• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1085-1100
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• 2023

For any given function f, we focus on the so-called prescribed mean curvature problem for the measure e^-f(|x|2)dx provided thate^-f(|x|2) ∈ L¹(ℝⁿ⁺¹). More precisely, we prove that there exists a smooth hypersurface M whose metric is ds² = dρ² + ρ²d𝜉² and whose mean curvature function is ${\frac{1}{n}}(\frac{u^p}{{\rho}^{\beta}})e^{f({\rho}^2)}{\psi}(\xi)$ for any given real constants p, β and functions f and ψ where u and ρ are the support function and radial function of M, respectively. Equivalently, we get the existence of a smooth solution to the following quasilinear equation on the unit sphere 𝕊ⁿ, $${\sum_{i,j}}({{\delta}_{ij}-{\frac{{\rho}_i{\rho}_j}{{\rho}^2+|{\nabla}{\rho}|^2}})(-{\rho}ji+{\frac{2}{{\rho}}}{\rho}j{\rho}i+{\rho}{\delta}_{ji})={\psi}{\frac{{\rho}^{2p+2-n-{\beta}}e^{f({\rho}^2)}}{({\rho}^2+|{\nabla}{\rho}|^2)^{\frac{p}{2}}}}$$ under some conditions. Our proof is based on the powerful method of continuity. In particular, if we take $f(t)={\frac{t}{2}}$, this may be prescribed mean curvature problem in Gauss measure space and it can be seen as an embedded result in Gauss measure space which will be needed in our forthcoming papers on the differential geometric analysis in Gauss measure space, such as Gauss-Bonnet-Chern theorem and its application on positive mass theorem and the Steiner-Weyl type formula, the Plateau problem and so on.

• The Pure and Applied Mathematics
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• v.25 no.3
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• pp.219-227
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• 2018

In this paper, we solve the additive ${\rho}$-functional equations $$(0.1)\;f(x+y)+f(x-y)-2f(x)={\rho}\left(2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)\right)$$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < 1, and $$(0.2)\;2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)={\rho}(f(x+y)+f(x-y)-2f(x))$$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < |2|. Furthermore, we prove the Hyers-Ulam stability of the additive ${\rho}$-functional equations (0.1) and (0.2) in non-Archimedean Banach spaces.

• Bulletin of the Korean Chemical Society
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• v.15 no.11
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• pp.985-990
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• 1994

Cross-interaction constants, ${\rho}^e_{XY}$, ${\rho}_{YZ}$ and ${\rho}_{XZ}$ are defined using observed rate constant, k_N=(k_1/k_{-1})k_2=Kk_2$, for the stepwise carbonyl addition reactions involving the rate-limiting breakdown of a tetrahedral intermediate $(T^{\pm})$. Abundant experimental evidence in the literature enables us to determine signs for the three constants for such mechanism, ${\rho}^e_{XY}$>0, ${\rho}_{YZ}$<0 and ${\rho}_{XZ}$0. These are in contrast to those for the concerted $S_N2$ mechanism, ${\rho}_{XY}$<0, ${\rho}_{YZ}$>0 and ${\rho}_{XZ}$, and provide useful mechanistic criteria. In the light of these criteria, mechanisms of some nucleophilic reactions of carbonyl compounds are re-examined.

• 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 $L^{t,{\rho}}_{{\varpi},{\sigma}}f(\zeta)$.

• Bulletin of the Korean Chemical Society
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• v.27 no.2
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• pp.224-230
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• 2006

Escherichia coli transcription termination factor Rho catalyzes the unwinding of RNA/DNA duplex in reactions that are coupled to ATP binding and hydrolysis. We report here the kinetic mechanism of presteady state ATP binding and hydrolysis by the Rho-RNA complex. Presteady state chemical quenched-flow technique under multiple turnover condition was used to probe the kinetics of ATP binding and hydrolysis by the Rho-RNA complex. The quenched-flow presteady state kinetics of ATP hydrolysis studies show that three ATPs are bound to the Rho-RNA complex with a rate of $4.4\;{\times}\;10^5M^{-1}s^{-1}$, which are subsequently hydrolyzed at a rate of $88s^{-1}$ and released during the initiation process. Global fit of the presteady state ATP hydrolysis kinetic data suggests that a rapid-equilibrium binding of ATP to Rho-RNA complex occurs prior to the first turnover and the chemistry step is not reversible. The initial burst of three ATPs hydrolysis was proposed to be involved in the initialization step that accompanies proper complex formation of Rho-RNA. Based on these results a kinetic model for initiation process for Rho-RNA complex was proposed relating the mechanism of ATP binding and hydrolysis by Rho to the structural transitions of Rho-RNA complex to reach the steady state phase, which is implicated during translocation along the RNA.

