• 대한수학회논문집
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• 제11권4호
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• pp.1147-1157
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• 1996

Nonlinear ill-posed problems arise in many application including parameter estimation and inverse scattering. We introduce a least squares regularization method to solve nonlinear ill-posed problems with constraints robustly and efficiently. The regularization method uses Trust-Region approach to handle the constraints on variables. The Generalized Cross Validation is used to choose the regularization parameter in computational tests. Numerical results are given to exhibit faster convergence of the method over other methods.

• Communications for Statistical Applications and Methods
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• 제16권4호
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• pp.659-667
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• 2009

Recently Song and Cheon (2006) and Cheon and Lim (2009) developed the generalized maximum entropy(GME) estimator to solve ill-posed problems for the regression coefficients in the simple panel model. The models discussed consider the individual and a spatial autoregressive disturbance effects. However, in many application in economics the data may contain nested groupings. This paper considers a two-way error component model with nested groupings for the ill-posed data and proposes the GME estimator of the unknown parameters. The performance of this estimator is compared with the existing methods on the simulated dataset. The results indicate that the GME method performs the best in estimating the unknown parameters in terms of its quality when the data are ill-posed.

• 대한수학회보
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• 제58권1호
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• pp.71-111
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• 2021

We consider the boundary value problem for the deflection of a finite beam on an elastic foundation subject to vertical loading. We construct a one-to-one correspondence �� from the set of equivalent well-posed two-point boundary conditions to gl(4, ℂ). Using ��, we derive eigenconditions for the integral operator ��M for each well-posed two-point boundary condition represented by M ∈ gl(4, 8, ℂ). Special features of our eigenconditions include; (1) they isolate the effect of the boundary condition M on Spec ��M, (2) they connect Spec ��M to Spec ����,α,k whose structure has been well understood. Using our eigenconditions, we show that, for each nonzero real λ ∉ Spec ����,α,k, there exists a real well-posed boundary condition M such that λ ∈ Spec ��M. This in particular shows that the integral operators ��M, arising from well-posed boundary conditions, may not be positive nor contractive in general, as opposed to ����,α,k.

• 대한수학교육학회지:학교수학
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• 제11권2호
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• pp.207-225
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• 2009

수학영재의 지적 욕구를 충족시키고 창의성을 신장시키는 문제해결 중심의 수업활동을 하기 위해서는 수학영재의 수준에 맞게 만들어진 문제가 필수적이다. 본 논문의 목적은 수학영재 지도교사의 교수 능력을 신장시키기 위한 심화 연수 과정의 일부인 원격 연수에 참여한 수학영재 지도교사가 만든 문제의 형태를 문제 접근 방법에 따라 '익숙한 문제', '익숙하지 않은 문제', '오류가 있는 문제'로 나누어 분석하여 수학영재 지도교사를 위한 원격 연수에서 교사의 문제만들기에 대한 실천적 방안을 제시하는데 있다.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.781-792
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• 2021

In this paper, we study well-posed problems and variational inequalities in locally convex Hausdorff topological vector spaces. The necessary and sufficient conditions are obtained for the existence of solutions of variational inequality problems and quasi variational inequalities even when the underlying set K is not convex. In certain cases, solutions obtained are not unique. Moreover, counter examples are also presented for the authenticity of the main results.

• Communications for Statistical Applications and Methods
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• 제21권5호
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• pp.395-409
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• 2014

Data limited, partial, or incomplete are known as an ill-posed problem. If the data with ill-posed problems are analyzed by traditional statistical methods, the results obviously are not reliable and lead to erroneous interpretations. To overcome these problems, we propose a dual generalized maximum entropy (dual GME) estimator for panel data regression models based on an unconstrained dual Lagrange multiplier method. Monte Carlo simulations for panel data regression models with exogeneity, endogeneity, or/and collinearity show that the dual GME estimator outperforms several other estimators such as using least squares and instruments even in small samples. We believe that our dual GME procedure developed for the panel data regression framework will be useful to analyze ill-posed and endogenous data sets.

