• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.401-419
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• 2024

Let K, H, K_II and H_II be the Gaussian curvature, the mean curvature, the second Gaussian curvature and the second mean curvature of a timelike tubular surface T_γ(α) with the radius γ along a timelike curve α(s) in Minkowski 3-space E³₁. We prove that T_γ(α) must be a (K, H)-Weingarten surface and a (K, H)-linear Weingarten surface. We also show that T_γ(α) is (X, Y)-Weingarten type if and only if its central curve is a circle or a helix, where (X, Y) ∈ {(K, K_II), (K, H_II), (H, K_II), (H, H_II), (K_II , H_II)}. Furthermore, we prove that there exist no timelike tubular surfaces of (X, Y)-linear Weingarten type, (X, Y, Z)-linear Weingarten type and (K, H, K_II, H_II)-linear Weingarten type along a timelike curve in E³₁, where (X, Y, Z) ∈ {(K, H, K_II), (K, H, H_II), (K, K_II, H_II), (H, K_II, H_II)}.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.503-511
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• 2010

We prove a common fixed point theorem for S-contraction mappings without continuity. Using this result we obtain an approximating curve for S-nonexpansive mappings in a Banach space and prove Browder's type strong convergence theorem for this approximating curve. The demiclosedness principle for S-nonexpansive mappings is also established.

• The Journal of Korean Academy of Prosthodontics
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• v.8 no.1
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• pp.30-36
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• 1968

The measurements on the various items, such as arch form, kinds of anterior dental arch, degree of curvature in anterior dental arches, relationship between direction of the disto-incisal edge of the canine and first premolar, and kinds of posterior dental arch in upper dental arches were studied on 311 cases of the Korean adults aged from 20 to 30years. The results were as follows. 1. The commonest type of the upper dental arches was U-type (53.7%), the remaining were O-type (25.4%) and V-type (20.0%). 2. A slight curvature type (71.87%) prevailed against angulated curvature type in upper anterior dental arches. 3. The degree of curvature from $121^{\circ}$ to $160^{\circ}$ in anterior dental arches was common, and the degree of curve of 1-type with on curvature was smaller than 4, 5 type with two curvature. 4. The direction of the disto-incisal edge of canine went between the tip of the buccal cusp and the lingual incline of the buccal cusp of the first premolar in most dental arches and went lingual incline of the buccal cusp of the first premolar in U-type, from buccal cusp to lingual cusp of the first premolar in O-type and were distributed from buccal edge to central groove of the first premolar in V-type. 5. A posterior dental arch with almost straight curvature was common in 60.87%, and 4-type with a half rounded curve from first premolar to second molar was next.

• Journal of the Korean Data and Information Science Society
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• v.25 no.1
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• pp.195-209
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• 2014

In this paper, we derive the estimators of the location parameter and the scale parameter in a logistic distribution based on multiply type-II censored samples by the approximate maximum likelihood estimation method. We use four modified empirical distribution function (EDF) types test for the logistic distribution based on multiply type-II censored samples using proposed approximate maximum likelihood estimators. We also propose the modified normalized sample Lorenz curve plot for the logistic distribution based on multiply type-II censored samples. For each test, Monte Carlo techniques are used to generate the critical values. The powers of these tests are also investigated under several alternative distributions.

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.903-914
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• 2014

The inverse Weibull distribution has been proposed as a model in the analysis of life testing data. Also, inverse Weibull distribution has been recently derived as a suitable model to describe degradation phenomena of mechanical components such as the dynamic components (pistons, crankshaft, etc.) of diesel engines. In this paper, we derive the approximate maximum likelihood estimators of the scale parameter and the shape parameter in the inverse Weibull distribution under multiply type-II censoring. We also develop four modified empirical distribution function (EDF) type tests for the inverse Weibull or extreme value distribution based on multiply type-II censored samples. We also propose modified normalized sample Lorenz curve plot and new test statistic.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2002.07a
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• pp.515-518
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• 2002

In this study, the ellipsoidal cap type magnetic pole structure was proposed for the electro-magnet in B-H curve tracer. From the simulation for the electro-magnet without specimen, the area of effective uniform field(99% range for the central field value) was considerably increased in case of the newly proposed ellipsoidal cap type magnetic pole than that of the conventional simple-inclined cap type magnetic pole. Also, through the simulation for the electro-magnet with permanent magnet specimen(NaFe30), the optimal Positions of the magnetic field measurement sensor(Hall sensor) were found out in each case and the errors were decreased in case of the newly proposed ellipsoidal cap type magnetic pole.

