• Transactions on Control, Automation and Systems Engineering
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• v.4 no.2
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• pp.124-129
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• 2002

This paper demonstrates that the largest Lyapunov exponent λ of recurrent neural networks can be controlled efficiently by a stochastic gradient method. An essential core of the proposed method is a novel stochastic approximate formulation of the Lyapunov exponent λ as a function of the network parameters such as connection weights and thresholds of neural activation functions. By a gradient method, a direct calculation to minimize a square error (λ - λ$\^$obj/)$^2$, where λ$\^$obj/ is a desired exponent value, needs gradients collection through time which are given by a recursive calculation from past to present values. The collection is computationally expensive and causes unstable control of the exponent for networks with chaotic dynamics because of chaotic instability. The stochastic formulation derived in this paper gives us an approximation of the gradients collection in a fashion without the recursive calculation. This approximation can realize not only a faster calculation of the gradient, but also stable control for chaotic dynamics. Due to the non-recursive calculation. without respect to the time evolutions, the running times of this approximation grow only about as N$^2$ compared to as N$\^$5/T that is of the direct calculation method. It is also shown by simulation studies that the approximation is a robust formulation for the network size and that proposed method can control the chaos dynamics in recurrent neural networks efficiently.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.533-546
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• 2018

The object of this work is to study the existence of solutions for a class of p(x)-Kirchhoff type problem under no-flux boundary conditions with dependence on the gradient. We establish our results by using the degree theory for operators of ($S_+$) type in the framework of variable exponent Sobolev spaces.

• Science of Emotion and Sensibility
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• v.18 no.3
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• pp.63-70
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• 2015

This study identified heart response of participants while listening to sounds which have 1/f fluctuations with exponent ${\alpha}$ gradient. The participants were engaged in emotional stress work. Prior studies related to 1/f fluctuation sound have reported that sound source can alleviate psychological and physiological state of users. Subjects of this study were exposed to sound with three levels of ${\alpha}$ gradient. Heart response of subjects were measured with Photoplethysmography(PPG) sensor simultaneously. The dependent variables of this study were beat per minute(BPM), very low frequency percent of pulse rate variability (VLF percent), the standard deviation of all normal RR intervals (SDNN), and high frequency power(HF power). Subject showed arousal response when exposed to sound with exponent ${\alpha}$ gradient of 3 whereas the sound with exponent ${\alpha}$ gradient of 1 and 2 resulted in relax effect. The characteristic of 1/f fluctuation sounds can be applied to alleviate stress for employers under emotional labor.

• Journal of the Korean Society of Safety
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• v.14 no.1
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• pp.19-24
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• 1999

A two dimensional thermo elasto-plastic finite clement stress analysis was performed to study stress distributions in functionally gradient material. The upper $ZrO_2$ surface is heated at 1200K until a steady state is established and cooled at 300K. The influences on the thermal stress distributions due to the difference of compositional gradient exponent p were investigated. In this study, we obtained the thermal stresses are low for p=1.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.494-494
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• 2000

This paper demonstrates that the largest Lyapunov exponent $\lambda$ of recurrent neural networks can be controlled by a gradient method. The method minimizes a square error $e_{\lambda}=(\lambda-\lambda^{obj})^2$ where $\lambda^{obj}$ is desired exponent. The $\lambda$ can be given as a function of the network parameters P such as connection weights and thresholds of neurons' activation. Then changes of parameters to minimize the error are given by calculating their gradients $\partial\lambda/\partialP$. In a previous paper, we derived a control method of $\lambda$via a direct calculation of $\partial\lambda/\partialP$ with a gradient collection through time. This method however is computationally expensive for large-scale recurrent networks and the control is unstable for recurrent networks with chaotic dynamics. Our new method proposed in this paper is based on a stochastic relation between the complexity $\lambda$ and parameters P of the networks configuration under a restriction. Then the new method allows us to approximate the gradient collection in a fashion without time evolution. This approximation requires only $O(N^2)$ run time while our previous method needs $O(N^{5}T)$ run time for networks with N neurons and T evolution. Simulation results show that the new method can realize a "stable" control for larege-scale networks with chaotic dynamics.

