• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.31 no.6_2
• /
• pp.577-583
• /
• 2013

Recently, massive archives of ground information imagery from new sensors have become available. To establish a functional relationship between the image and the ground space, sensor models are required. The rational functional model (RFM), which is used as an alternative to the rigorous sensor model, is an attractive option owing to its generality and simplicity. To determine the rational polynomial coefficients (RPC) in RFM, however, we encounter the problem of obtaining a stable solution. The design matrix for solutions is usually ill-conditioned in the experiments. To solve this unstable solution problem, regularization techniques are generally used. In this paper, we describe the effective determination of the optimal regularization parameter in the regularization technique during RPC derivation. A brief mathematical background of RFM is presented, followed by numerical approaches for effective determination of the optimal regularization parameter using the Euler Method. Experiments are performed assuming that a tilted aerial image is taken with a known rigorous sensor. To show the effectiveness, calculation time and RMSE between L-curve method and proposed method is compared.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.11 no.6
• /
• pp.904-912
• /
• 1987

The main mode of heat transfer of combustion gases at high temperature is thermal radiation of nonluminous gases, CO$_{2}$ and H$_{2}$O. Therefore the information of the emissivities of CO$_{2}$ and H$_{2}$O would be very important in the thermal performance analysis of furnace. In this study, an exponential model for the emissivities of CO$_{2}$ and H$_{2}$O was derived as function of P$_{g}$L and polynomial of reciprocal of temperature. Error analysis between the calculated values from present model and the valued of Hottel Chart was performed over temperature range of 1000-5000 R and a partial-pressure-length product range of 0.003 to 20 ft-atm. For CO$_{2}$ gray gas, the error percent between the calculated values and the values from Hottel Chart was distributed within 2.5% in case of using a polynomial in 1/T of degree 4. For H$_{2}$O gray gas, the model has an error range of 0 to 2.5% in case of using a polynomial in 1/T of degree 3.

• Journal of the Korean Geotechnical Society
• /
• v.21 no.2
• /
• pp.145-150
• /
• 2005

It is useful to select an appropriate mathematical model to predict landslide. Through observation and analysis of real-time measured time series, a reasonable mathematic model is chosen to do prediction of landslide. Two theoretical models, such as polynomial function and growth model, are suggested for the description and analysis of measured defermation from an active landslides. These models are applied herein to describe the main characteristics of defermation process for two types of landslide, namely polynomial and growth models. The TRS (tensiof rotation and settlement) sensors are applied to adopt two models, and the data analysis of two field (Neurpjae and Buksil) resulted in good coincidence between measured data and models.

• Journal of Korean Society for Quality Management
• /
• v.40 no.1
• /
• pp.49-59
• /
• 2012

In computer simulation models the output from the computer code is often deterministic, i.e., running the code twice with the same values for the input variables would give the same output. It is discussed why the response surface method with polynomial approximation for the true response function is a good approximation to the computer experiments model. A sequential strategy to find the proper reduced quadratic polynomial model is illustrated with a case study in the military war game computer simulation model.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.12
• /
• pp.3219-3226
• /
• 1994

A model is constructed to evaluate the stress intensity factors for a center crack subjected to polynomial anti-symmetric loading in a layered material. A Fredholm integral equation is derived by Fourier integral transform method. The integral equation is numerically analyzed to evaluate the effects of the ratios of shear modulus, Poisson's ratio and crack length to layer thickness as well as the number of layers on the stress intensity factor. The stress intensity factors are approached to constant values as the number of layers increase and decrease as the polynomial power of the loading increase. In case of the E-glass/Epoxy composite, dimensionless stress intensity factor is affected by cracked-resin layer thickness.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.17 no.2
• /
• pp.67-85
• /
• 2013

Reproducing Polynomial Particle Method (RPPM) is one of meshless methods that use meshes minimally or do not use meshes at all. In this paper, the RPPM is employed for free vibration analysis of shear-deformable plates of the first order shear deformation model (FSDT), called Reissner-Mindlin plate. For numerical implementation, we use flat-top partition of unity functions, introduced by Oh et al, and patchwise RPPM in which approximation functions have high order polynomial reproducing property and the Kronecker delta property. Also, we demonstrate that our method is highly effective than other existing results for various aspect ratios and boundary conditions.

• Proceedings of the IEEK Conference
• /
• 2006.06a
• /
• pp.173-174
• /
• 2006

High power amplifier (HPA), which is used in transmitter of wireless communication systems, usually works in near saturation point in order to achieve maximum efficiency. In this region, HPA can introduce undesirable nonlinear effects. In this paper, we present a polynomial modeling method for efficient techniques to compensate for nonlinear distortion introduced by nonlinear HPA. Proposed polynomial predistorter inverses actual amplifier. Namely, we derive polynomials of amplifiers from analytical method and the electrical parameters in the data sheet of an actual amplifier and then can derive polynomial predistorter by inversing them. It is an effective and a simple method to compensate nonlinear distortion. SSPA(Solid-state power amplifier) is considered. We also analyze the effects of predistortion on the SER performance of communication system with 16-QAM modulation format. The results have shown the efficiency of this model.

• Journal for History of Mathematics
• /
• v.36 no.1
• /
• pp.1-17
• /
• 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 IKEEE
• /
• v.25 no.1
• /
• pp.88-94
• /
• 2021

Public-key cryptographic algorithms such as RSA and ECC, which are currently in use, have used mathematical problems that would take a long time to calculate with current computers for encryption. But those algorithms can be easily broken by the Shor algorithm using the quantum computer. Lattice-based cryptography is proposed as new public-key encryption for the post-quantum era. This cryptographic algorithm is performed in the Polynomial Ring, and polynomial multiplication requires the most processing time. Therefore, a hardware model module is needed to calculate polynomial multiplication faster. Number Theoretic Transform, which called NTT, is the FFT performed in the finite field. The logic verification was performed using HDL, and the proposed design at the transistor level using Hspice was compared and analyzed to see how much improvement in delay time and power consumption was achieved. In the proposed design, the average delay was improved by 30% and the power consumption was reduced by more than 8%.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1998.06a
• /
• pp.83-86
• /
• 1998

In this paper, a fuzzy model based on the Polynomial Neural Network(PNN) structure is proposed to estimate the emission pattern for air pollutant in power plants. the new algorithm uses PNN algorithm based on Group Mehtod of Data Handling (GMDH) algorithm and fuzzy reasoning in order to identify the premise structure and parameter of fuzzy implications rules, and the least square method in order to identify the optimal consequence parameters. Both time series data for the gas furnace and data for the NOx emission process of gas turbine power plants are used for the purpose of evaluating the performance of the fuzzy model. The simulation results show that the proposed technique can produce the optimal fuzzy model with higher accuracy and feasibility than other works achieved previously.