• Proceedings of the KSME Conference
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• 2001.06b
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• pp.93-98
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• 2001

This paper studies on the design of an ILQ(Inverse Linear Quadratic optimal control) looper control system for hot strip mills. The looper which is placed between each stand plays an important role in controlling strip width by regulating strip tension variation generated from the velocity difference of main work rolls. The mathematical model for looper is firstly obtained by Taylor's linearization of nonlinear differential equations, where it is given as a linear and time invariant state-space equation. Secondly, a looper servo controller is designed by ILQ control algorithm, which is an inverse problem of LQ(Linear Quadratic optimal control) control. By tunning control gain arbitration parameters and time constants, it is shown that the ILQ looper servo controller has the performance that makes well to follow desired trajectories of both strip tension and looper angle.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.185-195
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• 2019

In this work, we study the conditions between null geodesic curves and timelike ruled surfaces in dual Lorentzian space. For this study, we establish a system of differential equations characterizing timelike ruled surfaces in dual Lorentzian space by using the invariant quantities of null geodesic curves on the given ruled surfaces. We obtain the solutions of these systems for special cases. Regarding to these special solutions, we give some results of the relations between null geodesic curves and timelike ruled surfaces in dual Lorentzian space.

• Bulletin of the Korean Mathematical Society
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• v.24 no.1
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• pp.31-37
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• 1987

I want to focus on developments in the areas of general relativity and gauge theory. The topics to be considered are the singularity theorms of Hawking and Penrose, the positivity of mass, instantons on the four-dimensional sphere, and the string picture of quantum gravity. I should mention that I will not have time do discuss either classical mechanics or symplectic structures. This is especially unfortunate, because one of the roots of differential geometry is planted firmly in mechanics, Cf. [GS]. The French geometer Elie Cartan first formulated his invariant approach to geometry in a series of papers on affine connections and general relativity, Cf. [C]. Cartan was trying to recast the Newtonian theory of gravity in the same framework as Einstein's theory. From the historical perspective it is significant that Cartan found relativity a convenient framework for his ideas. As about the same time Hermann Weyl in troduced the idea of gauge theory into geometry for purposes much different than those for which it would ultimately prove successful, Cf. [W]. Weyl wanted to unify gravity with electromagnetism and though that a conformal structure would fulfill thel task but Einstein rebutted this approach.

• Structural Engineering and Mechanics
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• v.49 no.4
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• pp.427-448
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• 2014

At present, the time of easy oil and gas is over. Now, the largest part of fossil fuels is concentrated in the deepest levels of tectonic structures and in the sea shelves. One of the most cumbersome operations of their extraction is the bore-hole drilling. In connection with austere tectonic and climate conditions, their drivage every so often is associated with great and diversified technological difficulties causing emergencies on frequent occasions. As a rule, they are linked with drill string accidents. A key role in prediction of these situations should play methods of theoretical modelling. For this reason, there is a growing need for development and implementation of new numerical methods for computer simulation of critical and post-critical behavior of drill strings (DSs). In this paper, the processes of non-linear deforming of a DS in cylindrical cavity of a deep bore-hole are considered. On the basis of the theory of curvilinear flexible rods, non-linear constitutive differential equations are deduced. The effects of the longitudinal non-uniform preloading, action of torque and interaction between the DS and the bore-hole surface are taken into account. Owing to the use of curvilinear coordinates in the constraining cylindrical surface and a specially chosen concomitant reference frame, it became possible to separate the desired variables and to reduce the total order of the equation system. To solve it, the method of continuation the solution by parameter and the transfer matrix technique are applied. As a result of the completed numerical analysis, the critical states of the DS loading in the cylindrical channels of inclined bore-holes are found. It is shown that the modes of the post-critical deforming of the DS are associated with its irregular spiral curving prevailing in the zone of bottom-hole-assembly. The possibility of invariant state generation during post-critical deforming is established, condition of its bifurcation is formulated. It is shown that infinite variety of loads can correspond to one geometrical configuration of the DS. They differ each from other by contact force functions.

• Journal of Korea Multimedia Society
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• v.9 no.5
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• pp.658-670
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• 2006

As the educational media tends to be more digitalized and individualized, the learning paradigm is dramatically changing into e-learning. Existing on-line courseware gives a learner more chances to learn when they are home with their own PCs. However, it is of little use when they are away from their digital media. Also, it is very labor-intensive to convert the original off-line contents to on-line contents. This paper proposes education mobile contents(EMC) that can supply the learners with dynamic interactions using various multimedia information by recognizing real images of off-line contents using mobile devices. Content-based image retrieval based on object shapes is used to recognize the real image, and shapes are represented by differential chain code with estimated new starting points to obtain rotation-invariant representation, which is fitted to computational resources of mobile devices with low resolution camera. Moreover we use a dynamic time warping method to recognize the object shape, which compensates scale variations of an object. The EMC can provide learners with quick and accurate on-line contents on off-line ones using mobile devices without limitations of space.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.781-794
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• 2008

