• Journal for History of Mathematics
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• v.36 no.1
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• pp.1-17
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• 2023

Paper folding is a versatile tool that can be used not only as a mathematical model for analyzing the geometric properties of plane and spatial figures but also as a visual method for finding the real roots of polynomial equations. The historical evolution of origami's geometric and algebraic techniques has led to the discovery of definitions and properties that can enhance one's cognitive understanding of mathematical concepts and generate mathematical interest and motivation on an emotional level. This paper aims to examine the history of origami geometry, the utilization of origami for solving polynomial equations, and the process of determining the real roots of quadratic, cubic, and quartic equations through origami techniques.

• Journal of Advanced Navigation Technology
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• v.18 no.4
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• pp.304-311
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• 2014

In this paper, we propose a ultra sound inspection technique for automatic defect detection and classification in aircraft composite materials. Using local maximum values of ultra sound wave, we choose peak values for defect detection. Distance data among peak values are used to construct histogram and to determine surface and back-wall echo from the floor of composite materials. C-scan image is then composed through this method. A threshold value is determined by average and variance of the peak values, and defects are detected by the values. PCA(principal component analysis) and QDA(quadratic discriminant analysis) are carried out to classify the types of defects. In PCA, 512 dimensional data are converted into 30 PCs(Principal Components), which is 99% of total variances. Computational cost and misclassification rate are reduced by limiting the number of PCs. A decision boundary equation is obtained by QDA, and defects are classified by the equation. Experimental result shows that our proposed method is able to detect and classify the defects automatically.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.413-424
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• 2008

In [21], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\parallel}\frac{1}{n}\sum\limits_{i=1}^{n}x_i{\parallel}^2+\sum\limits_{i=1}^{n}{\parallel}x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j{\parallel}^2=\sum\limits_{i=1}^{n}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\dots},x_n{\in}V$. We consider the functional equation $$nf(\frac{1}{n}\sum\limits^n_{i=1}x_i)+\sum\limits_{i=1}^{n}f(x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j)=\sum\limits_{i=1}^nf(x_i)$$ Using fixed point methods, we prove the generalized Hyers-Ulam stability of the functional equation $$(1)\;2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})=f(x)+f(y)$$.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.1
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• pp.52-58
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• 2005

We have developed a Group Method of Data Handling (GMDH) type algorithm for designing multi-layered neural networks. The algorithm is general enough that it will accept any number of inputs and any sized training set. Each neuron of the resulting network is a function of two of the inputs to the layer. The equation for each of the neurons is a quadratic polynomial. Several forms of the equation are tested for each neuron to make sure that only the best equation of two inputs is kept. All possible combinations of two inputs to each layer are also tested. By carefully testing each resulting neuron, we have developed an algorithm to keep only the best neurons at each level. The algorithm's goal is to create as accurate a network as possible while minimizing the size of the network. Software was developed to train and simulate networks using our algorithm. Several applications were modeled using our software, and the result was that our algorithm succeeded in developing small, accurate, multi-layer networks.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2003.10a
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• pp.148-151
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• 2003

In order to achieve reliable but cost-effective crash simulations of stamped parts, sheet forming process effects were incorporated in simulations using the ideal forming theory mixed with the 3D hybrid membrane/shell method, while the subsequent crash simulations were carried out using a dynamic explicit finite element code. Example solutions performed for forming and crash simulations of I- and S-shaped rails verified that the proposed approach is cost-effective without sacrificing accuracy. The method required a significantly small amount of additional computation time, less than 3% for the specific examples, to incorporate sheet forming effects to crash simulations. As for the constitutive equation, the combined isotropic-kinematic hardening law and the non-quadratic anisotropic yield stress potential as well as its conjugate strain-rate potential were used to describe the anisotropy of AA6114-T4 aluminum alloy sheets.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.6
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• pp.923-934
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• 1987

A flexible one-link robotic manipulator is modelled as a rotating cantilever beam with a hub and tip mass. An active control law is developed with consideration of the distributed flexibility of the arm. Equation of motion is derived by Hamilton's principle and, for modal control, represented as state variable form using Galerkin's mode summation method. Feedback coefficients are chosen to minimize the linear quadratic performance index(PI). To reconstruct the complete state vector from the measurements, an observer is proposed. In order to suppress vibration of the manipulator arm to desirable extent and to obtain accuracy of the positioning, weighting factor of input in PI is adjusted. Spillover effect due to the controller which controls several important modes is examined. Experiment is also performed to validate the theoretical analysis.

