• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.271-287
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• 2022

In this paper, starting with the geometric constants that can characterize Hilbert spaces, combined with the isosceles orthogonality of Banach spaces, the orthogonal geometric constant Ω_X(α) is defined, and some theorems on the geometric properties of Banach spaces are derived. Firstly, this paper reviews the research progress of orthogonal geometric constants in recent years. Then, this paper explores the basic properties of the new geometric constants and their relationship with conventional geometric constants, and deduces the identity of Ω_X(α) and γ_X(α). Finally, according to the identities, the relationship between these the new orthogonal geometric constant and the geometric properties of Banach Spaces (such as uniformly non-squareness, smoothness, convexity, normal structure, etc.) is studied, and some necessary and sufficient conditions are obtained.

• School Mathematics
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• v.13 no.1
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• pp.107-125
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• 2011

In this paper, we investigated how the GSP environments impact students' conjecturing of geometric properties. And we wanted to draw some implication in teaching and learning geometry in dynamic geometric environments. As results, we conclude that when students were given the problem situations which almost has no condition, they were not successful, and rather when the problem situations had appropriate conditions students were able to generate many conditions which were not given in the original problem situations, and consequently they were more successful in conjecturing geometric properties. And the geometric properties conjectured in GSP environments are more complex and difficult to prove than those in paper and pencil environments. Also the function of moving screen with 'Alt' key is frequently used in conjecturing geometric properties with functions of measurement and calculation of GSP. And students felt happier when they discovered geometric properties than when they could prove geometric properties.

• Structural Monitoring and Maintenance
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• v.9 no.2
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• pp.129-155
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• 2022

In this study, parametric analyses on a hoop-type PZT (lead-zirconate-titanate) interface are performed to estimate the effects of the PZT interface's materials and geometries on sensitivities of impedance responses under strand breakage. The paper provides a guideline for installing the PZT interface suitable in tendon anchorages for damage-sensitive impedance signatures. Firstly, the concept of the PZT interface-based impedance monitoring technique in prestressed tendon anchorage is briefly described. A FE (finite element) analysis is conducted on a multi-strands anchorage equipped with a hoop-type PZT interface for analyzing materials and geometric effects. Various material properties, geometric sizes of the interface, and PZT sensor are simulated under two states of prestressing force for acquiring impedance responses. Changes in impedance signals are statistically quantified to analyze the effect of these factors on damage-sensitive impedance monitoring in the tendon anchorage. Finally, experimental analyses are performed to demonstrate the effects of materials and geometrical properties of the PZT interface on damage-sensitive impedance monitoring.

• Korean Journal of Mathematics
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• v.21 no.3
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• pp.223-236
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• 2013

Schensted algorithm was first described in 1938 by Robinson [5], in a paper dealing with an attempt to prove the correctness of the Littlewood-Richardson rule. Schensted [9] rediscovered Schensted algorithm independently in 1961 and Viennot [12] gave a geometric interpretation for Schensted algorithm in 1977. In this paper we describe some properties of Schensted algorithm using Viennot's geometric interpretation.

• Journal of the Korean Data and Information Science Society
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• v.8 no.2
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• pp.135-141
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• 1997

In this paper, it is investigated the properties of the transformed geometric Poisson process when the intensity function of the process is a distribution of the continuous random variable. If the intensity function of the transformed geometric Poisson process is a Pareto distribution then the transformed geometric Poisson process is a strongly P-process.

• The Mathematical Education
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• v.47 no.4
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• pp.437-445
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• 2008

On the basis of the meaning and general process of geometric proof through transformation concept and understanding the geometric properties of linear transformation, this study showed that the centroid of geometrical figure and certain properties of a parabola and an ellipse in school mathematics can be explained as a conservative properties through linear transformation. From an educational perspective, this is a good example of showing the process of how several existing individual knowledge can be reorganized by a mathematical concept. Considering the fact that mathematical usefulness of linear transformation can be revealed through an invariable and conservation concept, further discussion is necessary on whether the linear transformation map included in the former curriculum have missed its point.

• East Asian mathematical journal
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• v.24 no.5
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• pp.527-545
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• 2008

One of the education purpose of the section "Figures" in the eighth grade is to develop students' deductive reasoning ability, which is basic and essential for living in a democratic society. However, most or middle school students feel much more difficulty or even frustration in the study of formal arguments for geometric situations than any other mathematical fields. It is owing to the big gap between inductive reasoning in elementary school education and deductive reasoning, which is not intuitive, in middle school education. Also, it is very burden for students to describe geometric statements exactly by using various appropriate symbols. Moreover, Usage of the same symbols for angle and angle measurement or segments and segments measurement makes students more confused. Since geometric relations is mainly determined by the measurements of geometric objects, students should be able to interpret the geometric properties to the algebraic properties, and vice verse. In this paper, we first compare and contrast inductive and deductive reasoning approaches to justify geometric facts and relations in school curricula. Convincing arguments are based on experiment and experience, then are developed from inductive reasoning to deductive proofs. We introduce teaching methods to help students's understanding for deductive reasoning in the textbook by using stepwise visualization materials. It is desirable that an effective proof instruction should be able to provide teaching methods and visual materials suitable for students' intellectual level and their own intuition.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.9 no.2
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• pp.119-124
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• 2000

In this paper based on geometric optics and geometric modeling aspheric surface of the side mirror mold with dead angle reduced have been designed and machined in a CNC machining center, Surface roughness of the mold was evaluat-ed by usin the surface shaping system. Surface generating simulation of a ball endmill process is investigated. Through the simulation based on the surface-shaping system 3-D engineered surfaces and properties of engineered surfaces are obtained, Computer simulation provides the effective working conditions through the prediction of geometric properties of engineered surfaces. The rear view mirror and room mirror play important role on the safe driving condition as a observation of environment but the rear view mirror can not provide complete information of driving environments due to the existence of the dead angle. The analysis on the shape of formed mirror shows that the proposed me？ improves range of a driver's sight.

• International Journal of Reliability and Applications
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• v.9 no.1
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• pp.31-52
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• 2008

In this paper generalized version of the geometric distribution is introduced. This distribution can be considered as a two-parameter generalization of the discrete geometric distribution. The main statistical and reliability properties of this distribution are discussed. Two methods of estimation, namely maximum likelihood method and the method of moments are used to estimate the parameters of this distribution. Simulation is utilized to calculate these estimates and to study some of their properties. Also, asymptotic confidence limits are established for the maximum likelihood estimates. Finally, the appropriateness of this new distribution for a set of real data, compared with the geometric distribution, is shown by using the likelihood ratio test and the Kolmogorove-Smirnove test.

• Journal of the Korea Computer Graphics Society
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• v.7 no.1
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• pp.19-25
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• 2001

In this paper, we study the special geometric reparametization of the (plane polynomial) Pythagorean Hodograph curves in the view point of their roots. The PH curves are completely determined by the roots of their hodographs. we show that the loci of roots of the PH curves satisfy some interesting geometric properties.