• Journal of Mechanical Science and Technology
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• v.18 no.1
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• pp.106-113
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• 2004

Recently, a new issue in designing spot welded structures such as automobile and train car bodies is to predict an economical fatigue design criterion. One of the most typical and traditional methods is to use a ΔP-N$\sub$f/ curve. However, since the fatigue data on the ΔP-N$\sub$f/ curve vary according to the welding conditions, materials, geometry of joint and fatigue loading conditions, it is necessary to perform the additional fatigue tests for determining a new fatigue design criterion of spot-welded lap joint having specific dimension and geometry. In this study, the stress distributions around spot welds of various spot welded lap joints such as in-plane bending type (IB type), tension shea. type (TS type) and cross tension type (CT type) were numerically analyzed. Using these results, the ΔP-N$\sub$f/ curves Previously obtained from the fatigue tests for each type were rearranged into the Δ$\sigma$-N$\sub$f/ relations with the maximum stresses at the nugget edge of the spot weld.

• Journal of the Korean Geotechnical Society
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• v.24 no.11
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• pp.121-131
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• 2008

In constructing a slurry trench cutoff wall, bentonite-water slurry is used to secure the stability of sidewalls during excavation before the wall is completed by backfilling. Unexpectedly, a thin but relatively impermeable layer called filter cake can be formed on the excavation surface, which significantly influences the result of slug test analysis in the cutoff wall if not considered. This study is to examine the effect of filter cake on evaluating hydraulic conductivity of the vertical cutoff wall through slug test analysis with the aid of the verified numerical program Slug_3D. The no-flux boundary conditions were adopted in Slug_3D to simulate the filter cake on the interface between the wall and the natural soil. A new set of type curves were built for applying the type curve method. New modification factors were obtained for using the modified line-fitting method. With consideration of filter cake, the type curve method and the modified line-fitting method were adopted to reanalyze the case study taken from EMCON (1995). The previous results achieved by Choi and Daniel (2006) without consideration of filter cake were compared with the present results obtained in this paper. The comparison emphasizes the necessity of considering filter cake when analyzing slug test results in vertical cutoff walls.

• Journal of Korean Medicine Rehabilitation
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• v.25 no.4
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• pp.83-92
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• 2015

Objectives To measure and analyze the curvature of the cervical spine for university students. Methods This study carried out on 132 students. The cervical spine curvature was measured by six measuring methods. The type and numeric value of cervical spine curvature was analyzed by Angle of cervical curve (C1~C7), Angle of cervical curve (C2~C7), Jackson's angle, Ishihara Index, Depth of cervical curve and Method of Jochumsen. Cervical spine curvatures between male and female are compared by Mann-Whitney test. Rate of type of cervical curvature between male and female are compared by linear by linear association. Results 1. The average of angle of cervical curve (C1~C7) is $33.78{\pm}9.85^{\circ}$, angle of cervical curve (C2~C7) is $10.28{\pm}8.12^{\circ}$. The average of Jackson's angle is $14.02{\pm}10.01^{\circ}$, average of Ishihara Index is $8.46{\pm}10.58%$. The average of Depth of cervical curve is $5.15{\pm}4.72mm$ and average of Method of Jochumsen is $0.94{\pm}3.83mm$. 2. More than half of student's cervical curvature showed hypolordosis except Ishihara index. 3. There was significant difference in numeric value of cervical curvature between male and female both groups in terms of Ishihara index. 4. There were insignificant differences between male and female in terms of type of cervical curvature. Conclusions According to above results, we found out average of student's cervical curve. And the results suggest that most of the student's cervical curvature decrease.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.523-537
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• 2011

A receiver operating characteristic (ROC) curve plots the true positive rate of a classier against its false positive rate, both of which are accuracy measures of the classier. The ROC curve has several interesting geometrical properties, including concavity which is a necessary condition for a classier to be optimal. In this paper, we study the nonparametric maximum likelihood estimator (NPMLE) of a concave ROC curve and its modification to reduce bias. We characterize the NPMLE as a solution to a geometric programming, a special type of a mathematical optimization problem. We find that the NPMLE is close to the convex hull of the empirical ROC curve and, thus, has smaller variance but positive bias at a given false positive rate. To reduce the bias, we propose a modification of the NPMLE which minimizes the $L_1$ distance from the empirical ROC curve. We numerically compare the finite sample performance of three estimators, the empirical ROC curve, the NMPLE, and the modified NPMLE. Finally, we apply the estimators to estimating the optimal ROC curve of the variance-threshold classier to segment a low depth of field image and to finding a diagnostic tool with multiple tests for detection of hemophilia A carrier.