• The Pure and Applied Mathematics
• /
• v.16 no.3
• /
• pp.255-258
• /
• 2009

It is well known that for a sequence a = ($a_0,\;a_1$,...) the general term of the dual sequence of a is $a_n\;=\;c_0\;^n_0\;+\;c_1\;^n_1\;+\;...\;+\;c_n\;^n_n$, where c = ($c_0,...c_n$ is the dual sequence of a. In this paper, we find the general term of the sequence ($c_0,\;c_1$,... ) and give another method for finding the inverse matrix of the Pascal matrix. And we find a simple proof of the fact that if the general term of a sequence a = ($a_0,\;a_1$,... ) is a polynomial of degree p in n, then ${\Delta}^{p+1}a\;=\;0$.

• East Asian mathematical journal
• /
• v.35 no.3
• /
• pp.285-288
• /
• 2019

Let $F_n$, $n{\in}{\mathbb{N}}$ be the n - th Fibonacci number, and let (p, q) be one of ordered pairs ($F_{n+2}$, $F_n$) or ($F_{n+1}$, $F_n$). Then we show that the multiplicative inverse of q mod p as well as that of p mod q are again Fibonacci numbers. For proof of our claim we make use of well-known Cassini, Catlan and dOcagne identities. As an application, we determine the number $N_{p,q}$ of nonzero term of a polynomial ${\Delta}_{p,q}(t)=\frac{(t^{pq}-1)(t-1)}{(t^p-1)(t^q-1)}$ through the Carlitz's formula.

• Wind and Structures
• /
• v.31 no.6
• /
• pp.549-560
• /
• 2020

Methods for stochastic simulation of non-Gaussian wind pressure have increasingly addressed the efficiency and accuracy contents to offer an accurate description of the extreme value estimation of the long-span and high-rise structures. This paper presents a linear prediction and z-transform (LPZ) based Cumulative distribution function (CDF) mapping algorithm for the simulation of multivariate non-Gaussian fluctuating wind pressure. The new algorithm generates realizations of non-Gaussian with prescribed marginal probability distribution function (PDF) and prescribed spectral density function (PSD). The inverse linear prediction and z-transform function (ILPZ) is deduced. LPZ is improved and applied to non-Gaussian wind pressure simulation for the first time. The new algorithm is demonstrated to be efficient, flexible, and more accurate in comparison with the FFT-based method and Hermite polynomial model method in two examples for transverse softening and longitudinal hardening non-Gaussian wind pressures.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.17 no.4
• /
• pp.83-93
• /
• 2017

In everyday life, the ratio of credit card aspect ratio is 1: 1.56, and A4 printer paper is 1: 1.414, which is relatively balanced golden ratio. In this paper, we show the Fibonacci Golden ratio as a polynomial based on the golden ratio, which is the most balanced and ideal visible ratio, and show that the application of Euler and symmetric jacket polynomial is related to BPSK and QPSK constellation. As a proof method, we have derived Fibonacci Golden and Galois field element polynomials. Then mathematically, We have newly derived a golden jacket code that can be used to generate an appropriate code with orthogonal properties and can simply be used for inverse calculation. We also obtained a channel capacity according to the channel correlation change using a block jacket matrix in a MIMO mobile communication.

• The KIPS Transactions:PartB
• /
• v.10B no.4
• /
• pp.373-380
• /
• 2003

Most of low cost digital cameras reveal relatively high lens distortion. The purpose of this research is to compensate the degradation of image quality due to the geometrical distortion of a lens system. The proposed method consists of two stages : calculation of a lens distortion coefficient by a simplified version of Tsai´s camera calibration and subsequent image warping of the original distorted image to remove geometrical distortion based on the calculated lens distortion coefficient. In the lens distortion coefficient calculation stage, a practical method for handling scale factor ratio and image center is proposed, after which its feasibility is shown by measuring the performance of distortion correction using a quantitative image quality measure. On the other hand, in order to apply image warping via inverse spatial mapping using the result of the lens distortion coefficient calculation stage, a cubic polynomial derived from an adopted radial distortion lens model must be solved. In this paper, for the purpose of real-time operation, which is essential for embedding into an information device, an approximated solution to the cubic polynomial is proposed in the form of a solution to a quadratic equation. In the experiment, potential for real-time implementation and equivalence in performance as compared with that from cubic polynomial solution are shown.

