• 한국수학교육학회지시리즈E:수학교육논문집
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• 제24권3호
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• pp.709-730
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• 2010

본 연구에서 함수를 어려워하는 원인이 함수의 가역성에 기인하는지 살펴보고자 가역적 사고가 요구되는 무리함수의 개념과 가역성을 분석하였다. 함수와 관련하여 저학년에서 형성된 개념이 불균형 상태로 고착화되어 있다. 하위권 학생들의 시각화, 기호 이해, 특히 가역적 사고 능력이 부족하여 오류 현상을 보이고 있다. 저학년부터 생활 주변의 가역적인 사고를 요하는 내용을 다루지만, 학생들은 가역성이 내포된 함수 내용을 어려운 대상으로만 간주하고 인지 구조의 조절 과정을 의도적으로 회피하거나, 인출하여도 연결성이 부족하고 부정확한 개념으로 응답하고, 특히 가역성이 내포된 문제에 대하여 반응율과 정답율이 낮으며 다양한 오류 현상이 나타났다.

• 대한수학회보
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• 제50권2호
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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.

• 대한수학회보
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• 제51권2호
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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.

• 대한수학회지
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• 제46권2호
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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.

• 대한수학회지
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• 제46권1호
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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.

• 초등상담연구
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• 제6권1호
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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.

• 한국학교수학회논문집
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• 제11권2호
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• pp.221-247
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• 2008

생명 나노 관련 분야의 대학 기초수학 교육 내용의 구성과 그 방안을 찾기 위하여, 그 분야의 대학생들이 기본함수(2차 함수, 유리함수, 무리함수, 로그함수, 삼각함수)에 대한 그래프 표현과 그래프에 내포한 기본정보에 대하여 어느 정도 알고 있는지, 고등학교 기초 수학 내용을 어느 정도 알고 있는지에 대하여 조사하였다. 그리고 그 분야와 관련된 전공 서적에서 사용되고 있는 수학 내용을 조사하였다. 조사 결과, 기본함수에 대한 그래프 표현과 그래프에 내포한 정보에 대한 이해 및 고등학교 기초 수학 내용에 대한 이해가 부족한 것으로 나타났다. 그리고 생명 나노 관련 분야의 각 전공에 사용되고 있는 수학 내용의 양과 내용의 깊이에 차이가 있었다. 이러한 조사 결과에 따르면, 생명 나노 관련 분야의 대학 기초수학 교육 내용 구성에서, 각 전공 분야의 대학생들의 고등학교 기초수학 내용에 대한 이해 정도를 반영하고 각 전공에 따라 수학 내용의 양적인 면과 내용의 깊이를 다양하게 고려하여야 할 것이다.

• 한국철도학회논문집
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• 제1권1호
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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.

• 한국환경복원기술학회지
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• 제3권3호
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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.

• 한국엔터테인먼트산업학회논문지
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• 제13권6호
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• pp.211-220
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• 2019

인간의 감성은 인간관계 속에서 발현되는 선험적으로 주체하지 못하는 감정의 오류를 현명하게 절제할 수 있도록 도와주며, 합리적인 선택을 할 수 있도록 감정에 명령하기 때문에 나와 타인의 행복(幸福)에 기여하게 된다. Abraham은 하나밖에 없는 아들, 그것도 백 세가다되어 얻은 아들을 제물로 바치라는 신의 명령에 고민에 빠졌을 것이다. 이때 그의 이성은 과연 합리적이었을까? 이성적 사유로는 자신의 아들을 바치는 행위가 적합한 행위라고 사유할 수 있겠지만, 인간의 마음으로는 그것이 과연 가능할 것인가? 또한 Aristoteles는 인간을 위한 선(善)에 있어서 인간적인 덕에 대해 정신의 덕이라고 하였다. 행복(幸福)도 정신의 활동이기 때문에 우리는 정신에 대해 어느 정도 알아야 한다고 말하였다. 이 ψυχή(psyche, 영혼) 정신(精神)은 비이성적인 요소로 눈에 보이지 않지만 이성적 원리에 개입하는 어떤 작용이다. 또한 C. G. Jung은 모든 인간은 눈에 드러나지는 않지만 역동적인 네 가지 심리기능을 가지고 있으며, 마음이 움직이는 것은 이러한 4가지 기능적 차원에 의한다는 것이다. 이것은 감각(S, Sensing), 직관(N, Intuition), 사고(T, Thinking), 감정(F, Feeling)의 요소가 복합적으로 작용하고 있다는 것이다. 또한 David Hume은 도덕은 이성에서 유래될 수 없다고 단정하면서 공감의 원리를 역설하였으며, Max Ferdinand Scheler는 어떤 사람의 시각적 특징을 파악하기 전에 이미 그 사람에 대한 전체적인 느낌을 마음속에 포착해 대응 태세를 취하게 되며, 이 느낌 속에 주어지는 것이 바로 가치이며, 이러한 과정을 통하여 가치가 부여됨으로써 인식 대상으로 고양되고, 가치를 파악하는 감정의 작용은 언제나 이성보다 선행하여 일어난다고 하였다. Emmanuel Levinas는 지극히 감정적인 사랑의 감정은 이성에 앞서며, 감성이 인간의 이성적 사유와 합리성에 앞선다는 것은 감정의 통제 불능에서 우리는 통제가능성과 절제의 요구로서 이성적 사유와 합리적이고 현명한 실천이성을 요구하게 되기 때문이라고 언급하였다. 인간의 감성적인 교육의 일환으로 도덕윤리과 교육과정에서는 Bloom의 인지적 정의적 행동적영역의 통합적인 사고를 갖춘 존재로서 도덕적 실천행위를 하는 존재를 이상형으로 지향하고 있다. 어떻게 하면 덕스러운 행위에 대한 감정의 지향성을 따르는 행위를 할 수 있으며, 또 어떻게 하면 부덕한 행위에 대한 감정의 지양성을 함양할 수 있을 것인가에 초점이 맞춰져 있다. 이러한 문제해결의 방향성은 바로 '덕감(德感) 강화'의 원리와 '부덕감(不德感)제거'의 원리로 우리는 인간의 감성(感性)과 행복감(幸福感) 함양에 대한 가능성과 방향성을 설계할 수 있다.