Let $\mathbb{H}_g$ and $\mathbb{D}_g$ be the Siegel upper half plane and the generalized unit disk of degree g respectively. Let $\mathbb{C}^{(h,g)}$ be the Euclidean space of all $h{\times}g$ complex matrices. We present a partial Cayley transform of the Siegel-Jacobi disk $\mathbb{D}_g{\times}\mathbb{C}^{(h,g)}$ onto the Siegel-Jacobi space $\mathbb{H}_g{\times}\mathbb{C}^{(h,g)}$ which gives a partial bounded realization of $\mathbb{H}_g{\times}\mathbb{C}^{(h,g)}$ by $\mathbb{D}_g{\times}\mathbb{C}^{(h,g)}$. We prove that the natural actions of the Jacobi group on $\mathbb{D}_g{\times}\mathbb{C}^{(h,g)}$. and $\mathbb{H}_g{\times}\mathbb{C}^{(h,g)}$. are compatible via a partial Cayley transform. A partial Cayley transform plays an important role in computing differential operators on the Siegel Jacobi disk $\mathbb{D}_g{\times}\mathbb{C}^{(h,g)}$. invariant under the natural action of the Jacobi group $\mathbb{D}_g{\times}\mathbb{C}^{(h,g)}$ explicitly.

• Journal of Korea Multimedia Society
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• v.7 no.12
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• pp.1680-1691
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• 2004

One of the representative methods of optical flow is a gradient method which estimates the movement of an object based on the differential of image brightness. However, the method is ineffective for large displacement of the object and many improved methods have been proposed to copy with such limitations. One of these improved techniques is the multigrid processing, which is used in many optical flow algorithms. As an alternative novel technique we have been proposing an orthogonal functional expansion method, where whole displacements are expanded from low frequency terms. This method is expected to be applicable to flow estimation with large displacement and deformation including expansion and contraction, which are difficult to cope with by conventional optical flow methods. In the orthogonal functional expansion method, the apparent displacement field is calculated iteratively by a projection method which utilizes derivatives of the invariant constraint equations of brightness constancy. One feature of this method is that differentiation of the input image is not necessary, thereby reducing sensitivity to noise. In this paper, we apply our method to several real images in which the objects undergo large displacement and/or deformation including expansion. We demonstrate the effectiveness of the orthogonal functional expansion method by comparing with conventional methods including our optimally scaled multigrid optical flow algorithm.

• Macromolecular Research
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• v.15 no.6
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• pp.553-559
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• 2007

Nanocomposite films were prepared by sol-gel synthesis from vanadium triisopropoxide with $poly((oxyethylene)_9$ methacrylate)-graft-poly(dimethyl siloxane), POEM-g-PDMS, producing in situ growth of vanadium oxide within the continuous ion-conducting POEM domains of micro phase-separated graft copolymer. The formation of vanadium oxide was confirmed by wide angle x-ray scattering (WAXS) and Fourier transform infrared (FT-IR) spectroscopy. Small angle x-ray scattering (SAXS) revealed the spatially-selective incorporation of vanadium oxide in the POEM domains. Upon the incorporation of vanadium oxide, the domain periodicity of the graft copolymer monotonously increased from 17.2 to 21.0 nm at a vanadium content 14 v%, above which it remained almost invariant. The selective interaction of vanadium oxide with POEM was further verified by differential scanning calorimetry (DSC) and FT-IR spectroscopy. The nanocomposite films exhibited excellent mechanical properties $(l0^{-5}-10^{-7}dyne/cm^2)$, mostly due to the confinement of vanadium oxide in the POEM chains as well as the interfaces created by the microphase separation of the graft copolymer.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.2
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• pp.65-77
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• 1994

This paper presents a derailed application procedure of the linear quadratic(LQ) theory for a SWATH heave and pitch control. A time domain model of coupled, linear time-invariant second order differential equations is derived from the frequency response model with the frequency dependent added mass and damping approximated as constant values at the heave natural frequency. Wave exciting forces are modeled as a sum of sinusoids. A systematic selection procedure of state and control weighting matrices is presented to obtain good transient behavior and acceptable fin movement. The validity of this controller design process is throughly investigated by simulations both in time domain and frequency domain and singular value plots of transfer function matrices. The finally designed control system shows good overall performances revealing that the applicability of the present study is proved successful.

• Journal of the Korea Computer Industry Society
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• v.7 no.4
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• pp.427-436
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• 2006

State-space method for the analysis of the dynamic characteristics of a body motion is set up as mathematical tool for the solution of differential equation by computer. Representation of a system is described as a simple form of matrix calculation and unique form of model is available for the linear or nonlinear, time variant or time invariant, mono variable or multi variable system etc. For the analysis of state-space method a complicated vector calculation is required, but this analysis can be simplified with the specific functions of a software package. Recently as the Graphical User Interface softwares are well-developed, then it is very simplified to execute the simulation of the dynamic characteristics for the state-space model with the interactive graphics treatment. The purpose of this study is to developed the simulator for the educational analysis of the dynamic characteristics of body motion, and for the analysis of the longitudinal dynamic characteristics of an aircraft that is primarily to design the simulator for the analysis of the transient response of an aircraft longitudinal stability.