• The Mathematical Education
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• v.43 no.4
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• pp.391-398
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• 2004

It is well-known in the literature that the general term of a sequence can be represented by a linear combination of binomial coefficients. The theorem and its known proofs are not easy for highschool students to understand. In this paper we prove the theorem by a pictorial method and by a very short and easy inductive method to make the problem easy and accessible enough for highschool students.

• Journal of the Korean Society for Precision Engineering
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• v.27 no.2
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• pp.109-116
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• 2010

It is important to make a mechanical structure precisely and reasonably in predicting the dynamic characteristics, controlling the vibration, and designing the structure dynamics. In finite element analysis model updating is appropriate as the design parameter is used to analyze the dynamic system. The errors can be contained from the physical parameters and the element modeling. From the dynamic test, more precise dynamic characteristics can be obtained. In this paper, model updating algorithm is developed using frequency difference between experiment and calculation. Modal frequencies are obtained by experiment and finite element analysis for beams with various cross section and shapes which have added masses and holes in the middle. For plates with and without groove, experiment and analyses are carried out by applying free boundary conditions as well. Mass and stiffness matrices are updated by comparing test and analytical modal frequencies. The result shows that the updated frequencies become closer to the test frequencies in case that both matrices are updated. An improved analytical model is obtained by changing model parameters such that the discrepancy between test and finite element frequencies is minimized. For beam and plate models updating of mass and stiffness matrices can improve the dynamical behavior of the model by acting on the physical parameters such as masses and stiffness.

• Journal of the Optical Society of Korea
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• v.10 no.1
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• pp.1-10
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• 2006

Optical transparency and high diffraction efficiency are two essential factors for high performance of the photopolymer. Optical transparency mainly depends on the miscibility between polymer binder and photopolymerized polymer, while diffraction efficiency depends on the refractive index modulation between polymer binder and photopolymerized polymer. For most of organic materials, the large refractive index difference between two polymers accompanies large structural difference that leads to the poor miscibility and thus poor optical quality via light scattering. Therefore, it is difficult to design a high-performance photopolymer satisfying both requirements. In this work, first, we prepared a new phase-stable photopolymer (PMMA) with large refractive index modulation and investigated the optical properties. Our photopolymer is based on modified poly (methyl methacrylate) as a polymer binder, acryl amide as a photopolymerizable monomer, triethanolamine as initiator, and yellow eosin as a photosensitizer at 532 nm. Diffraction efficiency over 85% and optical transmittance over 90% were obtained for the photopolymer. Second, Organic-inorganic nanocomposite films were prepared by dispersing an aromatic methacrylic monomer and a photo- initiator in organic-inorganic hybrid sol-gel matrices. The film properties could be controlled by optimizing the content of an organically modified silica precursor (TSPEG) in the sol-gel matrices. The photopolymer film modified with the organic chain (TSPEG) showed high diffraction efficiency (> 90%) under an optimized condition. High diffraction efficiency could be ascribed to the fast diffusion and efficient polymerization of monomers under interference light to generate refractive index modulation. The TSPEG modified photopolymer film could be successfully used for holographic memory.

• Korea-Australia Rheology Journal
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• v.17 no.4
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• pp.149-156
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• 2005

A simple constitutive model for viscoelastic suspensions is discussed in this paper. The model can be used to predict the rheological properties (relative viscosity and all stresses) for viscoelastic suspensions in shear and elongational flow, and the constitutive equations combine a 'viscoelastic' behaviour component and a 'Newtonian' behaviour component. As expected, the model gives a prediction of positive first normal stress difference and negative second normal stress difference; the dimensionless first normal stress difference strongly depends on the shear rate and decreases with the volume fraction of solid phase, but the dimensionless second normal stress difference (in magnitude) is nearly independent of the shear rate and increases with the volume fraction. The relative viscosities and all the stresses have been tested against available experimental measurements.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.283-296
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• 2005

It is well known that the ordering of the unknowns can have a significant effect on the convergence of a preconditioned iterative method and on its implementation on a parallel computer. To do so, we introduce a block red-black coloring to increase the degree of parallelism in the application of the block ILU preconditioner for solving sparse matrices, arising from convection-diffusion equations discretized using the finite difference scheme (five-point operator). We study the preconditioned PGMRES iterative method for solving these linear systems.

