• Journal for History of Mathematics
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• v.24 no.2
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• pp.1-15
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• 2011

Approximation is a very useful approach in mathematics research. It was the same in traditional Chinese and Chosun mathematics. This study derived five characteristics from approximation approaches which were found in Chinese and Chosun mathematical books: improvement of approximate values, common and inevitable use of approximate values, recognition of approximate values and their reasons, comparison of their exactness, application of approximate principles. Through these characteristics, we can infer what Chinese and Chosun mathematicians recognized approximate values and how they manipulated them. They took approximate approaches by necessity or for the sake of convenience in mathematical study and its applications. Also, they tried to improve the degree of exactness of approximate values and use the inverse calculations to check them.

• Journal of Satellite, Information and Communications
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• v.8 no.4
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• pp.130-134
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• 2013

This paper describes the basic principles of 3D broadcast system and proposes new 3D broadcast technology that reduce the amount of data by applying CS(Compressed Sensing). Differences between Sampling theory and the CS technology concept was described. Recently proposed CS algorithm AMP(Approximate Message Passing) and CoSaMP(Compressive Sampling Matched Pursuit) was described. Image data that compressed and restored by these algorithm was compared. Calculation time of the algorithm having a low complexity is determined.

• Journal of Satellite, Information and Communications
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• v.10 no.3
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• pp.57-61
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• 2015

This paper describes the basic principles of 3D broadcast system and proposes new 3D broadcast technology that reduces the amount of data by applying CS(Compressed Sensing). Differences between Sampling theory and the CS technology concept was described. CS algorithm SS-CoSaMP(Single-Space Compressive Sampling Matched Pursuit) and AMP(Approximate Message Passing) was described. Image data compressed and restored by these algorithm was compared. Calculation time of the algorithm having a low complexity is determined.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1065-1092
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• 2018

This manuscript is involved with a category of second-order impulsive functional integro-differential equations with nonlocal conditions in Banach spaces. Sufficient conditions for existence and approximate controllability of mild solutions are acquired by making use of the theory of cosine family, Banach contraction principle and Leray-Schauder nonlinear alternative fixed point theorem. An illustration is additionally furnished to prove the attained principles.

• Interaction and multiscale mechanics
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• v.1 no.3
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• pp.329-337
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• 2008

This paper presents the derivation of the generalized governing equations in theory of elasticity, their weak forms and the some applications in the numerical analysis of structural mechanics. Unlike the differential equations in classical elasticity theory, the generalized equations of the equilibrium and compatibility equations presented here take the form of integral equations, and the generalized equilibrium equations contain the classical differential equations and the boundary conditions in a single equation. By using appropriate test functions, the weak forms of these generalized governing equations can be established. It can be shown that various variational principles in structural analysis are merely the special cases of these weak forms of generalized governing equations in elasticity. The present weak forms of elasticity equations extend greatly the choices of the trial functions for approximate solutions in the numerical analysis of various engineering problems. Therefore, the weak forms of generalized governing equations in elasticity provide a powerful modeling tool in the computational structural mechanics.

• Progress in Medical Physics
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• v.32 no.1
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• pp.1-17
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• 2021

The evolution of X-ray computed tomography (CT) has been based on the discovery of X-rays, the inception of the Radon transform, and the development of X-ray digital data acquisition systems and computer technology. Unlike conventional X-ray imaging (general radiography), CT reconstructs cross-sectional anatomical images of the internal structures according to X-ray attenuation coefficients (approximate tissue density) for almost every region in the body. This article reviews the essential physical principles and technical aspects of the CT scanner, including several notable evolutions in CT technology that resulted in the emergence of helical, multidetector, cone beam, portable, dual-energy, and phase-contrast CT, in integrated imaging modalities, such as positron-emission-tomography-CT and single-photon-emission-computed-tomography-CT, and in clinical applications, including image acquisition parameters, CT angiography, image adjustment, versatile image visualizations, volumetric/surface rendering on a computer workstation, radiation treatment planning, and target localization in radiotherapy. The understanding of CT characteristics will provide more effective and accurate patient care in the fields of diagnostics and radiotherapy, and can lead to the improvement of image quality and the optimization of exposure doses.

• Nuclear Engineering and Technology
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• v.42 no.3
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• pp.271-278
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• 2010

While the deterministic lattice physics/depletion codes use leakage-corrected critical spectrum (although approximate due to the B1 buckling search employed), Monte Carlo depletion codes currently in use do not have such a feature in spite of their heterogeneity and continuous-energy modeling capability. This paper describes an approach to Monte Carlo depletion with leakage-corrected critical spectrum derived from first principles. This is based on the concept of albedo eigenvalue treated as weight of the reflected neutron in Monte Carlo simulation.

• Computational Structural Engineering
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• v.8 no.1
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• pp.173-186
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• 1995

It is well known that structures constructed by bonding two or more materials and then subjected to temperature change experience thermal stress. This stress results from thermal expansion mismatch of materials. The present paper derives formulas for the stresses in a bimaterial axisymmetric disk which is subjected to a uniform temperature change. First, an approximate solution following strength-of-materials principles is developed. However, the strength-of-materials solution has difficulty in predicting both the peak value of interfacial stresses and its associated distribution. Next, a solution consistent with the theory of elasticity is developed by way of an eigenfunction expansion approach. The eigenfunction analysis is compared with finite element stress analysis results for a specific numerical example. Finite element analysis results show that the interfacial stresses are adequately predicted by eigenfunction solution. Therefore, the method developed in this paper will be useful in determination of the interfacial stress state.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.3
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• pp.267-273
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• 2004

The purpose of this paper is to develop a systematic design method for the suspension system hard points and compliance elements, which have great influence on the handling stability of a vehicle. In this paper, a method to optimize J-turn responses is presented based on the principles of design of experiments, multi-body dynamic analysis and optimum design technique. The design variables associated with the J-turn maneuver are selected through the experimental design sensitivity analysis using the perturbation method. An objective function is defined as an approximate function for the J-turn characteristics using the TSA(Taylor series approximation). The values of the design variables, which make the optimized J-turn characteristics, are obtained using the conjugate gradient method. The result of the J-turn simulation shows that the optimized vehicle has more improved handling stability than the optimized vehicle.

• Journal of the Korean Institute of Intelligent Systems
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• v.3 no.2
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• pp.3-17
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• 1993

The fuzzy pattern matching technique has been developed in the framework of fuzzy set and possibility theory in order to take into account the imprecision and the uncertainty pervading values which have to be compared to requirements (which may be fuzzy) in a pattern matching process. This paper restates the basic principles and extends them to situations where (sub)patterns are only required to be satisfied up to a given tolerance (which may be fuzzy), or where the different subparts of a compound pattern may have various levels of importance. Both cases correspond to a weakening of elementary patterns. which can be expressed by a fuzzy relations modelling an approximate equality or an uncertain strict equality respectively. We also study the more sophisticated case where some elementary patterns have not to be satisfied with the highest priority provided that weaker requirements remain satisfied. The fuzzy pattern matching technique applies in a variety of problems including the evaluation of soft queries with respect to a fuzzy database, the evaluation of the fuzzy condition parts of rules in approximate reasoning, or the evaluation of the belonging of an ill-known object to a flexible class in classification problems.