• Journal of Korean Physical Therapy Science
• /
• v.2 no.4
• /
• pp.739-747
• /
• 1995

The purpose of this study was to evaluate and compare the Limits of stability(LOS) in hemiplegic patients who can walking independently. The LOS was measured at stable surface, unstable surface with eye open and eye closed. In this study, 18 out-patients were evaluated who were treated at Yonsei University Medical Center Rehabilitation Hospital. In order to determine the statistical significance of results, T-test, paired t-test, and Kruskal-Wallis 1-way ANOVA were applied at 0.05 level of significance. The results were as follows: 1. The mean of lateral limits of stability was 9.89 degree. 2. The mean of anteroposterior limits of stability was 6.43 degree. 3. There was a significant difference of limits of stability between sound side and affected side(p<0.05). 4. The limits of stability was significantly decreased with eye closed(p<0.05) 5. The limits of stability was significantly decreased at unstable surface(p<0.05). 6. The limits of stability was a significant difference as spasticity degree of ankle plantar flexors(p<0.05). These results showed that the limits of stability in hemiplegic patients was more decreased than that of normal adult. In order to improve the balance in hemiplegic patients, we need to increase the limits of stability.

• Journal of Korean Physical Therapy Science
• /
• v.3 no.2
• /
• pp.963-973
• /
• 1996

The purpose of this study was to evaluate and compare the limits of stability(LOS) at different sensory conditions in normal 20 years of age. The LOS was measured at stable surface, and unstable surface and the subjects stood with the feet contacted and 4 inches between the feet with the eyes open and the eyes closed. In this study, 20 physical therapy major subjects were evaluated at Wonkwang Public Health Junior College. In this study applied the paired t-test, and Kruskal-Wallis 1-way ANOVA to determine the statistical significance of results at 0.01 level of significance. The results were as follows: 1. The mean of lateral limits of stability was b.67 degree at stable surface with the eyes open and standing with the feet contacted. 2. The mean of anteroposterior limits of stability was 9.78 degree at stable surface with the eyes open and standing with the feet contacted. 3. The mean of lateral limits of stability was 15.10 degree at stable surface with the eyes open and standing with 4 inches between the feet. 4. The mean of anteroposterior limits of stability was 11.72 degree at stable surface with the eyes open and standing with 4 inches between the feet. 5. The anterior-posterior and lateral limits of stability significantly decreased with the eyes closed(p<0.01). 6. The anterior-posterior and lateral limits of stability significantly decreased at unstable surface(p<0.01). 7. There was no significant difference of limits of stability as the height and foot length(p>0.01).

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.11 no.1
• /
• pp.145-153
• /
• 1987

Stability limits of a double concentric jets flame and the structure of recirculation zone formed behind a thick burner rim were investigated. To control the flame stability, swirled secondary air flow ranging 0.13-0.71 of swirl number, and air, fuel, and mixture gas injection from an injection coaxial slit set on burner rim were examined. Flame stability limits, flame shapes, lengths of recirculation zone, temperature distributions, residence times, air ratios in the recirculation zone were measured. The following results were obtained. (1) Lean limits were considerably widened by a strong swirl because the recirculation zone was enlarged. (2) At fuel injection as well as mixture injection, lean limits were also extended. But, air injection had no effect on stability limits. (3) Injected gas seems to diffuse into the recirculation zone through its outer boundary surrounded the secondary air. Therefore, chemical structure in the recirculation zone with air injection coincides with that without injection. (4) Injection position had no effect on flame stability limits.

• Communications of the Korean Mathematical Society
• /
• v.24 no.1
• /
• pp.5-16
• /
• 2009

In this paper, we obtain the general solution and the generalized Hyers-Ulam-Rassias stability for a following functional equation $$\sum\limits_{i=1}^mf(x_i+\frac{1}{m}\sum\limits_{{i=1\atop j{\neq}i}\.}^mx_j)+f(\frac{1}{m}\sum\limits_{i=1}^mx_i)=2f(\sum\limits_{i=1}^mx_i)$$ for a fixed positive integer m with $m\;{\geq}\;2$. This is applied to investigate derivations and their stability on proper Lie $CQ^*$-algebras. The concept of Hyers-Ulam-Rassias stability originated from the Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300.

• The Pure and Applied Mathematics
• /
• v.29 no.2
• /
• pp.179-188
• /
• 2022

In this paper we investigate the Hyers-Ulam stability of the s-variable additive and l-variable quadratic functional equations of the form $$f\(\sum\limits_{i=1}^{s}x_i\)+\sum\limits_{j=1}^{s}f\(-sx_j+\sum\limits_{i=1,i{\neq}j}^{s}x_i\)=0$$ and $$f\(\sum\limits_{i=1}^{l}x_i\)+\sum\limits_{j=1}^{l}f\(-lx_j+\sum\limits_{i=1,i{\neq}j}^{l}x_i\)=(l+1)$$$\sum\limits_{i=1,i{\neq}j}^{l}f(x_i-x_j)+(l+1)\sum\limits_{i=1}^{l}f(x_i)$ (s, l ∈ N, s, l ≥ 3) in quasi-Banach spaces.

