• Communications of Mathematical Education
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• v.24 no.3
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• pp.709-730
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• 2010

The inverse function of a one-to-one correspondence is explained with a graph, a numerical formula or other useful expressions. The purpose of this paper is to know how low achieving students understand the learning contents needed reversible thinking about irrational functions. Low achieving students in this study took paper-pencil test and their written answers were collected. They made various mistakes in solving problems. Their error types were grouped into several classes and identified in this analysis. Most students did not connected concepts that they learned in the lower achieving students to think in reverse order in case of and to visualize concepts of functions. This paper implies that it is very important to take into account students' accommodation and reversible thinking activity.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.601-610
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• 2013

In [3] and [2], Atanassov introduced the two arithmetic functions $$I(n)=\prod_{p^{\alpha}{\parallel}n}\;p^{1/{\alpha}}\;and\;R(n)=\prod_{p^{\alpha}{\parallel}n}\;p^{{\alpha}-1}$$ called the irrational factor and the restrictive factor, respectively. Alkan, Ledoan, Panaitopol, and the authors explore properties of these arithmetic functions in [1], [7], [8] and [9]. In the present paper, we generalize these functions to a larger class of elements of $PSL_2(\mathbb{Z})$, and explore some of the properties of these maps.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.443-455
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• 2014

Atanassov introduced the irrational factor function and the strong restrictive factor function, which he defined as $I(n)=\displaystyle\prod_{p^{\alpha}||n}^{}p^{1/{\alpha}}$ and $R(n)=\displaystyle\prod_{p^{\alpha}||n}^{}p^{{\alpha}-1}$ in [2] and [3]. Various properties of these functions have been investigated by Alkan, Ledoan, Panaitopol, and the authors. In the prequel, we expanded these functions to a class of elements of $PSL_2(\mathbb{Z})$, and studied some of the properties of these maps. In the present paper we generalize the previous work by introducing real moments and considering a larger class of maps. This allows us to explore new properties of these arithmetic functions.

• Journal of the Korean Mathematical Society
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• v.46 no.2
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• pp.363-447
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• 2009

The author previously defined the spectral invariants, denoted by $\rho(H;\;a)$, of a Hamiltonian function H as the mini-max value of the action functional ${\cal{A}}_H$ over the Novikov Floer cycles in the Floer homology class dual to the quantum cohomology class a. The spectrality axiom of the invariant $\rho(H;\;a)$ states that the mini-max value is a critical value of the action functional ${\cal{A}}_H$. The main purpose of the present paper is to prove this axiom for nondegenerate Hamiltonian functions in irrational symplectic manifolds (M, $\omega$). We also prove that the spectral invariant function ${\rho}_a$ : $H\;{\mapsto}\;\rho(H;\;a)$ can be pushed down to a continuous function defined on the universal (${\acute{e}}tale$) covering space $\widetilde{HAM}$(M, $\omega$) of the group Ham((M, $\omega$) of Hamiltonian diffeomorphisms on general (M, $\omega$). For a certain generic homotopy, which we call a Cerf homotopy ${\cal{H}}\;=\;\{H^s\}_{0{\leq}s{\leq}1}$ of Hamiltonians, the function ${\rho}_a\;{\circ}\;{\cal{H}}$ : $s\;{\mapsto}\;{\rho}(H^s;\;a)$ is piecewise smooth away from a countable subset of [0, 1] for each non-zero quantum cohomology class a. The proof of this nondegenerate spectrality relies on several new ingredients in the chain level Floer theory, which have their own independent interest: a structure theorem on the Cerf bifurcation diagram of the critical values of the action functionals associated to a generic one-parameter family of Hamiltonian functions, a general structure theorem and the handle sliding lemma of Novikov Floer cycles over such a family and a family version of new transversality statements involving the Floer chain map, and many others. We call this chain level Floer theory as a whole the Floer mini-max theory.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.151-170
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• 2009

Let m be a positive integer. We show that for any given real number ${\alpha}\;{\in}\;[0,\;1]$ and complex number $\mu$ with $|\mu|{\leq}1$ which satisfy $e^{2{\pi}i{\alpha}}{\mu}^m\;{\neq}\;1$, there exists a Blaschke product B of degree 2m + 1 which has a fixed point of multiplier ${\mu}^m$ at the point at infinity such that the restriction of the Blaschke product B on the unit circle is a critical circle map with rotation number $\alpha$. Moreover if the given real number $\alpha$ is irrational of bounded type, then a modified Blaschke product of B is quasiconformally conjugate to some rational function of degree m + 1 which has a fixed point of multiplier ${\mu}^m$ at the point at infinity and a Siegel disk whose boundary is a quasicircle containing its critical point.

