• 대한수학회지
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• 제58권1호
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• pp.123-132
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• 2021

Let K be a number field and L a finite abelian extension of K. Let E be an elliptic curve defined over K. The restriction of scalars ResKLE decomposes (up to isogeny) into abelian varieties over K $$Res^L_KE{\sim}{\bigoplus_{F{\in}S}}A_F,$$ where S is the set of cyclic extensions of K in L. It is known that if L is a quadratic extension, then AL is the quadratic twist of E. In this paper, we consider the case that K is a number field containing a primitive third root of unity, $L=K({\sqrt[3]{D}})$ is the cyclic cubic extension of K for some D ∈ K×/(K×)3, E = Ea : y2 = x3 + a is an elliptic curve with j-invariant 0 defined over K, and EaD : y2 = x3 + aD2 is the cubic twist of Ea. In this case, we prove AL is isogenous over K to $E_a^D{\times}E_a^{D^2}$ and a property of the Selmer rank of AL, which is a cubic analogue of a theorem of Mazur and Rubin on quadratic twists.

• 제어로봇시스템학회논문지
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• 제21권1호
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• pp.1-6
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• 2015

This paper investigates the longitudinal flight dynamics and stability of flapping-wing micro air vehicles. Periodic external forces and moments due to the flapping motion characterize the dynamics of this system as NLTP (Non Linear Time Periodic). However, the averaging theorem can be applied to an NLTP system to obtain an NLTI (Non Linear Time Invariant) system which allows us to use a standard eigen value analysis to assess the stability of the system with linearization around a reference point. In this paper, we investigate the dynamics and stability of a hawkmoth-scale flapping-wing air vehicle by establishing an LTI (Linear Time Invariant) system model around a hovering condition. Also, a direct time integration of full nonlinear equations of motion of the flapping-wing micro air vehicle is conducted to see how the longitudinal flight dynamics appear in the time domain beyond the reference point, i.e. hovering condition. In the study, the flapping-wing air vehicle exhibited three distinct dynamic modes of motion in the longitudinal plane of motion: two stable subsidence modes and one unstable oscillatory mode. The unstable oscillatory mode is found to be a combination of a pitching velocity state and a forward/backward velocity state.

• 제어로봇시스템학회논문지
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• 제9권4호
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• pp.259-269
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• 2003

This paper considers the problem of determining a set of PI, PD and PID controller gains, for a given linear time invariant plant, that meets or exceeds the closed loop step response specifications. The proposed method utilizes two recent results: for a given system, (1) finding a set of stabilizing PI, PD and PID gains and (2) the relationship between time response (overshoot and speed) and the coefficients of the characteristic polynomial. The method allows us to extract a subset of PI, PD and PID gains that meets stability as well as time domain performance requirements. The intersections of two dimensional sets described by linear and quadratic inequalities in the controller design space are need to be Identified through numerical computation. The procedure is illustrated by examples.

• 제어로봇시스템학회논문지
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• 제10권7호
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• pp.658-668
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• 2004

This paper is concerned with a control allocation strategy using the dynamic inversion and the pseudo inverse control which generates the nominal control input trajectories. In addition, an autopilot design method is proposed by using time-varying control technique which is time-varying version of the pole placement of linear time-invariant system for an agile missile with aerodynamic fin and thrust vectoring control. The control allocation proposed in this paper is capable of extracting the maximum performance by combining each control effector, aerodynamic fin and thrust vectoring control. The adopted time-varying control technique for the autopilot design enhances the robustness of the tracking performance for a reference command. The main results are validated through the nonlinear simulations with aerodynamic data.

