• Journal of Institute of Control, Robotics and Systems
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• v.15 no.12
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• pp.1216-1222
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• 2009

This article describes a simple method for generating the walking trajectory for the biped humanoid robot. The method used a simple inverted model instead of complex multi-mass model and a reasonable explanation for the model simplification is included. The problem of gait trajectory generation is to find the solution from the desired ZMP trajectory to CoG trajectory. This article presents the analytic solution for the bipedal gait generation on the bases of ZMP trajectory. The presented ZMP trajectory has Fourier series form, which has finite or infinite summation of sine and cosine functions, and ZMP trajectory can be designed by calculating the coefficients. From the designed ZMP trajectory, this article focuses on how to find the CoG trajectory with analytical way from the simplified inverted pendulum model. Time segmentation based approach is adopted for generating the trajectories. The coefficients of the function should be designed to be continuous between the segments, and the solution is found by calculating the coefficients with this connectivity conditions. This article also has the proof and the condition of solution existence.

• Membrane Journal
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• v.3 no.3
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• pp.108-116
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• 1993

In PVC/PS pelyblend laminated membranes, perrneabilities were increased as increasing the blend ratio of PS and selectivities were increased with increasing the blend ratio of PVC. The gas permeation mechanism was shifted from the combination of Poiseuille and Knudsen flow model to the solution-diffusion model as decreasing the PS blend ratio. The structure of polyblend laminated membranes showed series model, where PS rich phase was formed at air side and PVC rich phase was at water side. The model of permeation in the polyblend laminated membranes also showed series model structure.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.31-48
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• 2007

The paper deals with the solution of some fractional partial differential equations obtained by substituting modified Riemann-Liouville derivatives for the customary derivatives. This derivative is introduced to avoid using the so-called Caputo fractional derivative which, at the extreme, says that, if you want to get the first derivative of a function you must before have at hand its second derivative. Firstly, one gives a brief background on the fractional Taylor series of nondifferentiable functions and its consequence on the derivative chain rule. Then one considers linear fractional partial differential equations with constant coefficients, and one shows how, in some instances, one can obtain their solutions on bypassing the use of Fourier transform and/or Laplace transform. Later one develops a Lagrange method via characteristics for some linear fractional differential equations with nonconstant coefficients, and involving fractional derivatives of only one order. The key is the fractional Taylor series of non differentiable function $f(x+h)=E_{\alpha}(h^{\alpha}{D_x^{\alpha})f(x)$.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.729-736
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• 2022

To help solving intractable nonlinear evolution equations (NLEEs) of waves in the field of fluid dynamics we develop an algorithm to find new high order solutions of the class of Abel, Bernoulli, Chini and Riccati equations of the form y' = ayⁿ + by + c, n > 1, with constant coefficients a, b, c. The role of this class of equations in NLEEs is explained in the introduction below. The basic algorithm to compute the coefficients of the power series solutions of the class, emerged long ago and is further developed in this paper. Practical application for hitherto unknown solutions is exemplified.

• Journal of Advanced Marine Engineering and Technology
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• v.22 no.6
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• pp.792-799
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• 1998

Further improvement of existing $H_{2}O/LiBr$ absorption refrigeration machine is absolutely neces-sary to promote the utilization of gas-cooling system Among various methods to improve the per-formance of the absorption refrigeration machine this research has focused on the use of a new working fluid that has better properties than the existing $H_{2}O/LiBr$ working fluid. In the series of the research, $H_{2}O/LiBr+HO{(CH_{2})}_{3}OH$ system was selected as the most promisable candidate. The absorption refrigeration machine is water-cooled double-effect, $H_{2}O/LiBr+HO{(CH_{2})}_{3}OH$ sys-tem with series flow type. In this study we found out the characteristic of new working solution through the cycle simulation and compared the result with that of LiBr solution to evaluate. Theoptimum designs and operating conditions were determined based on the operating constraints and the coefficient of performance. Results demonstrate that new working fluid subsrantially increases COP by as much as 10% and has a wider working range with 8% higher crystallization limits compared to the conventional $H_{2}O/LiBr$.

• Journal of Korean Society of Steel Construction
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• v.22 no.3
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• pp.241-251
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• 2010

This paper presents the development of a new analytical solution to the governing differential equation for isotropic annular sector plates subjected to uniform loading in a three-dimensional polar coordinate system. The 4th order governing partial differential equation (PDE) was converted to an ordinary differential equation (ODE) by assuming the Levy-type series solution form and the subsequent mathematical operations. Finally, a series-type solution was assembled with homogeneous and nonhomogeneous solution parts after operating real values and complex conjugates derived from the characteristic equation. To demonstrate the convergence rate and the accuracy of the featured method, several examples with various sector angles were selected and solved. The deflections and internal moments in the example annular sector plates that were obtained from the proposed solution were compared with those obtained from other analytical studies and numerical analyses using the finite element analysis package program, ABAQUS. Very good agreement with the results of other analytical and numerical methodologies was shown.

