• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.521-533
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• 2019

In this paper, we define a mean of two positive numbers called the k-golden mean and study some properties of it. Especially, we show that the 2-golden mean refines the harmonic and the geometric means. As an application, we define the k-golden ratio and give some properties of it as an generalization of the golden ratio. Furthermore, we define the matrix k-golden mean of two positive-definite matrices and give some properties of it. This is an improvement of Lim's results [2] for which the matrix golden mean.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.285-294
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• 2016

We define new inductive mean constructed by a mean on a complete metric space, and see its convergence when the intrinsic mean is given. We also give many examples of inductive matrix means and claim that the limit of inductive mean constructed by the intrinsic mean is not the Karcher mean, in general.

• Journal of Korean Society for Atmospheric Environment
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• v.30 no.3
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• pp.223-232
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• 2014

Monthly variations of radiative forcing (RF) and mean temperature changes by greenhouse gases emitted from commercial aircraft were estimated based on the simplified expression at four international airports (Incheon, Gimpo, Jeju, and Gimhae Airports) during the years of 2009~2010. The highest RF and mean temperature change in the study area occurred at Incheon Airport, whereas the lowest RF and mean temperature change at Gimhae Airport. During 2009~2010, the mean RF and mean temperature change estimated from aircraft $CO_2$ emissions at Incheon Airport were approximately 30.0 $mW/m^2$ and $0.022^{\circ}K$, respectively. The mean RF and mean temperature changes caused by other greenhouse gas $N_2O$ was significantly small (<<0.1 $mW/m^2$ and << $1{\times}10^{-3}^{\circ}K$). Meanwhile, $CH_4$ emissions caused negative mean RF ($-4.45{\times}10^{-3}mW/m^2$ at Incheon Airport) and the decrease of mean temperature ($-3.83{\times}10^{-6}^{\circ}K$) due to consumption of atmospheric $CH_4$ in the aircraft engine.

• Journal of Korean Neurosurgical Society
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• v.50 no.2
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• pp.95-98
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• 2011

Objective : This study aimed to evaluate the surgical outcomes of selective median neurotomy (SMN) for spastic wrist and fingers. Methods : We studied 22 patients with wrist and finger spasticity refractory to optimal oral medication and physical therapy. The authors evaluated spasticity of the wrist and finger muscles by comparing preoperative states with postoperative states using the modified Ashworth scale (MAS). We checked patients for changes in pain according to the visual analog scale (VAS) and degree of satisfaction based on the VAS. Results : The preoperative mean MAS score was $3.27{\pm}0.46$ ($mean{\pm}SD$), and mean MAS scores at 3, 6, and 12 months after surgery were $1.82{\pm}0.5$, $1.73{\pm}0.7$, and $1.77{\pm}0.81$ ($mean{\pm}SD$), respectively. On the last follow-up visit, the mean MAS score measured $1.64{\pm}0.9$ ($mean{\pm}SD$). Wrist and finger spasticity was significantly decreased at 3, 6, and 12 months after the operation (p<0.01). The preoperative mean pain VAS score was $5.85{\pm}1.07$ ($mean{\pm}SD$), and the mean pain VAS score on the last follow-up visit after surgery was $2.28{\pm}1.8$ ($mean{\pm}SD$). Compared with the preoperative mean pain VAS score, postoperative mean pain VAS score was decreased significantly (p<0.01). On the basis of a VAS ranging from 0 to 100, the mean degree of patient satisfaction was $64.09{\pm}15.93$ ($mean{\pm}SD$, range 30-90). Conclusion : The authors propose SMN as a possible effective procedure in achieving useful, long-lasting tone and in gaining voluntary movements in spastic wrists and fingers with low morbidity rates.

• The Mathematical Education
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• v.49 no.2
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• pp.199-221
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• 2010

The purpose of the study were to investigate how secondary pre-service teachers conceptualize arithmetic mean and how their conceptualization was formed for solving the problems involving arithmetic mean. As a result, pre-service teachers' conceptualization of arithmetic mean was categorized into conceptualization by "mathematical knowledge(mathematical procedural knowledge, mathematical conceptual knowledge)", "analog knowledge(fair-share, center-of-balance)", and "statistical knowledge". Most pre-service teachers conceptualized the arithmetic mean using mathematical procedural knowledge which involves the rules, algorithm, and procedures of calculating the mean. There were a few pre-service teachers who used analog or statistical knowledge to conceptualize the arithmetic mean, respectively. Finally, we identified the relationship between problem types and conceptualization of arithmetic mean.

• Transactions of the Korean Society of Automotive Engineers
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• v.14 no.3
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• pp.133-141
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• 2006

The Low cycle fatigue behavior of 11.7Cr-1.1Mo heat-resisting steel has been investigated under strain-controlled conditions with mean stresses at room temperature and $300^{\circ}C$. For the tensile mean stress test, the initial high tensile mean stress generally relaxed to zero at room temperature, however, at $300^{\circ}C$ initial tensile mean stress relaxed to compressive mean stress. Low cycle fatigue lives under mean stress conditions are usually correlated using modifications to the strain-life approach. Based on the fatigue test results from different stain ratio of -1, 0, 0.5, and 0.75 at room temperature and $300^{\circ}C$, the fatigue damage of the steel was represented by using cyclic strain energy density. Total strain energy density considering mean stress indicated well better than not considering mean stress at $300^{\circ}C$. Predicted fatigue life using Smith-Watson-Topper's parameter correlated fairly well with the experimental life at $300^{\circ}C$.

• Honam Mathematical Journal
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• v.28 no.4
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• pp.549-558
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• 2006

In this paper, we classify non-developable ruled surfaces in a Euclidean 3-spaces satisfying some algebraic equations in terms of the second mean curvature, the mean curvature and the Gaussian curvature.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.285-289
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• 2000

An additional term between the arithmetic mean and the geometric mean is presented.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.909-913
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• 2009

For a family of graphs $\mathcal{H}$ and an integer k, we denote by $R^k(\mathcal{H})$ the corresponding k-Ramsey number, which is defined to be the smallest integer n such that every k-coloring of the edges of $K_n$ contains a monochromatic copy of a graph in $\mathcal{H}$. The local k-Ramsey number $R^k_{loc}(\mathcal{H})$ and the mean k-Ramsey number $R^k_{mean}(\mathcal{H})$ are defined analogously. Let $\mathcal{G}$ be the family of non-bipartite graphs and $T_n$ be the family of all trees on n vertices. In this paper we prove that $R^k_{loc}(\mathcal{G})=R^k_{mean}(\mathcal{G})$, and $R^2(T_n)$ < $R^2_{loc}(T_n)4 = $R^2_{mean}(T_n)$ for all $n\;{\ge}\;3$.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1199-1217
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• 2006

The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the T-th hyper-Kloosterman sums Kl(h, k+1, r;q) and the hyper Cochrane sums C(h, q; m, k), and give an interesting mean value formula.