• 대한수학회지
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• 제32권4호
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• pp.725-737
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• 1995

Let $X_t = (X_t^(1), X_t^(2))', t \geqslant 0$, be a real stationary 2-dimensional Gaussian process with $EX_t^(1) = EX_t^(2) = 0$ and $$ EX_0 X'_t = (_{\rho(t) r(t)}^{r(t) \rho(t)}), $$ where $r(t) \sim $\mid$t$\mid$^-\alpha, 0 < \alpha < 1/2, \rho(t) = o(r(t)) as t \to \infty, r(0) = 1, and \rho(0) = \rho (0 \leqslant \rho < 1)$. For $t > 0, u > 0, and \upsilon > 0, let L_t (u, \upsilon)$ be the time spent by $X_s, 0 \leqslant s \leqslant t$, above the level $(u, \upsilon)$.

• 대한수학회지
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• 제31권3호
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• pp.367-373
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• 1994

Let us consider the Cauchy problem $$ {\rho_t + \upsilon \cdot \nabla\rho = 0 {\rho[\upsilon_t + (\upsilon \cdot \nabla)\upsilon] + \nabla p + \rho f {div \upsilon = 0 (1.1) {\rho$\mid$_t = 0 = \rho_0(x) {\upsilon$\mid$_t = 0 = \upsilon_0(x) $$ in $Q_T = R^3 \times [0,T]$, where $f(x,t), \rho_0(x) and \upsilon_0(x)$ are given, while the density $\rho(x,t)$, the velocity vector $\upsilon(x,t) = (\upsilon^1(x,t),\upsilon^2(x,t),\upsilon^3(x,t))$ and the pressure p(x,t) are unknowns. The equations $(1.1)_1 - (1.1)_3$ describe the motion of a nonhomogeneous ideal incompressible fluid.

• Nonlinear Functional Analysis and Applications
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• 제26권3호
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• pp.553-563
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• 2021

As hypergeometric meromorphic multivalent functions of the form $$L^{t,{\rho}}_{{\varpi},{\sigma}}f(\zeta)=\frac{1}{{\zeta}^{\rho}}+{\sum\limits_{{\kappa}=0}^{\infty}}{\frac{(\varpi)_{{\kappa}+2}}{{(\sigma)_{{\kappa}+2}}}}\;{\cdot}\;{\frac{({\rho}-({\kappa}+2{\rho})t)}{{\rho}}}{\alpha}_{\kappa}+_{\rho}{\zeta}^{{\kappa}+{\rho}}$$ contains a new subclass in the punctured unit disk ${\sum_{{\varpi},{\sigma}}^{S,D}}(t,{\kappa},{\rho})$ for -1 ≤ D < S ≤ 1, this paper aims to determine sufficient conditions, distortion properties and radii of starlikeness and convexity for functions in the subclass $L^{t,{\rho}}_{{\varpi},{\sigma}}f(\zeta)$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제24권3호
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• pp.179-190
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• 2017

In this paper, we introduce and solve the following quadratic (${\rho}_1$, ${\rho}_2$)-functional inequality (0.1) $$N\left(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y),t\right){\leq}min\left(N({\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y)),t),\;N({\rho}_2(4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y)),t)\right)$$ in fuzzy normed spaces, where ${\rho}_1$ and ${\rho}_2$ are fixed nonzero real numbers with ${{\frac{1}{{4\left|{\rho}_1\right|}}+{{\frac{1}{{4\left|{\rho}_2\right|}}$ < 1, and f(0) = 0. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (${\rho}_1$, ${\rho}_2$)-functional inequality (0.1) in fuzzy Banach spaces.

• Journal of Advanced Marine Engineering and Technology
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• 제29권1호
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• pp.17-24
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• 2005

The characteristics of diesel spray have effect on the engine Performance such as power. fuel consumption and emissions. Therefore, This study was Performed to investigate the effect of various injection parameters. In this study. the experiment is performed by using the high temperature and high pressure chamber. Spray behaviors are visualized by using the high speed camera and spray angle. Penetration etc. are measured. Experimental results are summarized as follows ; 1) Correlations of spray Penetration is expressed as follows $$0 $$t_b 2) Correlations of spray Angle is expressed as follows $$T_a=293K \;;\; tan({\theta}/2)=0.59({\rho}_a/{\rho}_f)^{0.437}$$ $$T_a=473K\;;\; tan({\theta}/2)=0.588({\rho}_a/{\rho}_f)^{0.404}$$ 3) The measured macro characteristics - spray tip penetration and spray angle agreed well with established correlations.

• Journal of Mechanical Science and Technology
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• 제19권6호
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• pp.1321-1328
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• 2005

The characteristics of the diesel spray have affected certain aspects of engine performance, such as the power, fuel consumption, and emissions. Therefore, this study was performed to investigate the effects of various injection parameters. In order to obtain the effect of injection parameters on diesel spray characteristics, the experiment is performed by using a high temperature and pressure chamber. The behaviors of the spray are visualized by using a high speed video camera, spray angle, penetration, and various other things. The results of the experiment are summarized as follows. (1) The correlation of the spray penetration can be expressed as follows. $$0< t $$t_{b} (2) The correlation of the spray angle can be expressed as follows $$T_a=293K\;tan({\theta}/2)=0.59({\rho}a/{\rho}f)^{0.437}$$ $$T_a=473K\;tan({\theta}/2)=0.588({\rho}a/{\rho}f)^{0.404}$$ (3) The measured macro characteristics that include the spray tip penetration and spray angle corresponded with the established correlations.

