• Physical Therapy Korea
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• v.12 no.1
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• pp.45-54
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• 2005

The quadriceps-angle (Q-angle) and the ratio of hamstring/quadriceps (H/Q) are important for the stability of the knee and for protection from excessive stress. The aim of this study was to examine the association between Q-angle and H/Q ratio with and without knee osteoarthritis. We compared knee osteoarthritis patients with symptom-free women. The mean age of the patients in the arthritis group (25 women, osteoarthritis) was 59.7 years. The non-arthritis group consisted of 25 women with a mean age of 55.2 years. Of the 25 women with osteoarthritis, 5 had the condition in their left knee, 5 had it in their right knee, and 15 had it on both sides. There was no significant difference in the knee Q-angle of the left and right knees of the arthritis group and the non-arthritis-group (p>.05). The strength of all the muscles around the involved right knee in the arthritis group was significantly weaker than that of the non-arthritis group (p<.05). However, in the left knee, only the strength of the knee extensors and internal rotators was significantly weaker than that of the non-arthritis group (p<.05). The Q-angle was not associated with the H/Q ratio and internal rotators/external rotators ratio of the involved knee in the arthritis group (p>.05). Neither was the Q-angle associated with the pain level of an involved knee in the arthritis group (p>.05). The knee pain was not associated with the H/Q ratio of the involved knee in the arthritis group (p>.05). The Q-angle was not associated with the ratio of H/Q and pain level of the involved knee in the osteoarthritis women.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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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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• v.47 no.4
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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.

• Journal of Korean Tunnelling and Underground Space Association
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• v.10 no.4
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• pp.383-395
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• 2008

The grouting is one of the improved techniques which is aim to decrease the permeability and to strengthen the soft ground. But The grouting method has many problems about a suitability of grouting procedure and an effectiveness of grouting after grouting work because of a technical characteristic operated inside the soil. The grouting $p{\sim}q{\sim}t$ chart of a typical index about grouting rate and time alteration of grouting pressure is one method to estimate the suitability of grouting factor with monitoring during grouting procedure. This study is automatic grouting system (AGS) which can control the testing and grouting procedures. It can make the detailed $p{\sim}q{\sim}t$ chart and analyze the grouting characters of the ground by comparing the detailed pattern of $p{\sim}q{\sim}t$ chart with standard pattern. If using the $p{\sim}q{\sim}t$ chart derived from AGS in the grouting work, it is an objective standard estimating the suitability of grouting factor with grouting materials, grouting method, grouting rate and grouting pressure, as results it expects successfully to improve reliability of the grouting work.

• Kyungpook Mathematical Journal
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• v.64 no.1
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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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• v.6 no.2
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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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• v.13 no.1
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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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• 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 applied mathematics & informatics
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• v.36 no.3_4
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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.

• 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 $B^s_{p,q}$.