• The Korean Journal of Elementary Counseling
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• v.6 no.1
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• pp.141-169
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• 2007

One of the most common feelings in everyday life is anger. Anger plays an important role in activating emotional energy and increasing intolerance when confronted with hardships, frustration and improper treatments. And it provides us with controlling interpersonal behavior, organizing internal, physiological, psychological process and various adaptive functions. If anger is not properly expressed, it brings about offensive attitude, leading to not only physical impairment but also anxiety in interpersonal relations and maladaptive to everyday life. For elementary school students, frequent quarrels, abusive words and defiant attitude toward adults are also caused by students' anger. Therefore, students' anger is one of the most difficult problems to be dealt with not only psychologically but also in elementary schools. In this respect, after investigating frequently experienced anger- inducing situations and inventing anger-inducing situation questionnaire, we postulated specific situations changing irrational belief into rational one. Based on these situations, we accounted for how to cope with anger inducing factors and change irrational belief into rational one, introducing several strategies needed to control anger, invented cognitive behavioral anger control program and tried to clarify the relationship between anger inducing experience and anger regulation ability. In order to derive usual anger-inducing situations, we made 180 students with fifth and sixth grade to record the reason why he/she got angry, mood, thought, behavior and result. Through this process, we could derive 47 situations bringing about anger and prepared anger-inducing situation questionnaire. It can be divided into 3 anger inducing situations by using factor analysis into 500 elementary students of fifth and sixth grade. Cognitive behavioral anger control program used in this study consists of 13 sessions. From first to fifth session, it is composed of 10 anger control methods to make students be aware of and control their anger. From sixth through thirteenth session, the relationship between irrational belief and anger inducing is introduced is focused on how irrational belief is changed into rational one. To examine the effects of the program, high anger students and the students lacking anger control are selected. Thirty students through pre-test using anger-inducing questionnaire and anger control ability questionnaire are taught the goals and procedures. Volunteer students and students with parents' consent allocated to experimental group (12 students) and the rest of the students are control group (12 students). Cognitive Behavioral Anger Control Program are applied every 50 minutes twice a week for 7 weeks and 4 weeks before and after this program, anger-inducing situation questionnaire and anger control ability questionnaire are practiced. Data collected in this study analyzed by SPSS and Kwakstat. In the middle of this program, quarterly reports and satisfaction measuratings were evaluated to examine whether there is verbal and non-verbal behavior change and students feel satisfied with the program. The results of this study are as follows: First, Cognitive-behavioral anger control program used in this study effectively reduced anger experience and lasted for 4 weeks. Second, cognitive behavioral anger control program increased students' ability to control anger inducing situations and also effective for 4 weeks. And its effect on verbal and non-verbal behaviour was very impressive Students come to realize that irrational belief is the cause of their anger and actively apply cognitive-behavioral anger control technique to themselves as well. Students became improved in their peer relations and felt confident in everyday life. The overall evaluation of this program can be listed as follows; "very satisfactory (91.67%)", "satisfactory (8.33%)", "very helpful (91.67%)", "helpful (8.33%). In this study we first investigated several anger-inducing situations and invented anger-inducing situation questionnaire and then applied cognitive behavioral anger control program in order to control their. anger and not to experience it. By creating workbooks and manuals this method can easily be used in school education settings.

• Journal of the Korean School Mathematics Society
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• v.11 no.2
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• pp.221-247
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• 2008

In order to find the structure and scheme of basic mathematics education in life and nano-related areas in university, I've studied how much the freshmen in those fields in the university know about the graphic expressions for the basic functions(quadratic function, rational function, irrational function, log function and trigonometric function), basic information contained in those graphs and basic high school mathematics. Also, I've examined mathematics used in books for majors related to those areas. The result of the study shows that there is a lack of understanding of the graphic expressions for basic functions, information contained in those graphs and basic high school mathematics. I've also found out that there is a difference in the amount and depth of mathematics used in each major in life and nano-related areas. According to the result of this study, the amount of understanding of freshmen with each major in basic high school mathematics needs to be reflected in structuring basic mathematics education in life and nano-related areas in university, and the amount and dept of content of mathematics should be considered in each major.

• Journal of the Korean Society for Railway
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• v.1 no.1 s.1
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• pp.30-39
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• 1998

The functions of diaphragms at abutments and piers of PSC box girder railway bridge are to transfer forces from the superstructure onto bearings or columns and to stiffen the superstructure cross-section against in -plane deformation. Due to stress disturbance at diaphragm, the design for the diaphragm using conventional design method is relatively irrational than those for other structural members. And, due to contribution to boundary condition of deck slab by the diaphragm, the behavior of deck slab near the diaphragm is different from that of the deck slab obtained from two dimensional analysis of the bridge, which is basis for the design of deck slab. In this paper, three dimensional behavior of deck slab near the diaphragm of prestressed concrete (PSC) box girder railway bridge constructed by the precast span method are analyzed by using three dimensional finite element modeling and using the strut-and-tie model design of the diaphragm are presented. The modeling techniques used in this paper can be applied effectively to examine the causes of cracks at deck slab near diaphragm and to design diaphragm rationally.

