• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제6권1호
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• pp.67-80
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• 2002

We formulate a pair of nondifferentiable symmetric dual variational problems with a square root term. Under invexity assumptions, we establish weak, strong, converse and self duality theorems for our variational problems by using the generalized Schwarz inequality. Also, we give the static case of our nondifferentiable symmetric duality results.

• 한국임상약학회지
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• 제31권3호
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• pp.216-230
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• 2021

Objective: Taking action on health inequalities starts with the production of information laying out the problems of inequalities, but Korean society has no national database to view related data at a glance. This study aimed to compare Korean national database with the Public Health Profile (PHP), a health inequality database of the UK. Methods: Data were collected from the websites of government and relevant organizations in the both countries between March and August 2020, which was updated in August 2021. Two themes including Co-occurring substance misuse and mental health issues in mental health and INteractive Health Atlas of Lung conditions in England were selected for comparison in terms of data accessibility, data usability and data visualization. Results: The British PHP is being served on a web-based platform, Fingertips. The data collected at the regional level were presented on 31 health inequality themes. The data are displayed at a level that can be compared between comparable communities, and visualized into various tables and figures. Comparable Korean data were scattered in several themes and websites, and mostly provided as a 17 administrative region base, which was too vast to make a meaningful comparisons. Conclusion: The findings proposed several considerations which could be useful for establishing a database of health inequality in the Korean society.

• Kyungpook Mathematical Journal
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• 제59권4호
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• pp.703-723
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• 2019

In this paper, we consider a common solution of three problems in real Hilbert spaces: the Ky Fan inequality problem, the variational inequality problem and the fixed point problem for demicontractive single-valued and quasi-nonexpansive multi-valued mappings. To find the solution we present a new iterative algorithm and prove a strong convergence theorem under mild conditions. Moreover, we provide a numerical example to illustrate the convergence behavior of the proposed iterative method.

• 대한수학회지
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• 제45권2호
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• pp.559-573
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• 2008

In this paper, two classes of functions, involving a parameter and the classical Euler gamma function, and two functions, involving the classical Euler gamma function, are verified to be logarithmically completely monotonic in $(-\frac{1}{2},\infty)$ or $(0,\infty)$; some inequalities involving the classical Euler gamma function are deduced and compared with those originating from certain problems of traffic flow, due to J. Wendel and A. Laforgia, and relating to the well known Stirling's formula.

• 대한전기학회논문지:전력기술부문A
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• 제48권5호
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• pp.560-570
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• 1999

This paper formulates the suboptimal robust Kalman filtering problem into two coupled Linear Matrix Inequality (LMI) problems by applying Lyapunov theory to the augmented system which is composed of the state equation in the uncertain linear system and the estimation error dynamics. This formulations not only provide the sufficient conditions for the existence of the desired filter, but also construct the suboptimal robust Kalman filter. The proposed filter can guarantee the optimized upper bound of the estimation error variance for uncertain systems with parametric uncertainties in both the state and measurement matrices. In addition, this paper shows how the problem of finding the minimizing solution subject to Quadratic Matrix Inequality (QMI), which cannot be easily transformed into LMI using the usual Schur complement formula, can be successfully modified into a generic LMI problem.

• Kyungpook Mathematical Journal
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• 제58권2호
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• pp.333-346
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• 2018

An approximation scheme utilizing Bezier curves is considered for solving time-delayed optimal control problems with terminal inequality constraints. First, the problem is transformed, using a $P{\acute{a}}de$ approximation, to one without a time-delayed argument. Terminal inequality constraints, if they exist, are converted to equality constraints. A computational method based on Bezier curves in the time domain is then proposed for solving the obtained non-delay optimal control problem. Numerical examples are introduced to verify the efficiency and accuracy of the proposed technique. The findings demonstrate that the proposed method is accurate and easy to implement.

• International Journal of Computer Science & Network Security
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• 제21권3호
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• pp.295-303
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• 2021

The relevance of the research is due to the fact that the issue of poverty is one of the most acute social problems of the beginning of the third millennium. The phenomenon of poverty is widespread in third world countries as well as it is observed in relatively developed countries. Poverty rates in Latin America are threatening. Consequently, the issue of social and economic inequality in these countries has become extremely acute. The purpose of the research: to identify the causes of poverty and social inequality and substantiate the main directions of poverty reduction in third world countries. The research methods: comparative analysis; index method; systematization; grouping; generalization. Results. The classification of the causes of poverty has been carried out and the directions of its overcoming in the countries of Latin America on groups of indicators have been defined, namely: 1) political; 2) economic; 3) demographic; 4) regional-geographical; 5) social; 6) qualification; 7) personal. Based on the Net Domestic Product indicator, a comparison of economic indicators of the studied countries has been carried out. It has been revealed that from 1990 to 2018 income inequality increased in 52 of 119 countries studied, and decreased in 57 states. Inequality has increased in the world's most populous countries, particularly China and India. In general, countries with growing inequality are home to more than two-thirds (71%) of the world's population. Trends in the distribution of income in the world have been investigated by applying the Gini index, the high level of which is observed in Latin America (Colombia 48,9%, Panama 46,1%, Chile and Mexico 45,9%). The forecast of the impact of the Covid-19 pandemic on this issue has been outlined; the ways of its impact on the economies of the countries have been studied. As a result of the study, the main directions and mechanisms of the strategy for poverty reduction and social inequality in the third world countries have been identified. The implementation of the poverty reduction strategy presented in this academic paper may have a positive impact on the economic situation of the population of Latin American countries.

