• Korean Journal of Remote Sensing
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• v.30 no.5
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• pp.617-625
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• 2014

The Rational Function Model has been used as a replacement sensor model in most commercial photogrammetric systems due to its capability of maintaining the accuracy of the physical sensor models. Although satellite images with rational polynomial coefficients have been used to determine three-dimensional position, it has limitations in the accuracy for large scale topographic mapping. In this study, high resolution stereo satellite images, QuickBird-2, were used to investigate how much the three-dimensional position accuracy was affected by the No. of ground control points, polynomial order, and distribution of GCPs. As the results, we can confirm that these experiments satisfy the accuracy requirements for horizontal and height position of 1:25,000 map scale.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.297-304
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• 2022

Fixed point theory has many useful applications in applied sciences. The object of this paper is to obtain fixed point for continuous self mappings in Hilbert C^*-module with rational conditions.

• Journal of the Korean Association of Geographic Information Studies
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• v.12 no.1
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• pp.106-118
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• 2009

Satellite imagery with high resolution of about one meter is used widely in commerce and government applications ranging from earth observation and monitoring to national digital mapping. Due to the expensiveness of IKONOS Pro and Precision products, it is attractive to use the low-cost IKONOS Geo product with vendor-provided rational polynomial coefficients (RPCs), to produce highly accurate mapping products. The imaging geometry of IKONOS high-resolution imagery is described by RFs instead of rigorous sensor models. This paper presents four different polynomial models, that are the offset model, the scale and offset model, the Affine model, and the 2nd-order polynomial model, defined respectively in object space and image space to improve the accuracies of the RF-derived ground coordinates. Not only the algorithm for RF-based ground coordinates but also the algorithm for accuracy improvement of RF-based ground coordinates are developed which is based on the four models, The experiment also evaluates the effect of different cartographic parameters such as the number, configuration, and accuracy of ground control points on the accuracy of geopositioning. As the result of a experimental application, the root mean square errors of three dimensional ground coordinates which are first derived by vendor-provided Rational Function models were averagely 8.035m in X, 10.020m in Y and 13.318m in Z direction. After applying polynomial correction algorithm, those errors were dramatically decreased to averagely 2.791m in X, 2.520m in Y and 1.441m in Z. That is, accuracy was greatly improved by 65% in planmetry and 89% in vertical direction.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.121-133
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• 2008

In this article, we define Minkowski Pythagorean-hodograph (MPH) curves in the Minkowski plane $\mathbb{R}^{1,1}$ and obtain $C^1$ Hermite interpolations for MPH quintics in the Minkowski plane $\mathbb{R}^{1,1}$. We also have the envelope curves of MPH curves, and make surfaces of revolution with exact rational offsets. In addition, we present an example of $C^1$ Hermite interpolations for MPH rational curves in $\mathbb{R}^{2,1}$ from those in $\mathbb{R}^{1,1}$ and a suitable MPH preserving mapping.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1201-1222
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• 2019

In this paper, we introduce the notion of modified TAC-Suzuki-Berinde type F-contraction and modified TAC-(${\psi}$, ${\phi}$)-Suzuki type rational mappings in the frame work of complete metric spaces, we also establish some fixed point results regarding this class of mappings and we present some examples to support our main results. The results obtained in this work extend and generalize the results of Dutta et al. [9], Rhoades [18], Doric, [8], Khan et al. [13], Wardowski [25], Piri et al. [17], Sing et al. [23] and many more results in this direction.

• ETRI Journal
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• v.30 no.6
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• pp.818-825
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• 2008

This paper proposes an exponentiation method with Frobenius mappings. The main target is an exponentiation in an extension field. This idea can be applied for scalar multiplication of a rational point of an elliptic curve defined over an extension field. The proposed method is closely related to so-called interleaving exponentiation. Unlike interleaving exponentiation methods, it can carry out several exponentiations of the same base at once. This happens in some pairing-based applications. The efficiency of using Frobenius mappings for exponentiation in an extension field was well demonstrated by Avanzi and Mihailescu. Their exponentiation method efficiently decreases the number of multiplications by inversely using many Frobenius mappings. Compared to their method, although the number of multiplications needed for the proposed method increases about 20%, the number of Frobenius mappings becomes small. The proposed method is efficient for cases in which Frobenius mapping cannot be carried out quickly.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.10
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• pp.1259-1268
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• 1995

This note presents the robust root clustering problem of interval systems whose characteristic equation might be given as either a family of interval polynomials or a family of polytopes. Corresponding to damping ratio and robustness margin approximately, we consider a certain class of D-region such as parabola, left-hyperbola, and ellipse in complex plane. Then a simpler D-stability criteria using rational function mapping is presented and prove. Without .lambda. or .omega. sweeping calculation, the absolute criteria for robust D-stability can be determined.

• Agricultural and Biosystems Engineering
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• v.5 no.1
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• pp.1-4
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• 2004

Community-based precision farming is a new concept of agricultural systems, which leads to organize groups of wise farmers and technology platforms in Japan. The wisdom farmers create a rational farming system to manage hierarchical variability: variability in farmers' community as well as variability of within-field and between-field. The technology platform develops and provides three key-technologies: mapping technology, variable-rate technology, and decision support systems available for rural constraints. Advancement of bio-production robots leads precision farming to the next level, where two technological innovations: how to produce and manage information-oriented fields and information-added products, can be attained.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.405-417
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• 2010

We prove the generalized Hyers-Ulam stability of the generalized quadratic functional equation $$f(rx\;+\;sy)\;=\;r^2f(x)\;+\;s^2f(y)\;+\;\frac{rs}{2}[f(x\;+\;y)\;-\;f(x\;-\;y)]$$ in fuzzy Banach spaces, where r, s are non-zero rational numbers with $r^2\;+\;s^2\;{\neq}\;1$.

• Journal of information and communication convergence engineering
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• v.15 no.2
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• pp.97-103
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• 2017

Implementation of faster pairing calculation is the basis of efficient pairing-based cryptographic protocol implementation. Generally, pairing is a costly operation carried out over the extension field of degree $k{\geq}12$. But the twist property of the pairing friendly curve allows us to calculate pairing over the sub-field twisted curve, where the extension degree becomes k/d and twist degree d = 2, 3, 4, 6. The calculation cost is reduced substantially by twisting but it makes the discrete logarithm problem easier if the curve parameters are not carefully chosen. Therefore, this paper considers the most recent parameters setting presented by Barbulescu and Duquesne [1] for pairing-based cryptography; that are secure enough for 128-bit security level; to explicitly show the quartic twist (d = 4) and sextic twist (d = 6) mapping between the isomorphic rational point groups for KSS (Kachisa-Schaefer-Scott) curve of embedding degree k = 16 and k = 18, receptively. This paper also evaluates the performance enhancement of the obtained twisted mapping by comparing the elliptic curve scalar multiplications.