• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.113-124
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• 2006

In this paper we consider the numerical solution of the sunflower equation. We prove that if the sunflower equation has a Hopf bifurcation point at a = ao, then the numerical solution with the Euler-method of the equation has a Hopf bifurcation point at ah = ao + O(h).

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.267-296
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• 2018

This paper studies the Cauchy problem and blow-up phenomena for a new generalized Camassa-Holm equation with cubic nonlinearity in the nonhomogeneous Besov spaces. First, by means of the Littlewood-Paley decomposition theory, we investigate the local well-posedness of the equation in $B^s_{p,r}$ with s > $max\{{\frac{1}{p}},\;{\frac{1}{2}},\;1-{\frac{1}{p}}\},\;p,\;r{\in}[0,{\infty}]$. Second, we prove that the equation is locally well-posed in $B^s_{2,r}$ with the critical index $s={\frac{1}{2}}$ by virtue of the logarithmic interpolation inequality and the Osgood's Lemma, and it is shown that the data-to-solution mapping is $H{\ddot{o}}lder$ continuous. Finally, we derive two kinds of blow-up criteria for the strong solution by using induction and the conservative property of m along the characteristics.

• Journal of Korea Society of Digital Industry and Information Management
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• v.9 no.4
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• pp.103-110
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• 2013

In Information Technology era, various amazing IT technologies, for example Big Data, are appearing and are available as the amount of information increase. The number of counselling for violation of personal data protection is also increasing every year that it amounts to over 160,000 in 2012. According to Korean Privacy Act, in the case of treating unique personal identification information, appropriate measures like encipherment should be taken. The technologies of encipherment are the most basic countermeasures for personal data invasion and the base elements in information technology. So various cryptography algorithms exist and are used for encipherment technology. Therefore studies on safer new cryptography algorithms are executed. Cryptography algorithms started from classical replacement enciphering and developed to computationally secure code to increase complexity. Nowadays, various mathematic theories such as 'factorization into prime factor', 'extracting square root', 'discrete lognormal distribution', 'elliptical interaction curve' are adapted to cryptography algorithms. RSA public key cryptography algorithm which was based on 'factorization into prime factor' is the most representative one. This paper suggests algorithm utilizing telescoping series as a safer cryptography algorithm which can maximize the complexity. Telescoping series is a type of infinite series which can generate various types of function for given value-the plain text. Among these generated functions, one can be selected as a original equation. Some part of this equation can be defined as a key. And then the original equation can be transformed into final equation by improving the complexity of original equation through the command of "FullSimplify" of "Mathematica" software.

• Smart Structures and Systems
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• v.26 no.6
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• pp.693-701
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• 2020

The conventional Kalman Filter (KF) provides a promising way for structural state estimation. However, the physical parameters of structural systems or models should be available for the estimation. Moreover, it is not applicable when the loadings applied to the structures are unknown. To circumvent the aforementioned limitations, a two-stage KF with unknown input approach is proposed for the simultaneous identification of structural parameters and unknown loadings. In stage 1, a modified observation equation is employed. The structural state vector is estimated by KF on the basis of structural parameters identified at the previous time-step. Then, the unknown input is identified by Least Squares Estimation (LSE). In stage 2, based on the concept of sensitivity matrix, the structural parameters are updated at the current time-step by using the estimated structural states obtained from stage 1. The effectiveness of the proposed approach is numerically validated via a five-story shearing model under random and earthquake excitations. Shaking table tests on a five-story structure are also employed to demonstrate the performance of the proposed approach. It is demonstrated from numerical and experimental results that the proposed approach can be used for the identification of parameters of structure and the external force applied to it with acceptable accuracy.

• Smart Structures and Systems
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• v.31 no.2
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• pp.131-140
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• 2023

As well-known, the extended Kalman filter (EKF) is a powerful tool for parameter identification with limited measurements. However, traditional EKF is not applicable when the external excitation is unknown. By using least-squares estimation (LSE) for force identification, an EKF with unknown input (EKF-UI) approach was recently proposed by the authors. In this approach, to ensure the influence matrix be of full column rank, the sensors have to be deployed at all the degrees-of-freedom (DOFs) corresponding to the unknown excitation, saying collocated measurements are required. However, it is not easy to guarantee that the sensors can be installed at all these locations. To circumvent this limitation, based on the idea of first-order-holder discretization (FOHD), an improved EKF with unknown input (IEKF-UI) approach is proposed in this study for the simultaneous identification of structural parameters and unknown excitation. By using projection matrix, an improved observation equation is obtained. Few displacement measurements are fused into the observation equation to avoid the so-called low-frequency drift. To avoid the ill-conditioning problem for force identification without collocated measurements, the idea of FOHD is employed. The recursive solution of the structural states and unknown loads is then analytically derived. The effectiveness of the proposed approach is validated via several numerical examples. Results show that the proposed approach is capable of satisfactorily identifying the parameters of linear and nonlinear structures and the unknown excitation applied to them.

