• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.731-737
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• 1994

Let $(\Omega, F, P)$ be a probability space with F a $\sigma$-algebra of subsets of the measure space $\Omega$ and P a probability measures on $\Omega$. Suppose $a > 0$ and let $(F_t)_{t \in [0,a]}$ be an increasing family of sub-$\sigma$- algebras of F. If $r > 0$, let $J = [-r, 0]$ and $C(J, R^n)$ the Banach space of all continuous paths $\gamma : J \to R^n$ with the sup-norm $\Vert \gamma \Vert_C = sup_{s \in J} $\mid$\gamma(x)$\mid$$ where $$\mid$\cdot$\mid$$ denotes the Euclidean norm on $R^n$. Let E and F be separable real Banach spaces and L(E,F) be the Banach space of all continuous linear maps $T : E \to F$ with the norm $\Vert T \Vert = sup {$\mid$T(x)$\mid$_F : x \in E, $\mid$x$\mid$_E \leq 1}$.

• Journal of KSNVE
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• v.9 no.2
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• pp.340-347
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• 1999

The acoustic performance of reactive type single expansion chamber can be calculated theoretically by plane wave theory. But higher order model should be considered to widen the frequency range. Mode matching method has been developed to consider higher order modes, but very complicated algebra should be used. Munjal suggested a numerical collocation method, which can overcome the shortcomings of mode matching method, using the compatibility conditions for acoustic pressure and particle velocity at the junctions of area discontinuities. But the restriction of Munjal's method is that the ratio between the area of inlet(or outlet) pipe and that of chamber must be natural number. In this paper, the new method was suggested to overcome the shortcomings of Munjal's method. The predictions by this method was also compared with those by the finite element method and Munjal's method in order to demonstrate the accuracy of the modified method presented here.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1387-1408
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• 2022

Let R be a commutative ring with a non-zero identity, S be a multiplicatively closed subset of R and M be a unital R-module. In this paper, we define a submodule N of M with (N :_R M)∩S = ∅ to be weakly S-prime if there exists s ∈ S such that whenever a ∈ R and m ∈ M with 0 ≠ am ∈ N, then either sa ∈ (N :_R M) or sm ∈ N. Many properties, examples and characterizations of weakly S-prime submodules are introduced, especially in multiplication modules. Moreover, we investigate the behavior of this structure under module homomorphisms, localizations, quotient modules, cartesian product and idealizations. Finally, we define two kinds of submodules of the amalgamation module along an ideal and investigate conditions under which they are weakly S-prime.

• Journal of the Korean Association of Geographic Information Studies
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• v.12 no.1
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• pp.64-72
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• 2009

The method to generate a digital elevation model(DEM) from contour lines causes a problem in which the low relief landform cannot be clearly presented due to the fact that it is significantly influenced by the expression of micro landform elements according to the interval of contours. Thus, this study attempts to develop a landcover burning method that recovers the micro relief landform of the DEM, which applies buffering and map algebra methods by inputting the elevation information to the landcover. In the recovering process of the micro landform, the DEM was recovered using the buffering method and elevation information through the map algebra for the landcover element for the micro landform among the primary DEM generation, making landcover map, and landcover elements. The recovering of the micro landform was applied based on stream landforms. The recovering of landforms using the buffering method was performed for the bar, which is a polygonal element, and wetland according to the properties of concave/convex through generating contours with a uniform interval in which the elevation information applied to the recovered landform. In the case of the linear elements, such as bank, road, waterway, and tributary, the landform can be recovered by using the elevation information through applying a map algebra function. Because the polygonal elements, such as stream channel, river terrace, and artificial objects (farmlands) are determined as a flat property, these are recovered by inputting constant elevation values. The results of this study were compared and analyzed for the degree of landform expression between the original DEM and the recovered DEM. In the results of the analysis, the DEM produced by using the conventional method showed few expressions in micro landform elements. The method developed in this study well described wetland, bar, landform around rivers, farmland, bank, river terrace, and artificial objects. It can be expected that the results of this study contribute to the classification and analysis of micro landforms, plain and the ecology and environment study that requires the recovering of micro landforms around streams and rivers.

