• 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.

• Journal of Energy Engineering
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• v.23 no.4
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• pp.141-149
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• 2014

In the present study, pure RHO zeolite was hydrothermally synthesized by using 18-crown-6 ether as a structure directing agent(SDA), and the small gases adsorption was investigated. Synthesized RHO zeolite was a cube shape particle of which average edge length was around $1.2{\mu}m$ and composed of primary crystallites having a diameter of around 100 to 200 nm. RHO zeolite structure was stable under 3h calcination at $600^{\circ}C$. Water adsorption data announced that RHO zeolite has a specific surface area of 483.32 m2/g and its micropore diameter was about 4 A. Gas adsorption was studied in the pressure range of 50 to 500 kPa for $CO_2$, $N_2$, $O_2$ and $H_2$. It was evident that RHO zeolite showed a strong $CO_2$ adsorption behavior. Especially, RHO zeolite showed a transient $CO_2$ adsorption behavior. The 3h $CO_2$ up-take at 50 kPa and 500 kPa was 1.283 and 3.357 mmol/g, respectively. The $CO_2/H_2$ selectivity was around 16 at 500 kPa. Compared with gas adsorption data for some representative microporous adsorbents, it was certain that RHO zeolite is a beneficial adsorbent for $CO_2/H_2$ separation.

• Journal of Microbiology and Biotechnology
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• v.30 no.10
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• pp.1488-1494
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• 2020

Rho guanine nucleotide dissociation inhibitor 1 (RhoGDI1) plays important roles in numerous cellular processes, including cell motility, adhesion, and proliferation, by regulating the activity of Rho GTPases. Its expression is altered in various human cancers and is associated with malignant progression. Here, we show that RhoGDI1 interacts with Cullin 3 (CUL3), a scaffold protein for E3 ubiquitin ligase complexes. Ectopic expression of CUL3 increases the ubiquitination of RhoGDI1. Furthermore, potassium channel tetramerization domain containing 5 (KCTD5) also binds to RhoGDI1 and increases its interaction with CUL3. Ectopic expression of KCTD5 increases the ubiquitination of RhoGDI1, whereas its knockdown by RNA interference has the opposite effect. Depletion of KCTD5 or expression of dominant-negative CUL3 (DN-CUL3) enhances the stability of RhoGDI1. Our findings reveal a previously unknown mechanism for controlling RhoGDI1 degradation that involves a CUL3/KCTD5 ubiquitin ligase complex.

• The Pure and Applied Mathematics
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• v.24 no.2
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• pp.109-127
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• 2017

In this paper, we solve the following quadratic ${\rho}-functional$ inequalities ${\parallel}f({\frac{x+y+z}{2}})+f({\frac{x-y-z}{2}})+f({\frac{y-x-z}{2}})+f({\frac{z-x-y}{2}})-f(x)-f(y)f(z){\parallel}$ (0.1) ${\leq}{\parallel}{\rho}(f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z)){\parallel}$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < ${\frac{1}{{\mid}4{\mid}}}$, and ${\parallel}f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z){\parallel}$ (0.2) ${\leq}{\parallel}{\rho}(f({\frac{x+y+z}{2}})+f({\frac{x-y-z}{2}})+f({\frac{y-x-z}{2}})+f({\frac{z-x-y}{2}})-f(x)-f(y)f(z)){\parallel}$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < ${\mid}8{\mid}$. Using the direct method, we prove the Hyers-Ulam stability of the quadratic ${\rho}-functional$ inequalities (0.1) and (0.2) in non-Archimedean Banach spaces and prove the Hyers-Ulam stability of quadratic ${\rho}-functional$ equations associated with the quadratic ${\rho}-functional$ inequalities (0.1) and (0.2) in non-Archimedean Banach spaces.

• Biotechnology and Bioprocess Engineering:BBE
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• v.9 no.1
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• pp.23-34
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• 2004