• Journal of Korea Multimedia Society
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• v.6 no.7
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• pp.1277-1285
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• 2003

In this paper, we present a conference key authentication mechanism by employing an algebraic method on IMT-2000 environment. To accomplish this, the symmetric balanced incomplete block design is applied for generating a conference key and then this key is distributed to participants. Through the technique for creation of a conference key and mutual authentications peformed based on identification information, a communication protocol is designed. The protocol proposed minimizes the communication complexity for generating a conference key. On a special case the complexity is O(equation omitted), where v is the number of participants. The security of the mechanism, which is a significant problem in construction of secure systems, can be assured since finding discrete logarithms is generally a hard problem.

• Journal of the Optical Society of Korea
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• v.13 no.3
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• pp.379-385
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• 2009

The vergence control of binocular stereoscopic camera is the most essential factor for acquiring high quality stereoscopic images. In this paper, we proposed a binocular stereoscopic camera vergence control method using disparity information by the simple image processing and estimate the quantity of vergence control using the Lagrange interpolation equation. The method of extracting disparity information through image processing is as follows: first the key-object in left & right images was extracted through labeling of the central area of the image, and then a simple method was used for calculating the disparity value of the same key-object in the labeled left and right images. The vergence control method uses disparity information and keeps the convergence distance of left & right cameras and the distance of the key-object the same. According to the proposed method, variance in the distance of the key-object and application of calculated disparity information of obtained left & right images to the quadratic Lagrange interpolation equation could estimate the quantity of vergence control, which confirmed that the method of stereoscopic camera vergence control can be simplified through experiments on various key-objects and other convergence distance.

• Steel and Composite Structures
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• v.39 no.1
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• pp.21-33
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• 2021

This paper aims to improve the current state-of-the-art in long-term deflection prediction in steel-concrete composite beams. The efficiency of a time-dependent finite element model based on linear creep theory is verified with available experimental data. A parametric numerical study is then carried out, which focuses on the effects of concrete creep and/or shrinkage, ultimate shrinkage strain and reinforcing bars in the slab. The study shows that the long-term deformations in composite beams are dominated by concrete shrinkage and that a higher area of reinforcing bars leads to lower long-term deformations and steel stresses. The AISC model appears to overestimate the shrinkage-induced deflection. A modified ACI equation is proposed to quantify time-dependent deflections in composite beams. In particular, a modified reduction factor reflecting the influence of reinforcing bars and a coefficient reflecting the influence of ultimate shrinkage are introduced in the proposed equation. The long-term deflections predicted by this equation and the results of extensive numerical analyses are found to be in good agreement.

• Bulletin of the Korean Chemical Society
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• v.35 no.9
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• pp.2699-2703
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• 2014

We solve the Klein-Gordon equation with the modified Rosen-Morse potential energy model. The bound state energy equation has been obtained by using the supersymmetric shape invariance approach. The relativistic vibrational transition frequencies for the $6^1{\Pi}_u$ state of the $^7Li_2$ molecule have been computed by using the modified Rosen-Morse potential model. The calculated relativistic vibrational transition frequencies are in good agreement with the experimental RKR values.

• Wind and Structures
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• v.25 no.5
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• pp.415-432
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• 2017

The nonlinear aerodynamic instability of a tensioned plane orthotropic membrane structure is theoretically investigated in this paper. The interaction governing equation of wind-structure coupling is established by the Von $K\acute{a}rm\acute{a}n's$ large amplitude theory and the D'Alembert's principle. The aerodynamic force is determined by the potential flow theory of fluid mechanics and the thin airfoil theory of aerodynamics. Then the interaction governing equation is transformed into a second order nonlinear differential equation with constant coefficients by the Bubnov-Galerkin method. The critical wind velocity is obtained by judging the stability of the second order nonlinear differential equation. From the analysis of examples, we can conclude that it's of great significance to consider the orthotropy and geometrical nonlinearity to prevent the aerodynamic instability of plane membrane structures; we should comprehensively consider the effects of various factors on the design of plane membrane structures; and the formula of critical wind velocity obtained in this paper provides a more accurate theoretical solution for the aerodynamic stability of the plane membrane structures than the previous studies.