• 대한수학회보
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• 제50권1호
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• pp.105-116
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• 2013

In this paper, we consider the positive solution to a Cauchy problem in $\mathbb{B}^N$ of the fast diffusive equation: ${\mid}x{\mid}^mu_t={div}(\mid{\nabla}u{\mid}^{p-2}{\nabla}u)+{\mid}x{\mid}^nu^q$, with nontrivial, nonnegative initial data. Here $\frac{2N+m}{N+m+1}$ < $p$ < 2, $q$ > 1 and 0 < $m{\leq}n$ < $qm+N(q-1)$. We prove that $q_c=p-1{\frac{p+n}{N+m}}$ is the critical Fujita exponent. That is, if 1 < $q{\leq}q_c$, then every positive solution blows up in finite time, but for $q$ > $q_c$, there exist both global and non-global solutions to the problem.

• Kyungpook Mathematical Journal
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• 제47권4호
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• pp.501-517
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• 2007

In this paper, we introduce and study a new class containing absolutely summing multilinear mappings and polynomials, which we call multiple weakly summing multilinear mappings and polynomials. We investigate some interesting properties about multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing multilinear mappings and polynomials defined on Banach spaces: In particular, we prove a kind of Dvoretzky-Rogers' Theorem and an ideal property for multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing multilinear mappings and polynomials. We also prove that the Aron-Berner extensions of multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing multilinear mappings and polynomials are also multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing.

• 한국터널지하공간학회 논문집
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• 제10권4호
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• pp.383-395
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• 2008

연약지반개량 기술 중의 하나인 그라우팅이 차수 보강 목적으로 다양한 건설공사에서 널리 활용되고 있지만 그라우팅공법이 지반내부에서 시행되는 기술적 특성상 그 시공과정의 적합성 및 시공 후 효과확인 방법에 대한 문제점이 많다. 본 연구 대상의 그라우팅 p-q-t chart는 주입속도(q)와 주입압(p)의 경시변화(t)에 대한 관계를 나타내는 지표로서 그라우팅 시공과정을 모니터링하여 시공인자의 적합성을 평가하여 조정할 수 있는 유일한 수단이다. 본 연구에서는 시험 및 시공과정을 일괄적으로 관리할 수 있는 자동 주입관리 시스템(AGS; automatic grouting system)를 이용하여 정밀한 p-q-t chart를 검출할 수 있었으며, 검출된 p-q-t chart의 유형을 표준유형과 비교분석을 통해서 대상지반의 주입특성에 대한 정보를 추정할 수 있었다. 향후 본 연구에서 적용한 자동 주입관리 시스템을 이용하여 도출된 p-q-t chart를 활용한다면 주입재료, 주입공법, 주입속도 및 주입압 등 시공인자의 적합성을 판정하고 조정하는 객관적 지표로 활용하여 그라우팅 시공의 신뢰성을 획기적으로 향상시킬 수 있을 것으로 기대된다.

• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.113-131
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• 2024

In this paper we give conditions for the existence of, and describe the asymtotic behavior of, radial positive solutions of the nonlinear elliptic equation of Emden-Fowler type with convection term ∆_p u + 𝛼|u|^q-1u + 𝛽x.∇(|u|^q-1u) = 0 for x ∈ ℝ^N, where p > 2, q > 1, N ≥ 1, 𝛼 > 0, 𝛽 > 0 and ∆_p is the p-Laplacian operator. In particular, we determine ${\lim}_{r{\rightarrow}}{\infty}\,r^{\frac{p}{q+1-p}}\,u(r)$ when $\frac{{\alpha}}{{\beta}}$ > N > p and $q\,{\geq}\,{\frac{N(p-1)+p}{N-p}}$.

