• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1141-1160
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• 2016

In this paper, a symbolic algorithm for solving a regular initial value problem (IVP) for a system of linear differential-algebraic equations (DAEs) with constant coeffcients has been presented. Algebra of integro-differential operators is employed to express the given system of DAEs. We compute a canonical form of the given system which produces another simple equivalent system. Algorithm includes computing the matrix Green's operator and the vector Green's function of a given IVP. Implementation of the proposed algorithm in Maple is also presented with sample computations.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.886-889
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• 2004

A simple macro triangle with drilling d.o.f.'s is proposed for plane stress problems based on IET(Individual element test) and finite element template. Three-node triangular element has geometrical advantages in preprocessing but suffers from bad performance comparing to other shapes of elements -especially quadrilateral. Main purpose of this study is to construct a high-performance linear triangular element with limited supplementary d.o.f.'s. A triangle is divided by three sub-triangles with drilling d.o.f.'s. The sub-triangle stiffness come from IET passing force-lumping matrix, so this assures the consistency of the element. The macro element strategy takes care of the element‘s stability and accuracy like higher-order stiffness in the F.E. template. The resulting element fits on the uses of conventional three-node. Benchmark examples show proposed element in closed form stiffness from CAS (Computer algebra system) gives the improved results without more computational efforts than others.

• Industrial Engineering and Management Systems
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• v.8 no.3
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• pp.155-161
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• 2009

We focus on discrete event systems with a structure of parallel processing, synchronization, and no-concurrency. We use max-plus algebra, which is an effective approach for controller design for this type of system, for modeling and formulation. Since a typical feature of this type of system is that the initial schedule is frequently changed due to unpredictable disturbances, we use a simple model and numerical examples to examine the possibility of applying the concepts of the feeding buffer and the project buffer of critical chain project management (CCPM) on max-plus linear discrete event systems in order to control the occurrence of an undesirable state change. The application of a CCPM-based framework on a max-plus linear discrete event system was proven to be effective.

• Journal of KIBIM
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• v.7 no.2
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• pp.1-7
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• 2017

Urban planning involves many different disciplines. In order for the related stakeholders to have better understanding and acceptable outcomes, planners are required to present a methodology that would properly reflect people's interest. In order to justify the demand and distribute people's interest, planners actively utilized the suitability analysis. Accordingly, a suitability analysis to find the optimal route for high-speed rail was performed in this paper. With ArcGIS and geographic data sets, simple map algebra could be used. The final product of this research was a map indicating the suitable routes for high-speed rail using the shortest path analysis.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.67.5-67
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• 2001

A closed loop system with a linear plant and nonlinearity in the feedback connection is analyzed for its quasi-static orbital stability by a state-space approach. First a periodic orbit is assumed to exist in the loop which is determined by describing function method for the given nonlinearity. This is possible by selecting a proper nonlinearity and a rigorous justification of the describing function method.[1-3, 18, 20]. Then by introducing residual operator, a linear perturbed model can be formulated. Using various transformations like a modified eigenstructure decomposition, periodic-averaging, charge of variables and coordinate transformation, the stability of the periodic orbit, as a solution of harmonic balance, can be shown by investigating a simple scalar function and result of linear algebra. This is ...

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.953-967
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• 2011

We show that the characteristic function $1S_{\underline{\alpha}}$ of any Harder-Narasimhan strata $S{\underline{\alpha}}\;{\subset}\;Coh_X^{\alpha}$ belongs to the spherical Hall algebra $H_X^{sph}$ of a smooth projective curve X (defined over a finite field $\mathbb{F}_q$). We prove a similar result in the geometric setting: the intersection cohomology complex IC(${\underline{S}_{\underline{\alpha}}$) of any Harder-Narasimhan strata ${\underline{S}}{\underline{\alpha}}\;{\subset}\;{\underline{Coh}}_X^{\underline{\alpha}}$ belongs to the category $Q_X$ of spherical Eisenstein sheaves of X. We show by a simple example how a complete description of all spherical Eisenstein sheaves would necessarily involve the Brill-Noether stratas of ${\underline{Coh}}_X^{\underline{\alpha}}$.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.11
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• pp.505-513
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• 2001

This paper presents the new three-level optimal control scheme for the large scale nonlinear systems, which is based on fast walsh transform. It is well known that optimization for nonlinear systems leads to the resolution of a nonlinear two point boundary value problem which always requires a numerical iterative technique for their solution. However, Three-level costate coordination can avoid two point boundary condition in subsystem. But this method also has the defect that must solve high order differential equation in intermediate level. The proposed method makes use of fast walsh transform, therefore, is simple in computation because of solving algebra equation instead of differential equation.

• Journal of Convergence for Information Technology
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• v.9 no.5
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• pp.7-13
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• 2019

Role-based access or attribute-based access control in cloud environment or big data environment need requires a suitable mathematical structure to represent a hierarchical model. This paper define the notion of multipliers and simple multipliers of lattice implication algebras that can implement a hierarchical model of role-based or attribute-based access control, and prove every multiplier is simple multiplier. Also we research the relationship between multipliers and homomorphisms of a lattice implication algebra L, and prove that the lattice [0, u] is isomorphic to a lattice $[u^{\prime},1]$ for each $u{\in}L$ and that L is isomorphic to $[u,1]{\times}[u^{\prime},1]$ as lattice implication algebras for each $u{\in}L$ satisfying $u{\vee}u^{\prime}=1$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1531-1548
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• 2016

Let C[0, t] denote the space of real-valued continuous functions on [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}\mathbb{R}^n$ by $Z_n(x)=(\int_{0}^{t_1}h(s)dx(s),{\ldots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $ t_n=t$ is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. Using a simple formula for a conditional expectation on C[0, t] with $Z_n$, we evaluate a generalized analytic conditional Wiener integral of the function $G_r(x)=F(x){\Psi}(\int_{0}^{t}v_1(s)dx(s),{\ldots},\int_{0}^{t}v_r(s)dx(s))$ for F in a Banach algebra and for ${\Psi}=f+{\phi}$ which need not be bounded or continuous, where $f{\in}L_p(\mathbb{R}^r)(1{\leq}p{\leq}{\infty})$, {$v_1,{\ldots},v_r$} is an orthonormal subset of $L_2[0,t]$ and ${\phi}$ is the Fourier transform of a measure of bounded variation over $\mathbb{R}^r$. Finally we establish various change of scale transformations for the generalized analytic conditional Wiener integrals of $G_r$ with the conditioning function $Z_n$.

• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.2
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• pp.129-143
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• 1998

The vibrations of steering wheel are required to be reduced for convenient ride quality and good controllability. This phenomenon, vibration of steering wheel, is occured by interaction with suspension system, steering system, vehicle body, engine/transmission and tire complicately. But reviewing the current research activities, most researches are performed for the vibration analysis of steering wheel with a simple model, and mot easy to be applied to the variation of each component element connected with steering system as well as that of the steering system. In this study, suspension system and steering system are modelled by the T.L.H. coordinate system which is usually used by a passenger car maker. Also, rigid body motions of engine and elastic motions of vehicle body in the previous study are considered. Derive the equation of motion in 29 d.o.f. and the vibration of steering wheel is analyzed numerically and verify the midelling of steering system by comparison with test results for real car. And then, the optimal design values of the engine mount system obtained from the previous study are applied to the verified steering system model and investigate the effects of various engine mount design values on the vibration of steering wheel.