• 대한수학회지
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• 제57권6호
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• pp.1347-1372
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• 2020

We study bifurcation for the following fractional Schrödinger equation $$\{\left.\begin{eqnarray}(-{\Delta})^su+V(x)u&=&{\lambda}f(u)&&{\text{in}}\;{\Omega}\\u&>&0&&{\text{in}}\;{\Omega}\\u&=&0&&{\hspace{32}}{\text{in}}\;{\mathbb{R}}^n{\backslash}{\Omega}\end{eqnarray}\right$$ where 0 < s < 1, n > 2s, Ω is a bounded smooth domain of ℝⁿ, (-∆)^s is the fractional Laplacian of order s, V is the potential energy satisfying suitable assumptions and λ is a positive real parameter. The nonlinear term f is a positive nondecreasing convex function, asymptotically linear that is $\lim_{t{\rightarrow}+{\infty}}\;{\frac{f(t)}{t}}=a{\in}(0,+{\infty})$. We discuss the existence, uniqueness and stability of a positive solution and we also prove the existence of critical value and the uniqueness of extremal solutions. We take into account the types of Bifurcation problem for a class of quasilinear fractional Schrödinger equations, we also establish the asymptotic behavior of the solution around the bifurcation point.

• 한국경영과학회지
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• 제29권4호
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• pp.61-72
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• 2004

In this paper, we design sampling inspections and service capacities simultaneously for multi-products. Particularly, we extend Kim(2003) by introducing the fixed cost of providing services. We show that, due to the fixed cost considered, the cost function of a product is no longer linear or convex in terms of the level of service provision, and the total inspection is prefered to the small level of service capacity which results in high burden of the fixed cost. And we develop a simple framework to deal with this joint design problem for a product. Also we consider the problem of allocating the given number of the total service capacities among products. A dynamic programming algorithm is developed to determine the optimal allocation which minimizes the overall total cost of the system and the optimal allocation can be obtained with the considerably smaller computations than the total number of possible allocations. The results can be used to support planning decisions and to aid the joint design of inspections and service capacities for products.

• 대한수학회지
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• 제48권4호
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• pp.775-795
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• 2011

The disturbance attenuation problem for a class of discretetime switched linear systems with exponential uncertainties via switched state feedback and switched dynamic output feedback is investigated, respectively. By using Taylor series approximation and convex polytope technique, exponentially uncertain discrete-time switched linear system is transformed into an equivalent switched polytopic model with additive norm bounded uncertainty. For such equivalent switched model, one designs its switching strategy and associated state feedback controllers and dynamic output feedback controllers so that whole switched model is asymptotical stabilization with H-in nity disturbance attenuation base on switched Lyapunov function and LMI approach. Finally, two numerical examples are presented to illustrate our results.

• 대한수학회지
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• 제54권1호
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• pp.319-357
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• 2017

There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions in a way such that uniformly bounded sequences of functions that converge pointwise in the weak (or norm) topology of E are sent to sequences that converge in the weak, norm or weak* topology of the target space. As an application, a new description of uniform closures of convex subsets of C(X, E) is given. Also new and strong results on integral representations of continuous linear operators defined on C(X, E) are presented. A new classes of vector measures are introduced and various bounded convergence theorems for them are proved.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2005년도 제36회 하계학술대회 논문집 D
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• pp.2564-2566
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• 2005

This paper presents an iterative linear matrix inequality (LMI) method for $H_2$ and $H_{\infty}$ optimal static output feedback (SOF) control, which is expressed in terms of LMIs subject to an additional rank condition. We propose a linear Penalty function to penalize the rank constraint so that static $H_2$ and $H_{\infty}$ synthesis results in solving a series of convex LMI optimization problems. Numerical experiments for various $H_2$ and $H_{\infty}$ SOF synthesis were performed to demonstrate the effectiveness of the proposed algorithm.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 1999년도 봄 학술발표회 논문집(I)
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• pp.245-250
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• 1999

In this study, the development of graphic user interface(GUI) program for optimum design of RC continuous beam is dealt. Optimum design problem that satisfies strength, serviceability, durability and geometrical conditions is formulated as a non-linear programming problem(NLP) in which the objective function as well as the constraints are highly non-linear on design variables such as cross sectional dimensions and steel ratio. Optimum design problem is solved by NLP techniques namely, sequential linear programming(SLP), sequential convex programming(SCP). Numerical examples of R.C. continuous beam using GUI system are given to show usefulness of GUI system for practical design work and efficiency of algorithm for the NLP techniques.

• Journal of Advanced Marine Engineering and Technology
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• 제31권1호
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• pp.58-66
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• 2007

Genetic Algorithms (GA) have some difficulties in practical applications because of too many function evaluations. To overcome these limitations, an approximated modeling method such as Response Surface Modeling(RSM) is coupled to GAs. Original RSM method predicts linear or convex problems well but it is not good for highly nonlinear problems cause of the average effect of the least square method(LSM). So the locally approximated methods. so called as moving least squares method(MLSM) have been used to reduce the error of LSM. In this study, the efficient evolutionary GAs tightly coupled with RSM with MLSM are constructed and then a 2-dimensional inviscid airfoil shape optimization is performed to show its efficiency.

• 산업경영시스템학회지
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• 제15권26호
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• pp.67-76
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• 1992

변수의 어떤 값들에 대해 도함수를 가질 수 없는 함수를 최적화해야 하는 등. OR 에서는 여러 상황이 존재한다. 이것은 Convex Analysis〔12〕서 이론적인 differential calculus를 근저로 하는 Non-differentiable Optimization 또는 Non-smooth Optimization 을 취급하는 것이 된다. 이러한 종류의 미분이 가능하지 않은 최적화문제는 연속함수를 위한 종래의 최적화법으로는 그 해법자체가 갖고 있는 연속성의 한계를 극복할 수 없다. 따라서, 이러한 문제를 해결하기 위해 Demyanov〔4〕가 제시한 quasi-differental function의 정의와 이들 함수에 따른 몇가지 주요정리들을 언급하고, 그것들을 토대로 Non-differentiable optimization problem의 수치적인 방법을 수행하기 위해 일종의 modified gradient 법을 제시한다. 이를 이용해서 numerical experiment를 위한 방법을 구체화하여, unrestricted non-differentable optimization problem에 적응하여, 그 수치해 결과를 보여서 그 타당성음 검토하였다.

• 대한수학회보
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• 제47권1호
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• pp.89-102
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• 2010

This paper concerns the problem of global robust stability of a time-delay discontinuous system with a positive-defined connection matrix under polytopic-type uncertainty. In order to give the stability condition, we firstly address the existence of solution and equilibrium point based on the properties of M-matrix, Lyapunov-like approach and the theories of differential equations with discontinuous right-hand side as introduced by Filippov. Second, we give the delay-independent and delay-dependent stability condition in terms of linear matrix inequalities (LMIs), and based on Lyapunov function and the properties of the convex sets. One numerical example demonstrate the validity of the proposed criteria.

• 대한수학회보
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• 제51권5호
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• pp.1551-1559
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• 2014

We consider functions that map the open unit disc conformally onto the complement of an unbounded convex set with opening angle ${\pi}{\alpha}$, ${\alpha}{\in}(1,2]$, at infinity. We derive the exact interval for the variability of the real Taylor coefficients of these functions and we prove that the corresponding complex Taylor coefficients of such functions are contained in certain discs lying in the right half plane. In addition, we also determine generalized central functions for the aforesaid class of functions.