• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1359-1380
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• 2018

In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Hardy type inequality with the same exponent n ($n{\geq}3$), then it has exactly the n-dimensional volume growth. Besides, three interesting applications of this fact have also been given. The first one is that we prove that complete noncompact smooth metric measure space with non-negative weighted Ricci curvature on which the Hardy type inequality holds with the best constant are isometric to the Euclidean space with the same dimension. The second one is that we show that if a complete n-dimensional Finsler manifold of nonnegative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then its flag curvature is identically zero. The last one is an interesting rigidity result, that is, we prove that if a complete n-dimensional Berwald space of non-negative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then it is isometric to the Minkowski space of dimension n.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.1-3
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• 2009

Recently, Carlsson, Full\acute{e}$r and Majlender [1] presented the concept of possibilitic correlation representing an average degree of interaction between marginal distribution of a joint possibility distribution as compared to their respective dispersions. They also formulated the weak and strong forms of the possibilistic Cauchy-Schwarz inequality. In this paper, we define a new probability measure. Then the weak and strong forms of the Cauchy-Schwarz inequality are immediate consequence of probabilistic Cauchy-Schwarz inequality with respect to the new probability measure.

• The Journal of Korea CHUNA Manual Medicine
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• v.5 no.1
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• pp.19-29
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• 2004

Objectives : Visual check and X-ray are commonly used by chiropractors to estimate ieg length inequality, This study have three categories: diagnosis for anatomic leg length inequality; difference between anatomic and functional leg length inequality; theraphies for anatomic or functional leg length inequality. Methods : We referred to a PubMed site by using word of 'leg length [JU] J Manipulative Physiol Ther', only items with abstracts. Results : We searched 26 articles in J Manipulative Physiol Ther with the key word-Ieg length. Conclusion : 1. Radiographs were most accurate and commonly used by chiropractors to measure anatomic leg length inequality, clinically wood block, tape measure, visual check are acceptable. 2. There was no article about difference between anatomic and functional leg length inequality. 3. Heel lift was commonly used with conservative theraphy for anatomic leg length Inequality. 4. Chiropractors have not yet proved that the supposed positive effects are a result of a reduction of subluxation, The detection of the manipulative lesion in the sacroiliac joint depends on valid and reliable tests, Because such tests have not been established, the presence of the manipulative lesion remains hypothetical. Great effort is needed to develop, establish and enforce valid and reliable test procedures.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.543-551
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• 1997

We prove a norm inequality of the form $\left\$\mid$ \upsilon \right\$\mid$ \leq (r - 1) \left\$\mid$ u \right\$\mid$_p, 1 < p < \infty$, between a non-negative subharmonic function u and a smooth function $\upsilon$ satisfying $$\mid$\upsilon(0)$\mid$ \leq u(0), $\mid$\nabla\upsilon$\mid$ \leq \nabla u$\mid$$ and $\mid$\Delta\upsilon$\mid$ \leq \alpha\Delta u$, where $\alpha$ is a constant with $0 \leq \alpha \leq 1$. This inequality extends Burkholder's inequality where $\alpha = 1$.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1363-1372
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• 2007

We investigate the containment measure of one domain to contain in another domain in a plane $X^{\kappa}$ of constant curvature. We obtain some Bonnesen-type inequalities involving the area, length, radius of the inscribed and the circumscribed disc of a domain D in $X^{\kappa}$.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.649-659
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• 1995

The purpose of this paper is to generalize the Carleson inequality, which is known to play important roles in harmonic analysis. The result given here is a generalization of Coifmann, Meyer, Stein [CMS]. A similar result is shown by Deng [D].

• Journal of Preventive Medicine and Public Health
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• v.41 no.3
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• pp.165-172
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• 2008

Objectives : Despite various government initiatives, including the expansion of national health insurance coverage, health inequality has been a key health policy issue in South Korea during the past decade. This study describes and compares the extent of the total health inequality and the income-related health inequality over time among Korean adults. Methods : This study employs the 1998, 2001 and 2005 Korean National Health and Nutrition Examination Surveys (KNHANESs). The self-assessed health (SAH) ordinal responses, measured on a five-point scale, resealed to cardinal values to measure the health inequalities with using interval regression. The boundaries of each threshold for the interval regression analysis were obtained from the empirical distribution of the EuroQol-5 Dimension (EQ-5D) valuation weights estimated from the 2005 KNHANES. The final model predicting the individuals' health status included age, gender, educational attainment, occupation, income, and the regional prosperity index. The concentration index was used to measure and analyze the health inequality. Results : The KNHANES data showed an unequal distribution of the total health inequality in favor of the higher income groups, and this is getting worse over time (0.0327 in 1998, 0.0393 in 2001 and 0.0924 in 2005). The income-related health inequality in 2005 was 0.0278, indicating that 30.1% of the total health inequality can be attributed to income. Conclusions : The findings indicate there are health inequalities across the sociodemographic and income groups despite the recent government's efforts. Further research is warranted to investigate what potential policy actions are necessary to decrease the health inequality in Korea.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.71-75
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• 2009

The purpose of this paper is to prove a Jensen type inequality for Choquet integrals with respect to a non-additive measure which was introduced by Choquet [1] and Sugeno [20]; $$\Phi((C)\;{\int}\;fd{\mu})\;{\leq}\;(C)\;\int\;\Phi(f)d{\mu},$$ where f is Choquet integrable, ${\Phi}\;:\;[0,\;\infty)\;\rightarrow\;[0,\;\infty)$ is convex, $\Phi(\alpha)\;\leq\;\alpha$ for all $\alpha\;{\in}\;[0,\;{\infty})$ and ${\mu}_f(\alpha)\;{\leq}\;{\mu}_{\Phi(f)}(\alpha)$ for all ${\alpha}\;{\in}\;[0,\;{\infty})$. Furthermore, we give some examples assuring both satisfaction and dissatisfaction of Jensen type inequality for the Choquet integral.

• Journal of the Korean Statistical Society
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• v.26 no.4
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• pp.445-452
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• 1997

A more generalized version of the information inequality based on diffusivity which is a natural measure of dispersion for median-unbiased estimators developed by Sung et al. (1990) is presented. This non-Bayesian L$_{1}$ information inequality is free from regularity conditions and can be regarded as an analogue of the Chapman-Robbins inequality for mean-unbiased estimation. The approach given here, however, deals with a more generalized situation than that of the Chapman-Robbins inequality. We also develop a Bayesian version of the L$_{1}$ information inequality in median-unbiased estimation. This latter inequality is directly comparable to the Bayesian Cramer-Rao bound due to the van Trees inequality.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.901-914
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• 2013

Kwon and Bae gave an interpolation for a continuous form of H$\ddot{o}$lder's inequality for a real-valued bounded measurable function on a product of measure spaces. It is given some generalizations of their result.