• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.211-219
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• 2010

Let P be a Jacobian polynomial such as deg P = $deg_y$ P. Suppose the Jacobian polynomial P satisfies the intersection condition satisfying $dim_C$ C[x, y]/$P_y$> = deg P - 1, we can prove that the Keller map which has P as one of coordinate polynomial always has its inverse.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1485-1500
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• 2021

A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are geodesics on hypercones. We later use this association to characterize rectifying curves that are also slant helices in three-dimensional space as geodesics of circular cones. In addition, we consider curves that lie on a moving hyperplane normal to (i) one of the normal vector fields of the Frenet frame and to (ii) a rotation minimizing vector field along the curve. The former class is characterized in terms of the constancy of a certain vector field normal to the curve, while the latter contains spherical and plane curves. Finally, we establish a formal mapping between rectifying curves in an (m + 2)-dimensional space and spherical curves in an (m + 1)-dimensional space.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1477-1496
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• 2023

A class of normalized univalent functions f defined in an open unit disk of the complex plane is introduced and studied such that the values of the quantity zf'(z)/f(z) lies inside the evolute of a nephroid curve. The inclusion relations of the newly defined class with other subclasses of starlike functions and radius problems concerning the second partial sums are investigated. All the obtained results are sharp.

• Journal of Oral Medicine and Pain
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• v.25 no.2
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• pp.205-214
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• 2000

This study was performed to investigate the relationship between mandibular midline shift and anteroposterior first molar occlusal relation, and their effects on the mandibular height and the occlusal plane angle. For this study, 49 patients with temporomandibular disorders were selected. They did not show facial asymmetry and their facial midline coincide with maxillary dental midline. Upper and lower mandibular impression were taken and the casts were fabricated. Amount and direction of the mandibular midline shift and the anteroposterior shift between the two occluding first molars were measured on the casts. Several items related to height such as mandibular height from top of the articular surface of the condyle to curve changing point between antegonial notch and mandibular angle, condylar height which was the vertical distance from the articular surface to retroepicondyle of the condyle, and sigmoid height from the deepest point of sigmoid notch to the curve changing point and the occlusal plane angle were also measured on the panoramic and on the transcranial radiographs. Correlation between midline shift and anteroposterior first molar relation and comparison between right and left mandibular height by the midline shift and the first molar relation were analysed by SPSS windows program. The results of this study were as follows : 1. Mean amount of midline shift in the subjects with midline shift were 2.0mm for both side, respectively. The first molar relation of the ipsilateral side of midline shift showed Angle class II tendency and the contralateral side showed Angle class III tendency, which meant drift of the dentition to the side of the midline shift. 2. The occlusal plane angle on the panoramic radiograph were $13.0^{\circ}$ in right, and $12.5^{\circ}$ in left side, and their were no correlation between occlusal plane angle and mandibular midline shift and the first molar occlusal relation. 3. Angle's classification for both sides of the first molar relation were same in about half of all the subjects. Amount of deviation from class I first molar relation, however, were decreased in the contralateral side of observed side. 4. Mandibular height of the ipsilateral side to which mandibular midline shift showed tendency of lower than that of the contralateral side, and there was a tendency that the height was higher in class III subjects, then class II subjects, and lower in class I subjects. However, condylar height did not show any difference in the subjects with midline shift and also show no difference by the first molar occlusal relation.

• The korean journal of orthodontics
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• v.30 no.5 s.82
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• pp.521-533
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• 2000

This study was investigated to evaluate the morphologic characteristics of openbite and deep bite in Class I malocclusion patients and to find skeletodental factors which contributed to vertical discrepancy in Class I malocclusion. The subjects were consisted of 40 control subjects (male 20, female 20) and 40 Class I openbite patients and 40 Class I deep bite patients. Lateral cephalograms in centric occlusion were taken, traced and digitized lot each subjects. The computerized statistical analysis were carried out with SPSS program. The results were as follows. 1. The pattern of vortical discrepancy in Class I malocclusion is mainly influenced by the skeletodental factors under palatal plane. 2. In openbite group, vortical discrepancy is prominent on anterior lower face and is closely related with skeletal factors such as mandibular form and inclination. 3. In deep bite group, dental factors such as ewe of Spee, vertical height of maxillary molar and skeletal factor such as articular angle were contributed to the vertical discrepancy. 4. The multiple regression analysis showed that overbite in Class I molar relationship was determined mainly by dental factors such as lower incisor to occlusal plane angle, curve of Spee, interincisal angle, and ODI.

