• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.557-564
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• 2012

This study concerns the existence of positive solution for the following nonlinear system $$\{-div(|x|^{-ap}|{\nabla}u|^{p-2}{\nabla}u)=|x|^{-(a+1)p+c_1}({\alpha}_1f(v)+{\beta}_1h(u)),x{\in}{\Omega},\\-div(|x|^{-bq}|{\nabla}v|q^{-2}{\nabla}v)=|x|^{-(b+1)q+c_2}({\alpha}_2g(u)+{\beta}_2k(v)),x{\in}{\Omega},\\u=v=0,x{\in}{\partial}{\Omega}$$, where ${\Omega}$ is a bounded smooth domain of $\mathbb{R}^N$ with $0{\in}{\Omega}$, 1 < $p,q$ < N, $0{{\leq}}a<\frac{N-p}{p}$, $0{{\leq}}b<\frac{N-q}{q}$ and $c_1$, $c_2$, ${\alpha}_1$, ${\alpha}_2$, ${\beta}_1$, ${\beta}_2$ are positive parameters. Here $f,g,h,k$ : $[0,{\infty}){\rightarrow}[0,{\infty})$ are nondecresing continuous functions and $$\lim_{s{\rightarrow}{\infty}}\frac{f(Ag(s)^{\frac{1}{q-1}})}{s^{p-1}}=0$$ for every A > 0. We discuss the existence of positive solution when $f,g,h$ and $k$ satisfy certain additional conditions. We use the method of sub-super solutions to establish our results.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.195-212
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• 2023

In this paper, two weight conditions are introduced and the multiple weighted strong and weak characterizations of the multilinear fractional new maximal operator 𝓜_ϕ,β are established. Meanwhile, we introduce the ${\mathcal{S}}_{({\vec{p}},q),{\beta}}({\varphi})$ and $B_{({\vec{p}},q),{\beta}}({\varphi})$ conditions and obtain the characterization of two-weighted inequalities for 𝓜_ϕ,β. Finally, the relationships of the conditions ${\mathcal{S}}_{({\vec{p}},q),{\beta}}({\varphi}),\,{\mathcal{A}}_{({\vec{p}},q),{\beta}}({\varphi})$ and $B_{({\vec{p}},q),{\beta}}({\varphi})$ and the characterization of the one-weight $A_{({\vec{p}},q),{\beta}}({\varphi})$ are given.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.87-101
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• 2018

The purpose of this paper is to define a new class of hyperholomorphic functions spaces, which will be called $F^{\alpha}_{{\omega},G}$(p, q, s) type spaces. For this class, we characterize hyperholomorphic weighted ${\alpha}$-Bloch functions by functions belonging to $F^{\alpha}_{{\omega},G}$(p, q, s) spaces under some mild conditions. Moreover, we give some essential properties for the extended weighted little ${\alpha}$-Bloch spaces. Also, we give the characterization for the hyperholomorphic weighted Bloch space by the integral norms of $F^{\alpha}_{{\omega},G}$(p, q, s) spaces of hyperholomorphic functions. Finally, we will give the relation between the hyperholomorphic ${\mathcal{B}}^{\alpha}_{{\omega},0}$ type spaces and the hyperholomorphic valued-functions space $F^{\alpha}_{{\omega},G}$(p, q, s).

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.117-121
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• 2009

For $1{\leq}p$, $q{\leq}{\infty}$ and $s{\in}\mathbb{R}$, it is proved that there exists a constant C > 0 such that for any $f{\in}B^{s+2}_{p,q}(\mathbb{R}^n)$ $${\parallel}f{\parallel}_{B^{s+2}_{p,q}(\mathbb{R}^n)}{\leq}C{\parallel}f\;-\;{\Delta}f{\parallel}_{B^{s}_{p,q}(\mathbb{R}^n)}$$, which tells us that the operator $I-\Delta$ is $B^{s+2}_{p,q}$-coercive on the Besov space $B^s_{p,q}$.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.2
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• pp.231-237
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• 2018

Hardy's inequality is refined non-trivially as the form $${\int_{0}^{{\infty}}}\{{\frac{1}{x}}{\int_{0}^{x}}f(t)dt\}^pdx{\leq}Q_f{\times}({\frac{p}{p-1}})^p{\int_{0}^{x}}f^p(x)dx$$ for some $Q_f:0{\leq}Q_f{\leq}1$. $P{\acute{o}}lya$-Knopp's inequality is also refined by the similar form.

• Asian Pacific Journal of Cancer Prevention
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• v.16 no.9
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• pp.3723-3727
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• 2015

The p53 tumor suppressor protein is a principal mediator of growth arrest, senescence, and apoptosis in response to a broad array of cellular damage. p53 is a substrate for the ubiquitin-proteasome system, however, the ubiquitin-conjugating enzymes (E2s) involved in p53 ubiquitination have not been well studied. UBE2Q1 is a novel E2 ubiquitin conjugating enzyme gene. Here, we investigated the effect of UBE2Q1 overexpression on the level of p53 in the MDA-MB-468 breast cancer cell line as well as the interaction between UBE2Q1 and p53. By using a lipofection method, the p53 mutated breast cancer cell line, MDA-MB-468, was transfected with the vector pCMV6-AN-GFP, containing UBE2Q1 ORF. Western blot analysis was employed to verify the overexpression of UBE2Q1 in MDA-MB-468 cells and to evaluate the expression level of p53 before and after cell transfection. Immunoprecipitation and GST pull-down protocols were used to investigate the binding of UBE2Q1 to p53. We established MDA-MB-468 cells that transiently expressed a GFP fusion proteins containing UBE2Q1 (GFP-UBE2Q1). Western blot analysis revealed that levels of p53 were markedly lower in UBE2Q1 transfected MDA-MB-468 cells as compared with control MDA-MB-468 cells. Both in vivo and in vitro data showed that UBE2Q1 co-precipitated with p53 protein. Our data for the first time showed that overexpression of UBE2Q1can lead to the repression of p53 in MDA-MB-468 cells. This repression of p53 may be due to its UBE2Q1 mediated ubiquitination and subsequent proteasome degradation, a process that may involve direct interaction of UBE2Q1with p53.

