• The Mathematical Education
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• v.47 no.4
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• pp.447-465
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• 2008

The purpose of this study is to suggest effective teaching methods on the concept of infinity for students to obtain the right concept in the middle school curriculum. Many people have thought that infinity is something vouge and unapproachable. But, nowadays it is rather something with a precise definition that lies at the core of modern mathematics. To understand mathematics and science very well, it is necessary to comprehend the concept of infinity. But students tend to figure out the properties of infinite objects and limit concepts only through their experience closely related to finite process, and so they are apt to have their spontaneous intuition and misconception about it. Since most of them have cognitive obstacles in studying the infinite concepts and misconception, mathematics teachers need to help them overcome the obstacles and establish the right secondary intuition for the concepts through good examples and appropriate explanation. In this study, we consider the developing process of the concept of infinity in human history and give some comments and suggestions in teaching methods relative to that concept with new suitable examples.

• Journal for History of Mathematics
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• v.31 no.2
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• pp.73-91
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• 2018

This study begins with the awareness of problem that the education of mathematics teachers has failed to link the limit and the infinite set conceptually. Thus, this study analyzes the historical and reciprocal development of the limit and the infinite set, and discusses how to improve the education of these concepts and their relation based on the outcome of this analysis. The results of the study confirm that the infinite set is the historical tool of linking the limit and the real numbers. Also, the result shows that the premise of 'the component of the straight line is a point.' had the fundamental role in the construction of the real numbers as an arithmetical continuum and that the moral certainty of this premise would be obtained through a thought experiment using an infinite set. Based on these findings, several proposals have been made regarding the teacher education of awakening someone to the fact that 'the theoretical foundation of the limit is the real numbers, and it is required to introduce an infinite set for dealing with the real numbers.' in this study. In particular, by presenting one method of constructing the real numbers as an arithmetical continuum based on a thought experiment about the component of the straight line, this study opens up the possibility of an education that could get the limit values psychologically connected to the infinite set in overcoming the epistemological obstacle related to the continuum concept.

• Geomechanics and Engineering
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• v.31 no.2
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• pp.223-235
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• 2022

Bearing capacity of shallow foundations is often determined for either dry or saturated soils. In some occasions, foundations may be subjected to external loading which is inclined and/or eccentric. In this study, the ultimate bearing capacity of shallow foundations resting on partially saturated coarse-grained cohesionless and fine-grained cohesive soils subjected to a wide range of combined vertical (V) - horizontal (H) - moment (M) loadings is rigorously evaluated using the well-established limit equilibrium method. The unified effective stress approach as well as the suction stress concept is effectively adopted so as to simulate the behaviour of the underlying unsaturated soil medium. In order to obtain the bearing capacity, four equilibrium equations are solved by adopting Coulomb failure mechanism and Bishop effective stress concept and also considering a linear variation of the induced matric suction beneath the foundation. The general failure loci of the shallow foundations resting on unsaturated soils at different hydraulic conditions are presented in V - H - M spaces. The results indicate that the matric suction has a marked influence on the bearing capacity of shallow foundations. In addition, the effect of induced suction on the ultimate bearing capacity of obliquely-loaded foundations is more pronounced than that of the eccentrically-loaded footings.

• School Mathematics
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• v.14 no.4
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• pp.409-429
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• 2012

This paper reports the process two 11th grade students went through in reinventing derivatives on their own via a context problem involving the concept of velocity. In the reinvention process, one of the students conceived a tangent line as the limit of a secant line, and then the other student explained to a peer that the slope of a tangent line was the geometric mean of derivative. The students also used technology to concentrate on essential thinking to search for mathematical concepts and help visually understand them. The purpose of this study was to provide meaningful implications to school practices by describing students' process of reinvention of derivatives. This study revealed certain characteristics of the students' reinvention process of derivatives and changes in the students' thinking process.

• Earthquakes and Structures
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• v.8 no.3
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• pp.591-617
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• 2015

Standards for seismic assessment and retrofitting of buildings provide deformation limit states for structural members and connections. However, in order to perform fully consistent performance-based seismic analyses of soil-structure systems; deformation limit states must also be available for foundations that are vulnerable to nonlinear actions. Because such limit states have never been established in the past, a laboratory testing program was conducted to study the rotational capacity of small-scale foundation models under combined axial load and moment. Fourteen displacement-controlled monotonic and cyclic tests were performed using a cohesionless soil contained in a $2.0{\times}2.0{\times}1.2m$ container box. It was found that the foundation models exhibited a stable hysteretic behavior for imposed rotations exceeding 0.06 rad and that the measured foundation moment capacity complied well with Meyerhof's equivalent width concept. Simplified code-based soil-structure analyses of an 8-story building under an array of strong ground motions were also conducted to preliminary evaluate the implication of finite rotational capacity of vulnerable foundations. It was found that for the same soil as that of the experimental program foundations would have a deformation capacity that far exceeds the imposed rotational demands under the lateral load resisting members so yielding of the soil may constitute a reliable source of energy dissipation for the system.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1993.10a
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• pp.248-255
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• 1993

