• Journal of applied mathematics & informatics
• /
• 제24권1_2호
• /
• pp.141-154
• /
• 2007

The connectivity problem is a fundamental problem in graph theory. The best known algorithm to solve the connectivity problem on general graphs with n vertices and m edges takes $O(K(G)mn^{1.5})$ time, where K(G) is the vertex connectivity of G. In this paper, an efficient algorithm is designed to solve vertex connectivity problem, which takes $O(n^2)$ time and O(n) space for a trapezoid graph.

• Journal of applied mathematics & informatics
• /
• 제9권1호
• /
• pp.45-60
• /
• 2002

Some error estimates in terms of the p-norms of the fourth derivative for the remainder in a perturbed trapezoid formula are given. Applications for the expectation of a random variable and the Hermite-Hadamard divergence in Information Theory are also pointed out.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제45권2호
• /
• pp.177-189
• /
• 2006

This study focuses on the analysis of prospective elementary teachers' representation of trapezoid area and teacher educator's reflecting in the context of a mathematics course. In this study, I use my own teaching and classroom of prospective elementary teachers as the site for investigation. 1 examine the ways in which my own pedagogical content knowledge as a teacher educator influence and influenced by my work with students. Data for the study is provided by audiotape of class proceeding. Episode describes the ways in which the mathematics was presented with respect to the development and use of representation, and centers around trapezoid area. The episode deals with my gaining a deeper understanding of different types of representations-symbolic, visual, and language. In conclusion, I present two major finding of this study. First, Each representation influences mutually. Prospective elementary teachers reasoned visual representation from symbolic and language. And converse is true. Second, Teacher educator should be prepared proper mathematical language through teaching and learning with his students.

• East Asian mathematical journal
• /
• 제31권2호
• /
• pp.167-188
• /
• 2015

Formula for the area of a trapezoid is an educational material that can handle algebraic and geometric perspectives simultaneously. In this note, we will make up the expression equivalent algebraically to the formula for the area of a trapezoid, and deal with the conversion of a geometric point of view, in algebraic terms of translating and interpreting the expression geometrically. As a result, the geometric conversion model, the first algebraic model, the second algebraic model are obtained. Therefore, this problem is a good material to understand the advantages and disadvantages of the algebraic and geometric perspectives and to improve the mathematical insight through complementary activity. In addition, these activities can be used as material for enrichment and gifted education, because it helps cultivate a rich perspective on diverse and creative thinking and mathematical concepts.

• 대한치과의사협회지
• /
• 제54권7호
• /
• pp.529-540
• /
• 2016

Objective: The objective of this study was to evaluate the osseointegration of narrow-diameter implant with trapezoid-shape and to evaluate the effect of coronal microthreads on trapezoid-shape narrow-diameter implant. Materials and Methods: The experimental narrow-diameter implants were classified into two groups according to absence or presence of coronal microthreads: trapezoid-shape narrow diameter implant (TN group) and trapezoid-shape narrow-diameter implant with microthreads (TNM group). They were installed alternately in bilateral mandible in three dogs. After 8 weeks, the animals were sacrificed. Resonance frequency analysis, removal torque test, and histometric analysis were performed. Results: Statistically higher implant stability quotient (ISQ) values were observed in TNM group than in TN group at the time of implant installation. However, significant ISQ values difference was not observed between groups at 8 weeks. Both groups showed significantly increased ISQ values at 8 weeks, compared to the time of implant installation. There was no significant difference between groups in removal torque test. Bone-implant contact ratio also showed no significant difference between groups in total and coronal part. Conclusion: Within the limitation of this study, it could be concluded that the trapezoid-shape design on narrow-diameter implant showed successful ossointegration, and the microthreads on coronal part did not result in significant bone-implant contact and biomechanical stability at 8 weeks.

• Journal of applied mathematics & informatics
• /
• 제32권5_6호
• /
• pp.635-647
• /
• 2014

In this paper, a generalized perturbed midpoint rule is established. Various error bounds for this generalization are also obtained.

