• 대한수학회보
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• 제49권1호
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• pp.33-47
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• 2012

In this paper, the log-convexity of another class one-parameter mean is investigated. As applications, some new upper and lower bounds of logarithmic mean, new estimations for identric mean and new inequalities for power-exponential mean and exponential-geometric mean are first given.

• 대한수학회논문집
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• 제34권1호
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• pp.239-251
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• 2019

In this paper we introduce a new formulation of symmetric homogeneous bivariate means that depends on the variation of a given continuous strictly increasing function on (0, ${\infty}$). It turns out that this class of means includes a lot of known bivariate means among them the arithmetic mean, the harmonic mean, the geometric mean, the logarithmic mean as well as the first and second Seiffert means. Using this new formulation we introduce a lot of new bivariate means and derive some mean-inequalities.

• 소음진동
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• 제6권6호
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• pp.735-747
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• 1996

In this paper, buckling reliability analyses of stiffened cylinder with random initial geometric imperfection under axial impact load are performed by the combined response surface method. The effect of random geometric imperfection on the failure probability and reliability is recognized quantitatively. Buckling reliability decreases with the increase of mean value, cov of initial geometric imperfection under the same external load. Buckling probability under impact load is greater than those under static load with the same condition. From the probabilistic characteristics of imapct buckling load, relation between reliability index and safety parameter can be obtained in addition to the relation between load and reliability index. And those results can be used to determine the range of required safety parameter and acceptable imperfaction.

• Kyungpook Mathematical Journal
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• 제47권1호
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• pp.133-150
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• 2007

In a development of efficient primal-dual interior-points algorithms for self-scaled convex programming problems, one of the important properties of such cones is the existence and uniqueness of "scaling points". In this paper through the identification of scaling points with the notion of "(metric) geometric means" on symmetric cones, we extend several well-known matrix inequalities (the classical L$\ddot{o}$wner-Heinz inequality, Ando inequality, Jensen inequality, Furuta inequality) to symmetric cones. We also develop a theory of spectral geometric means on symmetric cones which has recently appeared in matrix theory and in the linear monotone complementarity problem for domains associated to symmetric cones. We derive Nesterov-Todd inequality using the spectral property of spectral geometric means on symmetric cones.

• 대한수학회지
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• 제53권5호
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• pp.1077-1100
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• 2016

We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of geometric functions. We prove a fundamental existence and uniqueness theorem in terms of these functions. On any Lorentz surface with parallel normalized mean curvature vector field we introduce special geometric (canonical) parameters and prove that any such surface is determined up to a rigid motion by three invariant functions satisfying three natural partial differential equations. In this way we minimize the number of functions and the number of partial differential equations determining the surface, which solves the Lund-Regge problem for this class of surfaces.

• 한국멀티미디어학회논문지
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• 제11권6호
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• pp.777-786
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• 2008

Human face avatar is important information in nowadays, such as describing real people in virtual world. In this paper, we have presented a face avatar creation and warping algorithm by using face feature analysis method, in order to detect face feature, we utilized local mean method based on facial feature appearance and face geometric information. Then detect facial candidates by using it's character in $YC_bC_r$ color space. Meanwhile, we also defined the rules which are based on face geometric information to limit searching range. For analyzing face feature, we used face feature points to describe their feature, and analyzed geometry relationship of these feature points to create the face avatar. Then we have carried out simulation on PC and embed mobile device such as PDA and mobile phone to evaluate efficiency of the proposed algorithm. From the simulation results, we can confirm that our proposed algorithm will have an outstanding performance and it's execution speed can also be acceptable.

• Kyungpook Mathematical Journal
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• 제24권2호
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• pp.159-172
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• 1984

• Journal of Preventive Medicine and Public Health
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• 제20권2호
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• pp.261-269
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• 1987

In order to investigate working conditions of underground coal mines, this work was undertaken to evaluate the respirable dust and the concentration of quartz in Taeback and Kangneung areas. The concentration of quartz was determined by Fourier Transform Infrared Spectrophotometry. The results were as follows; 1) The concentration of respirable dust of drilling and coal face in Taeback and Kangneung areas were as followed; Arithmetic $Mean{\pm}S.D.(mg/m^3)$ Taeback Drilling: $2.00{\pm}1.56$ Taeback Coal Face: $3.74{\pm}3.14$ Kangneung Drilling: $4.55{\pm}4.51$ Kangneung Coal Face: $5.77{\pm}4.53$ Geometric $Mean{\pm}S.D.(mg/m^3)$ Taeback Drilling: $1.34{\pm}2.81$ Taeback Coal Face : $2.55{\pm}2.61$ Kangneung Drilling : $2.44{\pm}3.63$ Kangneung Coal Face: $4.24{\pm}2.37$ 2) Distribution of respirable dust was well fitted to the log-normal distribution and geometric mean value was $log^{-1}\;0.37{\pm}log^{-1}\;0.47(2.34{\pm}2.95)mg/m^3$. 3) The difference of respirable dust concentrations in Taeback and Kangneung areas was not significant statistically (p>0.05). 4) The concentration of quartz of drilling and coal face in Taeback and Kangneung areas were as followed; Arithmetic $Mean{\pm}S.D.(%)$ Taeback Drilling: $6.18{\pm}5.52$ Taeback Coal Face: $1.89{\pm}1.54$ Kangneung Drilling: $3.54{\pm}2.12$ Kangneung Coal Face: $2.05{\pm}3.37$ Geometric $Mean{\pm}S.D.(%)$ Taeback Drilling: $4.24{\pm}2.59$ Coal Face: $1.39{\pm}2.22$ Kangneung Drilling : $2.55{\pm}3.08$ Kangneung Coal Face : $1.24{\pm}2.33$ 5) Distribution of quartz concentrations was well fitted to the log-normal distribution and geometric mean value was $log^{-1}\;0.33{\pm}log^{-1}\;0.45(2.14{\pm}2.82)%$. 6) The difference of quartz concentrations in Taeback and Kangneung areas was not significant (p>0.05), but significant at drilling sites and coal faces (p<0.05).

• Journal of the Korean Statistical Society
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• 제22권2호
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• pp.201-208
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• 1993

Given the specific mean shift outlier model, the score test for multiple outliers in nonlinear regression is discussed as an alternative to the likelihood ratio test. The geometric interpretation of the score statistic is also presented.

• Journal of the Korean Statistical Society
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• 제24권2호
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• pp.419-437
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• 1995

Given the specific mean shift outlier model, several standard approaches to obtaining test statistic for outliers are discussed. Each of these is developed in detail for the nonlinear regression model, and each leads to an equivalent distribution. The geometric interpretations of the statistics and accuracy of linear approximation are also presented.