• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.333-340
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• 2013

In this paper, we prove that on a K$\ddot{a}$hler spin foliatoin of codimension $q=2n$, any eigenvalue ${\lambda}$ of type $r(r{\in}\{1,{\cdots},[\frac{n+1}{2}]\})$ of the basic Dirac operator $D_b$ satisfies the inequality ${\lambda}^2{\geq}\frac{r}{4r-2}\;{\inf}_M{\sigma}^{\nabla}$, where ${\sigma}^{\nabla}$ is the transversal scalar curvature of $\mathcal{F}$.

• 대한수학회논문집
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• 제25권3호
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• pp.451-456
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• 2010

In this paper, we construct explicitly K$\ddot{a}$hler metrics on the ellipsoids and calculate their sectional curvatures. Using MAPLE [3], we obtain some geodesic curves on an ellipsoid so that if some conditions are dropped in Question 2.1 [4], then Question 2.1 is not true.

• 대한수학회보
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• 제49권2호
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• pp.329-338
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• 2012

In this paper, we define the almost h-slant submersion and the h-slant submersion which may be the extended version of the slant submersion [11]. And then we obtain some theorems which come from the slant submersion's cases. Finally, we construct some examples for the almost h-slant submersions and the h-slant submersions.

• 대기
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• 제28권2호
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• pp.211-222
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• 2018

Cloud droplet activation process is well described by $K{\ddot{o}}hler$ theory and several parameterizations based on $K{\ddot{o}}hler$ theory are used in a wide range of models to represent this process. Here, we test the two different method of calculating the solute effect in the $K{\ddot{o}}hler$ equation, i.e., osmotic coefficient method (OSM) and ${\kappa}-K{\ddot{o}}hler$ method (KK). To do that, each method is implemented in the cloud droplet activation parameterization module of WRF-CHEM (Weather Research and Forecasting model coupled with Chemistry) model. It is assumed that aerosols are composed of five major components (i.e., sulfate, organic matter, black carbon, mineral dust, and sea salt). Both methods calculate similar representative hygroscopicity parameter values of 0.2~0.3 over the land, and 0.6~0.7 over the ocean, which are close to estimated values in previous studies. Simulated precipitation, and meteorological variables (i.e., specific heat and temperature) show good agreement with reanalysis. Spatial patterns of precipitation and liquid water path from model results and satellite data show similarity in general, but on regional scale spatial patterns and intensity show some discrepancy. However, meteorological variables, precipitation, and liquid water path do not show significant differences between OSM and KK simulations. So we suggest that the relatively simple KK method can be a good alternative to the OSM method that requires various information of density, molecular weight and dissociation number of each individual species in calculating the solute effect.

• Journal of Trauma and Injury
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• 제18권1호
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• pp.64-69
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• 2005

Purpose: We report the radiologic and the clinical results for surgical treatment of calcaneal fractures involving the subtalar joint. Methods: We evaluated the findings of radiographs and computed tomographs of 39 patients (40 cases) with intra-articular calcaneal fractures. The fractures were treated with open reduction via an extended lateral approach and internal fixation using a plate. We assessed the radiologic results, such as the $B{\ddot{o}}hler$ angle, the Gissane angle, and the height/width ratio. We assessed the clinical results based on the critieria of Salama et al. Results: According to the Essex-Lopresti classification, 9 cases were classified as tongue type and 31 cases as joint depression type. According to the Sanders classification, 10 cases were classified as type IIA, 4 cases as IIB, 16 cases as IIIAB, 4 cases as IIIAC, and 6 cases as type IV. The mean preoperative $B{\ddot{o}}hler$ angle was 7.7, the mean postoperative $B{\ddot{o}}hler$ angle was 21.1, and the mean last follow-up $B{\ddot{o}}hler$ angle was 16.8. Clinical results classified as 10 excellent, 13 good, 11 fair, and 6 poor. Conclusion: In the treatment of intra-articular fractures of the calcaneus, open reduction via an extended lateral approach seems to be a useful method in that it can provide direct exposure of the subtalar joint with little morbidity.