• Journal of Korea Water Resources Association
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• v.32 no.4
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• pp.489-499
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• 1999

This research investigated the applicapability of an improved algorithm to calculate the topographic index, ln($\alpha$/tan B), for the topography of Korea employing channel initiation threshold area(CIT) and an exponent for the gradient(H). hanjaechun subwatershed in Cheongdochun and Dongok subwatershed in Wichun test watershed were selected as study areas. The digital elevation models(DEM) of study areas have been made with the resolution from 10m to 100m. Application of CIT to the traditional algorithm provide reasonable computation method in considering channel pixel impact. Introduction of the gradient exponent(H) made it possible to obtain better flow convergence effect in concave topography comparing with the traditional multiple flow direction algorithm. The improved algorithm shows the capability to relax the overestimation problem of rising limb of hydrograph through reducing overestimated high value of topographic index.

• Steel and Composite Structures
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• v.42 no.3
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• pp.397-405
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• 2022

The existing researches on the dynamics of the fluid-conveying pipes only focus on stability and vibration problems, and there is no literature report on the wave propagation of the fluid-conveying pipes. Therefore, the purpose of this paper is to explore the propagation characteristics of longitudinal and flexural waves in the fluid-conveying pipes. First, it is assumed that the material properties of the fluid-conveying pipes vary based on a power function of the thickness. In addition, it is assumed that the material properties of both the fluid and the pipes are closely depended on temperature. Using the Euler-Bernoulli beam equation and based on the linear theory, the motion equations considering the thermal-mechanical-fluid coupling is derived. Then, the exact expressions of phase velocity and group velocity of longitudinal waves and bending waves in the fluid-conveying pipes are obtained by using the eigenvalue method. In addition, we also studied the free vibration frequency characteristics of the fluid-conveying pipes. In the numerical analysis, we successively studied the influence of temperature, functional gradient index and liquid velocity on the wave propagation and vibration problems. It is found that the temperature and functional gradient exponent decrease the phase and group velocities, on the contrary, the liquid flow velocity increases the phase and group velocities. However, for vibration problems, temperature, functional gradient exponent parameter, and fluid velocity all reduce the natural frequency.

• Advances in nano research
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• v.8 no.1
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• pp.49-58
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• 2020

This paper investigates the vibration characteristics of flexoelectric nanobeams resting on viscoelastic foundation and subjected to magneto-electro-viscoelastic-hygro-thermal (MEVHT) loading. In this regard, the Nonlocal strain gradient elasticity theory (NSGET) is employed. The proposed formulation accommodates the nonlocal stress and strain gradient parameter along with the flexoelectric coefficient to accurately predict the frequencies. Further, with the aid of Hamilton's principle the governing differential equations are derived which are then solved through Galerkin-based approach. The variation of the natural frequency of MEVHT nanobeams under the influence of various parameters such as the nonlocal strain gradient parameter, different field loads, power-law exponent and slenderness ratio are also investigated.

• Structural Engineering and Mechanics
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• v.71 no.3
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• pp.223-232
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• 2019

Since the actuators with small- scale structures may be exposed to external reciprocal actions lead to create undesirable loads causing instability, the buckling behaviors of them are interested to make reliable or accurate actions. Therefore, the purpose of this paper is to analyze plastic buckling behavior of the micro beam structures by adopting a Conventional Mechanism-based Strain Gradient plasticity (CMSG) theory. The effect of length scale on critical force is considered for three types of boundary conditions, i.e. the simply supported, cantilever and clamped - simply supported micro beams. For each case, the stability equations of the buckling are calculated to obtain related critical forces. The constitutive equation involves work hardening phenomenon through defining an index of multiple plastic hardening exponent. In addition, the Euler-Bernoulli hypothesis is used for kinematic of deflection. Corresponding to each length scale and index of the plastic work hardening, the critical forces are determined to compare them together.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2001.04a
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• pp.73-76
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• 2001

We have simulated the effect of fracture characteristics on reduction of effective permeability of the fractured rocks due to in-situ bacteria growth. A nutrient is injected continuously for growth of in-situ bacteria. We used a power law for fracture length distribution and a fBm for fracture aperture spatial distribution. The results show that in-situ bacteria growth reduces the Permeability hyperbolically, but the porosity of backbone fracture does not change significantly. It shows that reduction of the permeability proceeds at faster speed for smaller value of length exponent(a) and for larger value of Hurst exponent(H). The fracture length distribution has stronger effect on speed of reduction than the aperture spatial distribution. The time needed to reduce permeability is inversely proportional to the hydraulic gradient.