• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.967-983
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• 2010

Let M be an n-dimensional complete simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant $-{\kappa}^2$. Using the cone total curvature TC($\Gamma$) of a graph $\Gamma$ which was introduced by Gulliver and Yamada [8], we prove that the density at any point of a soap film-like surface $\Sigma$ spanning a graph $\Gamma\;\subset\;M$ is less than or equal to $\frac{1}{2\pi}\{TC(\Gamma)-{\kappa}^2Area(p{\times}\Gamma)\}$. From this density estimate we obtain the regularity theorems for soap film-like surfaces spanning graphs with small total curvature. In particular, when n = 3, this density estimate implies that if $TC(\Gamma)$ < $3.649{\pi}\;+\;{\kappa}^2\inf\limits_{p{\in}F}Area(p{\times}{\Gamma})$, then the only possible singularities of a piecewise smooth (M, 0, $\delta$)-minimizing set $\Sigma$ are the Y-singularity cone. In a manifold with sectional curvature bounded above by $b^2$ and diameter bounded by $\pi$/b, we obtain similar results for any soap film-like surfaces spanning a graph with the corresponding bound on cone total curvature.

• Restorative Dentistry and Endodontics
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• v.28 no.1
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• pp.41-49
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• 2003

There are increasing usage of Nickel-Titanium rotary files in modern clinical endodontic treatment because it is effective and faster than hand filing due to reduced step. This study was conducted to evaluate the effect of canal preparations using 3 different rotary Nickel-Titanium files that has different cross sectional shape and taper on the maintenance of canal curvature. Simulated resin block were instrumented with Profile(Dentsply, USA), GT rotary files(Dentsply, USA), Hero 642(Micro-Mega France), and Pro-Taper(Dentsply, USA). The image of Pre-instrumentation and Post-instrumentation were acquired using digital camera and overspreaded in the computer. Then the total differences of canal diameter, deviation at the outer portion of curvature, deviation at the inner portion of curvature, movement of center of the canal and the centering ratio at the pre-determined level from the apex were measured. Results were statistically analyzed by means of ANOVA, followed by Scheffe test at a significance level of 0.05. The results were as follows； 1. Deviation at the outer portion of curvature, deviation at the inner portion of curvature were showed largest in Pro-Taper so also did in the total differences of canal diameter(p＜0.05). 2. All the groups showed movements of center Profile combined with GT rotary files and Hero 642 has no difference but Pro-Taper showed the most deviation(p＜0.05). 3. At the 1, 2, 3mm level from the apex movements of center directed toward the outer portion of curvature, but in 4, 5 mm level directed toward the inner portion of curvature(p＜0.05). As a results of this study, it could be concluded that combined use of other Nickel-Titanium rotary files is strongly recommended when use Pro-Taper file because it could be remove too much canal structure and also made more deviation of canal curvature than others.

• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.103-109
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• 2000

In this paper, we present the proof of generalized Fenchel's theorem by estimating the Gauss-Kronecker curvature of the tube of a nondegenerate closed curve in R$^{n}$ .

• Publications of The Korean Astronomical Society
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• v.30 no.2
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• pp.309-313
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• 2015

If the present universe is slightly open then pre-inflation curvature would appear as a cosmic dark-flow component of the CMB dipole moment. We summarize current cosmological constraints on this cosmic dark flow and analyze the possible constraints on parameters characterizing the pre-inflating universe in an inflation model with a present-day very slightly open ${\Lambda}CDM$ cosmology. We employ an analytic model to show that for a broad class of inflation-generating effective potentials, the simple requirement that the observed dipole moment represents the pre-inflation curvature as it enters the horizon allows one to set upper and lower limits on the magnitude and wavelength scale of pre-inflation fluctuations in the inflaton field and the curvature parameter of the pre-inflation universe, as a function of the fraction of the total initial energy density in the inflaton field. We estimate that if the current CMB dipole is a universal dark flow (or if it is near the upper limit set by the Planck Collaboration) then the present constraints on ${\Lambda}CDM$ cosmological parameters imply rather small curvature ${\Omega}_k{\sim}0.1$ for the pre-inflating universe for a broad range of the fraction of the total energy in the inflaton field at the onset of inflation. Such small pre-inflation curvature might be indicative of open-inflation models in which there are two epochs of inflation.

