• 대한수학회보
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• 제60권4호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권3호
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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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• 제15권11호
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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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• 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 $L^{t,{\rho}}_{{\varpi},{\sigma}}f(\zeta)$.

• Bulletin of the Korean Chemical Society
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• 제27권2호
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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.

• 대한화학회지
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• 제38권12호
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• pp.915-920
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• 1994

치환(Z)-벤질(X)-아렌 술포네이트류와 치환(Y)-피리딘과의 Menschutkin형 반응을 $35\circC$ 아세토니트릴 용액에서 전기전도도법으로 측정하였다. 이 반응의 2차 반응속도상수로부터 Hammett $\rho$값을 구하였다. 음의 $\rho_Y$값은 전이 상태에서 친핵체로부터 기질의 벤질기에 하전이동이 일어나 친핵체의 질소에 양의 하전을 띤다. 양의 $\rho_X$값은 이탈기인 술포네이트에 음의 하전이 발달되어 있음을 나타내며 음의 $\rho_Z$값은 반응 중심인 벤질 탄소에 양의 하전을 띠고 있음을 각각 나타낸다. 복합 Hammett의 상호작용 항은 │$\rho_YZ$│ > │$\rho_XY$│ > │$\rho_ZX$│의 순으로 나타났으며 이들의 결과로부터 치환 benzyl arenesulfonate류와 치환 pyridine류의 반응은 dissociative $S_N2$으로 진행됨을 알 수 있었다.

• 한국인터넷방송통신학회논문지
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• 제17권6호
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• pp.19-25
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• 2017

본 논문은 비트코인 채굴에 필요한 SHA-256 암호 해시 값(n)을 구성하는 2개의 소수(p,q)를 빠르게 해독하는 소인수분해법을 다룬다. 본 논문에서는 Pollard's Rho 소인수분해 알고리즘의 수행횟수를 월등히 감소시킨 알고리즘을 제안하였다. Rho (${\rho}$) 알고리즘은 $(x_0,y_0)=(2,2)$ 초기치에 대해 $x_i=x^2_{i-1}+1(mod\;n)$과 $y_i=[(y^2_{i-1}+1)^2+1](mod\;n)$을 계산하여 1 < $gcd({\mid}x_i-y_i{\mid},n)$ < n으로 소인수를 구한다. 이 알고리즘은 특정 합성수에 대해서는 소인수 분해에 실패할 수 있다. 제안된 알고리즘은 Pollard Rho 알고리즘에 $(x_0,y_0)=(2^k,2^k)$와 ($2^k,2$), $2{\leq}k{\leq}10$을 적용하였다. 그 결과 모든 합성수에 대해 소인수분해를 할 수 있었으며, Pollard Rho 알고리즘의 수행횟수를 67.94% 감소시켰다.

• 생명과학회지
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• 제17권2호통권82호
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• pp.192-197
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• 2007

외부 병원체 침입으로 이동하고 있는 T 세포는 두가지 뚜렷한 형태적인 변화, 즉, leading edge와 uropod를 형성하여 효과적으로 T세포 이동에 영향을 미친다. Uropod 구조물은 이동하는 림프구들의 뒤쪽에서 관찰 할 수 있는 아주 독특한 구조로 CD44, ERM, F-actin과 같은 단백질들이 서로 영향을 미치며 모인다. F-actin cytoskeleton은 세포의 형태를 유지하는 기본적인 틀을 제공한다. Rho A small GTPase는 이러한 cytoskeleton을 재구성하는 organizer로 역할을 한다고 보고되어 왔다. 지금까지, 다양한 경로를 통하여 Rho A가 활성화 되어 진다고 보고 되었다. 본 실험에서 PDZ 도메인이 세포 내부 RHo A에 GDP가 결합된 불활성화 형태의 Rho A를 GTP가 결합된 활성화 형태로 전환한다는 것을 알았고, F-actin cytoskeleton을 재구성 하며, PDZ 도메인을 함유한 세포는 uorpod 구조물이 없어졌으며 세포 이동 속도도 감소하는 것을 알았다. 따라서 Rho A와 F-actin cytoskeleton 사이의 신호 전달 과정이 uropod 형성에 아주 중요한 기능을 할 것이라는 것을 알았다.

• The Korean Journal of Physiology and Pharmacology
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• 제23권6호
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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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• 제48권6호
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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.