• East Asian mathematical journal
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• v.35 no.3
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• pp.285-288
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• 2019

Let $F_n$, $n{\in}{\mathbb{N}}$ be the n - th Fibonacci number, and let (p, q) be one of ordered pairs ($F_{n+2}$, $F_n$) or ($F_{n+1}$, $F_n$). Then we show that the multiplicative inverse of q mod p as well as that of p mod q are again Fibonacci numbers. For proof of our claim we make use of well-known Cassini, Catlan and dOcagne identities. As an application, we determine the number $N_{p,q}$ of nonzero term of a polynomial ${\Delta}_{p,q}(t)=\frac{(t^{pq}-1)(t-1)}{(t^p-1)(t^q-1)}$ through the Carlitz's formula.

• Journal of Nutrition and Health
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• v.38 no.7
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• pp.570-577
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• 2005

The purpose of this study was to investigate the effect of bone mineral density on life styles, dietary habits and nutrient intakes among the male college students. The subjects were divided into four groups; $Q_1$ (calcaneus BMD < 25 percentile, n = 117), $Q_2$ (25 percentile $\le$ calcaneus BMD < 50 percentile, n = 118), $Q_3$ (50 percentile $\le$ calcaneus BMD < 75 percentile, n = 118) $Q_4$ (calcaneus BMD $\ge$ 75 percentile, n = 116). And they were asked about general characteristics, life style, dietary habit, and nutrient intake using questionnaire and 24-hr recall method. They were measured the bone mineral density of calcaneus using quantitative ultrasound. The average age of the subjects of the study was 23.0 yews and the average height, weight, and BMI were 174.7 cm, 69.0 kg, $22.5 kg/m^2$. The bone mineral density in calcaneus was $0.43 g/cm^2$ in $Q_1,\;0.50 g/cm^2$ in $Q_2,\;0.56 g/cm^2$ in $Q_3$, and $0.69 g/cm^2$ in $Q_4$ (p < 0.001). The results showed that $Q_1$ tended to have irregular exercise compared to the other three groups. Compared with $Q_1$ and $Q_2$, the frequency of skipping breakfast was lower in $Q_3$ and $Q_4$. Also the results showed that the $Q_4$ was significantly more often to drink coffee compared with the other three groups (p < 0.01). The mean daily energy intake was 2210.6 kcal ($88.4\%$ of RDA). The intake of energy, vitamin $B_2$, calcium, and zinc did not meet the Korean RDA. Also the $Q_2$consumed significantly lower intakes of protein (p < 0.05) and plant protein (p < 0.05) compared to the $Q_3$ and $Q_4$. The $Q_1$ and $Q_2$ consumed significantly lower intakes of vitamin $B_2$ (p < 0.01) compared to the $Q_3$ and $Q_4$. In conclusion, male student in lower bone mineral density appeared to have unhealthy life styles and dietary habits in terms of irregular exercise, high frequency of skipping breakfast and lower intakes of protein, vitamin $B_2$ showing a strong need proper education on meal practices and exercise habits for the bone health.

• Journal of the Korean Statistical Society
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• v.21 no.1
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• pp.47-58
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• 1992

The autocorrelation function structures of bilinear time series model BL(p, q, r, s), $r \geq s$ are obtained and shown to be analogous to those of ARMA(p, l), l=max(q, s). Simulation studies are performed to investigate the adequacy of Akaike information criteria for identification between ARMA(p, l) and BL(p, q, r, s) models and for determination of orders of BL(p, q, r, s) models. It is suggested that the model of having minimum Akaike information criteria is selected for a suitable model.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.479-484
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• 2002

Let I be an ideal in a Gorenstein local ring A with the maximal ideal m and d = dim A. Then we say that I is a good ideal in A, if I contains a reduction $Q=(a_1,a_2,...,a_d)$ generated by d elements in A and $G(I)=\bigoplus_{n\geq0}I^n/I^{n+1}$ of I is a Gorenstein ring with a(G(I)) = 1-d, where a(G(I)) denotes the a-invariant of G(I). Let S = A[Q/a$_1$] and P = mS. In this paper, we show that the following conditions are equivalent. (1) $I^2$ = QI and I = Q:I. (2) $I^2S$ = $a_1$IS and IS = $a_1$S：sIS. (3) $I^2$Sp = $a_1$ISp and ISp = $a_1$Sp ：sp ISp. We denote by $X_A(Q)$ the set of good ideals I in $X_A(Q)$ such that I contains Q as a reduction. As a Corollary of this result, we show that $I\inX_A(Q)\Leftrightarrow\IS_P\inX_{SP}(Qp)$.