• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.255-271
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• 2023

In this paper, we deal with random attractors for dynamical systems forced by a deterministic noise. These kind of systems are modeled as skew products where the dynamics of the forcing process are described by the base transformation. Here, we consider skew products over the Bernoulli shift with the unit interval fiber. We study the geometric structure of maximal attractors, the orbit stability and stability of mixing of these skew products under random perturbations of the fiber maps. We show that there exists an open set U in the space of such skew products so that any skew product belonging to this set admits an attractor which is either a continuous invariant graph or a bony graph attractor. These skew products have negative fiber Lyapunov exponents and their fiber maps are non-uniformly contracting, hence the non-uniform contraction rates are measured by Lyapnnov exponents. Furthermore, each skew product of U admits an invariant ergodic measure whose support is contained in that attractor. Additionally, we show that the invariant measure for the perturbed system is continuous in the Hutchinson metric.

• Physical Therapy Korea
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• v.15 no.4
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• pp.18-26
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• 2008

The present study was aimed at investigating the postural control ability of volleyball players with functional ankle instability. The subjects were 26 male volleyball players were divided into 2 groups (13 subjects with functional ankle instability and 13 subjects with ankle stability) who could evaluate Questionnaire. All the male participants were tested by a Balance Master System. This study were to measure of static balance ability, dynamic balance ability, motor function the difference between functional ankle instability group and control group. Ankle instability group and stable group in postural sway ($^{\circ}/sec$) on film surface with eye closed in modified clinical test sensory interaction on balance, and left unilateral stance with eye opened and closed were significantly different (p<.05). The ankle instability group and stable group in limit of stability were significantly different (p<.05). The ankle instability group and stable group in left/right rhythmic weight shirt were significantly different (p<.05). The ankle instability group and stable group in turn time (sec) & turn sway ($^{\circ}$) during step/quick turn and end sway ($^{\circ}/sec$) in tandem walk were significantly different (p<.05). This study showed that volleyball players with functional ankle in stability were effected postural control ability by static balance & dynamic balance ability. Further study is needed to measure various athletic with functional ankle instability for clinical application.

• The Journal of Korean Physical Therapy
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• v.28 no.4
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• pp.221-226
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• 2016

Purpose: This study was conducted to evaluate the effects of neck and trunk stabilization exercise on static and dynamic balance in older adults. Methods: A total of 30 older adults participated in this study. Participants were randomly assigned to the neck and trunk stabilization exercise group (NTSG) (n=15) or the trunk stabilization exercise group (TSG) (n=15). The NTSG performed a trunk stabilization exercise added to a neck stabilization exercise that included biofeedback. Both groups received training for 30 minutes per day three times per week for eight weeks. The anterior, posterior limit of stability and sway length was used to measure static balance ability, while the timed up and go (TUG) test was used to measure dynamic balance ability. Results: Participants showed significant differences in sway length, anterior limit of stability, posterior limit of stability, and the results of the TUG test between their pre- and post mediation evaluations (p<0.05). The NTSG showed a more significant increase than the TSG (p<0.05). Conclusion: According to the results of this study, both exercises effectively improved static and dynamic balance ability. However, the neck and trunk stabilization exercise is more efficient for increasing the balance ability of older adults.

• Bulletin of the Korean Chemical Society
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• v.20 no.1
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• pp.35-41
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• 1999

Stability characteristics of hyperbolic reaction-diffusion equations with a reversible Brusselator model are investigated as an extension of the previous work. Intensive stability analysis is performed for three important parameters, Nrd, β and Dx, where Nrd is the reaction-diffusion number which is a measure of hyperbolicity, β is a measure of reversibility of autocatalytic reaction and Dx is a diffusion coefficient of intermediate X. Especially, the dependence on Nrd of stability exhibits some interesting features, such as hyperbolicity in the small Nrd region and parabolicity in the large Nrd region. The hyperbolic reaction-diffusion equations are solved numerically by a spectral method which is modified and adjusted to hyperbolic partial differential equations. The numerical method gives good accuracy and efficiency even in a stiff region in the case of small Nrd, and it can be extended to a two-dimensional system. Four types of solution, spatially homogeneous, spatially oscillatory, spatio-temporally oscillatory and chaotic can be obtained. Entropy productions for reaction are also calculated to get some crucial information related to the bifurcation of the system. At the bifurcation point, entropy production changes discontinuously and it shows that different structures of the system have different modes in the dissipative process required to maintain the structure of the system. But it appears that magnitude of entropy production in each structure give no important information related for states of system itself.