• Korean Journal of Mathematics
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• 제6권2호
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• pp.221-229
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• 1998

Let $k$ be a real abelian field and $k_{\infty}$ be its $\mathbb{Z}_p$-extension for an odd prime $p$. Let $A_n$ be the Sylow $p$-subgroup of the ideal class group of $k_n$, the $nth$ layer of the $\mathbb{Z}_p$-extension. By using the main conjecture of Iwasawa theory, we have the following: If $p$ does not divide $\prod_{{{\chi}{\in}\hat{\Delta}_k},{\chi}{\neq}1}B_{1,{\chi}{\omega}^{-1}$, then $A_n$ = {0} for all $n{\geq}0$, where ${\Delta}_k=Gal(k/\mathbb{Q})$ and ${\omega}$ is the Teichm$\ddot{u}$ller character for $p$. The converse of this statement does not hold in general. However, we have the following when $k$ is of prime conductor $q$: Let $q$ be an odd prime different from $p$. and let $k$ be a real subfield of $\mathbb{Q}({\zeta}_q)$. If $p{\mid}{\prod}_{{\chi}{\in}\hat{\Delta}_{k,p},{\chi}{\neq}1}B_{1,{\chi}{\omega}}-1$, then $A_n{\neq}\{0\}$ for all $n{\geq}1$, where ${\Delta}_{k,p}$ is the $Gal(k_{(p)}/\mathbb{Q})$ and $k_{(p)}$ is the decomposition field of $k$ for $p$.

• Asian Pacific Journal of Cancer Prevention
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• 제13권1호
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• pp.225-229
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• 2012

Background: Males have a higher prevalence of hepatocellular carcinoma (HCC) than females in general, but the reasons for the sex disparity are still obscure. DNA copy number alteration (CNA) is a major feature of solid tumors including HCC, but whether CNA plays a role in sex-related differences in HCC development has never been evaluated. Methods: High-resolution array comparative genomic hybridization (CGH) was used to examine 17 female and 46 male HCC patients with chronic hepatitis B virus (HBV) infection in Shanghai, China. Two-tailed Fisher's exact or ${\chi}^2$ tests was used to compare CNAs between females and males. Results: The overall frequencies and patterns of CNAs in female and male cases were similar. However, female HCC tumors presented more copy number gains compared to those in males on 1q21.3-q22 (76.5% vs. 37.0%, P = 0.009), 11q11 (35.3% vs. 0.0%, P = 0.0002) and 19q13.31-q13.32 (23.5% vs. 0.0%, P = 0.004), and loss on 16p11.2 (35.3% vs. 6.5%, P = 0.009). Relative to females, male cases had greater copy number loss on 11q11 (63.0% vs. 17.6%, P = 0.002). Further analyses showed that 11q11 gain correlated with 19q13.31-q13.32 gain (P = 0.042), 11q11 loss (P = 0.011) and 16p11.2 loss (P = 0.033), while 1q21.3-q22 gain correlated with 19q13.31-q13.32 gain (P = 0.046). Conclusions: These findings suggest that CNAs may play a role in sex-related differences in HBVassociated HCC development.

• Korean Journal of Mathematics
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• 제26권1호
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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 applied mathematics & informatics
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• 제36권3_4호
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• pp.285-299
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• 2018

In this article, we present the Stancu generalization of (p, q)-$Sz{\acute{a}}sz$-Mirakyan Kantorovich type linear positive operators. Using Korovkin's result, approximation properties are investigated. First, we evaluate moments and direct results. By choosing p and q, the convergence rate have been estimated for better approximation. For the particular case ${\alpha}=0$, ${\beta}=0$ we obtain results for (p, q)-$Sz{\acute{a}}sz$-Mirakyan Kantorovich type operators.

• 충청수학회지
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• 제22권1호
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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 $B^s_{p,q}$.

• 충청수학회지
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• 제33권1호
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• pp.147-156
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• 2020

The functional equation related to a distance measure f(pr, qs) + f(ps, qr) = M(r, s)f(p, q) + M(p, q)f(r, s) can be generalized a sum form functional equation as follows $${\frac{1}{n}}{\sum\limits_{i=0}^{n-1}}f(P{\cdot}{\sigma}_i(Q))=M(Q)f(P)+M(P)f(Q)$$ where f, g is information measures, P and Q are the set of n-array discrete measure, and σ_i is a permutation for each i = 0, 1, ⋯, n-1. In this paper, we obtain the hyperstability of the above type functional equation.