• Journal of Korean Society for Quality Management
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• v.19 no.1
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• pp.129-140
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• 1991

This paper deals with on (S-1, S) spare-part inventory model for multi-stage machine repair problem with attrition. The steady-state availability of the system is maximized under some constraints such as total cost, available space etc.. The problem is formulated as a closed queueing network and the system availability is calculated by Buzen's computational algorithm. In order to find the optimal numbers of spare units and repair channels for each operating stage, the problem is formulated as a non-linear integer programming(NLIP) problem and an efficient algorithm. which is a natural extension of the new Lawler-Bell algorithm of Sasaki et el., is used to solve the NLIP problem. A numerical example is given to illustrate the algorithm.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.183-197
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• 2021

Recently several authors have extended the Beta function by using its integral representation. However, in many cases no expression of these extended functions in terms of classic special functions is known. In the present paper, we introduce a further extension by defining a family of functions G_r,s : ℝ^*₊ → ℂ, with r, s ∈ ℂ and ℜ(r) > 0. For given r, s, we prove that this function satisfies a second-order linear differential equation with rational coefficients. Solving this ODE, we express G_r,s as a combination of confluent hypergeometric functions. From this we deduce a new integral relation satisfied by Tricomi's function. We then investigate additional specific properties of G_r,1 which take the form of new non trivial integral relations involving exponential and error functions. We discuss the connection between G_r,1 and Stokes' first problem (or Rayleigh problem) in fluid mechanics which consists in determining the flow created by the movement of an infinitely long plate. For $r{\in}{\frac{1}{2}}{\mathbb{N}}^*$, we find additional relations between G_r,1 and Hermite polynomials. In view of these results, we believe the family of extended beta functions G_r,s will find further applications in two directions: (i) for improving our knowledge of confluent hypergeometric functions and Tricomi's function, (ii) and for engineering and physics problems.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.689-706
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• 2008

In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

• Steel and Composite Structures
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• v.27 no.5
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• pp.567-576
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• 2018

The objective of this work is to analyze large deflections of a fiber reinforced composite cantilever beam under point loads. In the solution of the problem, finite element method is used in conjunction with two dimensional (2-D) continuum model. It is known that large deflection problems are geometrically nonlinear problems. The considered non-linear problem is solved considering the total Lagrangian approach with Newton-Raphson iteration method. In the numerical results, the effects of the volume fraction and orientation angles of the fibre on the large deflections of the composite beam are examined and discussed. Also, the difference between the geometrically linear and nonlinear analysis of fiber reinforced composite beam is investigated in detail.

• Structural Engineering and Mechanics
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• v.44 no.3
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• pp.405-416
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• 2012

In this study the investigation of large deflections subject in compliant mechanisms is presented using homotopy perturbation method (HPM). The main purpose is to propose a convenient method of solution for the large deflection problem in compliant mechanisms in order to overcome the difficulty and complexity of conventional methods, as well as for the purpose of mathematical modeling and optimization. For simplicity, a cantilever beam of linear elastic material under horizontal, vertical and bending moment end point load is considered. The results show that the applied method is very accurate and capable for cantilever beams and can be used for a large category of practical problems for the aim of optimization. Also the consequence of effective parameters on the large deflection is analyzed and presented.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.4
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• pp.668-676
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• 2008

In this paper, we considered the $H_{\infty}$ tracking control for time-delayed linear systems with saturating actuators. The considered time delay is a time varying one having bounded magnitude and rate, and the considered tracking reference is a general one only known its bounds of magnitude and rate. First, we have converted the $H_{\infty}$ tracking control problem into an equivalent $H_{\infty}$ disturbance attenuation problem using two steps of transformations. Next, based on a new Lyapunov-Krasovskii functional, we have derived the result in the form of LMI with two non-convex parameters. Finally, by numerical examples, we have shown the usefulness and effectiveness of our result.

