• Journal of the Korean Society of Propulsion Engineers
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• v.3 no.1
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• pp.86-94
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• 1999

Measured shock wave effects were investigated by changing shock strength and position with particular emphasis on the stability limits of hydrogen-air jet flames. For this purpose, a supersonic nonpremixed, jet-like flame was stabilized along the axis of a Mach 2.5 wind tunnel, and wedges were mounted on the sidewall in order to interact oblique shock waves with the flame. This experiment was the first reacting flow experiment interacting with shock waves. Schilieren visualization pictures, wall static pressures, and flame stability limits were measured and compared to corresponding flames without shock-flame interaction. Substantial improvements in the flame stability limits were achieved by properly interacting the shock waves with the flameholding recirculation zone. The reason for the significant improvement in flame stability limits is believed to be the adverse pressure gradient caused by the shock, which can elongate the recirculation zone.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.397-409
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• 2018

In this paper, we investigate the generalized Hyers-Ulam stability of the functional equation $$f\({\sum\limits_{i=1}^{n}}x_i\)+{\sum\limits_{1{\leq}i<j{\leq}n}}f(x_i-x_j)-n{\sum\limits_{i=1}^{n}f(x_i)=0$$ for integer values of n such that $n{\geq}2$, where f is a mapping from a vector space V to a Banach space Y.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.413-424
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• 2008

In [21], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\parallel}\frac{1}{n}\sum\limits_{i=1}^{n}x_i{\parallel}^2+\sum\limits_{i=1}^{n}{\parallel}x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j{\parallel}^2=\sum\limits_{i=1}^{n}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\dots},x_n{\in}V$. We consider the functional equation $$nf(\frac{1}{n}\sum\limits^n_{i=1}x_i)+\sum\limits_{i=1}^{n}f(x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j)=\sum\limits_{i=1}^nf(x_i)$$ Using fixed point methods, we prove the generalized Hyers-Ulam stability of the functional equation $$(1)\;2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})=f(x)+f(y)$$.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.12
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• pp.180-187
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• 1998

The stability and theoretical performance limits of the feedback controlled force reflecting haptic manipulator have been discussed. All the virtual environment which interact physically with the haptic system have its own stable performance limit. Three different realization of the interfaces have been compared using the driving point admittance. The haptic system which is separated from the human hand or finger is superior to its stable interaction provided that there is a means to apply a direct damping between the haptic manipulator and the human finger Electro-magnetic force is used for its digital implementation of the simple separated type haptic device. The stable limits of a virtual wall is calculated and experimental results show that there is performance limits in this implementation.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.12
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• pp.3344-3351
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• 1995

The stability of diffusion flame formed behind a bluff body with fuel injection slits was experimentally investigated in various fuel injection angles, fuel injection ratios, grids and extension ducts. The flame stability limits, temperature distributions and length of recirculation zones, direct photographs of flames were measured in order to discuss the stabilization mechanism of the diffusion flame. The results from this study are as follows. The fuel injection angle is an important factor in determining the flame stability. Stability limits can be improved by variety of the fuel injection ratio. When the grid and extension duct are set, stability characteristics are varied with the blockage ratios, grid intervals, and grid numbers. The recirculation zone not only serves as a steady ignition source of combustion stream but also governs the stabilization mechanism.

• Physical Therapy Korea
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• v.6 no.1
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• pp.35-46
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• 1999

The purposes of this study were to evaluate and compare the limits of stability(LOS) at different body positioning(standing and one leg standing) in normal 20 years of age. Fourty subjects participated in the study. Subjects comprised 20 males and 20 females who without neurologic, orthopaedic impairments and balance performance impaired. The LOS was measured at Two Feet Forceplate and One Leg Forceplate with BPM(Balance Performance Monitor) Dataprint Software Version 5.3. The subjects stood 4 inches between the feet at Two Feet Forceplate and stood one legged at One Leg Forceplate. In this study applied the paired t-test and independent t-test to determine the statistical significance of results at 0.01 and 0.05 level of significance. The results of this study were as follows: 1) The anteroposterior LOS significantly increased with one legged stance(p<0.05). 2) The mediolateral LOS significantly decreased with one legged stance(p<0.01). 3) There were significant difference posterior LOS in standing and anterior LOS in one legged stance according to sexual difference(p<0.05). 4) The mediolateral LOS was not significant difference between standing and one legged stance according to sexual difference(p>0.05).