• Honam Mathematical Journal
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• v.41 no.4
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• pp.725-744
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• 2019

In this paper we introduce some new types of double difference sequence spaces defined by a new definition of convergence of double sequences and a double series with the help of sequence of Orlicz functions and a four dimensional bounded regular matrices A = (a_rtkl). We also make an effort to study some topological properties and inclusion relations between these sequence spaces. Finally, we compute the closed ideals in the space 𝑙²_∞.

• Journal of Advanced Marine Engineering and Technology
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• v.22 no.2
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• pp.174-180
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• 1998

Robust stability of discrete-time regulators which utilize state predictors to compensate computation delays is considered. Novel expressions for the return difference matrices and the complementary sensitivity matrices at the input and the output of the regulator are found to obtain simple bounds for unstructured perturbations. Robust stability for pertubations of the system matrix and /or the gain matrix is also considered. under certain restriction on the nominal system simple bounds for the pertubations are obtained directly from the characteristic equation. It is shown that as far as the effect of the computation delays concerns these bounds have explicit relation to those for the unstructured pertubations.

• Proceedings of the KIEE Conference
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• 1983.07a
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• pp.135-138
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• 1983

This paper studies a variable structure adaptive model following control system which can control a plant in which the parameters of the controlled plant can not be estimated because they vary with time and in which the controlled plant has noise. The values of the feedback gain matrices for given states are obtained the equivalent control law, and the adaptive controller has been designed using the adaptive mechanism which switches the matrices. The adaptive controller minimizes the state error vector, that is, the difference between the state vector of the model and the state vector of the controlled plant. A controlled plant which has time varying parameters, a controlled plant which has only noise, and a controlled plant which has both have been controlled by the designed adaptive controller. The continuous single input-output system has been analysed by computer. This control system may be used to control practical systems by the addition of a microcomputer.

• Structural Engineering and Mechanics
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• v.46 no.2
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• pp.269-294
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• 2013

This paper is concerned with the determination of exact buckling loads and vibration frequencies of variable thickness isotropic plates using well known finite difference technique. The plates are subjected to uni, biaxial compression and shear loadings and various combinations of boundary conditions are considered. The buckling load is found out as the in plane load that makes the determinant of the stiffness matrix equal to zero and the natural frequencies are found out by carrying out eigenvalue analysis of stiffness and mass matrices. New and exact results are given for many cases and the results are in close agreement with the published results. In this paper, like finite element method, finite difference method is applied in a very simple manner and the application of boundary conditions is also automatic.

• Journal of Biosystems Engineering
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• v.27 no.6
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• pp.529-536
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• 2002

The performance of stilting engine, in particular, its energy conversion efficiencies are critically influenced by the regenerator characteristics. The regenerator characteristics are influenced by effectiveness, void fraction. heat transfer loss and fluid friction loss in the regenerator matrix. These factors were influenced by the surface geometry and material properties of the regenerator matrix. The regenerator design goals arc good heat transfer and low pressure drop of working Bas across the regenerator. Various data for designing a wire screen matrix have been given by Kays and London(1984). The mesh number of their experiment. however, was confined below the No. 60. which seems rather small for the Stirling engine applications. In this paper. in order to provide a basic data for the design of regenerator matrix, characteristics of heat transfer and flow friction loss were investigated by a packed mettled of matrix in oscillating flow as the same condition of operation in a Stirling engine. Seven kinds of sing1e wire screen meshes were used as the regenerator matrices. The results are summarized as follows; 1. While the working fluid flew slowly in the regenerator. the temperature difference was great at the both hot-blow(the working fluid flows from healer to cooler) and cold-blow(the working fluid flows from cooler to healer). On the other hand. while the working fluid flew fast. the temperature difference was not distinguished. 2. The No.150 wire screen used as the regenerator matrix showed excellent performance than tile others. 3. Phase angle variation and filling rate affected heat transfer or regenerator matrices. 4. Temperature difference between the inlet and outlet of the regenerator is very hish in degree of 120 phase angle.