• The Journal of the Korea Contents Association
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• v.7 no.12
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• pp.322-332
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• 2007

We consider a deformation method suitable for fractal. In IFS fractal, the position of a point is characterized by its code as well as by its coordinates. Code has a meaning of address for fractal. If we move a point by changing its code, the resulting movement shows fractal behavior. We propose three deformation methods based on code information. For the deformation vector of a point in fractal, 1) we use the vector of a given vector field at the point obtained by code transformation, 2) we use the vector constructed by adding predefined displacement vectors according to the code information of the point. Both methods show a fractal-like character as well as an ordinary continuous deformation character. Also, 3) we can deform fern-fractal more naturally by restricting its deforming region using code form.

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1109-1127
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• 2021

We study the long-term dynamics for a family of incompressible three-dimensional Leray-α-like models that employ the spectral fractional Laplacian operators. This family of equations interpolates between incompressible hyperviscous Navier-Stokes equations and the Leray-α model when varying two nonnegative parameters 𝜃₁ and 𝜃₂. We prove the existence of a finite-dimensional global attractor for the continuous semigroup associated to these models. We also show that an operator which projects the weak solution of Leray-α-like models into a finite-dimensional space is determining if it annihilates the difference of two "nearby" weak solutions asymptotically, and if it satisfies an approximation inequality.

• Steel and Composite Structures
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• v.6 no.2
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• pp.87-101
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• 2006

The deformation and dynamic behavior mechanism of submerged shell-like lattice structures with membranes are in principle of a non-conservative nature as circulatory system under hydrostatic pressure and disturbance forces of various types, existing in a marine environment. This paper deals with a characteristic analysis on quasi-periodic and chaotic behavior of a circular arch under follower forces with small disturbances. The stability region chart of the disturbed equilibrium in an excitation field was calculated numerically. Then, the periodic and chaotic behaviors of a circular arch were investigated by executing the time histories of motion, power spectrum, phase plane portraits and the Poincare section. According to the results of these studies, the state of a dynamic aspect scenario of a circular arch could be shifted from one of quasi-oscillatory motion to one of chaotic motion. Moreover, the correlation dimension of fractal dynamics was calculated corresponding to stochastic behaviors of a circular arch. This research indicates the possibility of making use of the correlation dimension as a stability index.

• BMB Reports
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• v.48 no.12
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• pp.677-684
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• 2015

Cardiovascular function is regulated by the rhythmicity of circadian, infradian and ultradian clocks. Specific time scales of different cell types drive their functions: circadian gene regulation at hours scale, activation-inactivation cycles of ion channels at millisecond scales, the heart's beating rate at hundreds of millisecond scales, and low frequency autonomic signaling at cycles of tens of seconds. Heart rate and rhythm are modulated by a hierarchical clock system: autonomic signaling from the brain releases neurotransmitters from the vagus and sympathetic nerves to the heart's pacemaker cells and activate receptors on the cell. These receptors activating ultradian clock functions embedded within pacemaker cells include sarcoplasmic reticulum rhythmic spontaneous Ca²⁺ cycling, rhythmic ion channel current activation and inactivation, and rhythmic oscillatory mitochondria ATP production. Here we summarize the evidence that intrinsic pacemaker cell mechanisms are the end effector of the hierarchical brain-heart circadian clock system.