• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.277-284
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• 2004

An m-transversal to a family of convex sets in the plane is an m-point set which intersects every members of the family. One of Grubaum's conjectures says that a planar family of translates of a convex compact set has a 3-transversal provided that any two of its members intersect. Recently the conjecture has been proved affirmatively (see [4]). In the present paper we provide a different and straightforward proof for the conjecture for the family of translates of a closed trapezoid in the plane and give several concrete 3-transversals.

• Proceedings of the Korea Concrete Institute Conference
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• 1996.04a
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• pp.300-305
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• 1996

Reinforced concrete column is an effective structural element to take advantage of high strength concrete. This paper presents an experimental and analytical strength of high strength concrete rectangular tied column sections under eccentric loading. The test variables are concrete strength, steel ratios, slenderness and eccentricity. The analytical results of the ACI's rectangular stress block, Zia's modified rectangular stress block, and a trapezoid block are compared with experimentally obtained data. It may be concluded that the trapezoid stress block provided the most reasonable column section capacities for high strength concrete columns.

• Journal of Energy Engineering
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• v.13 no.1
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• pp.28-33
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• 2004

The objective of the study was to investigate the characteristics of heat transfer and flow in 2-dimensional impinging air jet system, in which trapezoid rods have been set up in front of impinging plate in order to increase heat transfer. Experiments were carried out first using without the rods to establish the baseline heat transfer performance. And this result compared with the experimentation with rods. When rods are installed in front of the impinging plate, the acceleration of the flow and the eddies due to the rods seem to contribute to the heat transfer enhancement. Heat transfer performance was best under the condition of C=1 n and as the pitch is 30 mm. In this case, maximum rate of heat transfer augmentation is about 1.62 times greater compared to that without trapezoid rods.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.253-267
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• 2013

The newly revised mathematics curriculum of 2007 speaks of ultimate goal to develop ability to think and communicate mathematically, in order to develop ability to rationally deal with problems arising from the life around, which puts emphasize on mathematical communication. In this study, analysis on mathematical communication and analogical thinking process of group of students with similar level of academic achievement and that with different level, and thus analyzed if such communication has affected analogical thinking process in any way. This study contains following subjects: 1. Forms of mathematical communication took placed at the two groups based on achievement level were analyzed. 2. Analogical thinking process was observed through trapezoid's area obtaining activity and analyzed if communication within groups has affected such process anyhow. A framework to analyze analogical thinking process was developed with reference of problem solving procedure based on analogy, suggested by Rattermann(1997). 15 from 24 students of year 5 form of N elementary school at Gunpo Uiwang, Syeonggi-do, were selected and 3 groups (group A, B and C) of students sharing the same achievement level and 2 groups (group D and E) of different level were made. The students were led to obtain areas of parallelogram and trapezoid for twice, and communication process and analogical thinking process was observed, recorded and analyzed. The results of this study are as follow: 1. The more significant mathematical communication was observed at groups sharing medium and low level of achievement than other groups. 2. Despite of individual and group differences, there is overall improvement in students' analogical thinking: activities of obtaining areas of parallelogram and trapezoid showed that discussion within subgroups could induce analogical thinking thus expand students' analogical thinking stage.

• Transactions of Materials Processing
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• v.8 no.1
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• pp.14-21
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• 1999

Trapezoid cups and square ones have been deep-drawn to 45mm in depth. Displacements and strains have been analysed by FEM and experiment. Strains and effective strains in the corner flanges of trapezoid cups have been compared with those in square cups. The results have shown that because of shear strains on the corner flange, it is necessary to adopt effective strain for comparing strains, mean vale of effective strains in the corner flange with a corner angle of 72 degrees is narly equal to those with a corner angle of a right angle and mean value of effective strains with a corner angle of 102 degrees is smaller than those with a corner angle of a right angle.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.978-981
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• 2005

In order to manufacture a doubly curved sheet metal effectively, a flexible incremental roll forming process has been developed by adopting the advantages of the incremental forming process and the roll forming process by combining inherent flexibility of the incremental forming process and continuous deformation of the roll forming process. The forming method has been further enhanced to form general quadrilateral blanks (including a square, a rectangle, a symmetrical trapezoid and an asymmetrical trapezoid, etc.) into doubly curved shapes by controlling the forming paths developed by various experiments.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.165-167
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• 2003

To evaluate the thermal and water stress of vegetation canopy in Southern Qu$\'{e}$bec, leaf water status was evaluated from vegetation indices derived from SPOT VEGETATION images and surface temperature from NOAA AVHRR images. This study was conducted by investigating vegetation conditions for two different periods, from June to August, 1999 and 2000. The vegetation indices were integrated for the evaluating vegetation conditions as a new index, normalized moisture index (NMI). A trapezoid was defined by the NMI and surface temperature, and the thermal and water status of the vegetation canopy was determined according to separate small sections within the trapezoid.

• Structural Engineering and Mechanics
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• v.28 no.5
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• pp.587-601
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• 2008

In this study, a numerical procedure based on the finite element method for materially and geometrically nonlinear analysis of reinforced and prestressed concrete slender columns with arbitrary section subjected to combined biaxial bending and axial load is developed. In order to overcome the low computer efficiency of the conventional section integration method in which the reinforced concrete section is divided into a large number of small areas, an efficient section integration method is used to determine the section tangent stiffness. In this method, the arbitrary shaped cross section is divided into several concrete trapezoids according to boundary vertices, and the contribution of each trapezoid to section stiffness is determined by integrating directly the trapezoid. The space frame flexural theory is utilized to derive the element tangent stiffness matrix. The nonlinear full-range member response is traced by an updated normal plane arc-length solution method. The analytical results agree well with the experimental ones.

• Food Science and Preservation
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• v.7 no.2
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• pp.166-170
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• 2000

In order to improve cut-flower export packaging on the distribution process, newly developed T-type(trapezoid type) container was tested and evaluated on the viewpoints of the protection, workability, and economics. T-type container performed better in protection and workability comparing to 0201 and modified 0201 type containers. Especially, load efficiency of T-type container was 33 percent higher than others, indicating that total distribution costs from Korea to Japan can be saved up to 1.7million dollars per year. T-type container is also advantageous because of its superior display performance and environmentally friendly design. We recommend that T-type container is suitable for most of cut-flowers which are usually horizontally packed such as roses, chrysanthemums, and lilies.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.791-815
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• 2014

We show amongst other that if $f,g:[a,b]{\rightarrow}\mathbb{C}$ are two functions of bounded variation and such that the Riemann-Stieltjes integral $\int_a^bf(t)dg(t)$ exists, then for any continuous functions $h:[a,b]{\rightarrow}\mathbb{C}$, the Riemann-Stieltjes integral $\int_{a}^{b}h(t)d(f(t)g(t))$ exists and $${\int}_a^bh(t)d(f(t)g(t))={\int}_a^bh(t)f(t)d(g(t))+{\int}_a^bh(t)g(t)d(f(t))$$. Using this identity we then provide sharp upper bounds for the quantity $$\|\int_a^bh(t)d(f(t)g(t))\|$$ and apply them for trapezoid and Ostrowski type inequalities. Some applications for continuous functions of selfadjoint operators on complex Hilbert spaces are given as well.