• East Asian mathematical journal
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• v.37 no.4
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• pp.401-426
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• 2021

In order to propose ways to implement mathematical connection between algebra and geometry, this study reinterpreted and visualized the Khayyam's geometric method solving the cubic equations using two conic sections and the Al-Kāshi's method of constructing of angle trisection using a cubic equation. Khayyam's method is an example of a geometric solution to an algebraic problem, while Al-Kāshi's method is an example of an algebraic a solution to a geometric problem. The construction and property of conics were presented deductively by the theorem of "Stoicheia" and the Apollonius' symptoms contained in "Conics". In addition, I consider connections that emerged in the alternating process of algebra and geometry and present meaningful Implications for instruction method on mathematical connection.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.539-550
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• 2004

We consider communication or computer systems that have the average memory occupancy and congestion. A certain system may be reduced further if new processes are admitted only when the number of processes queued at the processor is below a certain threshold, run queue cutoff(RQ). We show that response time of a process is invariant with respect to RQ when processes do not communicate each other. The invariance property is considered with the evolution of the queue lengths as point processes and demonstrate it numerically using matrix-geometric methods. We illustrate the RQ invariance property.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.2
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• pp.93-99
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• 2001

A new type geometric and mathematical network reduction model is introduced. Large-scale network is analyzed with analytic approach. The graph has many nodes, branches and loops. Circuit equation are obtained from these elements and connection rule. In this paper, the analytic relation between voltage source has a mutual different graphic property. Node-reduction procedure is achieved with this circuit property. Consequently voltage source value is included into the adjacent node-analyzing equation. A resultant model equations are reduced as much as voltage source number. Matrix rank is (n-1-k), where n, k is node and voltage source number. The reduction procedure is described and verified with geometric principle and circuit theory. Matrix type circuit equation can be composed with this technique. The last results shall be calculated by using computer.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1988.10a
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• pp.30-35
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• 1988

An analytical study was conducted using the Galerkin technique to determine the behaviour of thin fibre-reinforced and laminated composite pipes under soil pressure. Geometric nonlinearity and material linearity have been assumed. We assumed that vertical and lateral soil pressure are proportional to the depth and lateral displacement of the pipe respectively. And we also assumed that radial shear stress is negligible because the ratio of the thickness to the radius of pipe is very small. We, in this paper, discuss the effect of the number of layer, fiber orientation, and soil property.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.16 no.1
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• pp.1-7
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• 1998

SAR data can be achieved independently of weather conditions or sun illumination which is main limitation of electro-optical sensor to get image. The information from imagery can be more enlarged using Shh data be-cause SAR data offers different information from electro-optical sensor. SAR data contains various distortions caused by the radar specification and geometric properties of data acquisition. These distortions should be removed to get the information with acceptable accuracy. In this study, we aimed to correct the radiometric distortion in Shh image caused by the geometric property of the object. For this purpose, we simulated the SAR image by modelling of the power of return beam which is variable according to the geometric configuration between SAR antenna and ground object. Dividing the SAR image by the simulation image, then, we can get the radiometrically corrected image. As a result of this study, we could minimize the effect of radiometric distortion in achieving some qualitative information from SAR image for the related field, such as Geospatial Information System.

• Journal of the Chungcheong Mathematical Society
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• v.11 no.1
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• pp.35-44
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• 1998

Let {X(t), $t{\in}\mathbb{R}^n$} be a $S{\alpha}S$ H-sssis Chentsov random field with control measure m. We consider a geometric construction for L$\acute{e}$vy-Chentsov random fields and Takenaka random fields. Finally, we proved some property of conjugate classes and a.s. H$\ddot{o}$lder unboundedness of $S{\alpha}S$ H-sssis Chentsov random fields for all order ${\gamma}$ > H.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.813-820
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• 2006

We consider a MAR model with ARCH type conditional heteroscedasticity. MAR-ARCH model can be derived as a smoothed version of the double threshold AR-ARCH model by adding a random error to the threshold parameters. Easy to check sufficient conditions for strict stationarity, ${\beta}-mixing$ property and existence of moments of the model are given via Markovian representation technique.

• Proceeding of KASS Symposium
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• 2005.05a
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• pp.125-132
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• 2005

Membrane structures, a kind of lightweight soft structural system, are used for spatial structures. The material property of the membrane has strong axial stiffness, but little bending stiffness. The design procedure of membrane structures are needed to do shape finding, stress-deformation analysis and cutting pattern generation. In shape finding, membrane structures are unstable structures initially. These soft structures need to be introduced initial stresses because of its initial unstable state, and it happens large deformation phenomenon. And also there are highly varied in their size, curvature and material stiffness. So, the approximation inherent in cutting pattern generation methods is quite different. Therefore, in this study, to find the structural shape after large deformation caused by Initial stress, we need the shape analysis considering geometric nonlinear ten And the geodesic line on surface of initial equilibrium shape and the cutting pattern generation using the geodesic line is introduced.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.893-912
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• 2005

We discuss a certain geometric property $X_{{\theta},{\gamma}}$ of dual algebras generated by a polynomially bounded operator and property ($\mathbb{A}_{N_0,N_0}$; these are central to the study of $N_{0}\timesN_{0}$-systems of simultaneous equations of weak$^{*}$-continuous linear functionals on a dual algebra. In particular, we prove that if T $\in$ $\mathbb{A}$$^{M}$ satisfies a certain sequential property, then T $\in$ $\mathbb{A}^{M}_{N_0}(H) if and only if the algebra $A_{T}$ has property $X_{0, 1/M}$, which is an improvement of Li-Pearcy theorem in [8].

• Journal of the Korean Society of Hazard Mitigation
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• v.7 no.5
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• pp.99-110
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• 2007

A single slab concrete pavement has been modeled and analyzed by ABAQUS program. The stress and displacement of the JCP slab under traffic load with frictionless contact interaction between slab and base calculated by ABAQUS program have been compared with the results obtained by KENSLABS program. The results of the stresses of the two modeling show similar tendency and the difference of the two modeling is very small however the results of the displacement of the two modeling show some dissimilarity. In order to analyze the effects of material and geometric properties on the responses of slab, some varying parameters were chosen as input for the modeling. The changing parameters include the thickness and elastic modulus of the concrete slab, the thickness and elastic modulus of base and the elastic modulus of the subgrade. The contact interaction between the slab and base layer had been also studied and different friction coefficient 0, 2.5, 6.6, 7.5, 8.9 had been used to simulate the different friction interface condition. The results of the analysis showed that the responses of the concrete slab vary with the material and geometric properties of the pavement structure and the slab-base friction condition.