• 대한수학교육학회지:수학교육학연구
• /
• 제8권2호
• /
• pp.565-586
• /
• 1998

Like many other school subjects, terminology is a starting point of mathematical thinking, and plays a key role in mathematics learning. Among several areas in mathematics, geometry is the area in which students usually have the difficulty of learning, and the new terms are frequently appeared. This is why we started to investigate geometric terms first. The purpose of this study is to investigate geometric terminology in school mathematics. To do this, we traced the historical transition of geometric terminology from the first revised mathematics curriculum to the 7th revised one, and compared the geometric terminology of korean, english, Japanese, and North Korean. Based on this investigation, we could find and structuralize the following four issues. The first issue is that there are two different perspectives regarding the definitions of geometric terminology: inclusion perspective and partition perspective. For example, a trapezoid is usually defined in terms of inclusion perspective in asian countries while the definition of trapezoid in western countries are mostly based on partition perspective. This is also the case of the relation of congruent figures and similar figures. The second issue is that sometimes there are discrepancies between the definitions of geometric figures and what the name of geometric figures itself implies. For instance, a isosceles trapezoid itself means the trapezoid with congruent legs, however the definition of isosceles trapezoid is the trapezoid with two congruent angles. Thus the definition of the geometric figure and what the term of the geometric figure itself implies are not consistent. We also found this kind of discrepancy in triangle. The third issue is that geometric terms which borrow the name of things are not desirable. For example, Ma-Rum-Mo(rhombus) in Korean borrows the name from plants, and Sa-Da-Ri-Gol(trapezoid) in Korean implies the figure which resembles ladder. These terms have the chance of causing students' misconception. The fourth issue is that whether we should Koreanize geometric terminology or use Chinese expression. In fact, many geometric terms are made of Chinese characters. It's very hard for students to perceive the ideas existing in terms which are made of chines characters. In this sense, it is necessary to Koreanize geometric terms. However, Koreanized terms always work. Therefore, we should find the optimal point between Chines expression and Korean expression. In conclusion, when we name geometric figures, we should consider the ideas behind geometric figures. The names of geometric figures which can reveal the key ideas related to those geometric figures are the most desirable terms.

• Steel and Composite Structures
• /
• 제51권6호
• /
• pp.587-600
• /
• 2024

In order to investigate the seismic performance of regionally confined concrete circular column with trapezoid stirrups (TRCCC) under high axial compression ratio, the confinement mechanism of regionally confined concrete was analyzed. Three regionally confined concrete circular columns with trapezoid stirrups were designed, and low cyclic loading tests were conducted at three different axial compression ratios (0.9, 1.1, 1.25) to study the failure mode, hysteresis curve, skeleton curve, deformation capacity, stiffness degradation and energy dissipation capacity of the specimens. The results indicate that the form of regional confinement concrete provides more uniform confinement to the normal confinement, and the confinement efficiency at the edges is 1.4 times that of normal confined concrete. The ductility coefficients of the specimens were all greater than 3 under high axial compression ratios, and the stiffness and horizontal bearing capacity increased with the increase of axial compression ratio. Therefore, it is recommended that the code of design specifications can appropriately relax the axial compression ratio limit for TRCCC. Finally, the spacing between stirrups of TRCCC was analyzed using ABAQUS software. The results showed that as the spacing between the stirrups decreased, the cracking load and peak load of TRCCC increased continuously, but the rate of increase decreases.

• Wind and Structures
• /
• 제19권1호
• /
• pp.75-88
• /
• 2014

The computational fluid dynamic is used to explore new aspects of the hill flow. This analysis focuses on flow dependency and the comparison of results from measurements and simulations to show an optimization turbulent model and the possibility of replacing measurements with simulations. The first half of the paper investigates a suitable turbulence model for determining a suitable site for a wind turbine. Results of the standard k-${\varepsilon}$ model are compared precisely with the measurements taken in front of the hilltop, The Reynolds Stress Model showed exact results after 1.0 times of hill steepness but the standard k-${\varepsilon}$ model and standard k-${\omega}$ model showed greater underestimation. In addition, velocity flow over Pha Taem hill topography and the reference geometry shape were compared to find a suitable site for a turbine in case the actual hill structure was associated with the trapezoid geometric shape. Further study of geometry shaped hills and suitable sites for wind turbines will be reported elsewhere.

• Journal of applied mathematics & informatics
• /
• 제12권1_2호
• /
• pp.21-29
• /
• 2003

Let G be a graph with n vertices and n edges. The problem of constructing a spanning tree is to find a connected subgraph of G with n vertices and n -1 edges. In this paper, we propose an O(log n) time parallel algorithm with O(n/ log n) processors on an EREW PRAM for constructing a spanning tree on trapezoid graphs.