• Transactions of the Korean hydrogen and new energy society
• /
• v.17 no.2
• /
• pp.158-165
• /
• 2006

In order to provide the database for designing microcombustors, the combustion characteristics of premixed methane and propane air microflames at normal and elevated temperatures and atmospheric pressure generated on a microtube were studied experimentally and computationally. The stability limits of premixed microflames and the propensity of the microflames near the stability limits were experimentally determined, while the structure of the microflame at the fuel-leanest limit was obtained using a two-dimensional CFD simulation with a reduced kinetic mechanism. For all the microflames, the stability limits were observed only in the fuel-rich region. Results also show substantial extension of stability limits with elevated temperature that is realistic condition for micro fuel processing and significant fuel dilution immediately near the tube exit due to a low Peclet number times Lewis number effect.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.32 no.10
• /
• pp.93-101
• /
• 2004

A method to calculate stability limits is investigated to predict the characteristics of high-frequency combustion instability in liquid-propellant rocket engine. It is based on the theory of linear stability analysis proposed in previous works and useful to predict combustion stability at the beginning stage of engine development. The system of equations governing reactive flow in combustor has the simplified and linearized forms. The overall equation expressing stability limits is adopted. The procedures to evaluate quantitatively each term included in the equation are proposed. The thermo-chemical properties and flow variables required in the evaluation can be obtained from calculation of thermodynamic equilibrium, CFD results, and experimental test data. Based on the existent data, stability limits are calculated with actual rocket engine (KSR-III rocket engine). The present calculations show the reasonable stability limits in a quantitative manner and the stability characteristics of the engine are discussed. The prediction from linear stability analysis could be serve as the first approximation to the true prediction.

• Bulletin of the Korean Mathematical Society
• /
• v.45 no.3
• /
• pp.587-600
• /
• 2008

In this paper we establish the general solution and investigate the Hyers-Ulam-Rassias stability of the following functional equation in quasi-Banach spaces. $${\sum\limits_{{{1{\leq}i<j{\leq}4}\limits_{1{\leq}k<l{\leq}4}}\limits_{k,l{\in}I_{ij}}}\;f(x_i+x_j-x_k-x_l)=2\;\sum\limits_{1{\leq}i<j{\leq}4}}\;f(x_i-x_j)$$ where $I_{ij}$={1, 2, 3, 4}\backslash${i, j} for all $1{\leq}i<j{\leq}4$. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc.

• Journal of the Chungcheong Mathematical Society
• /
• v.33 no.3
• /
• pp.319-326
• /
• 2020

In this paper, we establish a general solution of the following functional equation $$mf\({\sum\limits_{k=1}^{n}}x_k\)+{\sum\limits_{t=1}^{m}}f\({\sum\limits_{k=1}^{n-i_t}}x_k-{\sum\limits_{k=n-i_t+1}^{n}}x_k\)=2{\sum\limits_{t=1}^{m}}\(f\({\sum\limits_{k=1}^{n-i_t}}x_k\)+f\({\sum\limits_{k=n-i_t+1}^{n}}x_k\)\)$$ where m, n, t, i_t ∈ ℕ such that 1 ≤ t ≤ m < n. Also, we study Hyers-Ulam-Rassias stability for the generalized quadratic functional equation with n-variables and m-combinations form in quasi-𝛽-normed spaces and then we investigate its application.

• Journal of the Korean Academy of Clinical Electrophysiology
• /
• v.10 no.1
• /
• pp.1-5
• /
• 2012

Purpose : In this study, stroke patients' limits of stability and functional reach test and tibialis anterior, gastrocnemius muscle of lower extremity muscle activities to evaluate the correlation. Methods : 30 adult stroke patients to participate in this study. Limits of stability were measured using biorescue, tibialis anterior and gastrocnemius muscle of muscles activities were measured with functional reach test when there was movement. Results : Limits of stability and functional reach test (r=0.753, p<0.01), RMS value of the limits of stability and tibialis anterior muscle (r=0.706, p<0.01), RMS value of the limits of stability and gastrocnemius muscle (r=0.766, p<0.01), RMS value of the functional reach test and tibialis anterior muscle (r=0.835, p<0.01), RMS value of the functional reach test and gastrocnemius muscle (r=0.663, p<0.01), RMS value of the tibialis anterior and gastrocnemius muscle (r=0.816, p<0.01) correlations are shown as statistically significant. Conclusion : The balance and lower extremity muscle activities of stroke patients were studied, and were positively correlated with the RMS value of the limits of stability and functional reach test, tibialis anterior muscle, and gastrocnemius muscle. This study has shown that stroke patients' ankle joint muscle activity can greatly.