• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.621-634
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• 2022

The scaled inverse of a nonzero element a(x) ∈ ℤ[x]/f(x), where f(x) is an irreducible polynomial over ℤ, is the element b(x) ∈ ℤ[x]/f(x) such that a(x)b(x) = c (mod f(x)) for the smallest possible positive integer scale c. In this paper, we investigate the scaled inverse of (xⁱ - x^j) modulo cyclotomic polynomial of the form Φ_p^s (x) or Φ_p^sq^t (x), where p, q are primes with p < q and s, t are positive integers. Our main results are that the coefficient size of the scaled inverse of (xⁱ - x^j) is bounded by p - 1 with the scale p modulo Φ_p^s (x), and is bounded by q - 1 with the scale not greater than q modulo Φ_p^sq^t (x). Previously, the analogous result on cyclotomic polynomials of the form Φ_2ⁿ (x) gave rise to many lattice-based cryptosystems, especially, zero-knowledge proofs. Our result provides more flexible choice of cyclotomic polynomials in such cryptosystems. Along the way of proving the theorems, we also prove several properties of {x^k}_k∈ℤ in ℤ[x]/Φ_pq(x) which might be of independent interest.

• Journal of the Korea Society of Computer and Information
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• v.17 no.12
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• pp.187-198
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• 2012

International standard for software quality evaluation, ISO/IEC 9126 defines the quality characteristics and sub-characteristics consisting of quality of the software. Also, in this standard, the quality assessment items are presented in metrics based on maturity, fault tolerance, recoverability and compliance which are sub-characteristics of reliability. However, this reliability assessment items which are presented are not applied now due to the mathematical difficulties and the problems caused by collection of data. In order to resolve these problems, this study introduces measures to develop a specific test technique by quality attributes and to measure the quality. In other words, the detailed guidelines are presented to be utilized as a standard by summarizing test activities and techniques by each development life the most commonly used. The SW quality results are derived by assigning weights to software in order of the most important quality characteristics of respective software using checklist that can be easily utilized and applying test technique that can be utilized for detailed evaluation items and checklist. This improves problems that include reliability assessment item of ISO/IEC 9126 as the measures to measure new reliability quality of software.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.365-380
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• 2012

Non-negative matrix factorization (NMF) is a very efficient method to explain the relationship between functions for finding basis information of multivariate nonnegative data. The multiplicative update (MU) algorithm is a popular approach to solve the NMF problem, but it fails to approach a stationary point and has inner iteration and zero divisor. So the elementwisely alternating projected gradient (eAPG) algorithm was proposed to overcome the defects. In this paper, we use the fact that the equilibrium point is stable to prove the convergence of the eAPG algorithm. By using a classic model, the equilibrium point is obtained and the invariant sets are constructed to guarantee the integrity of the stability. Finally, the convergence conditions of the eAPG algorithm are obtained, which can accelerate the convergence. In addition, the conditions, which satisfy that the non-zero equilibrium point exists and is stable, can cause that the algorithm converges to different values. Both of them are confirmed in the experiments. And we give the mathematical proof that the eAPG algorithm can reach the appointed precision at the least iterations compared to the MU algorithm. Thus, we theoretically illustrate the advantages of the eAPG algorithm.

• Transactions of Materials Processing
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• v.8 no.1
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• pp.65-77
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• 1999

In recent years, the quality requirements from the customers of hot rolled steel strip have been steadily increasing in diversity and strictness. To meet these quality requirements as well as to improve productivity, steel mills have been doing their efforts for developing high performance Automatic Gauge Control (AGC) system. However, it is very time consuming and also needs a lot of money to develop the new technologies of AGC in actual mill. So, there has been a demand for developing the Dynamic Hot Rolling Simulator since late 80's. It is a kind of software packages and can analyze the dynamic behaviors of hot finishing rolling process without laborious experiments in actual mill. It can also be used as a designing tool of Automatic Gauge Controller. In this work, the Dynamic Hot Rolling Simulator which is applicable to 6 sands hot strip mill rolling was developed. The MATLAB with SIMLINK was used as a software developer for making the main part of simulator because it is very powerful tool for modeling, integrating, controller design, and simulation. In this paper, the structures and the mathematical models of the simulator were briefly described and the results of simulation on the transient phenomena of hot rolling process with actual mill data were also presented.

