• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.41-63
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• 2024

In this paper, we study complete Riemannian immersions into a semi-Riemannian warped product obeying suitable curvature constraints. Under appropriate differential inequalities involving higher order mean curvatures, we establish rigidity and nonexistence results concerning these immersions. Applications to the cases that the ambient space is either an Einstein manifold, a steady state type spacetime or a pseudo-hyperbolic space are given, and a particular investigation of entire graphs constructed over the fiber of the ambient space is also made. Our approach is based on a parabolicity criterion related to a linearized differential operator which is a divergence-type operator and can be regarded as a natural extension of the standard Laplacian.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.5
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• pp.549-554
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• 2012

In this paper, we consider the optimal fuzzy filter of nonlinear discrete-time with estimation error variance constraint. First, the Takagi and Sugeno(T-S) fuzzy model is employed to approximate the nonlinear system. Next, the error state is mean square bounded, and the steady state variance of the estimation error of each state is not more than the individual predefined value. It is shown that, the addressed problem can be carried out by solving linear matrix inequality(LMI) and some algebraic quadratic matrix inequalities. Finally, some examples are provided to illustrate the design procedure and expected performance through simulations.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1095-1103
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• 2016

B. Y. Chen introduced a series of curvature invariants, known as Chen invariants, and proved sharp estimates for these intrinsic invariants in terms of the main extrinsic invariant, the squared mean curvature, for submanifolds in Riemannian space forms. Special classes of submanifolds in Sasakian manifolds play an important role in contact geometry. F. Defever, I. Mihai and L. Verstraelen [8] established Chen first inequality for C-totally real submanifolds in Sasakian space forms. Also, the differential geometry of slant submanifolds has shown an increasing development since B. Y. Chen defined slant submanifolds in complex manifolds as a generalization of both holomorphic and totally real submanifolds. The slant submanifolds of an almost contact metric manifolds were defined and studied by A. Lotta, J. L. Cabrerizo et al. A Chen first inequality for slant submanifolds in Sasakian space forms was established by A. Carriazo [4]. In this article, we improve this Chen first inequality for special contact slant submanifolds in Sasakian space forms.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.979-998
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• 2009

Involving the Ricci curvature and the squared mean curvature, we obtain a basic inequality for a submanifold of an S-space form tangent to structure vector fields. Equality cases are also discussed. As applications we find corresponding results for almost semi-invariant submanifolds, $\theta$-slant submanifolds, anti-invariant submanifold and invariant submanifolds. A necessary and sufficient condition for a totally umbilical invariant submanifold of an S-space form to be Einstein is obtained. The inequalities for scalar curvature and a Riemannian invariant $\Theta_k$ of different kind of submanifolds of a S-space form $\tilde{M}(c)$ are obtained.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.105-122
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• 2007

In this paper we analyze various studies on $Erd\ddot{o}s-Mordell$ inequality(from a point O inside a given triangle ABC the perpendiculars OP, OQ, OR are drawn to its sides, then OA+OB+OC${\ge}$2(OP+OQ+OR)). We find out three trends of studies on $Erd\ddot{o}s-Mordell$ inequality: studies on various proof methods, studies on related means, studies on $Erd\ddot{o}s-Mordell$ type inequalities.

• Kyungpook Mathematical Journal
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• v.47 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.26 no.1
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• pp.35-42
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• 1989

Let .ohm.$_{n}$ and Pm $t_{n}$ denote the sets of all n*n doubly stochastic matrices and the set of all n*n permutation matrices respectively. For m*n matrices A=[ $a_{ij}$ ], B=[ $b_{ij}$ ] we write A.leq.B(A$a_{ij}$ .leq. $b_{ij}$ ( $a_{ij}$ < $b_{ij}$ ) for all i=1,..,m; j=1,..,n. Let $I_{n}$ denote the identity matrix of order n, let $J_{n}$ denote the n*n matrix all of whose entries are 1/n, and let $K_{n}$=n $J_{n}$. For a complex square matrix A, the permanent of A is denoted by per A. Let $E_{ij}$ denote the matrix of suitable size all of whose entries are zeros except for the (i,j)-entry which is one.hich is one.

• Journal of Preventive Medicine and Public Health
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• v.41 no.5
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• pp.300-306
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• 2008

Objectives : This study was performed to compare the standardized mortality ratios among different small areas and to explore the usefulness of standardized mortality ratios in South Korea. Methods : To calculate the standardized mortality ratio (SMR), we obtained the national deaths certificate data (2004-2006) and national registration population data (2003-2006), and these were provided by the National Statistical Office. The small areas (Eup.Myoun.Dong) were based on the subdivisions of counties. Among the 3,580 small areas classified by the National Statistical Office, 3,571 areas were included in this study. The basic statistics and decile distributions of the SMRs for all the regional levels were calculated, and the small area maps were also produced for some selected regions. To evaluate the precision of SMR, we calculated the 95% confidence intervals of the SMR in selected small areas. Results : The mean and the standard deviation of the SMRs among all small areas were 100.8 and 17.0, respectively. The range was 30.6-211.7 and the inter-quartile range was 20.7. Seoul metropolitan city displayed the lowest mean SMR among 16 regions in South Korea, and 34.6 percent of the small area SMRs belonged to the first decile(the lowest group). On the contrary, the mean SMR of Gyeongsangnam province was highest, and 26.1 percent of the small area SMRs belonged to the tenth decile(the highest group). In some areas, the precision of the SMR, which was calculated by the 95% confidence intervals, remained questionable, yet it was quite stable for almost areas. Conclusions : The standardized mortality ratios can be useful for allocating health resources at the small area level in Korea.

• Journal of Electrical Engineering and Technology
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• v.11 no.1
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• pp.200-214
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• 2016

This paper investigates the problem of stability analysis and robust H_∞ controller for time-delayed systems with parameter uncertainties and stochastic disturbances. It is assumed parameter uncertainties are norm bounded and mean and variance for disturbances of them are known. Firstly, by constructing a newly augmented Lyapunov-Krasovskii functional, a stability criterion for nominal systems with time-varying delays is derived in terms of linear matrix inequalities (LMIs). Secondly, based on the result of stability analysis, a new controller design method is proposed for the nominal form of the systems. Finally, the proposed method is extended to the problem of robust H_∞ controller design for a time-delayed system with parameter uncertainties and stochastic disturbances. To show the validity and effectiveness of the presented criteria, three examples are included.

• Journal of Preventive Medicine and Public Health
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• v.47 no.2
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• pp.94-103
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• 2014

Objectives: The present study examined relationships between socioeconomic status (SES) and obesity and body mass index (BMI) as well as the effects of health-related behavioral and psychological factors on the relationships. Methods: A cross-sectional population-based study was conducted on Korean adults aged 20 to 79 years using data from the 2001, 2005, and 2007 to 2009 Korea National Health and Nutrition Examination Survey. Multivariate logistic and linear regression models were used to estimate odds ratios of obesity and mean differences in BMI, respectively, across SES levels after controlling for health-related behavioral and psychological factors. Results: We observed significant gender-specific relationships of SES with obesity and BMI after adjusting for all covariates. In men, income, but not education, showed a slightly positive association with BMI (p<0.05 in 2001 and 2005). In women, education, but not income, was inversely associated with both obesity and BMI (p<0.0001 in all datasets). These relationships were attenuated with adjusting for health-related behavioral factors, not for psychological factors. Conclusions: Results confirmed gender-specific disparities in the associations of SES with obesity and BMI among adult Korean population. Focusing on intervention for health-related behaviors may be effective to reduce social inequalities in obesity.