Recently, due to the increasing attention to the structural safety under uncertain environments, many researches on the structural reliability analysis have been peformed. Some useful methods are available to evaluate performance reliability of structures with explicit limit states. However, for large structures, in which structural behaviors can be analyzed with finite element models and the limit states are only expressed implicitly, Monte-Carlo simulation method has been mainly used. However, Monte-Carlo simulation method spends too much computational time on repetitive structural analysis. Many alternative methods are suggested to reduce the computational work required in Monte-Carlo simulation. Response surface method is widely used to improve the efficiency of structural reliability analysis. Response surface method is based on the concept of approximating simple polynomial function of basic random variables for the limit state which is not easily expressed in explicit forms of design random variables. The response surface method has simple algorithm. However, the accuracy of results highly depends on how properly the stochastic characteristics of the original limit state has been represented by approximated function, In this study, an improved response surface method is proposed in which the sampling points for creating response surface are modified to represent the failure surface more adequately and the combined use of a linear response surface function and Rackwitz-Fiessler method has been employed. The method is found to be more effective and efficient than previous response surface methods. In addition more consistent convergence is achieved, Accuracy of the proposed method has been investigated through example.

• Journal of the Korean Geosynthetics Society
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• v.6 no.4
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• pp.1-6
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• 2007

New procedure for evaluation of creep reduction factor by the limit creep strain concept was introduced through the analysis of creep test results. To determine the limit creep strain of the geogrids, the Sherby-Dorm Plots were applied and the results of this procedure were compared and interpreted, respectively. From this, it is seen that the creep reduction factors were 1.45 for the geogrid samples used in this study. Through the comparison of creep reduction factors in 10% creep strain criteria, it was confirmed that the range of creep reduction factor is about 0.06~0.14 for the geogrid samples in this study.

• International Journal of Naval Architecture and Ocean Engineering
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• v.8 no.6
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• pp.577-588
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• 2016

Due to the uncertainties related to the flaw assessment parameters, such as flaw size, fracture toughness, loading spectrum and so on, the probability concept is preferred over deterministic one in flaw assessment. In this study, efforts have been made to develop the reliability based flaw assessment procedure which combines the flaw assessment procedure of BS7910 and first-and second-order reliability methods (FORM/SORM). Both crack length and depth of semi-elliptical surface crack at weld toe were handled as random variable whose probability distribution was defined as Gaussian with certain means and standard deviations. Then the limit state functions from static rupture and fatigue perspective were estimated using FORM and SORM in joint probability space of crack depth and length. The validity of predicted limit state functions were checked by comparing it with those obtained by Monte Carlo simulation. It was confirmed that the developed methodology worked perfectly in predicting the limit state functions without time-consuming Monte Carlo simulation.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.04a
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• pp.88-96
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• 1995

Seismic design provisions in Korea has developed based on seismic provisions in United States (e.g., ATC 3-06). Current seismic design provisions in U .S. is moving toward adopting enhanced concept for design. Federal Emergence Management Agency (FEMA) Provides the NEHRP recommended Provisions for the Development of Seismic Regulations for New Buildings which can be used as a source document for use by any interested members of the building community. Current seismic design provisions in U .S. generally use a uni-level force. These provisions can not be satisfied if the limit state design is concerned. Limit state can be defined as a state causing undesirable performance o( a structure (e .g., serviceability, ultimate, buckling, etc.). Even if there are provision for controlling drift by two levels, it is still difficult to satisfy limit states using uni-level force. Architectural Institute of Japan (AIJ) uses a hi-level forces Int seismic loadings which can satisfy serviceability and ultimate limit state. However, the seismic parameters used in AIJ guideline are basically determined by subjective manner of code committee member and professions. These parameters need to be determined based on target quantities (target reliability, target energy dissipation, target displacement, target stress level, etc.). This study develops the method to determine the sesmic design parameters based on a certain taget level. Reliability is used as a target level and load factors in ANSI/ASCE 7-88 are selected as design parameters to be determined.

• The Korean Society of Law and Medicine
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• v.11 no.2
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• pp.75-112
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• 2010

This article analyses the concept of medicine in the legal context. It is not easy to define the concept of medicine because medical practice has various dimensions and the situation in which the practice is performed has a broad variety. The duty of medical law is to build the boundary of protection in that the nature of medicine would not be distorted by the factors of social systems like industry or governmental authorities. Without understanding the various dimensions - especially the dimension of Humanities and Sociology - of the medicine it is not possible to draw the limit on the performance of medicine appropriately. Concerning the medical practice (especially in the context of the regulation of medical licence), the enacted law (Medical Act) defines the concept just for form's sake and it finally depends on the interpretation of the legal enforcement authorities. Moreover, between the judgments of the courts there exists no coherent principles for the regulation and the interpretation of the Medical Act depends often on the riskiness, the abstract concept, which finally leads the interpretation to depend on the subject of the practice. On the contrary, the development and scientific movement of the technology tends to tighten the range of the medical professionals of medical practice and the perspectives of the medicine. Medical act is actually oriented at the patient's understanding of him- or herself. The above-mentioned tendency of the interpretation and the legal policy could lead the medicine away from its nature.