• Ocean and Polar Research
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• v.42 no.1
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• pp.77-88
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• 2020

This paper presents the coordinate systems used for trawl doors modeling, and provides matrix equations of connection between these systems. The projections of the forces acting on the door into axes of various coordinate systems were obtained, which were used in the door equilibrium equations. Six equilibrium conditions for the door as a solid were obtained: formulas that allow for the door area in plan to be determined; its weight in water; its mass; three moment equations for determining the position of the warp and backstrops fastening points to the door with triangular and quadrangular backstrop arrangements. It was found that the moment equilibrium equations of trawl doors are generally incompatible, which was not found by any of the authors who have previously conducted research into trawl doors. Using the Kronecker-Capelli theorem, the compatibility equation is obtained. This equation includes the coordinates of the backstrop fastening points to the door, which means that these points cannot be randomly selected. The technique of determining the warp and backstrops' fastening points position to the door is described. Conditions of directional (by angle of attack) and roll (in angle of roll) stability of the doors' equilibrium are presented. The equations presented in this paper comprise a mathematical model that allows, when designing the doors, to select optimal parameters, as well as to carry out adjustments for trawling purposes to ensure the stable movement of the doors and the entire trawl system.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.383-389
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• 2017

This paper devotes to the study of a diffusive model for unstirred membrane reactors with maintenance energy subject to a homogeneous Neumann boundary condition. It shows that the unique constant steady state is globally asymptotically stable when it exists. This result further implies the non-existence of the non-uniform steady state solution.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.1234-1239
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• 1993

We study how to design conventional feedback controllers to drive chaotic trajectories of the well-known systems to their equilibrium points or any of their inherent periodic orbits. The well-known chaotic systems are Heon map and Duffing's equation, which are used as illustrative examples. The proposed feedback controller forces the chaotic trajectory to the stable manifold as OGY method does. Simulation results are presented to show the effectiveness of the proposed design method.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.313-318
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• 1994

It is well known that the neural network can be used as an universal approximater for functions and functionals. But these theoretical results are just an existence theorem and do not lead to decide the suitable network structure. This doubfulness whether a certain network can approximate a given function or not, brings about serious stability problems when it is used to identify a system. To overcome the stability problem, We suggest successive identification and control scheme with supervisory controller which always assures the identification process within a basin of attraction of one stable equilibrium point regardless of fittness of the network.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.43.5-43
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• 2001

This paper considers a new synthesis of the optimally performing brain-state-in-a-box (BSB) neural associative memory given a set of prototype patterns to be stored as asymptotically stable equilibrium points with the large and uniform size of the domain of attraction (DOA). First, we propose a new theorem that will be used to provide a guideline in design of the BSB neural associative memory. Finally, a design example is given to illustrate the proposed approach and to compare with existing synthesis methods.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.1
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• pp.39-53
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• 2023

In this paper, we consider a delayed ratio-dependent predator-prey reaction-diffusion system with homogenous Neumann boundary conditions. We study the existence of nonnegative solutions and the stability of the nonnegative equilibria to the system. In particular, we provide a sufficient condition for the positive equilibrium to be globally asymptotically stable.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.257-279
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• 2023

Applying the Lyapunov-Schmidt reduction, we consider spectral stability of small amplitude stationary periodic solutions bifurcating from an equilibrium of the generalized Swift-Hohenberg equation. We follow the mathematical framework developed in [15, 16, 19, 23] to construct such periodic solutions and to determine regions in the parameter space for which they are stable by investigating the movement of the spectrum near zero as parameters vary.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.5
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• pp.617-624
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• 2007

This paper presents a novel quadstable monolithic mechanism (QsMM) which provides four stable equilibrium positions within its operation range. The quadstable mechanism has been realized from the use of both X- and Y-directional bistable structures which use curved snapping beams. A millimeter-scale brass mechanism was fabricated by ultra-precision milling to test the quadstability and the displacement-load behavior, and the prototype clearly demonstrated four distinct stable positions in its millimeter-scale planar operation. We discuss the design concept, finite element simulation for static and transient responses, fabrication by ultra-precision milling, and experimental measurement of the proposed quadstable mechanism.

• Proceedings of the KIEE Conference
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• 1997.07c
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• pp.1103-1105
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• 1997

Transient stability analysis is concerned with a power system's response to unwanted disturbance. Recently, direct method which utilize the stable region of stable equilibrium point is used to analyze transient stability This paper focuses on the controlling UEP method using the fractal behaviours. In the controlling UEP method, many algorithms are used to find controlling UEP However, the existence of fractal region gives difficulty in finding the controlling UEP. So, this paper observes the fractal feature arid introduce the fractal index to explain how much the fractal region occupies in the entire space. Using an improved algorithm from the view point of fractal index, we are going to find the controlling UEP.

• Wind and Structures
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• v.4 no.6
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• pp.469-480
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• 2001

The Leipzig Wind Profile is generally known as a typical neutral planetary boundary layer flow. But it became clear from the present research that it was not completely neutral but weakly stable. We examined whether we could simulate the Leipzig Wind Profile by using a ($k-{\varepsilon}$) turbulence model including the equation of potential temperature. By solving analytically the Second Moment Closure Model under the assumption of local equilibrium and under the condition of a stratified flow, we expressed the turbulent diffusion coefficients (both momentum and thermal) as functions of flux Richardson number. Our ($k-{\varepsilon}$) turbulence model which included the equation of potential temperature and the turbulent diffusion coefficients varying with flux Richardson number reproduced the Leipzig Wind Profile.