• 충청수학회지
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• 제13권1호
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• pp.139-144
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• 2000

The generalized noncommutative torus $T_{\rho}^d$ of rank m was defined in [2]. Assume that for the completely irrational noncommutative subtorus $A_{\rho}$ of rank m of $T_{\rho}^d$ there is no integer q > 1 such that $tr(K_0(A_{\rho}))=\frac{1}{q}{\cdot}tr(K_0(A_{\rho^{\prime}}))$ for $A_{\rho^{\prime}}$ a completely irrational noncommutative torus of rank m. All $C^*$-algebras ${\Gamma}({\eta})$ of sections of locally trivial $C^*$-algebra bundles ${\eta}$ over $M=\prod_{i=1}^{e}S^{2k_i}{\times}\prod_{i=1}^{s}S^{2n_i+1}$, $\prod_{i=1}^{s}\mathbb{PR}_{2n_i}$, or $\prod_{i=1}^{s}L_{k_i}(n_i)$ with fibres $T_{\rho}^d{\otimes}M_c(\mathbb{C})$ were constructed in [6, 7, 8]. We prove that ${\Gamma}({\eta}){\otimes}M_{p^{\infty}}$ is isomorphic to $C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C}){\otimes}M_{p^{\infty}}$ if and only if the set of prime factors of cd is a subset of the set of prime factors of p, that $\mathcal{O}_{2u}{\otimes}{\Gamma}({\eta})$ is isomorphic to $\mathcal{O}_{2u}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if and only if cd and 2u - 1 are relatively prime, and that $\mathcal{O}_{\infty}{\otimes}{\Gamma}({\eta})$ is not isomorphic to $\mathcal{O}_{\infty}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if cd > 1 when no non-trivial matrix algebra can be ${\Gamma}({\eta})$.

• 한국자기공명학회논문지
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• 제17권1호
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• pp.24-29
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• 2013

The structural characteristics of 4-coordinate $BO_4$ [B(1)] and 3-coordinate $BO_3$ [B(2)] groups in $BiB_3O_6$ were studied by $^{11}B$ magic angle spinning (MAS) and single-crystal nuclear magnetic resonance (NMR) spectroscopy. The spin-lattice relaxation time in the laboratory frame, $T_1$, for $^{11}B$ decreased slowly with increasing temperature, whereas the spin-lattice relaxation times in the rotating frame, $T_{1{\rho}}$, for B(1) and B(2), which differed from $T_1$, were nearly constant. Further, $T_{1{\rho}}$ for B(1) and B(2) showed very similar trends, although the $T_{1{\rho}}$ value of B(2) was shorter than that of B(1). The 3-coordinate $BO_3$ and 4-coordinate $BO_4$ were distinguished by $^{11}B$ MAS NMR spectrum and $T_{1{\rho}}$.

• Elastomers and Composites
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• 제38권3호
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• pp.235-242
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• 2003

이소프렌 고무(IR)로 개질된 천연고무계의 NR/CB 복합재료의 가교반응에 대하여 반응 도중의 전기적 성질 변화를 in-situ로 측정함으로서 주어진 샘플의 가교반응 특성을 연구하였다. 샘플의 전기적 성질이 가황반응이 진행되는 동안 샘플 내의 카본 블랙의 재정렬에 의해 연속적으로 변하기 때문에 샘플의 체적고유저항 값(${\rho}$)의 변화를 반응시간의 함수로 표시하였다. 이로부터, 반응온도에 따른 반응시작 안정화시간($t_i$), 최대반응속도 시간($t_p$), 및 이 때의 최대반응속도 체적고유저항값(${\rho}_p$)을 정의하여 이로부터 Arrhenius 도시를 이용한 해석을 시도하였다. 체적 고유저항값 ${\rho}$는 반응시작 전에는 ${\sim}10^8$ order의 높은 값을 보이다가 반응시작 후에 급격히 떨어지는 안정화 시간, $t_i$를 거친 후에 다시 최대반응속도를 보이는 $t_p$에서 피크를 보이며, 그 이후에는 단조 감소하여 일정한 값으로 수렴하는 것이 관찰되었다. 한편, 샘플의 반응온도가 높아질수록 $t_i$는 $1{\sim}2$분으로서 상대적으로 일정한 데 반하여, $t_p$는 점점 더 짧아져 $160^{\circ}C$의 반응온도에서는 3분 정도로까지 짧아지는 것이 관찰되었다. 또한 반응의 인가 주파수에 대한 변화로서, 약 1,000Hz이하의 저주파수에서는 상대적으로 낮은 활성화에너지($E_a$)값을 보였으나, 10,000Hz의 높은 측정주파수에서는 더 큰 $E_a$값을 나타냄으로서 반응온도변화에 민감함을 보여주었다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제27권1호
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• pp.25-33
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• 2020

In this paper, we consider the following quadratic (ρ₁, ρ₂)-functional equation (0, 1) $$N(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y)-{\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y))-{\rho}_2(4f({\frac{x+y}{2}})+f(x-y)-f(x)-f(y)),t){\geq}{\frac{t}{t+{\varphi}(x,y)}}$$, where ρ₂ are fixed nonzero real numbers with ρ₂ ≠ 1 and 2ρ₁ + 2ρ₂≠ 1, in fuzzy normed spaces. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (ρ₁, ρ₂)-functional equation (0.1) in fuzzy Banach spaces.