• Korean Journal of Applied Biomechanics
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• v.27 no.2
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• pp.133-140
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• 2017

Objective: The purpose of this study was to determine the relationship between center of pressure (CoP) and local stability of the lower joints, which was calculated based on approximate entropy (ApEn) during walking in elderly women. Method: Eighteen elderly women were recruited (age: $66.4{\pm}1.2yrs$; mass: $55.4{\pm}8.3kg$; height: $1.56{\pm}0.04m$) for this study. Before collecting data, reflective marker triads composed of 3 non-collinear spheres were attached to the lateral surface of the thigh and shank near the mid-segment to measure motion of the thigh and shank segments. To measure foot motion, reflective markers were placed on the shoe at the heel, head of the fifth metatarsal, and lateral malleolus, and were also placed on the right anterior-superior iliac spine, left anterior-superior iliac spine, and sacrum to observe pelvic motion. During treadmill walking, kinematic data were recorded using 6 infrared cameras (Oqus 300, Qualisys, Sweden) with a 100 Hz sampling frequency and kinetic data were collected from a treadmill (Instrumented Treadmill, Bertec, USA) for 20 strides. From kinematic data, 3D angles of the lower extremity's joint were calculated using Cardan technique and then ApEn were computed for their angles to evaluate local stability. Range of CoP was determined from the kinetic data. Pearson product-moment and Spearman rank correlation coefficient were applied to find relationship between CoP and ApEn. The level of significance was determined at p<.05. Results: There was a negative linear correlation between CoP and ApEn of hip joint adduction-abduction motion (p<.05), but ApEn of other joint motion did not affect the CoP. Conclusion: It was conjectured that ApEn, local stability index, for adduction/abduction of the hip joint during walking could be useful as a fall predictor.

• Journal of the Korean Society of Physical Medicine
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• v.8 no.3
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• pp.417-424
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• 2013

PURPOSE: We investigated the relationship between the segment of erector spinae during a core stability exercise according to visual control. METHODS: The subjects of this study were 20 healthy students. An 8-channel electromyograph was used to measure muscle activities of the erector spinae by segment(cervical, thoracic and lumbar) during a core stability exercise according to visual control. The collected data were analyzed using the independent t-test and Pearson-test. RESULTS: The activity of the erector spinae for all segment was higher without the vision than with. The activity of right cervical erector spinae was significantly increased by increasing the activity of the left thoracic erector spinae during a core stability exercise with vision (r= .555). The activity of left thoracic erector spinae was significantly increased by increasing the activity of the left lumbar erector spinae during a core stability exercise without vision (r= .472). CONCLUSION: There was a positive correlation between the cervical and thoracic segment of erector spinae during a core stability exercise with vision. There was a positive correlation between the thoracic and lumbar segment of erector spinae during a core stability exercise without vision.

• The Journal of Asian Finance, Economics and Business
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• v.7 no.12
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• pp.181-193
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• 2020

This study examines the relationship between gender diversity (women on the board and women on the audit committee) and a firm's financial stability. The ordinary least square analysis was used to determine the relationship. To measure the financial stability of Malaysian suspect firms, i.e., firms with the lowest positive earnings, the Altman (1993) Z-Score measurement was utilized. The results indicate that women on the board are significantly and negatively associated with the firm's financial stability. That is, they are related to low financial stability, which contradicts the agency and resource dependence theories. Regarding women directors on the audit committee, there is no significant relationship with financial stability, meaning that they cannot protect the company against financial distress. These results are robust and do not change when using different measurements of gender diversity, one-year lag of independent variables, and other methods of analysis, namely random effect panel data. This study is the first to alert policymakers, stakeholders, researchers, and society in general to the need to re-evaluate and strengthen the role of women directors in improving firms' financial stability, particularly in emerging economies like Malaysia.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.1049-1061
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• 2017

The paper presents a characterization of stable random measures, giving a canonical form of their Laplace transform. Domain of attraction of stable random measures is concerned in a theorem showing that a random measure belongs to domain of attraction of any stable random measures if and only if it varies regularly at infinity.

• Journal of the Korean Society of Safety
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• v.13 no.4
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• pp.137-141
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• 1998

The combustion instability of a rocket motor can be predicted by the linear stability analysis. The most important input data in this analysis is the combustion response function of the solid propellant. In many cases, it is very difficult to measure the function. But, in that case, the combustion response function can be theoretically evaluated by properties of the propellant. In this study, the theoretical values were compared with measured values by T-burner. Data are relatively so well agreed that theoretical values are enough to be used in linear stability analysis of the rocket motor using a newly developed propellant.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10b
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• pp.203-208
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• 1987

Design problem of output feedback controllers for discrete large scale systems using simplified model is investigated. It is shown that neglecting fast modes does not generally guarantee the stability of the closed loop system. In this paper, the design procedure is proposed to stabilize the system by minimizing a quadratic cost function for the simplified model and a measure of stability for the neglected fast model.