• 대한수학회보
• /
• 제50권1호
• /
• pp.83-96
• /
• 2013

Let K be a number field and fix a prime number $p$. For any set S of primes of K, we here say that an elliptic curve E over K has S-reduction if E has bad reduction only at the primes of S. There exists the set $B_{K,p}$ of primes of K satisfying that any elliptic curve over K with $B_{K,p}$-reduction has no $p$-torsion points under certain conditions. The first aim of this paper is to construct elliptic curves over K with $B_{K,p}$-reduction and a $p$-torsion point. The action of the absolute Galois group on the $p$-torsion subgroup of E gives its associated Galois representation $\bar{\rho}_{E,p}$ modulo $p$. We also study the irreducibility and surjectivity of $\bar{\rho}_{E,p}$ for semistable elliptic curves with $B_{K,p}$-reduction.

• Journal of Microbiology and Biotechnology
• /
• 제18권1호
• /
• pp.171-175
• /
• 2008

Here, we report that Vibrio parahaemolyticus induces a rapid remodeling of macrophage actin and activates RhoB GTPase. Mutational analysis revealed that the effects depend on type III secretion system 1 regulated translocation of a V. parahaemolyticus effector protein, VP1686, into the macrophages. Remodeling of actin is shown to be necessary for increased bacterial uptake followed by initiation of apoptosis in macrophages. This provides evidence for functional association of the VP1686 in triggering an eat me-and-die signal to the host.

• Molecules and Cells
• /
• 제26권4호
• /
• pp.396-403
• /
• 2008

The first ORF of the ARV S1133 S1 segment encodes the nonstructural protein p10, which is responsible for the induction of cell syncytium formation. However, p10-dependent signaling during syncytium formation is fully unknown. Here, we show that dominant negative RhoA, Rho inhibitor C3 exoenzyme, ROCK/Rho-kinase inhibitor Y-27632 and Rac1 inhibitor NSC23766 inhibit p10-mediated cell fusion. p10 over-expression is concomitant with activation and membrane translocation of RhoA and Rac1, but not cdc42. RhoA and Rac1 downstream events, including JNK phosphorylation and transcription factor AP-1 and $NF-{\kappa}B$ activation, as well as MLC expression and phosphorylation are simultaneously activated by p10. p10 point mutant T13M possessed 20% fusion-inducing ability and four p10 fusion-deficient mutants V15M, V19M, C21S and L32A reduced or lost their ability to activate RhoA and Rac1 signaling. We conclude that p10-mediated syncytium formation proceeds by utilizing RhoA and Rac1-dependent signaling.

• 대한수학회보
• /
• 제54권4호
• /
• pp.1141-1158
• /
• 2017

In this paper, we study the value distribution of the derivative of a Dirichlet L-function $L^{\prime}(s,{\chi})$ at the a-points ${\rho}_{a,{\chi}}={\beta}_{a,{\chi}}+i{\gamma}_{a,{\chi}}$ of $L^{\prime}(s,{\chi})$. We give an asymptotic formula for the sum $${\sum_{{\rho}_{a,{\chi}};0<{\gamma}_{a,{\chi}}{\leq}T}\;L^{\prime}({\rho}_{a,{\chi}},{\chi})X^{{\rho}_{a,{\chi}}}\;as\;T{\rightarrow}{\infty}$$, where X is a fixed positive number and ${\chi}$ is a primitive character mod q. This work continues the investigations of Fujii [4-6], $Garunk{\check{s}}tis$ & Steuding [8] and the authors [12].

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

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제23권2호
• /
• pp.145-153
• /
• 2016

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

• 대한수학회보
• /
• 제59권5호
• /
• pp.1305-1315
• /
• 2022

Let u be a function on a connected finite graph G = (V, E). We consider the mean field equation (1) $-{\Delta}u={\rho}\({\frac{he^u}{\int_Vhe^ud{\mu}}}-{\frac{1}{{\mid}V{\mid}}}\),$ where ∆ is 𝜇-Laplacian on the graph, 𝜌 ∈ ℝ\{0}, h : V → ℝ⁺ is a function satisfying min_x∈V h(x) > 0. Following Sun and Wang [15], we use the method of Brouwer degree to prove the existence of solutions to the mean field equation (1). Firstly, we prove the compactness result and conclude that every solution to the equation (1) is uniformly bounded. Then the Brouwer degree can be well defined. Secondly, we calculate the Brouwer degree for the equation (1), say $$d_{{\rho},h}=\{{-1,\;{\rho}>0, \atop 1,\;{\rho}<0.}$$ Consequently, the equation (1) has at least one solution due to the Brouwer degree d_𝜌,h ≠ 0.