• Communications of Mathematical Education
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• v.37 no.1
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• pp.65-84
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• 2023

The method of Lagrange multipliers, one of the most fundamental algorithms for solving equality constrained optimization problems, has been widely used in basic mathematics for artificial intelligence (AI), linear algebra, optimization theory, and control theory. This method is an important tool that connects calculus and linear algebra. It is actively used in artificial intelligence algorithms including principal component analysis (PCA). Therefore, it is desired that instructors motivate students who first encounter this method in college calculus. In this paper, we provide an integrated perspective for instructors to teach the method of Lagrange multipliers effectively. First, we provide visualization materials and Python-based code, helping to understand the principle of this method. Second, we give a full explanation on the relation between Lagrange multiplier and eigenvalues of a matrix. Third, we give the proof of the first-order optimality condition, which is a fundamental of the method of Lagrange multipliers, and briefly introduce the generalized version of it in optimization. Finally, we give an example of PCA analysis on a real data. These materials can be utilized in class for teaching of the method of Lagrange multipliers.

• Proceedings of the Korea Inteligent Information System Society Conference
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• 1999.10a
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• pp.281-289
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• 1999

The objective of this paper is to propose a brand new interface mechanism to provide more intelligent decision making support for EC problems. Its main virtue is based on a numerical process mechanism by using an Extended AND-OR Graph (EAOG)-based logic algebra. Using this mechanism, decision makers engaged in electronic commerce (EC) can effectively deal with complicated decision making problems. In the field of traditional expert systems research, AND-OR Graph approach has been suggested as a useful tool for representing the logic flowchart of the forward and/or backward chaining inference methods. However, the AND-OR Graph approach cannot be effectively used in the EC problems in which real-time problem-solving property should be highly required. In this sense, we propose the EAOG inference mechanism for EC problem-solving in which heurisric knowledge necessary for intelligent EC problem-solving can be represented in a form of matrix. Finally, we have proved the validity of our approach with several propositions and an illustrative EC example

• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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• pp.980-984
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• 1990

In order to find the optimal control law for the precise trajectory tracking of a robot manipulator, a perturbational control method is proposed based on a linearized manipulator dynamic model which can be obtained in a very compact and computationally efficient manner using the dual number algebra. Manipulator control can be decomposed into two parts: the nominal control and the corrective perturbational control. The nominal control is precomputed from the inverse dynamic model using the quantities of a desired trajectory. The perturbational control is obtained by applying the second-variational method on the linearized dynamic model. Simulation results for a PUMA-560 robot show that, by using this controller, the desired trajectory tracking performance of the robot can be achieved, even in the presence of large initial positional disturbances.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.565-570
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• 1994

In this article we prove a version of the Perron-Frobenius Theorem in linear algebra using the Brouwer's Fixed Point Theorem in topology. We will mostly concentrate on he qualitative aspect of the Perron-Frobenius Theorem rather than quantitative formulas, which would be enough for theoretical investigations in ergodic theory. By the nature of the method of the proof, we do not expect to obtain a numerical estimate. But we may regard it worthwhile to see why a certain type of result should be true from a topological and geometrical viewpoint. However, a geometric argument alone would give us a sharp numerical bounds on the size of the eigenvalue as shown in Section 2. Eigenvectors of a matrix A will be fixed points of a certain mapping defined in terms of A. We shall modify an existing proof of Frobenius Theorem and that will do the trick for Perron-Frobenius Theorem.

• Bulletin of the Korean Mathematical Society
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• v.28 no.2
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• pp.175-180
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• 1991

In [3], [4] and [5], Hochster and Huneke introduced the notions of the tight closure of an ideal and of the weak F-regularity of a ring. This notion enabled us to give new proofs of many results in commutative algebra. A regular ring is known to be F-regular, and a Gorenstein local ring is proved to be F-regular provided that one ideal generated by a system of parameters (briefly s.o.p.) is tightly closed. In fact, a Gorenstein local ring is weakly F-regular if and only if there exists a system of parameters ideal which is tightly closed [3]. But we do not know whether this fact is true or not if a ring is not Gorenstein, in particular, a ring is a Cohen Macaulay (briefly C-M) local ring. In this paper, we will prove this in the case of an 1-dimensional C-M local ring. For this, we study the F-rationality and the normality of the ring. And we will also prove that a C-M local ring is to be Gorenstein under some additional condition about the tight closure.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.12
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• pp.1168-1175
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• 2010

Excessive torsional vibrations from marine engine shafting systems can be reduced by using torsional vibration dampers. But in order to be tuned effectively, the dampers should be designed through the optimum design procedure. In this paper, the procedure to get the optimum values of system parameters of spring-viscous dampers using effective modal mass of inertia and stiffness is suggested and the damping is determined by the exact algebra optimization method. The validity of the suggested method is confirmed through the application to a 1800 kW four cycle diesel engine and generator system.