• Journal of the Korean Mathematical Society
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• v.32 no.4
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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 $(u, \upsilon)$.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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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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• v.26 no.3
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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 $L^{t,{\rho}}_{{\varpi},{\sigma}}f(\zeta)$.

• The Pure and Applied Mathematics
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• v.24 no.3
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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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• v.29 no.1
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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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• v.19 no.6
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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.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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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 ${\Gamma}({\eta})$.

• Journal of the Korean Magnetic Resonance Society
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• v.17 no.1
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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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• v.38 no.3
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• pp.235-242
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• 2003

A vulcanization reaction characteristics of an isoprene rubber (IR)-modified natural rubber/carbon black (NR/CB) composite was studied using in-situ electrical property measuring technique. Since the electrical conductivity of the sample composite would be changed continuously during the vulcanization reaction by rearranging of the carbon black particles within the sample, volume resistivity (${\rho}$) might be obtained as a function or reaction time. A stabilization time ($t_i$), maximum reaction speed time ($t_p$), and volume resistivity at that time(${\rho}_p$) were defined from the data for the Arrhenius analysis. Volume resistivity ${\rho}$ showed a comparatively high value of ${\sim}10^8$ order before the reaction started, and dramatically decreased to be stabilized within $1{\sim}2$ minutes as soon as the reaction started. As the more time elapsed, thereafter, ${\rho}$ decreased monotonously to a certain constant value through a peak, ${\rho}_p$ at time $t_p$, which was considered as the maximum reaction rate. As a result, while $t_i$ values were comparatively constant as $1{\sim}2$ minutes, $t_p$ values showed to become shorter and shorter as the reaction temperature.

• The Pure and Applied Mathematics
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• v.27 no.1
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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.