• Korean Journal of Mathematics
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• v.17 no.3
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• pp.283-291
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• 2009

We investigate the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the parabolic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\xi}_t=-L{\xi}+g_1(3{\xi}+{\eta})-s{\phi}_1-h_1(x,t)\;in\;{\Omega}{\times}(0,\;2{\pi}),\\{\eta}_t=-L{\eta}+g_2(3{\xi}+{\eta})-s{\phi}_1-h_2(x,t)\;in\;{\Omega}{\times}(0,\;2{\pi}).\end{array}$$ We show the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the parabolic system when the nonlinearity $g^{\prime}_1,\;g^{\prime}_2$ are bounded and $3g^{\prime}_1(-{\infty})+g^{\prime}_2(-{\infty})<{\lambda}_1,\;{\lambda}_n<3g^{\prime}_1(+{\infty})+g^{\prime}_2(+{\infty})<{\lambda}_{n+1}$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1693-1710
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• 2013

In this paper, we consider the biharmonic elliptic systems of the form $$\{{\Delta}^2u=F_u(u,v)+{\lambda}{\mid}u{\mid}^{q-2}u,\;x{\in}{\Omega},\\{\Delta}^2v=F_v(u,v)+{\delta}{\mid}v{\mid}^{q-2}v,\;x{\in}{\Omega},\\u=\frac{{\partial}u}{{\partial}n}=0,\; v=\frac{{\partial}v}{{\partial}n}=0,\;x{\in}{\partial}{\Omega},$$, where ${\Omega}{\subset}\mathbb{R}^N$ is a bounded domain with smooth boundary ${\partial}{\Omega}$, ${\Delta}^2$ is the biharmonic operator, $N{\geq}5$, $2{\leq}q$ < $2^*$, $2^*=\frac{2N}{N-4}$ denotes the critical Sobolev exponent, $F{\in}C^1(\mathbb{R}^2,\mathbb{R}^+)$ is homogeneous function of degree $2^*$. By using the variational methods and the Ljusternik-Schnirelmann theory, we obtain multiplicity result of nontrivial solutions under certain hypotheses on ${\lambda}$ and ${\delta}$.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.04a
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• pp.546-550
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• 2008

Impulsive excitation on vehicles produces shock-type vibration on the seat, usually which has major frequencies and damping ratios dependent on the characteristics of the suspension, the tire, the seat cushion and so on. The response of single degree of freedom model to a half-sine force input was considered as simple shock-type vibration signal. The quasi-apparent-mass for fifteen subjects was obtained with the shock-type vibration generated on the rigid seat, so its nonlinearity was found over 6.3 Hz according to the difference of magnitude of the shocks.

• Proceedings of the IEEK Conference
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• 2003.07e
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• pp.2367-2370
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• 2003

A fast pattern classification algorithm with Cellular Parallel Processing Network-based dynamic programming is proposed. The Cellular Parallel Processing Networks is an analog parallel processing architecture and the dynamic programming is an efficient computation algorithm for optimization problem. Combining merits of these two technologies, fast Pattern classification with optimization is formed. On such CPPN-based dynamic programming, if exemplars and test patterns are presented as the goals and the start positions, respectively, the optimal paths from test patterns to their closest exemplars are found. Such paths are utilized as aggregating keys for the classification. The pattern classification is performed well regardless of degree of the nonlinearity in class borders.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.9 no.1
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• pp.127-134
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• 1999

Boolean functions have an important role for designing block ciphers and hash functions. In this paper, we propose a method for designing optimum correlation immune functions. We also analyze their cryptographic properties - balancedness, nonlinearity, correlation value to the set of linear functions, correlation immunity, propagation characteristic, and algebraic degree. Such functions are special type of Semi-bent functions [2,5]

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.5
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• pp.558-563
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• 2008

Vibration/shock affects biggest taking a train subtraction of vehicle and durability decline. Therefore, absorber is used for vibration/shock isolation and various qualities of the material and design are applied to isolation. This paper proposes vibration/shock absorber that applies 'Disc' spring. Through comparison with 'Disc' spring that has nonlinearity and coil spring that is having linearity, see effect that nonlinearity of isolation gets in vibration/shock Isolation. Coil spring and 'Disc' spring are non-linear numerical analysis and simulation through theory for this, get and investigate comparison result through an experiment finally. Expressed and formulated shock through 'Runge-Kutta' method/impact response to nonlinear-vibration-equation of 1 degree of freedom for numerical analysis. Double half sine pulse of excitation used and analyzed result through spectrum response analysis here. Response of disc spring is compared to response of coil spring by changing $h_o/t$ ratio with computer simulation and the usage of disc spring is increased through analysis of effect of design factors. The purpose of this paper is that the shock response of disc spring is calculated through numerical simulation and to design the optimal absorber under the limited condition. And then, the isolation effect was analyzed through the shock test.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.04a
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• pp.990-993
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• 2008