• The korean journal of orthodontics
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• v.48 no.4
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• pp.236-244
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• 2018

Objective: The aim of this study is to compare the adaptation of a straight wire between brackets positioned at the mid-lingual surface and those placed gingivally by using a three-dimensional simulation software. Methods: This cross-sectional study was performed using OrthoAid, an in-house software. The subjects were 36 adolescents with normal Class I occlusion. For each dental cast, two bracket positioning approaches, namely the middle and gingival, were examined. In the middle group, the reference points were placed on the mid-lingual surface of each tooth, while in the gingival group, the reference points were positioned lingually on the anterior teeth. A 4th degree polynomial was adopted, and the in-plane and off-plane root mean squares (RMSs) of the distances between the reference points and the fitted polynomial curve were calculated using the software. Statistical analysis was performed using the paired-samples t-test (${\alpha}=0.05$). Results: The mean in-plane RMS of the polynomial curve to the bracket distance in the gingival group was significantly lower than that in the middle group (p < 0.001). The off-plane RMS was higher in the gingivally positioned brackets in the maxilla than in the middle group (p < 0.001). However, the off-plane RMS in mandible was not statistically significantly different between the two groups (p = 0.274). Conclusions: The results demonstrated that the gingival placement of lingual brackets on the anterior teeth could decrease the distance between a tooth and the straight wire.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.413-424
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• 2006

Let $\Gamma$ be a bounded rotation (BR) curve without cusps in the complex plane $\mathbb{C}$ and let G := int $\Gamma$. We prove that the rate of convergence of the interpolating polynomials based on the zeros of the Faber polynomials $F_n\;for\;\bar G$ to the function of the reflexive Smirnov-Orlicz class $E_M (G)$ is equivalent to the best approximating polynomial rate in $E_M (G)$.

• The korean journal of orthodontics
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• v.25 no.2 s.49
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• pp.153-163
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• 1995

In this study, Receiver Operating Characteristic(ROC) analysis was used to evaluate the ability of cephalometric measurements to identify patients with Class III malocclusions. ROC analysis is the method for determining the validity of a diagnostic measure and for evaluating the relative value of diagnostic tests. The sample consisted of 496 patients with malocclusion. Class III malocclusion is defined as the dental relationship for which The mesiobuccal groove of the lower first molar is deviated mesially from the mesiobuccal cusp of the upper first molar. Of the total sample of 496 patients, 245 had Class III malocclusions. 16 cephalometric measurements were selected, each of which was treated as a diagnostic test. The ROC curves were generated for each cephalometric measurement with intervals of $1.0^{\circ}$ for angular measurements, 1.0mm for linear measurements. The area under the ROC curves was measured for direct comparison among different diagnostic tests. The results were as follows; 1. The 'Wits' appraisal was found to be a better diagnostic criterion for the presence of Class III malocclusion than any other commonly'used cephalometric measurement. 2. AB plane angle, ANB angle, App-Bpp distance, AF-BF distance, APDI, Distance of point A and Pog to N perpendicular, maxillomandibular differential had high diagnostic value. 3. Cephalometric measurements which evaluate the position of the mandible had moderate diagnostic value. 4. Cephalometric measurements related to the maxilla discriminated least between patients with and without Class III malocclusion.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.29-41
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• 2014

In this paper, we prove that infinite-dimensional vector spaces of -dense curves are generated by means of the functional equations f(x)+f(2x)+${\cdots}$+f(nx) = 0, with $n{\geq}2$, which are related to the partial sums of the Riemann zeta function. These curves ${\alpha}$-densify a large class of compact sets of the plane for arbitrary small ${\alpha}$, extending the known result that this holds for the cases n = 2, 3. Finally, we prove the existence of a family of solutions of such functional equation which has the property of quadrature in the compact that densifies, that is, the product of the length of the curve by the $n^{th}$ power of the density approaches the Jordan content of the compact set which the curve densifies.

• 한국태양에너지학회:학술대회논문집
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• 2012.03a
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• pp.457-462
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• 2012

Daylighting software is an important component to predict the performance of daylighting system in advance of a field demonstration study with installing them in buildings. PHOTOPIA is a powerful software to generate a candela distribution curve(CDC) of an active daylighting system like a tracking dish concentrator. With PHOTOPIA, a set of candela distribution curves was generated under clear sky conditions and different solar altitude angles. The candela distribution curves were then imported to RADIANCE for rendering and analysis on the daylighting performance of a tracking dish concentrator when it installed in a actual class room without windows. As a result, the daylight collection efficiency of the dish concentrator was 68.4% when we assumed that there was no tracking error. It was found that candela(cd) and total lumens(lm) increased with solar altitude rising, whereas the distribution angle was fixed. The illuminance uniformity on the work plane in the class room was relatively low, 0.12, while the illuminance uniformity on the area of $2.7m^2$ to which the light was illuminated was considerably high, 0.60. The maximum illuminance was 1,340lux with a solar altitude angle of 80 degrees.