• 대한수학회논문집
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• 제15권4호
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• pp.605-616
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• 2000

We prove the non-homogeneous boundary value problem for population evolution equations is well-posed in Sobolev space H(sup)3/2,3/2($\Omega$). It provides a strictly mathematical basis for further research of population control problems.

• 대한치과교정학회지
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• 제48권3호
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• pp.182-188
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• 2018

Objective: This study was performed to validate the autonomous maximal smile (AMS) as a new reference for evaluating dental and gingival exposure. Methods: Digital video clips of 100 volunteers showing posed smiles and AMS at different verbal directives were recorded for evaluation a total of three times at 1-week intervals. Lip-teeth relationship width (LTRW) and buccal corridor width (BCW) were measured. LTRW represented the vertical distance between the inferior border of the upper vermilion and the edge of the maxillary central incisors. Intraclass correlation coefficients (ICCs) for reproducibility, and the m-value (minimum number of repeated measurements required for an ICC level over 0.75), were calculated. Results: LTRW and BCW of the AMS were 1.41 and 2.04 mm, respectively, greater than those of the posed smile (p < 0.05), indicating significantly larger dental and gingival exposure in the AMS. The reproducibility of the AMS (0.74 to 0.77) was excellent, and higher than that of the posed smile (0.62 to 0.65), which had fair-to-good reproducibility. Moreover, the m-value of the AMS (0.88 to 1.05) was lower than that of the posed smile (1.59 to 1.85). Conclusions: Compared to the posed smile, the AMS shows significantly larger LTRW and BCW, with significantly higher reproducibility. The AMS might serve as an adjunctive reference, in addition to the posed smile, in orthodontic and other dentomaxillofacial treatments.

• The Journal of Advanced Prosthodontics
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• 제15권1호
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• pp.1-10
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• 2023

PURPOSE. Accuracy of image matching between resting and smiling facial models is affected by the stability of the reference surfaces. This study aimed to investigate the morphometric variations in subdivided facial units during resting, posed and spontaneous smiling. MATERIALS AND METHODS. The posed and spontaneous smiling faces of 33 adults were digitized and registered to the resting faces. The morphological changes of subdivided facial units at the forehead (upper and lower central, upper and lower lateral, and temple), nasal (dorsum, tip, lateral wall, and alar lobules), and chin (central and lateral) regions were assessed by measuring the 3D mesh deviations between the smiling and resting facial models. The one-way analysis of variance, Duncan post hoc tests, and Student's t-test were used to determine the differences among the groups (α = .05). RESULTS. The smallest morphometric changes were observed at the upper and central forehead and nasal dorsum; meanwhile, the largest deviation was found at the nasal alar lobules in both the posed and spontaneous smiles (P < .001). The spontaneous smile generally resulted in larger facial unit changes than the posed smile, and significant difference was observed at the alar lobules, central chin, and lateral chin units (P < .001). CONCLUSION. The upper and central forehead and nasal dorsum are reliable areas for image matching between resting and smiling 3D facial images. The central chin area can be considered an additional reference area for posed smiles; however, special cautions should be taken when selecting this area as references for spontaneous smiles.

• Communications for Statistical Applications and Methods
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• 제9권1호
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• pp.87-100
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• 2002

Poorly-posed problems in the balanced discriminant analysis was considered. We restrict consideration to the case of observations and the number of variables are the same and small. When these problems exist, we do not use a maximum likelihood estimates(MLE) to estimate covariance matrices. Instead of MLE, an alternative estimate for the covariance matrices are proposed. This alternative method make good use of two regularization parameters, $\lambda$} and $\gamma$. A new test rule for the discriminant function is suggested and examined via limited hut informative simulation study. From the simulation study, it is shown that the suggested test rule gives better test result than other previously suggested method in terms of error rate criterion.