• Korean Journal of Mathematics
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• 제27권3호
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• pp.691-705
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• 2019

In the present paper is to classify Beta-almost (${\beta}$-almost) Ricci solitons and ${\beta}$-almost gradient Ricci solitons on almost $CoK{\ddot{a}}hler$ manifolds with ${\xi}$ belongs to ($k,{\mu}$)-nullity distribution. In this paper, we prove that such manifolds with V is contact vector field and $Q{\phi}={\phi}Q$ is ${\eta}$-Einstein and it is steady when the potential vector field is pointwise collinear to the reeb vectoer field. Moreover, we prove that a ($k,{\mu}$)-almost $CoK{\ddot{a}}hler$ manifolds admitting ${\beta}$-almost gradient Ricci solitons is isometric to a sphere.

• 대한족부족관절학회지
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• 제18권4호
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• pp.165-172
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• 2014

Purpose: We evaluated the correlation of postoperative clinical outcomes and radiologic findings using computed tomography and simple X-ray in intra-articular calcaneal fractures. Materials and Methods: The current study is based on 41 feet, 38 patients with displaced intra-articular fracture who underwent surgical treatment with at least one year of follow-up. Evaluation of clinical outcome included American Orthopaedic Foot and Ankle Society (AOFAS) ankle-hindfoot score, visual analogue scale (VAS) score, and subjective satisfaction. A simple X-ray was used in evaluation of preoperative and postoperative Gissane angle, B${\ddot{O}}$hler angle, and calcaneal fracture width. Computed tomography scan was performed for evaluation of preoperative and postoperative articular step-off and articular gap in all cases. Finally, we evaluated the correlation of the postoperative clinical outcomes and radiologic findings based on the measurement. Results: The average postoperative AOFAS score and VAS score was $84.1{\pm}8.5$ and $2.2{\pm}2.2$. Subjective satisfaction was excellent in 15 cases, good in 19 cases, and fair in seven cases. The average B${\ddot{O}}$hler angle was restored from $11.1^{\circ}$ to $24.7^{\circ}$(p<0.05), Gissane angle was changed from $121.0^{\circ}$ to $119.0^{\circ}$ (p>0.05), and the average width was restored from 45.8 to 35.0 mm (p<0.05). The average articular step-off and gap were decreased from 6.3 to 2.0 mm and from 11.1 to 4.6 mm, respectively (p<0.05). No significant correlations were observed between the clinical outcome and Gissane angle, B${\ddot{O}}$hler angle, and width, and there was no significant correlation between the clinical outcome and Sanders classification. However, postoperative articular step-off showed correlation with VAS and AOFAS score and articular gap showed correlation with VAS score. Conclusion: The clinical outcome did not show correlation with B${\ddot{O}}$hler angle and Gissane angle but did show correlation with anatomical reduction of the posterior facet joint.

• 대한수학회보
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• 제49권1호
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• pp.49-55
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• 2012

In this paper, we prove that a complex Finsler manifold is a complex locally Minkowski space if and only if it is a strictly K$\ddot{a}$hler-Berwald manifold with zero holomorphic sectional curvature.

• 호남수학학술지
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• 제35권2호
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• pp.119-128
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• 2013

In the present paper, we define a product-symmetric recurrent-metric connection in an almost Hermitian manifold and study some properties of this connection, in particular, its curvature properties.

• 대한수학회보
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• 제52권3호
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• pp.1027-1034
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• 2015

As a natural generalization of the contact metric manifolds, Kim, Park and Sekigawa discussed quasi contact metric manifolds based on the geometry of the corresponding quasi $K{\ddot{a}}hler$ cones. In this paper, we show that a quasi contact metric manifold is a contact manifold.