• Journal of Oral Medicine and Pain
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• v.21 no.1
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• pp.197-206
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• 1996

This study ws performed to investigate the relationship between cervical curvature and the spatial position of the posterior part of the atlas imaged in the lateral cephalograph. Sixty six patients with temporomandibular disorders(TMD) and twenty dental students were selected for patients group and control group, respectively. The average age of patients group was 26.3 years, and 24.9 years in control group. Measured variables were cervical depth, upper space between the atlas and the base of the occiput, lower space between the atlas and the spinous process of the axis, rea of the posterior part of the atlas imaged in the lateral cephalograph, and the cervical curvature passing through the uppermost point in dorsal side of Dens of the Axis to the lowermost and rearmost point of the 5th cervical vertebra. The reliability of the method used for measuring cervical curvature with curved ruler was also tested. The results obtained were as follows : 1. Cervical depth of patients group was 122.9mm and significantly shorter than that of control group, in which cervical depth was 131.9mm, and cervical depth was significantly correlated with other variables in all subjects. 2. Upper space was greater in patients group, but total space including upper and lower space showed no difference between the two groups. The average value of total space was 26.5mm. 3. Area of the posterior part of the atlas was 168.2$\textrm{mm}^2$ in patients group, and 186.5$\textrm{mm}^2$ in control group with significant difference between the two groups. 4. Average range of radius of cervical curvature were 33-40cm and there was no difference between the two groups. 5. There was no significant correlation between the cervical curvature and the area of the posterior arch of the atlas. 6. The method using curved ruler for measuring cervical curvature could be accepted as a reliable method.

• Restorative Dentistry and Endodontics
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• v.37 no.2
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• pp.104-109
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• 2012

Objectives: The purpose of this study was to evaluate the buccolingual curvature at the apical one third in type II mesial canals of mandibular molars using the radius and angle of curvature. Materials and Methods: Total 100 mandibular molars were selected. Following an endodontic access in the teeth, their distal roots were removed. #15 H- or K-files (Dentsply Maillefer) were inserted into the mesiobuccal and mesiolingual canals of the teeth. Radiographs of the teeth were taken for the proximal view. Among them, type II canals were selected and divided into two subgroups, IIa and IIb. In type IIa, two separate canals merged into one canal before reaching the apex and in type IIb, two separate canals merged into one canal within the apical foramen. The radius and angle of curvature of specimens were examined. Results: In type II, mean radius of curvature in mesiolingual and mesiobuccal canals were 2.82 mm and 3.58 mm, respectively. The radius of the curvature of mesiolingual canals were significantly smaller than that of mesiobuccal canals in type II, and especially in type IIa. However, there were no statistically significant differences in radius of curvature between mesiobuccal and mesiolingual canals in type IIb and there were no significant differences in angle of curvature between type IIa and IIb. Conclusion: In this study, type II mesial canals of mandibular molars showed severe curvature in the proximal view. Especially, mesiolingual canals of type IIa had more abrupt curvature than mesiobuccal canals at the apical one third.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.175-177
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• 1989

The following is the basic problem about the stability in Riemannian Geometry; given a Riemannian manifold N, find all stable complete minimal submanifolds of N. As answers of this problem, do Carmo-Peng [1] and Fischer-Colbrie and Schoen [3] showed that the stable minimal surfaces in R$^{3}$ are planes and Schoen-Yau [5] and Fischer-Colbrie and Schoen [3] gave a solution for the case where the ambient space is a three dimensional manifold with nonnegative scalar curvature. In this paper we will remove the assumption of finite absolute total curvature in [3, Theorem 3].

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.641-648
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• 2000

It has been conjectured that, on a compact 3-dimensional manifold, a critical point of the total scalar curvature functional restricted to the space of constant scalar curvature metrics of volume 1 is Einstein. In this paper we find a sufficient condition that a critical point is Einstein. This condition is equivalent for a critical point ot be conformally flat. Its relationship with the Fisher-Marsden conjecture is also discussed.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.511-517
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• 2024

Let (M, p) denote a noncompact manifold M together with arbitrary basepoint p. In [7], Kondo-Tanaka show that (M, p) can be compared with a rotationally symmetric plane M_m in such a way that if M_m satisfies certain conditions, then M is proved to be topologically finite. We substitute Kondo-Tanaka's condition of finite total curvature of M_m with a weaker condition and show that the same conclusion can be drawn. We also use our results to show that when M_m satisfies certain conditions, then M is homeomorphic to ℝⁿ.

• Proceedings of the Korea Concrete Institute Conference
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• 2002.10a
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• pp.111-116
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• 2002

The flexural ductility capacity of reinforced concrete columns can be expressed either in terms of curvature ductility or displacement ductility. To evaluate ductility capacity of reinforced concrete columns, analytical models and a non-linear analysis program, NARCC have been developed, which is applicable to the RC columns subjected to seismic loading. The analytical results by using computer program NARCC are in good agreement with the test results. In order to develop relationships between the curvature ductility and the displacement ductility, the analysis for total 21,600 RC circular columns using the computer program NARCC have been carried out for parametric studies. Based on the results from the parametric studies, a correlation equation between the curvature ductility and the displacement ductility was developed.