• 한국추진공학회지
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• 제3권1호
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• pp.86-94
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• 1999

충격파가 초음속 수소-공기 제트화염의 화염 안정한계에 미치는 영향을 충격파의 강도와 위치를 변화시키면서 연구하였다. 이러한 목적으로 마하수 2.5의 초음속 연소기 벽면에 쐐기를 부착시켜 경사 충격파를 발생시켰다. 본 실험은 충격파가 초음속 화염에 미치는 영향을 연구한 최초의 실험연구이다. 쉬릴렌 가시화 사진과 벽면 정압, 화염 안정 한계를 측정하였으며 충격파가 없는 경우와 비교하였다. 보염 재순환 영역에 충격파를 적절히 간섭시킴으로써 화염 안정 한계가 대폭 개선되었다. 화염 안정한계가 대폭 향상된 이유는 충격파에 의해 발생한 역압력구배로 화염안정화에 중요한 아음속 재순환 영역의 크기가 증대된 때문으로 여겨진다.

• Korean Journal of Mathematics
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• 제16권3호
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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 $$(1)\;2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})=f(x)+f(y)$$.

• 충청수학회지
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• 제31권4호
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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.

• 한국정밀공학회지
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• 제15권12호
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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.

• 대한기계학회논문집
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• 제19권12호
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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.

• 충청수학회지
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• 제21권4호
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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.

• 한국전문물리치료학회지
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• 제6권1호
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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).

• 대한수학회보
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• 제48권4호
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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,....

• 호남수학학술지
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• 제30권2호
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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.

• 한국연소학회:학술대회논문집
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• 한국연소학회 2015년도 제51회 KOSCO SYMPOSIUM 초록집
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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.