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.673-688
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• 2011

Let $n{\geq}2$ be an even integer. We investigate that if an odd mapping f : X ${\rightarrow}$ Y satisfies the following equation $2_{n-2}C_{\frac{n}{2}-1}rf\(\sum\limits^n_{j=1}{\frac{x_j}{r}}\)\;+\;{\sum\limits_{i_k{\in}\{0,1\} \atop {{\sum}^n_{k=1}\;i_k={\frac{n}{2}}}}\;rf\(\sum\limits^n_{i=1}(-1)^{i_k}{\frac{x_i}{r}}\)=2_{n-2}C_{{\frac{n}{2}}-1}\sum\limits^n_{i=1}f(x_i),$ then f : X ${\rightarrow}$ Y is additive, where $r{\in}R$. We also prove the stability in normed group by using shadowing property and the Hyers-Ulam stability of the functional equation in Banach spaces and in Banach modules over unital C-algebras. As an application, we show that every almost linear bijection h : A ${\rightarrow}$ B of unital $C^*$-algebras A and B is a $C^*$-algebra isomorphism when $h(\frac{2^s}{r^s}uy)=h(\frac{2^s}{r^s}u)h(y)$ for all unitaries u ${\in}$ A, all y ${\in}$ A, and s = 0, 1, 2,....

• Honam Mathematical Journal
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• v.30 no.2
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• pp.233-246
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• 2008

In this paper, we obtain the general solution of the following cubic type functional equation and establish the stability of this equation (0.1) $kf({{\sum}\limits^{n-1}_{j=1}}x_j+kx_n)+kf({{\sum}\limits^{n-1}_{j=1}}x_j-kx_n)+2{{\sum}\limits^{n-1}_{j=1}}f(kx_j)+(k^3-1)(n-1)[f(x_1)+f(-x_1)]=2kf({\sum\limits^{n-1}_{j=1}}x_j)=K^3{\sum\limits^{n-1}_{j=1}[f(x_j+x_n)+f(x_j-x_n)]$ for any integers k and n with k ${\geq}$ 2 and n ${\geq}$ 3.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.455-466
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• 2008

In, [7], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\left\|{\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i{\left\|^2+{\sum\limits_{i=1}^{n}}\right\|}{x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}x_j}}\right\|^2}={\sum\limits_{i=1}^{n}}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\cdots},x_{n}{\in}V$. Let V,W be real vector spaces. It is shown that if a mapping $f:V{\rightarrow}W$ satisfies $$(0.1){\hspace{10}}nf{\left({\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i \right)}+{\sum\limits_{i=1}^{n}}f{\left({x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}}x_i}\right)}\\{\hspace{140}}={\sum\limits_{i=1}^{n}}f(x_i)$$ for all $x_1$, ${\dots}$, $x_{n}{\in}V$ $$(0.2){\hspace{10}}2f\(\frac{x+y}{2}\)+f\(\frac{x-y}{2} \)+f\(\frac{y}{2}-x\)\\{\hspace{185}}=f(x)+f(y)$$ for all $x,y{\in}V$. Furthermore, we prove the generalized Hyers-Ulam stability of the functional equation (0.2) in real Banach spaces.

• 한국연소학회:학술대회논문집
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• 2015.12a
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• pp.247-250
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• 2015

The characteristics of opposed nonpremixed tubular flames with radiation heat loss are investigated using linear stability analysis and 2-D numerical simulations. Two extinction limits, as the $Damk{\ddot{o}}hler$ number is small or large, are confirmed using finite difference method with a simple continuation method. It is verified that the results of linear stability analysis predict the number of flame cells and the critical Da starting cellular instability or amplification of temperature near both extinction limits with good resolution.