• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제19권3호
• /
• pp.305-313
• /
• 2012

In this note we study Nesbitt's Inequality and modify it to make several inequalities. We prove some inequalities by using power series and Cauchy-Schwarz Inequality.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• 제9권1호
• /
• pp.1-3
• /
• 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.

• 대한수학회보
• /
• 제42권4호
• /
• pp.725-738
• /
• 2005

A reverse of the Cauchy-Bunyakovsky-Schwarz integral inequality for complex-valued functions and applications for the finite Fourier transform are given.

• 대한수학회논문집
• /
• 제33권4호
• /
• pp.1285-1301
• /
• 2018

This paper is devoted to the study of $Tur{\acute{a}}n$-type inequalities for some well-known special functions such as Gauss hypergeometric functions, generalized complete elliptic integrals and confluent hypergeometric functions which are derived by using a new form of the Cauchy-Bunyakovsky-Schwarz inequality. We also apply these inequalities for some sample of interest such as incomplete beta function, incomplete gamma function, elliptic integrals and modified Bessel functions to obtain their corresponding $Tur{\acute{a}}n$-type inequalities.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제15권1호
• /
• pp.93-101
• /
• 2008

In this article we shall characterize the Heinz-Kato-Furuta inequality in several ways, and the best bound for sharpening of the inequality is obtained by the method in [7].

• 대한수학회지
• /
• 제39권3호
• /
• pp.351-361
• /
• 2002

We extend the Holder-McCarthy inequality for a positive and an arbitrary operator, respectively. The powers of each inequality are given and the improved Reid's inequality by Halmos is generalized. We also give the bound of the Holder-McCarthy inequality by recursion.

• Kyungpook Mathematical Journal
• /
• 제54권4호
• /
• pp.531-543
• /
• 2014

The object of the present paper is to discuss some interesting properties of analytic functions f(z) associated with the subclasses $\mathcal{D}({\beta}_1,{\beta}_2,{\beta}_3;{\lambda})$, $\mathcal{G}({\theta},{\alpha})$ and $\mathcal{Q}({\theta},{\alpha})$. Also, radius problems of $\frac{1}{\delta}f({\delta}z)$ for f(z) in the class $\mathcal{D}({\beta}_1,{\beta}_2,{\beta}_3;{\lambda})$, $\mathcal{G}({\theta},{\alpha})$ and $\mathcal{Q}({\theta},{\alpha})$ are considered.

• 대한수학회지
• /
• 제58권3호
• /
• pp.791-797
• /
• 2021

In this corrigendum, we offer a correction to [J. Korean Math. Soc. 54 (2017), No. 2, 461-477]. We construct a counterexample for the strengthened Cauchy-Schwarz inequality used in the original paper. In addition, we provide a new proof for Lemma 5 of the original paper, an estimate for the extremal eigenvalues of the standard unpreconditioned FETI-DP dual operator.

• 전기학회논문지
• /
• 제62권11호
• /
• pp.1560-1565
• /
• 2013

This paper proposes the control method for compensating for unbalanced grid current and reducing a total harmonic distortion (THD) of the grid current at the three-phase grid-connected inverter systems under unbalancd and distorted grid voltage conditions. The THD of the grid current caused by grid voltage harmonics is derived by considering the phase delay and magnitude attenuation due to the hardware low-pass filter (LPF). The Cauchy-Schwarz inequality theory is used in order to search more easily for a minimum point of THD. Both the gain and angle of a compensation voltage at the minimum point of THD of the grid current are derived. The negative-sequence components in the three-phase unbalanced grid voltage are cancelled in order to achieve the balanced grid current. The simulation and experimental results show the validity of the proposed control methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제22권2호
• /
• pp.91-100
• /
• 2018

In this paper, we propose a new method for template matching, patch ratio, to inpaint unknown pixels. Before this paper, many inpainting methods used sum of squared differences(SSD) or sum of absolute differences(SAD) to calculate distance between patches and it was very useful for closest patches for the template that we want to fill in. However, those methods don't consider about geometric similarity and that causes unnatural inpainting results for human visuality. Patch ratio can cover the geometric problem and moreover computational cost is less than using SSD or SAD. It is guaranteed about finding the most similar patches by Cauchy-Schwarz inequality. For ignoring unnecessary process, we compare only selected candidates by priority calculations. Exeperimental results show that the proposed algorithm is more efficent than Criminisi's one.