Escherichia coli transcription termination factor Rho catalyzes the unwinding of RNA/DNA duplex in reactions that are coupled to ATP binding and hydrolysis. Fluorescence stopped-flow methods using ATP and the fluorescent 2'(3')-O-( N-methylanthraniloyl) derivatives (mant-derivatives) of ATP and ADP were used to probe the kinetics of nucleotide binding to and dissociation from the Rho-RNA complex. Presteady state nucleotide binding kinetics provides evidence for the presence of negative cooperativity in nucleotide binding among the multiple nucleotide binding sites on Rho hexamer. The binding of the first nucleotide to the Rho-RNA complex occurs at a bimolecular rate of 3.6${\times}$10$\^$6/ M$\^$-1/ sec$\^$-1/ whereas the second nucleotide binds at a slower rate of 4.7${\times}$10$\^$5/ M$\^$-1/ sec$\^$-1/ at 18$^{\circ}C$, RNA complexed with Rho affects the kinetics of nucleotide interaction with the active sites through conformational changes to the Rho hexamer, allowing the incoming nucleotide to be more accessible to the sites. Adenine nucleotide binding and dissociation is more favorable when RNA is bound to Rho, whereas ATP binding and dissociation step in the absence of RNA occurs significantly slower, at a rate ∼70- and ∼40-fold slower than those observed with the Rho-RNA complex, respectively.

• Korean Journal of Mathematics
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• v.23 no.2
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• pp.231-248
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• 2015

In this paper, we solve the following quadratic $\rho$-functional inequalities ${\parallel}f(\frac{x+y+z}{2})+f(\frac{x-y-z}{2})+f(\frac{y-x-z}{2})+f(\frac{z-x-y}{2})-f(x)-x(y)-f(z){\parallel}\;(0.1)\\{\leq}{\parallel}{\rho}(f(x+y+z+)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-f(z)){\parallel}$ where $\rho$ is a fixed complex number with ${\left|\rho\right|}<\frac{1}{8}$, and ${\parallel}f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z){\parallel}\;(0.2)\\{\leq}{\parallel}{\rho}(f(\frac{x+y+z}{2})+f(\frac{x-y-z}{2})+f(\frac{y-x-z}{2})+f(\frac{z-x-y}{2})-f(x)-f(y)-f(z)){\parallel}$ where $\rho$ is a fixed complex number with ${\left|\rho\right|}$ < 4. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic $\rho$-functional inequalities (0.1) and (0.2) in complex Banach spaces.

• Magazine of the Korea Concrete Institute
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• v.8 no.6
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• pp.141-149
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• 1996

The reinforced high-strength-concrete beam subjected to flexure moment behaves more brittly than the moderate-strength-concrete beam reinforced with equal reinforcement ratio($\rho$/$\rho_b$). Test results show that when the concrete strength exceeds 830kg/$cm^2$, the maximum reinforcement ratio should be less than $0.6{\rho}_b$ for ductile behavior (${\rho}_b$=balanced steel ratio). The ratio of flexural strength between experimental results and analytical results with rectangular stress block decrease as the compressive strength of concrete increase. The shape of the compressive stress block distributed triangularly. because the ascending part of the stress-strain curve shows fairly linear response up to maximum stress in contrast to the nonlinear behavior of the medium and low strength specimens.

• Journal of Microbiology and Biotechnology
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• v.4 no.1
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• pp.63-67
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• 1994

A microorganism showing degradative activity towards benzene, toluene and ${\rho}-xylene$ (BTX) was isolated from an activated sewage sludge and was tentatively identified as Pseudomonas fluorescence BE103. This strain was found to utilize benzene and toluene as growth substrates, but to degrade ${\rho}-xylene$ in the obligate presence of a growth substrate. The metabolic product resulted from the cometabolism of ${\rho}-xylene$ was identified as 3, 6-dimethylpyrocatechol by LC/MS analysis, and the metabolic pathway was analyzed to be similar to the tod pathway. From the kinetic studies done regarding BTX biodegradation using Pseudomonas fluorescence BE103, it was revealed that the cometabolism of ${\rho}-xylene$ is significantly affected by the ratio of growth substrate concentration to biomass concentration, and that the cometabolism of ${\rho}-xylene$ initiates only when this ratio was about 0.03.

• The Pure and Applied Mathematics
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• v.24 no.4
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• pp.243-251
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• 2017

In this paper, we solve the additive ${\rho}-functional$ equations (0.1) $f(x+y)+f(x-y)-2f(x)={\rho}(2f(\frac{x+y}{2})+f(x-y)-2f(x))$, and (0.2) $2f(\frac{x+y}{2})+f(x-y)-2f(x)={\rho}(f(x+y)+f(x-y)-2f(x))$, where ${\rho}$ is a fixed (complex) number with ${\rho}{\neq}1$, Using the direct method, we prove the Hyers-Ulam stability of the additive ${\rho}-functional$ equations (0.1) and (0.2) in ${\beta}-homogeneous$ (complex) F-spaces.