• The Korean Journal of Applied Statistics
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• v.24 no.4
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• pp.721-733
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• 2011

We consider the state price densities that are implicit in financial asset prices. In the pricing of an option, the state price density is proportional to the second derivative of the option pricing function and this relationship together with no arbitrage principle imposes restrictions on the pricing function such as monotonicity and convexity. Since the state price density is a proper density function and most of the shape constraints are caused by this, we propose to estimate the state price density directly by specifying candidate densities in a flexible nonparametric way and applying methods of regularization under extra constraints. The problem is easy to solve and the resulting state price density estimates satisfy all the restrictions required by economic theory.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.19 no.2
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• pp.288-294
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• 2010

In recent years, wind energy has been the world's fastest growing source of energy. This paper describes the structural design and analysis of composite blade for 2 kW-level HAWT (horizontal axis wind turbine). The aerodynamic design and force, which are required to design and analyze a composite blade structurally, are calculated through BEMT(blade element momentum theory) implemented in public code PROPID. To obtain the equivalent material properties of filament wound composite blades, the rule-of-mixture is applied using the basic material properties of fiber and matrix, respectively. Lay-up sequence, ply thickness and ply angle are designed to satisfy the loading conditions. Structural analysis by using commercial software ABAQUS is performed to compute the displacement and strength ratio of filament wound composite blades.

• YAKHAK HOEJI
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• v.21 no.2
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• pp.95-100
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• 1977

The effects of the particle size on the homogeneity of mixing and segregation of caffeine-lactose (1:99) mixture were studied. Using the two kinds of caffein, milled and unmilled caffein, V-type blender, the degree of mixing according to the particle size was predicted and the experiment on the change of mixedness by mixing time was carried out by the method derived from mixing index theory by Poole et al. and Hersey. the results could be summarized as follows; (1) The homogeneity of mixing was greatly affected by the particle size and the particle size should be reduced to the adepuate level to attain the desirable mixedness. (2) The homogeneity was not proportional to the mixing time and optimum mixing time for caffein-lactose was about 10 minutes. (3) Segregation tendency was increased by the particle size increase and greatly affected by the flow time in the segregation cell.

• The Korean Journal of Applied Statistics
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• v.3 no.2
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• pp.27-37
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• 1990

We consider the statistical control problem for the mixture model in which one can choose the values of independent variables that produce the values of the dependent variables as close to the target values as possible. The theory suggested for the problem is reviewed and an extended model with respect to the assumption of variance and the number of dependent variables is suggested. A Basyesian treatment is studied for the above problem with example as an illustration.

• Bulletin of the Korean Chemical Society
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• v.14 no.1
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• pp.34-34
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• 1993

The gelation phenomena of N-methylolated PAAm (M-PAAm) in aqueous media was studied. The critical gelation concentration (CGC) was very close to the calculated $C^*$ of the scaling theory. But the CGC of lower MW M-PAAm deviated from $C^*$ due to contamination of small molecules. We propose that the CGC is the close packing configuration of polymer molecules in solution. The experimental results of the gelation of M-PAAm/PAAm mixture proved that the close packing configuration is essential to make a gel. We calculated the minimum quantity of M-PAAm to make M-PAAm/PAAm mixture a gel by using the close packing configuration. We used a lattice model.

• Research in Mathematical Education
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• v.27 no.1
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• pp.129-150
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• 2024

This study utilized South Korean elementary and middle school student data to examine the longitudinal change trajectories of learning motivation types according to the longitudinal change trajectories of mathematics academic achievement. Growth mixture modeling, latent growth model, and multiple indicator latent growth model were used to examine various change trajectories for longitudinal data. As a result of the analysis, it was classified into 4 subgroups with similar longitudinal change trajectories of mathematics academic achievement, and the characteristics of the mathematics subject, which emphasize systematicity, appeared. Furthermore, higher mathematics academic achievement was associated with higher self-determination and higher academic motivation. And as the grade level increases, amotivation increases and self-determination decreases. This study suggests that teaching and learning support using this is necessary because the level of learning motivation according to self-determination is different depending on the level of mathematics academic achievement reflecting the characteristics of the student.

• Structural Engineering and Mechanics
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• v.48 no.4
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• pp.547-567
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• 2013

Nonlinear behavior of functionally graded material (FGM) plates under thermal loads is investigated here using an efficient sinusoidal shear deformation theory. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the sinusoidal distribution of transverse shear stress through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. Unlike the conventional sinusoidal shear deformation theory, the proposed efficient sinusoidal shear deformation theory contains only four unknowns. The material is graded in the thickness direction and a simple power law based on the rule of mixture is used to estimate the effective material properties. The neutral surface position for such FGM plates is determined and the sinusoidal shear deformation theory based on exact neutral surface position is employed here. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The non-linear strain-displacement relations are also taken into consideration. The thermal loads are assumed as uniform, linear and non-linear temperature rises across the thickness direction. Closed-form solutions are presented to calculate the critical buckling temperature, which are useful for engineers in design. Numerical results are presented for the present efficient sinusoidal shear deformation theory, demonstrating its importance and accuracy in comparison to other theories.

• Computers and Concrete
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• v.25 no.1
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• pp.37-57
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• 2020

This work investigates a new type of quasi-3D hyperbolic shear deformation theory is proposed in this study to discuss the statics and free vibration of functionally graded porous plates resting on elastic foundations. Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction. By including indeterminate integral variables, the number of unknowns and governing equations of the present theory is reduced, and therefore, it is easy to use. The present approach to plate theory takes into account both transverse shear and normal deformations and satisfies the boundary conditions of zero tensile stress on the plate surfaces. The equations of motion are derived from the Hamilton principle. Analytical solutions are obtained for a simply supported plate. Contrary to any other theory, the number of unknown functions involved in the displacement field is only five, as compared to six or more in the case of other shear and normal deformation theories. A comparison with the corresponding results is made to verify the accuracy and efficiency of the present theory. The influences of the porosity parameter, power-law index, aspect ratio, thickness ratio and the foundation parameters on bending and vibration of porous FG plate.

• Journal of Korean Society of Steel Construction
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• v.14 no.1
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• pp.105-111
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• 2002

A post-tensioned slab bridge is analyzed by the specially orthotropic laminates theory. Both the geometry and the material of the cross section of the slab are considered symmetrical with respect to the mid-surface so that the bending extension coupling stiffness, $B_{ij}=0$, and $D_{16}=D_{26}=0$. Each longitudinal and transverse steel layer is regarded as a lamina, and material constants of each lamina is calculated by the use of rule of mixture. This bridge with simple support is under uniformly distributed vertical and axial loads. In this paper, the finite difference method and the beam theory are used for analysis. The result of beam analysis is modified to obtain the solution of the plate analysis. The result of this paper can be used for post-tensioned slab bridge analysis by the engineers with undergraduate study in near future.

• Steel and Composite Structures
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• v.19 no.2
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• pp.369-384
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• 2015

This work presents a free vibration analysis of functionally graded metal-ceramic (FG) beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose, a simple displacement field based on higher order shear deformation theory is implemented. The proposed theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The most interesting feature of this theory is that it accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. In addition, it has strong similarities with Euler-Bernoulli beam theory in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. By employing the Hamilton's principle, governing equations of motion for coupled axial-shear-flexural response are determined. The validity of the present theory is investigated by comparing some of the present results with those of the first-order and the other higher-order theories reported in the literature. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.