• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.839-849
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• 2022

In this paper we consider a condition on the Ricci curvature involving vector fields which enabled us to achieve new results for volume comparison and Laplacian comparison. These results in special case obtained with considering volume non-collapsing condition. Also, by applying this condition we get new results of volume comparison for almost Ricci solitons.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.577-585
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• 2008

In this paper, we shall calculate the volume of normal tubes around geodesics under a curvature perturbation to establish a theorem of volume comparison type.

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.613-618
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• 1996

In this paper, M will always denote an n- dimensional complete Riemannian manifold and $\omega_n$ is the volume of $S^n$.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.213-220
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• 2004

In this paper, we generalize the Bishop-Gromov volume comparison theorem by considering an integral bound for the part of the radial Ricci curvature which lies below a given smooth function. We also establish a compactness theorem from this result.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.365-371
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• 1997

We prove some relation of volume with the covering radius of Riemannian manifolds and reprove well-known sphere rigidity theorems by using it.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.421-437
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• 2019

We establish some Hessian comparison theorems and volume comparison theorems for Riemann-Finsler manifolds under various line radial integral curvature bounds. As their applications, we obtain some results on first eigenvalue, Gromov pre-compactness and generalized Myers theorem for Riemann-Finsler manifolds under suitable line radial integral curvature bounds. Our results are new even in the Riemannian case.

• The Korean Journal of Food And Nutrition
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• v.10 no.3
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• pp.287-294
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• 1997

When bread making, the condition of thawing-fermentation for frozen dough were tested in variable temperature, and measured thawing-fermentation time and volume of frozen dough. L-Ascorbic acid (L-Aa) was added in frozen dough for the comparison test of develop volume in bread staling degree of baking bread were measured additive frozen dough which was stoppages in freezing, staling degrees were tested hardness with Rheometer. The test for comparison of thawing-fermentation time in variable temperature was shown the condition of dough conditioner at 3$0^{\circ}C$ was most effective for bread making, Because That condition was required very short time(74 min) But, in this comparison of volume in final products was shown the products in the condition of thawing-fermentation at 3$0^{\circ}C$ was smaller than the products at 5$^{\circ}C$(418 ml). The baking volume of L-Aa additive frozen dough which has under gone thawing-fermentation at 3$0^{\circ}C$, were shown baking volume of 420 ml in 2 weeks storage terms to 100 mg/kg L-Aa additive dough and shown baking volume of 454 ml in 4 weeks storage terms to dough of 200 mg/kg additive weight. Staling degrees of L-Aa additive frozen bread were measured with Rheometer. The hardness of 100 mg/kg L-Aa additive frozen bread was sown low level hardness in 1~2 weeks freezing term, 150 mg/kg L-Aa additive frozen bread was shown low level hardness in 3 weeks freezing term. In 4 weeks freezing term, 200 mg/kg L-Aa additive frozen bread was shown low level hardness compared with non-additive L-Aa frozen bread. In comparison of frozen bread quality, non-additive L-Aa products was better than additive L-Aa products in equality of baking shape and external apparence. But in total quality in external and internal apparence, additive L-Aa products was better than non-additive L-Aa products.

• Journal of Power Electronics
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• v.11 no.5
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• pp.621-631
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• 2011

In space qualified DC-DC converters, optimization of the following electrical characteristics is of greater interest in comparison with other specifications; power loss/efficiency, output voltage ripple and volume/weight. The main goal of this paper is to present an appropriate solution for optimizing the above mentioned characteristics. For this purpose, a comprehensive power loss model of a DC-DC converter is fully developed. Proper models are also demonstrated for assessment of the output voltage ripple and the utilized transformer volume as the bulkiest component in a DC-DC converter. In order to provide a test bed for evaluation of the proposed models, a 50W push-pull DC-DC converter is designed and implemented. Finally, a novel cost function with three assigned weight functions is proposed in order to have a trade-off among the power loss, the output voltage ripple and the utilized transformer volume of the converter. The cost function is optimized for applications in which volume has the highest priority in comparison with power loss and ripple. The optimization results show that the transformer volume can be decreased by up to 51% and this result is verified by experimental results. The developed models and algorithms in this paper can be used for other DC-DC converter topologies with some minor modifications.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.4
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• pp.397-409
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• 2021

The Bishop and Bishop-Gromov volume comparisons with the Bakry-Emery Ricci tensor in a metric measure space are studied by the comparisons of the Jacobi differential equations in a Riemannian and Lorentzian manifold.

• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.529-536
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• 2006

Investigators use either Euclidean distance or volume of a simplex defined composed of data points as agreement index to measure chance-corrected agreement among observers for multivariate interval data. The agreement coefficient proposed by Um(2004) is based on a volume of a simplex and does not depend on the variables' measuring units. We consider a comparison of Um(2004)'s agreement coefficient with others based on two unit-free distance measures, Pearson distance and Mahalanobis distance. Comparison among them is made using hypothetical data set.