• Journal of Korea Water Resources Association
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• v.34 no.5
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• pp.473-486
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• 2001

The WGR model was developed to represent meso-scale precipitation. As a conceptual model, this model shows a good link between atmospheric dynamics and statistical description of meso-scale precipitation(Waymire et al., 1984). However, as it has maximum 18 parameters along with its non-linear structure, its parameter estimation has been remained a difficult problem. There have been several cases of its parameter estimation for different fields using non-linear programming techniques(NLP), which were also difficult tasks to hamper its wide applications. In this study, we estimated the WGR model parameters of the Han river basin using the genetic algorithm(GA) and compared them to the NLP results(Yoo and Kwon, 2000). As a result of the study, we can find that the sum of square error from the GA provide more consistent parameters to the seasonal variation of rainfall. Also, we can find that the higher rainfall amount during summer season is closely related with the arrival rate of rain bands, not the rain cell intensity.

• The Journal of the Acoustical Society of Korea
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• v.40 no.2
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• pp.109-120
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• 2021

This paper proposes the H∞ norm based data association gate method to apply robustly the data association gate of passive sonar automatic target tracking which is on non-linear targets in dense cluttered environment. For target tracking, data association method selects the measurements within validated gate, which means validated measuring extent, as candidates for the data association. If the extent of the validated gate in the data association is not proper or the data association executes under dense cluttered environment, it is difficult to maintain the robustness of target tracking due to interference of clutter measurements. To resolve this problem, this paper proposes a novel gating method which applies H∞ norm based bisection algorithm combined with 3-σ gate method under Gaussian distribution assumption and tracking error covariance. The proposed method leads to alleviate the interference of clutters and to track the non-linear maneuvering target robustly. Through analytic method and simulation to utilize simulated data of horizontal and vertical bearing measurements, improvement of data association robustness is confirmed contrary to the conventional method.

• International Journal of Computer Science & Network Security
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• v.23 no.7
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• pp.49-60
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• 2023

The amount of data generated by electronic systems through e-commerce, social networks, and data computation has risen. However, the security of data has always been a challenge. The problem is not with the quantity of data but how to secure the data by ensuring its confidentiality and privacy. Though there are several research on cloud data security, this study proposes a security scheme with the lowest execution time. The approach employs a non-linear time complexity to achieve data confidentiality and privacy. A symmetric algorithm dubbed the Non-Deterministic Cryptographic Scheme (NCS) is proposed to address the increased execution time of existing cryptographic schemes. NCS has linear time complexity with a low and unpredicted trend of execution times. It achieves confidentiality and privacy of data on the cloud by converting the plaintext into Ciphertext with a small number of iterations thereby decreasing the execution time but with high security. The algorithm is based on Good Prime Numbers, Linear Congruential Generator (LGC), Sliding Window Algorithm (SWA), and XOR gate. For the implementation in C, thirty different execution times were performed and their average was taken. A comparative analysis of the NCS was performed against AES, DES, and RSA algorithms based on key sizes of 128kb, 256kb, and 512kb using the dataset from Kaggle. The results showed the proposed NCS execution times were lower in comparison to AES, which had better execution time than DES with RSA having the longest. Contrary, to existing knowledge that execution time is relative to data size, the results obtained from the experiment indicated otherwise for the proposed NCS algorithm. With data sizes of 128kb, 256kb, and 512kb, the execution times in milliseconds were 38, 711, and 378 respectively. This validates the NCS as a Non-Deterministic Cryptographic Algorithm. The study findings hence are in support of the argument that data size does not determine the execution.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.454-459
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• 2004

This paper considers the problem of satellite's orbit control and a solution based in Linear Matrix Inequalities (LMI) is proposed for the case of Low Earth Orbiters (LEO). In particular, the modelling procedure and the algorithm for control law synthesis are tested using as study case the European Gravity Field and Ocean Circulation Explorer satellite (GOCE), to be launched by the European Space Agency (ESA) in the year 2006. The scientific objective of this space mission is the recovering of the Earth gravity field with high accuracy (less than 10${\mu}m$/${\mu}m$) and spatial resolution (better than 100km). In order to meet these scientific requirements, the orbit control must guarantee stringent specifications in terms of environmental disturbances attenuation (atmospheric drag forces) even in presence of high levels of model uncertainty.