• International Journal of Aeronautical and Space Sciences
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• v.17 no.1
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• pp.101-108
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• 2016

The RCS characteristics of stealth modified three-surface aircraft are analyzed in this paper. Prototype A is built with CATIA software and the three-dimensional digital models of modified stealth three-surface B and C are also designed based on carrier-based aircraft Su-33; the numerical simulation of RCS characteristics of three-surface aircraft is conducted with RCSAnsys software based on physical optics method and the method of equivalent currents; The following results are obtained by comparative analysis and mathematical statistics: (1) by the use of physical optics method and equivalent electromagnetic current method, the scattering intensity for each part of the model and RCS characteristic of the aircraft can be analyzed efficiently and accurately; (2) compared with model A, the mean RCS value of model B is reduced to 14.1% in forward direction and 48.1% in lateral direction; (3) compared with model A, the mean RCS value of model C decreases to 11.4% in forward direction and 21.6% in lateral direction. The results are expected to provide theoretical basis and technical support to the conceptual design of aircraft and stealth technology research.

• The Transactions of the Korea Information Processing Society
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• v.5 no.9
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• pp.2345-2352
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• 1998

The hyper-geometric distribution software reliability growth model was recently developed and successfully applied Due to mathematical difficultv of the maximum likclihmd method, the least squares method has hem suggested for parameter estimation by the previous studies. We first summarize and compare the minimization criteria adopted by the previous studies. It is theo shown that the weighted least squares method is more appropriate hecause of the nonhomogeneous variability of the number of newly detected faults. The adequacy of the weighted least squares method is illustrated by two numerical examples. Finally, we propose a new method fur predicting the number of faults newly discovered by next test instances. The new prediction method can be used for determining the time to stop testing.

• Transactions of the Korean Society of Automotive Engineers
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• v.15 no.5
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• pp.180-187
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• 2007

This paper presents a mathematical vehicle model that is designed to analyze the dynamic performance and to develop various safety control systems. Wheel slip controllers for ABS is also formulated to improve the vehicle response and to increase the safety on slippery road. Validation of the model and controller is performed by comparison with a commercial software package, CarSim. The result shows that performances of developed vehicle model are in good accordance with those of the CarSim on various driving conditions. Developed ABS controller is applied to the vehicle model and CarSim model, and it achieves good control performance. ABS controller improves lateral stability as well as longitudinal one when a vehicle is in turning maneuver on slippery road. A driver model is also designed to control steer angle of the vehicle model. It also shows good performance because the vehicle tracks the desired lane very well.

• International Journal of Precision Engineering and Manufacturing
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• v.7 no.3
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• pp.3-7
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• 2006

For the purpose to improve and to automate designing of high-speed spindle units (SU's), we have developed the mathematical models and software to estimate SU performance characteristics, including the run-out of spindles running on ball bearings. In order to understand better the mechanics of high-speed SUs, the dynamic interaction of ball bearings and SU, and the influence of the bearing imperfections and SU's operational conditions on the run-out, we have carried out computer simulation and experimental studies. Through the study of SU's, we have found out that run-out of SU can vary drastically with variation of rpm. The influences of rotation speed and of accuracy parameters of bearings on the SU accuracy have the greatest importance. The influence of bearing preload has a secondary importance. Comparison of the results of these studies has demonstrated adequacy of the models and software developed to the real SU's.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.6
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• pp.1689-1699
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• 1990

Sendzimir rolling mill is widely used for rolling hard materials such as stainless steel due to its small work roll diameter and shape controllability using two effective actuators, AS-U-Roll crown adjustment and lst. intermediate roll shifting. However, in comparison with 4-high or 6-high mills, it is noteasy to get good strip or excellent flatness because Z-mill has small diameter of work rolls which are easily deformed by load. A new mathematical model based on the method of dividing roll and strip into multo-portions was used to develop strip profile prediction software. Using the developed software, several influencing factors related to rolled strip profile for Z-Mill were tested analytically and characterized for the effective shape control. The effects of adjusting shape control actuators of Z-Mill on strip profile were also examined and discussed in detail.

• Journal of IKEEE
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• v.17 no.3
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• pp.221-228
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• 2013

About functional parameters of a LED/UVLED (Light Emitting Diode/Ultra Violet LED), one of the most important parameters is the I-V characteristic. By researching factors affect to the I-V characteristic of uvled, we found that beside of the structure of the device itself, there is the influence of the electrode materials, electrode shapes, the process of wiring and packaging. In this work, we want to improve the performance of UVLED to find out the optimal mask design principles. The study is based on theoretical mathematical models, as well as the use of simulation software tool Comsol. From all results obtained, the team has improved mask design to manufacture electrodes for GaN-based UVLED. Electrode masks are designed by three softwares, which are Intellisuite, Klayout and AutoCad. Intellisuite masks would be used in fabrication simulation while Klayout and AutoCad are used to fabricate electrodes in experiments. As well as, we silmulated the structure of an uvled 355nm emission wavelength by TCAD software, in order to compare with uvled sample that has the same emission wavelength.