\leq}m,\;1{\leq}j{\leq}n]$ be the polynomial ring over a field $k$ with indeterminates $x_{ij}$. Let $I_t(X)$ be the determinantal ideal generated by the $t$-minors of an $m{\times}n$ matrix $X=(x_{ij})$. Eagon and Hochster proved that $I_t(X)$ is a perfect ideal of grade $(m-t+1)(n-t+1)$. We give a structure theorem for a class of determinantal ideals of grade 3. This gives us a characterization that $I_t(X)$ has grade 3 if and only if $n=m+2$ and $I_t(X)$ has the minimal free resolution $\mathbb{F}$ such that the second dierential map of $\mathbb{F}$ is a matrix defined by complete matrices of grade $n+2$.

• Journal of the Korean Institute of Educational Facilities
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• v.22 no.3
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• pp.13-20
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• 2015

This study was carried out to analyze moving awareness of students to physical conditions and attitudes on user's place to moving route. Moving awareness and route choice of students on variation type were grasped through questionnaire. As the results, the satisfaction degree, moving awareness and elapsed time for adaptation of students to physical facilities associated with moving class were antithetical to numbers of class and student. The more students, the more negative the moving itself. Especially, students showed a different tendency to route choice of high frequency moving and possession awareness of their belongings according to spatial nearness and composition of homebase. These basic data will be utilizable to suggest various model for composition and rearrangement of school space.

• The Mathematical Education
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• v.51 no.4
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• pp.429-453
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• 2012

The purpose of the study were to analyze teaching models of arithmetic operations of integers in Korean middle school mathematics textbooks of the first grade and Americans', from which we compare and analyze standards for choice of models of middle school teachers and preservice mathematics teachers. We also analyze the effect of the choice of teaching models for students to understand and appreciate number systems as a coherent body of knowledge. On the basis of that, we would like to find the best model to help students understand and reason the process of formulate the arithmetic operations of natural numbers and integers into the operation of the real number system. Furthermore, we help these series of the study to be applied effectively in the middle school mathematics class in Korea.