• Journal of applied mathematics & informatics
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• 제35권1_2호
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• pp.147-163
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• 2017

In this paper, we establish the necessary and sufficient Karush-Kuhn-Tucker (KKT) conditions for an optimization problem with difference of set-valued maps under generalized cone convexity assumptions. We also study the duality results of Mond-Weir (MW D), Wolfe (W D) and mixed (Mix D) types for the weak solutions of the problem (P).

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.251-261
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• 2008

In this paper second order cone convex, second order cone pseudoconvex, second order strongly cone pseudoconvex and second order cone quasiconvex functions are introduced and their interrelations are discussed. Further a MondWeir Type second order dual is associated with the Vector Minimization Problem and the weak and strong duality theorems are established under these new generalized convexity assumptions.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1395-1408
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• 2010

In this paper, a pair of Wolfe type second-order nondifferentiable multiobjective symmetric dual program over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under second-order (F, $\alpha$, $\rho$, d)-convexity assumptions. An illustration is given to show that second-order (F, $\alpha$, $\rho$, d)-convex functions are generalization of second-order F-convex functions. Several known results including many recent works are obtained as special cases.

• 대한수학회보
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• 제50권5호
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• pp.1639-1650
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• 2013

In this paper, a class of set-valued mappings is introduced, which is called uniformly same-order. For this sort of mappings, some minimax problems, in which the minimization and the maximization of set-valued mappings are taken in the sense of vector optimization, are investigated without any hypotheses of convexity.

• 대한수학회지
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• 제56권4호
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• pp.1001-1016
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• 2019

We are concerned with optimization methods for the $L^2$-Wasserstein least squares problem of Gaussian measures (alternatively the n-coupling problem). Based on its equivalent form on the convex cone of positive definite matrices of fixed size and the strict convexity of the variance function, we are able to present an implementable (accelerated) gradient method for finding the unique minimizer. Its global convergence rate analysis is provided according to the derived upper bound of Lipschitz constants of the gradient function.

• 대한치과교정학회지
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• 제40권3호
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• pp.134-144
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• 2010

성장기 아동의 상기도 협착은 두개안면 성장에 영향을 미칠 수 있다. 본 연구는 3차원 cone-beam computed tomography (CBCT)를 이용하여 제II급 부정교합 아동의 상기도 부피 및 단면적 계측치와 측모두부계측치를 비교하여 상기도와 안면 형태와의 연관성을 알아보고자 하였다. 37명의 아동(남자 17명, 여자 20명, 평균 연령 11.02세)의 CBCT를 촬영하였다. 연구 결과, 상기도의 PNS-posterior plane에서의 단면적($S_{PP}$)은 제II급 부정교합군에서 유의하게 작았다 (p < 0.05). 상기도 부피 계측치는 제II급 부정교합군에서 제I급 부정교합군보다 작았으나, 두 군 간 통계적으로 유의한 차이는 없었다. 제II급 부정교합군은 후안모고경(PFH), mandibular body length (p < 0.05), Pog to Nperp (p < 0.01)에서 제I급 부정교합군보다 유의하게 작은 값을 보였고, FMA (p < 0.05), ANB, facial convexity (p < 0.01)는 유의하게 큰 값을 보였다. 제II급 부정교합군의 PNS 전방의 상기도 부피($W_N$)는 ANB difference 각도와 음의 상관관계를 보였다 (p < 0.05). 제II급 부정교합 아동은 상대적으로 좁은 상기도 부피를 가지며 이에 따른 감소 된 후안모고경(PFH)과 하악골의 divergent한 안면 성장 양상을 보였다.

• Imaging Science in Dentistry
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• 제42권4호
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• pp.201-205
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• 2012

Purpose: This study was performed to assess the compatibility of cone beam computed tomography (CBCT) synthesized cephalograms with conventional cephalograms, and to find a method for obtaining normative values for three-dimensional (3D) assessments. Materials and Methods: The sample group consisted of 10 adults with normal occlusion and well-balanced faces. They were imaged using conventional and CBCT cephalograms. The CBCT cephalograms were synthesized from the CBCT data using OnDemand 3D software. Twenty-one angular and 12 linear measurements from each imaging modality were compared and analyzed using paired-t test. Results: The linear measurements between the two imaging modalities were not statistically different (p>0.05) except for the U1 to facial plane distance. The angular measurements between the two imaging modalities were not statistically different (p>0.05) with the exception of the gonial angle, ANB difference, and facial convexity. Conclusion: Two-dimensional cephalometric norms could be readily used for 3D quantitative assessment, if corrected for lateral cephalogram distortion.

• 대한치과교정학회지
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• 제43권3호
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• pp.113-119
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• 2013

Objective: To compare three-dimensionally the midfacial hard- and soft-tissue asymmetries between the affected and the unaffected sides and determine the relationship between the hard tissue and the overlying soft tissue in patients with nonsyndromic complete unilateral cleft lip and palate (UCLP) by cone-beam computed tomography (CBCT) analysis. Methods: The maxillofacial regions of 26 adults (18 men, 8 women) with nonsyndromic UCLP were scanned by CBCT and reconstructed by three-dimensional dental imaging. The frontal-view midfacial analysis was based on a $3{\times}3$ grid of vertical and horizontal lines and their intersecting points. Two additional points were used for assessing the dentoalveolar area. Linear and surface measurements from three reference planes (Basion-perpendicular, midsagittal reference, and Frankfurt horizontal planes) to the intersecting points were used to evaluate the anteroposterior, transverse, and vertical asymmetries as well as convexity or concavity. Results: Anteroposteriorly, the soft tissue in the nasolabial and dentoalveolar regions was significantly thicker and positioned more anteriorly on the affected side than on the unaffected side (p < 0.05). The hard tissue in the dentoalveolar region was significantly retruded on the affected side compared with the unaffected side (p < 0.05). The other midfacial regions showed no significant differences. Conclusions: With the exception of the nasolabial and dentoalveolar regions, no distinctive midfacial hard- and soft-tissue asymmetries exist between the affected and the unaffected sides in patients with nonsyndromic UCLP.