• Proceedings of the KIEE Conference
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• 2005.11b
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• pp.347-349
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• 2005

This paper presents an efficient algorithm to estimate the maximum load level for heavily loaded power systems with the load-generation variation vector obtained by ELD (Economic Load Dispatch) and/or short term load forecasting while utilizing the elliptic pattern of the P-e curve. It is well known the power flow equation in the rectangular coordinate is fully quadratic. However, the coupling between e and f makes it difficult to take advantage of this quadratic characteristic. In this paper, a simple technique is proposed to reflect the e-f coupling effects on the estimation of maximum loadability with theoretical analysis. An efficient estimation algorithm has been developed with the use of the elliptic properties of the P-e curve. The proposed algorithm is tested on IEEE 14 bus system, New England 39 bus system and IEEE 118 bus system, which shows that the maximum load level can be efficiently estimated with remarkable improvement in accuracy.

• Progress in Superconductivity
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• v.10 no.2
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• pp.69-73
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• 2009

For extraction of the self-energy from the angle resolved photoemission spectroscopy(ARPES) experiments for the cuprate superconductors, the momentum distribution curve(MDC) analysis is commonly used. There are two requirements for this method to work: the self-energy is momentum independent and the bare electron dispersion is known. Assuming that the first condition is satisfied in the cuprates, we checked the effects of the bare dispersion on the extracted self-energy. For this, we first generated the ARPES intensity using the tight-binding band of the B2212 by solving the Eliashberg equation. We then extracted the self-energy from the theoretically generated ARPES intensity using the linear and quadratic dispersions. By choosing the bare dispersion such that the Kramer-Kronig relation is best satisfied between the real and imaginary parts of the extracted self-energy, we confirmed that the quadratic dispersion is better for the bare electron band for Bi2212. The self-energy can be reasonably extracted from the ARPES experiments using the MDC analysis.

• Journal of the Korea Institute of Military Science and Technology
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• v.12 no.4
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• pp.540-547
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• 2009

In the near future, military robots are likely to be substituted for military personnel in the field of battle. The power system of a legged robot is considerably more complex than the one used for a land vehicle because of the coordination and stability issues due to the large number of degree of freedom. In this paper, a servovalve-piston combination system for a straight-line motion of robot leg is modeled as three degree of freedom based on double inputs and single output transfer function. The output is the displacement of piston from neutral. The inputs are valve displacement from neutral and arbitrary load force in this system. LQR(Linear Quadratic Regulator) technique is applied in order to achieve robust stability and fast responses of the system. The Kalman filter loop, rejection of disturbance and noise, riccati equation, filter gain matrix, and frequency domain equality are analyzed and designed.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.12C
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• pp.1201-1207
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• 2006

In this paper, we say the adaptive shading correction system supporting multi-resolution for mobile camera. The shading effect is caused by non-uniform illumination, non-uniform camera sensitivity, or even dirt and dust on glass (lens) surfaces. In general this shading effect is undesirable [1-3]. Eliminating it is frequently necessary for subsequent processing and especially when quantitative microscopy is the fine goal. The proposed system is available on thirty nine kinds of image resolutions scanned by interlaced and progressive type. Moreover, the system is using forty kinds of continuous quadratic equations instead of using the piece-wise linear curve which is composed of multiple line segments. Finally, the system could correct the shading effect without discontinuity in any image resolution. The proposed system is implemented in VLSI with cell library based on Hynix $0.25{\mu}m$ CMOS technology.