Vibration/shock affects biggest taking a train subtraction of vehicle and durability decline. Therefore, absorber is used for vibration/shock isolation and various qualities of the material and design are applied to isolation. This paper proposes vibration/shock absorber that applies 'Disc'spring. Through comparison with 'Disc' spring that has nonlinearity and coil spring that is having linearity, see effect that nonlinearity of isolation gets in vibration/shock isolation. Coil spring and 'Disc' spring are non-linear numerical analysis and simulation through theory for this, get and investigate comparison result through an experiment finally. Expressed and formulated shock through 'Runge-Kutta' method/impact response to nonlinear-vibration-equation of 1 degree of freedom for numerical analysis. Double half sine pulse of excitation used and analyzed result through spectrum response analysis here. Response of disc spring is compared to response of coil spring by changing ho/t ratio with computer simulation and the usage of disc spring is increased through analysis of effect of design factors. The purpose of this paper is that the shock response of disc spring is calculated through numerical simulation and to design the optimal absorber under the limited condition. And then, the isolation effect was analyzed through the shock test.

• The Korean Journal of Applied Statistics
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• v.32 no.5
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• pp.703-720
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• 2019

The influence of temperature on electricity demand is increasing due to extreme weather and climate change, and the climate impacts involves nonlinearity, asymmetry and complexity. Considering changes in government energy policy and the development of the fourth industrial revolution, it is important to assess the climate effect more accurately for stable management of electricity supply and demand. This study aims to analyze the effect of temperature change on electricity demand using the partial linear model. The main results obtained using the time-unit high frequency data for meteorological variables and electricity consumption are as follows. Estimation results show that the relationship between temperature change and electricity demand involves complexity, nonlinearity and asymmetry, which reflects the nonlinear effect of extreme weather. The prediction accuracy of in-sample and out-of-sample electricity forecasting using the partial linear model evidences better predictive accuracy than the conventional model based on the heating and cooling degree days. Diebold-Mariano test confirms significance of the predictive accuracy of the partial linear model.

• Journal of the Earthquake Engineering Society of Korea
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• v.7 no.4
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• pp.15-22
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• 2003

Seismic design codes developed taking into account the strong earthquakes may result in unnecessary economical loss in the low seismic area, and the importance of the performance based design considering the soil-structure interaction is recognized for the reasonable seismic design. In this study. elastic and inelastic seismic response analyses of a single degree of freedom system on the soft soil layer were performed considering the nonlinearity of the soil for the 1 weak earthquakes scaled to the nominal peak accelerations of 0.07g and 0.11g. The seismic response analyses were performed in one step applying the earthquake motions to the bedrock, utilizing a pseudo 3-D dynamic analysis software of the soil-structure system. The study results indicated that seismic response spectra of a system assuming the rigid base or the linear soil layer does not represent the true behavior of a structure-soil system, and it is necessary to take into account the nonlinear soil-structure interaction effects and to perform the performance based seismic design for the various soil layers, having different characteristics, rather than to follow the routine design procedures specified in the design codes for the reasonable seismic design. The nonlinearity of the soft soil excited with the weak seismic motions also affected significantly on the elastic and inelastic seismic response spectra of a system due to the nonlinear soil amplification of the earthquake motions, and it was pronounced especially for the elastic response spectra.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.13 no.1
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• pp.139-146
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• 2003

In this paper we demonstrate a cryptanalysis of the stream cipher LILI-128. Our approach to analysis on LILI-128 is to solve an overdefined system of multivariate equations. The LILI-128 keystream generato $r^{[8]}$ is a LFSR-based synchronous stream cipher with 128 bit key. This cipher consists of two parts, “CLOCK CONTROL”, pan and “DATA GENERATION”, part. We focus on the “DATA GENERATION”part. This part uses the function $f_d$. that satisfies the third order of correlation immunity, high nonlinearity and balancedness. But, this function does not have highly nonlinear order(i.e. high degree in its algebraic normal form). We use this property of the function $f_d$. We reduced the problem of recovering the secret key of LILI-128 to the problem of solving a largely overdefined system of multivariate equations of degree K=6. In our best version of the XL-based cryptanalysis we have the parameter D=7. Our fastest cryptanalysis of LILI-128 requires $2^{110.7}$ CPU clocks. This complexity can be achieved using only $2^{26.3}$ keystream bits.