• Journal of the Korean Chemical Society
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• v.38 no.12
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• pp.915-920
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• 1994

The Menschutkin type reactions of substituted (Z)-benzyl (X)-arenesulfonates with substituted(Y)-pyridines were studied by the electroconductometric method in acetonitrile at $35\circC$. Hammett $\rho$ values were calculated by the second order rate constants for the reaction of substituted (Z)-benzyl (X)-arenesulfonates with substituted (Y)-pyridines. The negative $\rho_Y$ values meant positive charge development on the nitrogen of pyridine at transition state owing to the charge development on the oxygen atom of benzenesulfonate. And the negative $\rho_Z$ values meant positive charge development on the benzylic carbon. Application of the multi-Hammett interaction,│$\rho_YZ$│ > │$\rho_XY$│ > │$\rho_ZX$│, the Menschutkin type reaction of substituted benzyl arenesulfonates with substituted pyridines was shown to be dissociative $S_N2$ mechanism.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.17 no.6
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• pp.19-25
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• 2017

This paper deals with integer factorization of two prime p,q of SHA-256 secure hash value n for Bit coin mining. This paper proposes an algorithm that greatly reduces the execution time of Pollard's rho integer factorization algorithm. Rho(${\rho}$) algorithm computes $x_i=x^2_{i-1}+1(mod\;n)$ and $y_i=[(y^2_{i-1}+1)^2+1](mod\;n)$ for intial values $(x_0,y_0)=(2,2)$ to find the factor 1 < $gcd({\mid}x_i-y_i{\mid},n)$ < n. It however fails to factorize some particular composite numbers. The algorithm proposed in this paper applies multiple initial values $(x_0,y_0)=(2^k,2^k)$ and ($2^k,2$), $2{\leq}k{\leq}10$ to the existing Pollard's Rho algorithm. As a results, the proposed algorithm achieves both the factorization of all the composite numbers and the reduction of the execution time of Pollard's Rho by 67.94%.

• Journal of Life Science
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• v.17 no.2 s.82
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• pp.192-197
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• 2007

Two distinct morphological features, leading edge and uropod, in mobile T lymphocyte are crucial for efficient directional movement. The uropod is a unique rear protrusion in migrating lymphocytes, in which several proteins, including CD44, ERM (ezrin/radixin/moesin), and F-actin cytoskeleton are concentrated and concerted. F-actin cytoskeleton is a basic mold for the shape maintenance. Rho A small GTPase acts as cytoskeleton organizer, So far, various pathways potentially can induce the Rho activation. PDZ domain is able to increase active Rho A form (Rho-GTP) level, reorganize F-actin cytoskeleton, disrupts the uropod structure and cell migration was diminished, suggesting that signaling pathways between Rho and F-artin cytoskeleton are related to uropod formation.

• The Korean Journal of Physiology and Pharmacology
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• v.23 no.6
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• pp.493-499
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• 2019

Macrophage-associated inflammation is crucial for the pathogenesis of diverse diseases including metabolic disorders. Rhodanthpyrone (Rho) is an active component of Gentiana rhodantha, which has been used in traditional Chinese medicine to treat inflammation. Although synthesis procedures of RhoA and RhoB were reported, the biological effects of the specific compounds have never been explored. In this study, the anti-inflammatory activity and mechanisms of action of RhoA and RhoB were studied in lipopolysaccharide (LPS)-stimulated macrophages. Pretreatment with RhoA and RhoB decreased inducible nitric oxide synthase and cyclooxygenase-2 expressions in RAW 264.7 cells and in thioglycollate-elicited mouse peritoneal macrophages. In addition, it downregulated transcript levels of several inflammatory genes in LPS-stimulated RAW 264.7 cells, including inflammatory cytokines/chemokines (Tnfa, Il6, and Ccl2) and inflammatory mediators (Nos2 and Ptgs2). Macrophage chemotaxis was also inhibited by treatment with the compounds. Mechanistic studies revealed that RhoA and RhoB suppressed the nuclear factor $(NF)-{\kappa}B$ pathway, but not the canonical mitogen activated protein kinase pathway, in LPS-stimulated condition. Moreover, the inhibitory effect of RhoA and RhoB on inflammatory gene expressions was attenuated by treatment with an $NF-{\kappa}B$ inhibitor. Our findings suggest that RhoA and RhoB play an anti-inflammatory role at least in part by suppressing the $NF-{\kappa}B$ pathway during macrophage-mediated inflammation.

• Structural Engineering and Mechanics
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• v.48 no.6
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• pp.833-848
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• 2013

Nine rectangular-section of High Strength Concrete(HSC) beams were designed and casted based on the American Concrete Institute (ACI) code provisons with varying of tensile reinforcement ratio as (${\rho}_{min}$, $0.2_{{\rho}b}$, $0.3_{{\rho}b}$, $0.4_{{\rho}b}$, $0.5_{{\rho}b}$, $0.75_{{\rho}b}$, $0.85_{{\rho}b}$, $_{{\rho}b}$, $1.2_{{\rho}b}$). Steel and concrete strains and deflections were measured at different points of the beam's length for every incremental load up to failure. The ductility ratios were calculated and the moment-curvature and load-deflection curves were drawn. The results showed that the ductility ratio reduced to less than 2 when the tensile reinforcement ratio increased to $0.5_{{\rho}b}$. Comparison of the theoretical ductility coefficient from CSA94, NZS95 and ACI with the experimental ones shows that the three mentioned codes exhibit conservative values for low reinforced HSC beams. For over-reinforced HSC beams, only the CSA94 provision is more valid. ACI bending provision is 10 percent conservative for assessing of ultimate bending moment in low-reinforced HSC section while its results are valid for over-reinforced HSC sections. The ACI code provision is non-conservative for the modulus of rupture and needs to be reviewed.