• Journal of the Korean Society of Environmental Restoration Technology
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• v.3 no.3
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• pp.45-76
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• 2000

The purposes of this study were to investigate and understand the present status of various types of "deserts", such as sand desert, gravel desert, rock desert, earth desert, salt desert, desert, rocky desert, gobi desert, sandy desert, clay desert, etc., and the general countermeasures for the combating "desertification" "desertization", and to develop the technologies on the revegetation and restoration for the combating desertification in China. The methods of this study were mainly composed of field surveys on the several experimental sites and research institutes related to combating desertification in China, and examinations on the various technologies for the combating desertification at the Daxing Experimental Station of Beijing Forestry University. The conclusion from this study may be summarized as follows; 1. Status and tendency of desertification in China : China is one of the countries seriously threatened by desertification. Desertification affected areas in China are mainly distributed in arid, semi-arid and dry sub-humid areas in China, covering the most regions of the Northeast China (eastern region of Inner-Mongolia), the northern part of the North China (middle and western region of Inner-Mongolia, Shaanxi, Ningsha, Gansu) and the western part of the Northwest China (Xinzang, Qinghai, Xizang). The total area affected by desertification in China is approximately 2.622 million $km^2$. It covers 27.3% of the total territory of China. Until recently, it is estimated that the annual spreading ratio of desertification in China is 2,460 $km^2$. Therefore, desertification is mostly serious problems facing to the Chinese people. 2. The causes and environmental effect of desertification : The desertification in China is mainly caused by compound factors, including natural condition and human activities. In China, the desertification is started by the decrease of precipitation, continuous dry and drought, strong wind, wind and water erosion, land degradation and loss of natural vegetation caused by climate variation, and accelerated by the human activities, such as over-cultivating, over-grazing, over-cutting of woods, irrational use of water resources. Because desertification has affected the geographical features, soil nutrients contents, salinity, vegetation coverage and the functions of ecosystem, the environmental deteriorations in the desertification affected areas are very seriously. 3. The fundamental strategies of combating desertification in China are the increase of education and awareness of people through various mass media, the revision of laws to guarantee operation of Desertification Combating Law and to improve many relating laws and regulations, the application of advanced technologies and training of experts, the establishment of discriminative policies, and increasing arrangement of budget-investment, and so on. China, as a signed country in UNCCD, has made efforts for the combating desertification. Korea is also signed country in UNCCD, so we should play an important role in the desertification combating projects of China for the northest asia and global environmental conservation as well as environmental conservation of Korea.

• Journal of Korea Entertainment Industry Association
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• v.13 no.6
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• pp.211-220
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• 2019

It helps to wisely abstain from errors of the a priori subjective emotions related to human emotions, and orders emotions to make rational choices. These emotional happiness of human and moral sensitivities work directly or indirectly in rational choice of rational thought and reason. Abraham would have been troubled by the divine mandate to sacrifice a son who was only one, and a son who had been healed. Was his reason reasonable at this time? In rational reason, it can be said that the act of dedicating his son is an appropriate act, but is it possible in the human mind? Aristoteles also called human virtue virtue in good for human beings. Because happiness is also a mental activity, we have to know a certain degree about the mind. This ψυχή(psyche, spirit) spirit is an irrational element that is invisible but an intervention in rational principles. Also C. G. Jung states that all human beings have four dynamic psychological functions that are not visible, and that the mind is driven by these four functional dimensions. This means that the elements of S, Sensing, N, Intuition, T, Thinking, and Feeling are combined. David Hume also emphasized the principle of empathy, asserting that morality can not be derived from reason, and Max Ferdinand Scheler, before grasping the visual characteristics of a person, has already captured the whole feeling of the person, And that the value given to this feeling is the value, and that the function of emotion that is elevated to the perceived object by grasping the value through this process and the value is always preceded by the reason. Emmanuel Levinas states that emotional emotions of love are ahead of reason and that emotions precede human reasoning and rationality is the inability of emotional control that we need rational thought and rational and wise action as reason of control and temperance. As part of human emotional education, in the 7th curriculum, Bloom's cognitive, perceptive, and behavioral domain, which is a person with integrated thinking, is trying to be a moral practitioner. It focuses on how to act according to the direction of emotions for virtuous acts and how to develop emotions for emotions on behalf of vicious acts. We can design the possibility and direction of cultivating human emotions and emotional happiness and happy sensitivities by the principle of strengthening virtue and the principle of elimination of ill feeling.