• 대한수학회보
• /
• 제51권3호
• /
• pp.641-651
• /
• 2014

Because of difficulty of using Schauder's fixed point theorem to the polynomial-like iterative equation, a lots of work are contributed to the existence of solutions for the polynomial-like iterative equation on compact set. In this paper, by applying the Schauder-Tychonoff fixed point theorem we discuss monotone solutions and convex solutions of the polynomial-like iterative equation on an open set (possibly unbounded) in $\mathbb{R}^N$. More concretely, by considering a partial order in $\mathbb{R}^N$ defined by an order cone, we prove the existence of increasing and decreasing solutions of the polynomial-like iterative equation on an open set and further obtain the conditions under which the solutions are convex in the order.

• Journal of applied mathematics & informatics
• /
• 제28권5_6호
• /
• pp.1395-1408
• /
• 2010

In this paper, a pair of Wolfe type second-order nondifferentiable multiobjective symmetric dual program over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under second-order (F, $\alpha$, $\rho$, d)-convexity assumptions. An illustration is given to show that second-order (F, $\alpha$, $\rho$, d)-convex functions are generalization of second-order F-convex functions. Several known results including many recent works are obtained as special cases.

• 호남수학학술지
• /
• 제27권2호
• /
• pp.251-265
• /
• 2005

In this paper, we introduce a generalized vector quasivariational like inequality for fuzzy mappings and show the existence of solutions under compact assumption.

• 호남수학학술지
• /
• 제26권4호
• /
• pp.533-547
• /
• 2004

In this paper, we introduce two kinds of generalized vector quasivariational-like inequalities for multivalued mappings and show the existence of solutions to those variational inequalities under compact and non-compact assumptions, respectively.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제6권1호
• /
• pp.33-37
• /
• 1999

We obtain a generalization of Behera and Panda's result on nonlinear scalar case to the vector version.

• Journal of applied mathematics & informatics
• /
• 제11권1_2호
• /
• pp.273-281
• /
• 2003

The purpose of this paper is to study the duality theorems in cone constrained multiobjective nonlinear programming for pseudo-invex objectives and quasi-invex constrains and the constraint cones are arbitrary closed convex ones and not necessarily the nonnegative orthants.

• 한국항공우주학회지
• /
• 제49권1호
• /
• pp.21-30
• /
• 2021

탐색기를 탑재한 유도탄의 중기궤적은 탐색기 시야(FOV : Field-Of-View) 내에서 표적을 탐지하며, 전환 시점에서의 기동성을 최대화하도록 설계하는 것이 요구된다. 유도탄의 비행궤적 최적화 문제는 여러 구속조건이 적용된 비선형 문제로 일반적인 해석해를 도출하기 어렵기 때문에 그 동안 다양한 계산적인 방법들이 제시되어 왔다. 본 논문에서는 추진-활공 유도탄의 중기궤적 최적화 문제를 컨벡스 최적화 기법인 2차 원뿔 프로그래밍을 이용하여 산출하였다. 먼저, 운동방정식의 상태변수를 최소화하기 위해서 제어변수 구속조건이 추가된 제어변수 추가 형태의 운동방정식을 구성하였다. 또한, 자유 종말시간 문제와 추진시간 문제를 대처하기 위하여 정규화된 시간 변수를 독립 변수로 설정하였다. 그리고, 운동방정식과 제어변수 구속조건을 컨벡스 형태로 변환하기 위하여 각각 부분 선형화와 무손실 컨벡스 변환을 적용하였다. 마지막으로, 본 논문에서 제시된 방안의 타당성을 확인하기 위하여 비선형 최적화 프로그래밍 결과와 비교하였다.

• Imaging Science in Dentistry
• /
• 제50권4호
• /
• pp.323-330
• /
• 2020

Purpose: The mastoid region is ideal for studying sexual dimorphism due to its anatomical position at the base of the skull. This study aimed to determine sex in the Iranian population based on measurements of the mastoid process using different data mining algorithms. Materials and Methods: This retrospective study was conducted on 190 3-dimensional cone-beam computed tomographic (CBCT) images of 105 women and 85 men between the ages of 18 and 70 years. On each CBCT scan, the following 9 landmarks were measured: the distance between the porion and the mastoidale; the mastoid length, height, and width; the distance between the mastoidale and the mastoid incision; the intermastoid distance (IMD); the distance between the lowest point of the mastoid triangle and the most prominent convex surface of the mastoid (MF); the distance between the most prominent convex mastoid point (IMSLD); and the intersecting angle drawn from the most prominent right and left mastoid point (MMCA). Several predictive models were constructed and their accuracy was compared using cross-validation. Results: The results of the t-test revealed a statistically significant difference between the sexes in all variables except MF and MMCA. The random forest model, with an accuracy of 97.0%, had the best performance in predicting sex. The IMSLD and IMD made the largest contributions to predicting sex, while the MMCA variable had the least significant role. Conclusion: These results show the possibility of developing an accurate tool using data mining algorithms for sex determination in the forensic framework.

• 대한수학회보
• /
• 제32권2호
• /
• pp.343-348
• /
• 1995

Let X and Y be two normed spaces and D a nonempty convex subset of X. Let $T : X \ to L(X,Y)$ be a mapping, where L(X,Y) is the space of all continuous linear mappings from X into Y. And let $C : D \to 2^Y$ be a set-valued map such that for each $x \in D$, C(x) is a convex cone in Y such that Int $C(x) \neq 0 and C(x) \neq Y$, where Int denotes the interior.

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