• Journal of Korean Society for Atmospheric Environment
• /
• v.13 no.6
• /
• pp.463-474
• /
• 1997

Metallic elements in dustfall have been known as notable air pollutants directly or indirectly influencing human health and wealth. The first aim of this study was to obtain precise spatial distribution patterns of 5 elements (Pb, Zn, K, Cr, and Al) in dustfall around Suwon area. To predict isometric lines of metal fluxes deposited on unsupervised random sites, the study has applied both spatial statistics as a receptor model and a GIS (geographic information system). Total of 31 sampling sites were selected in the study area (roughly 3 by 3 km grid basis) and dustfall samples were then collected monthly basis by the British deposit gauges from Dec., 1995 to Nov., 1996. The metallic elements in the dustfall were then analyzed by an atomic absorption spectrometer (AAS). On the other hand, a base map overlapped by 7 layers was constructed by using the AutoCAD R13 and ARC/INFO 3.4D. Four different spatial interpolation and expolation techniques such as IDW (inverse distance weighted averaging), TIN (triangulated irregular network), polynomial regression, and kriging technique were examined to compare spatial distribution patterns. Each pattern obtained by each technique was substantally different as varing pollutant types, land of use types, and topological conditions, etc. Thus, our study focused intensively on uncertainty analysis based on a concept of the jackknife and the sum of error distance. It was found that a kriging technique was the best applicalbe in this study area.

• The Journal of Society for e-Business Studies
• /
• v.11 no.2
• /
• pp.1-11
• /
• 2006

This paper proposes an efficient inversion algorithm for Galois field GF(2n) by using a modified multi-bit shifting method based on the Montgomery algorithm. It is well known that the efficiency of arithmetic algorithms depends on the basis and many foregoing papers use either polynomial or optimal normal basis. An inversion algorithm, which modifies a multi-bit shifting based on the Montgomery algorithm, is studied. Trinomials and AOPs (all-one polynomials) are tested to calculate the inverse. It is shown that the suggested inversion algorithm reduces the computation time up to 26 % of the forgoing multi-bit shifting algorithm. The modified algorithm can be applied in various applications and is easy to implement.

• Journal of the Korea Institute of Military Science and Technology
• /
• v.17 no.5
• /
• pp.680-687
• /
• 2014

PGA(phase gradient autofocus) has been widely used to remove motion induced phase errors in the ISAR(inverse synthetic aperture radar) imaging. The critical process for the processing time and image quality is windowing stage in PGA. In this paper, the new method to determine window size based on polynomial least square approximation is proposed. Moreover, dominant range bins are selected for efficient phase error estimation, which improve image quality and speed up convergence. The simulation results show that the proposed algorithm provides high quality ISAR images while computational efficiency of inherent PGA is retained.

• Safety and Health at Work
• /
• v.3 no.4
• /
• pp.294-297
• /
• 2012

Previous studies on the vast increase in suicide mortality in Southeast Asia have indicated that suicide rates increase in parallel with a rise in unemployment or during periods of economic recession. This paper examines the effects of economic recession on suicidal rates amongst agriculture, fisheries, and forestry workers in Korea. Monthly time-series gross domestic product (GDP) data were linked with suicidal rates gathered from the cause of death records between1993-2008. Data were analyzed using generalized additive models to analyze trends, while a polynomial lag model was used to assess the unconstrained time lag effects of changes in GDP on suicidal rate. We found that there were significant inverse correlations between changes in GDP and suicide for a time lag of one to four months after the occurrence of economic event. Furthermore, it was evident that the overall relative risks of suicide were high enough to bring about social concern.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.63 no.7
• /
• pp.929-933
• /
• 2014

The measurement of joint angle is important to evaluate the patient's disability. The modified fiber tip and light propagation of the developed fiber sensor were investigated to increase the range of angle detection. Different shapes of fiber tips were manufactured with a polishing machine to deliver light signal in various patterns. Output signals were analyzed to obtain joint angle change with inverse polynomial models. The measured joint angles were displayed with LabVIEW program and the reliability was tested by comparing with a commercial angle sensor. This method can be used in rehabilitation field to determine patient's progress.