• Honam Mathematical Journal
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• v.45 no.1
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• pp.160-183
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• 2023

In the present paper, we prove that our main inequality reduces to some trapezoid and Newton type inequalities for differentiable s-convex functions. These inequalities are established by using the well-known Riemann-Liouville fractional integrals. With the help of special cases of our main results, we also present some new and previously obtained trapezoid and Newton type inequalities.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.633-639
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• 2004

In this paper using integral representations for n-time differentiable mappings, we establish new generalizations of certain Ostrowski and Trapezoid type inequalities by using fairly elementary analysis.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.67-84
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• 2003

A quadrature rule for the finite Hilbert Trasnform via trapezoid type inequalities is obtained . Some numerical experiments for different divisions of the interval [a, b] are also presented.

• Journal of Ocean Engineering and Technology
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• v.15 no.1
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• pp.7-11
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• 2001

In this paper, trapezoid sections and prominence sections were examined to improve the performance of floating breakwater in long waves. The linear potential theory is used and the boundary element method with a matching boundary is employed for numerical computation. The effects of the side slope of the trapezoid section and the geometry ratio of the prominence section on the floating breakwater were examined. It was found that trapezoid sections show lower transmission coefficients than the rectangular sections in the long wave range. In prominence sections the size of the sides are more important than the size of the top. Proper choices of the pontoon type geometry may move the local minimum point of the wave transmission coefficient toward the longer wave ranges and improve the performance of the floating breakwater in the long wave range for a given wave period.

• 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.

• Education of Primary School Mathematics
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• v.24 no.4
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• pp.247-264
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• 2021

The area of a trapezoid is an important concept to develop mathematical thinking and competency, but many students tend to understand the formula for the area of a trapezoid instrumentally. A clue to solving these problems could be found in Dienes' theory of learning mathematics and Watson and Mason' concept of example spaces. The purpose of this study is to obtain implications for the teaching and learning of the area of the trapezoid. This study analyzed the example spaces constructed by students in learning the area of a trapezoid based on Dienes' theory of learning mathematics. As a result of the analysis, the example spaces for each stage of math learning constructed by the students were a trapezoidal variation example spaces in the play stage, a common representation example spaces in the comparison-representation stage, and a trapezoidal area formula example spaces in the symbolization-formalization stage. The type, generation, extent, and relevance of examples constituting example spaces were analyzed, and the structure of the example spaces was presented as a map. This study also analyzed general examples, special examples, conventional examples of example spaces, and discussed how to utilize examples and example spaces in teaching and learning the area of a trapezoid. Through this study, it was found that it is appropriate to apply Dienes' theory of learning mathematics to learning the are of a trapezoid, and this study can be a model for learning the area of the trapezoid.

• Fashion & Textile Research Journal
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• v.21 no.5
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• pp.677-686
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• 2019

This study helps out-size consumers purchase ready-made clothes and improve fitness by classifying the lower bodies of abdomen-obese adult males in their 20s and older; in addition, it creates a size system based on each size interval of obesity type. The criteria for the 559 male subjects surveyed in this study were over $25kg/m^2$ of BMI, over 90 cm of waist, and over 0.85 waist hip ratio. The results are as follows. First, the higher the age group, the higher the degree of abdominal obesity in each age group. The degree of obesity then decreases somewhat as their age increases; however, the risk of abdominal obesity also increases. Second, 3 clusters were categorized by cluster analysis, into abdominal obesity, larger oval-type, trapezoid-type and small cylinder-type. Third, the size system establishment according to lower-body types resulted in basic body sizes and reference body sizes being different according to types even in commonly-appeared size names in the sections of respective types. The above research findings show it is necessary to understand obesity types according to waist and hip sizes that represent basic sizes and to design patterns in consideration of the characteristics of obese body shapes when lower-half body clothes are designed among obesity groups.

• Fashion & Textile Research Journal
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• v.25 no.5
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• pp.615-625
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• 2023

This study aimed to analyze the characteristics of the lower-body shape of middle-aged males with abdominal obesity by type and consider dimensional distribution to present a suit-pants size. The criteria were having a waist circumference greater than 90 cm and a waist-to-hip ratio(WHR) greater than 0.90; a total of 566 middle-aged males were surveyed. The findings revealed that, first, compared to standard lower-body types, the average body size of abdomenobese middle-aged males was significantly larger, especially in the horizontal area than in the vertical ares. Second, through a cluster analysis, a total of three categories of abdominal obesity were defined: small oval, large cylinder, and trapezoid type. The coverage rates of each type were 93.8%, 75.9%, and 93.0%, respectively. Finally, the suit-pants size system established according to lower-body types indicated the basic body size and reference body size were different for each type and also for the KS K 0050 male adult's garments size system. According to the definition of abdominal obesity, the types of abdominal obesity and the dimensions of each area are different, even if they belong to the same obesity group, suggesting that it is necessary to develop a pattern based on the analysis of obesity types.

• Fashion & Textile Research Journal
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• v.14 no.2
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• pp.269-276
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• 2012

The aim of this study is to develop clothing size system according to each size interval for obese girls aged 10~12 by classifying the upper bodies. The criteria for subjects in this study were girls who had over 1.46 of the R$\ddot{o}$hrer Index. A total of 229 schoolgirls who met these criteria were enrolled. Results are as follows; 1st, 5 factors were extracted by factor analysis and 3 clusters were categorized by cluster analysis, cylinder-type, inverted triangle-type and inverted trapezoid-type. And 2nd, as a consequence of size system establishment, the basic body sizes and reference body sizes were different according to types even in commonly-appeared size names at sections of respective types. The research findings above suggest that it is necessary to figure out the obesity types according to height and bust girth sizes representing basic sizes and to design the patterns in consideration of the characteristics of obese body shapes. And it may be used as a basic data to decide the desirable output of production according to respective body types.

• Journal of the Korean Society of Clothing and Textiles
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• v.28 no.3_4
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• pp.499-508
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• 2004

The purpose of this research is to define body characteristics of middle-aged men at ages between 35 and 55 whose physical changes are very prominent, by comparing the measurement data collected from this age group. This research also classifies different body types, and provides basic data for designing slacks' original forms according to each body type. Based on factor analysis of the measured data, seven key factors are grouped. And five different body types are classified based on the cluster analysis using factor marks. Type 1 refers to those who are tall and standard. This body type is characterized by trapezoid body shape when looked from the front, and slim abdomen when looked from the side. Type 2 refers to short and a little fat body shapes, with trapezoid front and protruding hip and abdomen. Type 3 refers to tall and fat body shapes, with rectangular front, protruding abdomen, and slim hip. Type 4 refers to those who are of medium height and a little obese, with rectangular front and protruding abdomen and hip. Type 5 refers to short and obese body shapes, with rectangular front, slim abdomen, and protruding hip. 12 items are available to judge middle-aged men's low body types and the hit ratio is 90%.