• 한국노년학
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• 제32권3호
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• pp.759-776
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• 2012

본 연구는 EQ-5D를 이용하여 소득계층에 따른 노인들의 건강불평등을 측정하였다. 특히 건강불평등의 다양한 측면을 파악하기 위하여 집중지수를 EQ-5D의 하위차원 및 노인들의 하위집단에 따라 분해(decomposition)하였다. 분석 자료는 2010년 국민건강영양조사 원자료가 사용되었으며 이중 60세 이상인 자를 노인으로 정의하여 분석하였다. 본 연구의 분석결과를 요약하면 다음과 같다. 첫째, 노인들의 EQ-5D 집중지수는 .0254를 기록하였다. 이는 고소득층에 유리한 불평등이 있음을 의미한다. 나아가 EQ-5D를 구성하는 모든 하위차원 즉, 운동능력, 자기관리, 일상활동, 통증/불편, 불안/우울, 기능악화 등에서도 불건강이 저소득층에 집중되어 나타났다. 둘째, EQ-5D 집중지수를 가장 많이 설명하는 하위차원은 운동능력으로 EQ-5D 집중지수의 35.8%를 설명하였다. 그 다음으로 통증 및 불편(17.7%), 기능악화(17.7%), 일상관리(14.6%) 등의 순으로 설명력이 높다. 이러한 결과는 전 연령층을 분석한 선행연구의 결과와 대조를 이루는데, 선행연구들에서 기여도가 매우 낮았던 운동능력(3.9%)이 크게 상승한 반면 불안/우울의 기여도는 약화되었다. 셋째, 성별, 지역, 배우자 유무에 따라 EQ-5D 집중지수를 분해한 결과 세 집단이 집중지수를 설명하는 정도는 비슷하게 나타났다. 세 집단은 각각 건강형평성의 1/10정도를 설명하였다. 넷째, EQ-5D 집중지수를 하위집단에 따라 분해한 결과, 남성보다는 여성이, 도시지역보다는 농어촌지역이, 그리고 배우자가 있는 노인보다는 없는 노인의 내부불평등이 더 크게 나타났다. 내부 불평등이 큰 세 집단의 경우 모두 EQ-5D 평균값도 낮았는데, 이는 저소득 여성노인일수록, 농어촌지역 저소득 노인일수록, 배우자가 없는 저소득 노인일수록 건강관련 삶의 질이 떨어짐을 의미하는 것이었다. 마지막으로 하위집단의 내부불평등이 집중지수를 설명하는 정도는 여성노인집단, 도시지역 노인집단, 배우자가 있는 노인집단이 크게 나타났다.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.227-245
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• 2011

In this paper, we introduce a new iterative method for finding a common element of the set of solutions for mixed equilibrium problem, the set of solutions of the variational inequality for a ${\beta}$inverse-strongly monotone mapping and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Ces$\`{a}$ro mean approximation method. We prove that the sequence converges strongly to a common element of the above three sets under some mind conditions. Our results improve and extend the corresponding results of Kumam and Katchang [A viscosity of extragradient approximation method for finding equilibrium problems, variational inequalities and fixed point problems for nonexpansive mapping, Nonlinear Analysis: Hybrid Systems, 3(2009), 475-86], Peng and Yao [Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems, Mathematical and Computer Modelling, 49(2009), 1816-828], Shimizu and Takahashi [Strong convergence to common fixed points of families of nonexpansive mappings, Journal of Mathematical Analysis and Applications, 211(1) (1997), 71-83] and some authors.

• 대한수학회보
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• 제50권2호
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• pp.375-388
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• 2013

In this paper, we introduce an iterative sequence for finding solution of a system of mixed equilibrium problems and the set of fixed points of a nonexpansive mapping in Hilbert spaces. Then, the weak and strong convergence theorems are proved under some parameters controlling conditions. Moreover, we apply our result to fixed point problems, system of equilibrium problems, general system of variational inequalities, mixed equilibrium problem, equilibrium problem and variational inequality.