• 제어로봇시스템학회논문지
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• 제9권11호
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• pp.861-867
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• 2003

We propose a sliding surface design method for linear systems with mismatched uncertainties in the state space model. In terms of LMIs, we derive a necessary and sufficient condition for the existence of a linear sliding surface such that the reduced-order equivalent sliding mode dynamics restricted to the linear sliding surface is not only stable but completely invariant to mismatched uncertainties. We give an explicit formula of all such linear switching surfaces in terms of solution matrices to the LMI existence condition. We also give a switching feedback control law, together with a design algorithm. Additionally, we give some hints for designing linear switching surfaces guaranteeing pole clustering constraints or linear quadratic performance bound constraints. Finally, we give a design example in order to show the effectiveness of the proposed methodology.

• 제어로봇시스템학회논문지
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• 제12권3호
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• pp.241-247
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• 2006

We propose a character recognition system to extract the component reference names from printed circuit boards (PCBs) automatically. The names are written in horizontal, vertical, reverse-horizontal and reverse-vertical directions. Also various symbols and figures are included in PCBs. To recognize the character and orientation effectively, we divide the recognizer into two stages: character classification stage and orientation classification stage. The character classification stage consists of two sub-recognizers and a verifier. The rotaion-invarint features of input pattern are then used to identify the character independent of orientation. Each recognizer is implemented as a neural network, and the weight values of verifier are obtained by genetic algorithm. In the orientation classification stage, the input pattern is compared with reference patterns to identify the orientation. Experimental results are presented to verify the usefulness of the proposed system.

• 제어로봇시스템학회논문지
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• 제8권4호
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• pp.292-298
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• 2002

We focus on the slicing off some sub-nets using the transitive matrix. Control flows in the Petri nets is done based on the token flows. One control f]ow explains the independent tokens status and if the token-in divides into several tokens after firing a transition then the control flow divides to several flows, as well. Accordingly, we define that the basic unit of concur-rency (short BUC) is a set of the executed control flows based on the behavioral properties in the net. The BUC is S-invariant which has one control flow. We show the usefulness of transitive matrix to slice off some subnets from the original net based on BUC-through on an example.

• 대한수학회보
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• 제48권2호
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• pp.315-324
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• 2011

In this paper, we study the effects of a deformation mapping on the resulting deformation d/BCK-algebra obtained via such a deformation mapping. Besides providing a method of constructing d-algebras from BCK-algebras, it also highlights the special properties of the standard BCK-algebras of posets as opposed to the properties of the class of divisible d/BCK-algebras which appear to be of interest and which form a new class of d/BCK-algebras insofar as its not having been identified before.

• Korean Journal of Mathematics
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• 제15권2호
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• pp.195-206
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• 2007

We investigate the multiplicity of $2{\pi}$-periodic solutions of the nonlinear Hamiltonian system with perturbed polynomial and exponential potentials, $\dot{z}= JG^{\prime}(z)$, where $z:R{\rightarrow}R^{2n}$, $\dot{z}={\frac{dz}{dt}}$, $J=\(\array{0&-I\\I&0}\)$, I is the identity matrix on $R^n,G:R^{2n}{\rightarrow}R$, G(0, 0) = 0 and $G^{\prime}$ is the gradient of G. We look for the weak solutions $z=(p,q){\in}E$ of the nonlinear Hamiltonian system.

• 한국전산유체공학회지
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• 제6권4호
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• pp.15-25
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• 2001

Numerical prediction of the diffusion controlled transition in a turbine gas pass is important because it can change the local heat transfer rate over a turbine blade as much as three times. In this study, the gas flow over turbine blade is simplified to the flat plate boundary layer, and an adaptive grid scheme redistributing grid points within the computation domain is proposed with a great emphasis on the construction of the grid control function. The function is sensitized to the second invariant of the mean strain tensor, its spatial gradient, and the interaction of pressure gradient and flow deformation. The transition process is assumed to be described with a κ-ε turbulence model. An elliptic solver is employed to integrate governing equations. Numerical results show that the proposed adaptive grid scheme is very effective in obtaining grid independent numerical solution with a very low grid number. It is expected that present scheme is helpful in predicting actual flow within a turbine to improve computation efficiency.