• The Pure and Applied Mathematics
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• v.25 no.1
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• pp.39-48
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• 2018

In this work, by applying the binomial expansion, some refinements of the Young and Heinz inequalities are proved. As an application, a determinant inequality for positive definite matrices is obtained. Also, some operator inequalities around the Young's inequality for semidefinite invertible matrices are proved.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.1021-1026
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• 2001

In this paper, we give an improvement of Carleman’s inequality by using the strict monotonicity of the power mean of n distinct positive numbers.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.377-388
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• 2002

In this paper, we obtain an extension of an analogue of Hilbert's inequality involving series of nonnegative terms. The integral analogies of the main results are also given.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.105-110
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• 2013

A logarithmic composition inequality in Besov spaces is derived which generalizes Vishik's inequality: ${\parallel}f{\circ}g{\parallel}_{B^s_{p,1}}{\leq}(1+{\log}({\parallel}{\nabla}g{\parallel}_{L^{\infty}}{\parallel}{\nabla}g^{-1}{\parallel}_{L^{\infty}})){\parallel}f{\parallel}_{B^s_{p,1}}$, where $g$ is a volume-preserving diffeomorphism on ${\mathbb{R}}^n$.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.207-222
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• 2008

A new counterpart of Bessel's inequality for orthonormal families in real or complex 2-inner product spaces is obtained. Applications for some Gr$\"{u}$ss inequality for determinantal integral inequalities are also provided.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.171-175
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• 2009

Let $A_1,\;A_2,\;{\cdots},\;A_n$ be a sequence of events on a given probability space. Let $m_n$ be the number of those $A_{i}{^{\prime}}s$ which occur. We establish an improved lower bounds of Univariate Bonferroni-Type inequality by using the linearity of binomial moments $S_1,\;S_2,\;S_3,\;S_4$ and$S_5$.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.701-708
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• 2001

In this article, using the properties of power mean, some new generalizations of the strengthened Hardy's inequalities are given.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.267-271
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• 2011

Let 0 < s < 1. For $f^{\ast}$ representing the symmetric radial decreasing rearrangement of f, we build up a fractional version of Polya-$Szeg{\ddot{o}}$ inequality: $${\int}_{\mathbb{R}^n}{\mid}(-\Delta)^{s/2}f^{\ast}(x){\mid}^2dx{\leq}{\int}_{\mathbb{R}^n}{\mid}(-\Delta)^{s/2}f(x){\mid}^2dx$$.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.491-506
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• 2019

In this paper, we show the existence and uniqueness of solution to stochastic differential equations under weakened $H{\ddot{o}}lder$ condition and a weakened linear growth condition. Furthermore, the properties of their solutions investigated and estimate for the error between Picard iterations $x_n(t)$ and the unique solution x(t) of SDEs.

• Journal of muscle and joint health
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• v.19 no.1
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• pp.27-36
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• 2012

Purpose: The purpose of this study was to investigate the leg length Inequality, habitual posture, and pain in women's college students. Methods: The subjects were 281 students, in 8 women's college in Korea. The tapelines were used for measuring leg length Inequality and questionnaires were used for measuring habitual posture, and pain. The data were collected between August and October 2010 and analyzed using SPSSWIN 11.5. length Inequality(<1 cm). The subjects of 2.8% were the length differences of above 2cm. The worst habitual posture were leaning habits. Especially, the habits of crossing her legs were significantly different to leg length Inequality(F=3.342, $p$=.037). The subjects of 84% were felt a severe pain on the upper body such as waist, back, scapula, neck or shoulder. But there is no difference between pain and leg length Inequality. Habitual posture are related to pain(r=.212, $p$=.001). Conclusion: To protect the severe health problem of musculoskeletal system, this study results will be give aid to health education in women's college students.