• Journal of the Korean Ceramic Society
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• v.18 no.2
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• pp.91-98
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• 1981

Synthetic zeolite A was prerared from domestic Hadong kaolin with sodium hydroxide solution and their ion exchange isotherms of $K^+$, $NH^{4+}$, $Li^+$ and $Ag^+$ ion were presented. The optimum reaction conditions for synthetic zeolite A from calcinated kaolin were 2 fold excess of 2N sodium hydroxide solution, 10$0^{\circ}C$ and 8 hours. It was observed that before the crystallization of zeolite A the samples reacted with sodium hydroxide solution had rather higher ion exchange capacities than zeolite A. The $K^+$-$Na^+$ and $Ag^+$$Na^+$ ion exchange isotherms were signoidal. The initial selectivity series was in the order $Ag^+$$K^+$>$Na^+$>$NH_4$>$Li^+$. Between approximately 33 and 67% replacement of soium ions the selectivity series became $Na^>$ and above 67% became $Ag^+$>$K^+$. Evidence were also presented to demonstrate that 8 out of 12 sodium ions per pseudo unit cell were not easily replaceable by lithium ions and 4 out of 12 not easily replaceable by ammonium ions.

• Journal of Soil and Groundwater Environment
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• v.20 no.5
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• pp.26-33
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• 2015

Batch experiments were performed to investigate the feasibility of a surfactant-enhanced soil washing process for soils heavily contaminated with crude oil in Kuwait. TPH concentration of the contaminated soil was 223,754 mg/kg, sampled from the bottom of a vaporized oil extraction pond in the Burgan reservoir field. Commercialized eight nonionic surfactants (Tween and Tergitol series) were used to measure the aqueous solubility for the crude oil. Among them, two Tergitol surfactants were used to evaluate the TPH removal efficiency of the surfactant-enhanced soil washing for heavily contaminated Kuwait soil. The solubility of the crude oil in surfactant solution was in the order Tergitol 15-S-7 > Tergitol 15-S-9 > Tergitol 15-S-12 > Tween-80 > Tween-20 > Tween-60, which showed that the crude oil solubilities of the Tergitol series were higher than those of the Tween series. The TPH removal efficiencies of 2% and 5% Tergitol 15-S-9 solution were 59% and 65%, respectively. Because the residual TPH concentration in the washed soil was still higher than the clean-up level (10,000 mg/kg), the soil washing process was repeated five times. After the fifth washing, the residual TPH concentration in the soil went down to 7,680 mg/kg and its removal efficiency was 97%.

• Proceedings of the Membrane Society of Korea Conference
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• 1997.10a
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• pp.39-45
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• 1997

Introduction : Polyimides are one of the most important classes of the high performance polymers due to their excellent electrical, thermal, and high-temperature mechanical properties. But their uses are limited because of their poor solubility. Most polyimide derivatives are processed in the form of polyamic acids, which are subsequently converted into the imide structures.Recently, it has been found that the soluble polyimides with large molecular weight sufficient to application. For enhancing processability, the majority of approaches have involved the following factors. As much as, the separation of the imide ring along the back-bone, that is to say, reducing the density of imide ring in the repeat structure. The introduction of bulky substituents along the back-bone, in order to enhance the free volume of main-chain. The incorporation of flexible or thermally stable linkages in the main-chain, reducing the packing force. The disruption of symmetry or recurrence regularity through copolymerization in order to reduce crystallnity.The objectives of this investigation are the synthesis and characterization of soluble polyimides as membrane materials by the single-step polymerization and the preparation of the asymmetric polyimide membrane by using phase inversion technique. In the present study, three series of polyimide derivatives are synthesized; H series is homopolyimides, A series is prepared from single dianhydride and two diamines, B series is yielded from two dianhydrides and a diamine. The dope solution was directly prepared from the PI solution via one step polymerization from monomers.

• Journal of the Korean Solar Energy Society
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• v.38 no.5
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• pp.27-36
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• 2018

The purpose of this paper is to apply the numerical solution procedure to compute conduction time series factors (CTSF) for construction materials with large thermal capacities. After modifying the procedure in Ref. [9], it is applied to find the CTSF for the wall type 19 and the roof type 18 of ASHRAE. The response periods for one hr pulse load are longer than 24hrs for these wall and roof. The CTSF generated using modified procedure agree well with the values presented in the ASHRAE handbook. The modified procedure is a general procedure that can be applied to find CTSF for materials with complex structures. For the large thermal capacity materials, it should be checked whether thermal response period of the material is over 24hr or not. With suggested solution procedure, it is easy to check the validity of the CTSF based on 24hr period.