• BMB Reports
• /
• 제51권6호
• /
• pp.296-301
• /
• 2018

Mitochondrial DNA (mtDNA) mutations are often observed in various cancer types. Although the correlation between mitochondrial dysfunction and cancer malignancy has been demonstrated by several studies, further research is required to elucidate the molecular mechanisms underlying accelerated tumor development and progression due to mitochondrial mutations. We generated an mtDNA-depleted cell line, ${\rho}^0$, via long-term ethidium bromide treatment to define the molecular mechanisms of tumor malignancy induced by mitochondrial dysfunction. Mitochondrial dysfunction in ${\rho}^0$ cells reduced drug-induced cell death and decreased the expression of pro-apoptotic proteins including p53. The p53 expression was reduced by activation of nuclear $factor-{\kappa}B$ that depended on elevated levels of free calcium in $HCT116/{\rho}^0$ cells. Overall, these data provide a novel mechanism for tumor development and drug resistance due to mitochondrial dysfunction.

• 전기의세계
• /
• 제32권8호
• /
• pp.486-493
• /
• 1983

기존 Echo제거기의 여파기계수를 binary representation할 때 bit수를 줄이기 위하여 자동이득 조절기를 사용한 새로운 Echo제거기를 제안하였다. 적응여파기 계수수가 55이고 .rho.e=16dB, P/S.leq. dB일때 P.leq.0 dB, S>-42 dB인 경우 새echo제거기는 20bit로서 8bit로 규격화된 디지탈 Processor 또는 기억소자등을 사용하면 30%의 bit절약을 가져온다. 수학적 operation은 대단히 경미하게 증가하며 수렴속도도 훨씬 빠르다.

• Investigative Magnetic Resonance Imaging
• /
• 제18권3호
• /
• pp.208-218
• /
• 2014

목적: 조영증강 MRI에서의 간혈관종의 조영증강속도와 겉보기확산계수 및 복셀내비결집운동 MR영상에서의 여러가지 지표인, 진성 확산계수 (D), 관류계수 (f), 가성 확산계수 ($D^*$), 겉보기확산계수 ($ADC_{fit}$)와의 상관관계를 알아보고자 하였다. 대상과 방법: 후향적인 연구로 IRB 승인을 받았다. 39명 환자에서 47개의 간혈관종을 연구대상으로 하였다. 이 중 남자가 20명 여자가 19명이었다. 간혈관종은 조영증강후 시행한 T1 강조영상에서의 조영증강 속도에 따라서 3가지 형으로 분류하였고, 빠른 조영증강을 보이는 간혈관종은 A형, 중간정도는 B형, 느린 조영증강을 보이는 경우는 C형으로 하였다. D, f, $D^*$ and $ADC_{fit}$ 값을 구하여 3가지형의 간혈관종 간에 차이를 비교하였다. 결과: $ADC_{fit}$와 D 값은 C형의 간혈관종이 A형의 간혈관종보다 유의하게 낮았다 (P = 0.0022, P = 0.0085). 하지만 f 와 $D^*$ 값은 세 군간에 차이가 없었다. 모든 b값에서의 (50, 200, 500 and $800sec/mm^2$) 겉보기확산계수값은 C형이 A형에 비해 유의하게 낮았다 (P < 0.012). 그리고 b값이 $800sec/mm^2$에서 C형의 겉보기확산계수 값이 B형보다 유의하게 낮았다 (P = 0.0021). 하지만 다른 b 값에서는 A형과 B형, B형과 C형 간의 차이는 없었다(P > 0.016). 간혈관종의 조영증강 속도와 각 b 값에서의 겉보기확산계수 값 $ADC_{50}$ (${\rho}=-0.357$, P = 0.014), $ADC_{200}$ (${\rho}=-0.537$, P = 0.0001), $ADC_{500}$ (${\rho}=-0.614$, P = 0.0001), $ADC_{800}$ (${\rho}=-0.607$, P = 0.0001)과는 부적 상관관계 (negative correlation)를 보였다. 따라서 $ADC_{50}$, $ADC_{200}$, $ADC_{500}$, and $ADC_{800}$에서의 겉보기확산계수 값은 조영증강속도가 느릴수록 감소하는 경향을 보였다. 결론: 간혈관종은 조영증강 속도에 따라 다양한 겉보기확산계수 값을 보이고, 느린 조영증강을 보이는 간혈관종이 감소된 겉보기확산계수 값을 보이는 것은 진성 분자확산과 관계가 있다.