• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.321-331
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• 2024

We consider the numerical treatment of blow-up problems having non-monotonic singular solutions that tend to infinity at some point in the domain. The use of standard numerical methods for solving problems with blow-up solutions can lead to significant errors. The reason being that solutions of such problems have singularities whose positions are unknown in advance. To be able to integrate such non-monotonic blow-up problems, we describe and use a method of non-local transformations. To show the efficiency of the method, we present a comparison of exact and numerical solutions in addition to some comparison with the work of other authors.

• Journal of Advanced Marine Engineering and Technology
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• v.29 no.7
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• pp.779-784
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• 2005

This paper presents the theory of similarity transformations applied to the momentum and energy equations for laminar, forced, external boundary layer flow over a horizontal flat plate which leads to a set of non-linear, ordinary differential equations of phase change material slurry(PCM Slurry). The momentum and energy equation set numerically to obtain the non-dimensional velocity and temperature profiles in a laminar boundary layer are solved. The heat transfer characteristics of PCM slurry was numerically investigated with similar method. It is clarified that the similar solution method of Newtonian fluid can be used reasonably this type of PCM slurry which has low concentration. The data of local wall heat flux and convective heat transfer coefficient of PCM slurry are higher than those of water more than 150$\~$200$\%$, approximately.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1221-1241
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• 2008

Most of domains people have studied are convex bounded projective (or affine) domains. Edith $Soci{\acute{e}}$-$M{\acute{e}}thou$ [15] characterized ellipsoid in ${\mathbb{R}}^n$ by studying projective automorphism of convex body. In this paper, we showed convex and bounded projective domains can be identified from local data of their boundary points using scaling technique developed by several mathematicians. It can be found that how the scaling technique combined with properties of projective transformations is used to do that for a projective domain given local data around singular boundary point. Furthermore, we identify even unbounded or non-convex projective domains from its local data about a boundary point.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37 no.7C
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• pp.554-564
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• 2012

The vehicle recognition consists of two steps; the vehicle region detection step and the vehicle identification step based on the feature extracted from the detected region. Features using linear transformations have the effect of dimension reduction as well as represent statistical characteristics, and show the robustness in translation and rotation of objects. Among the linear transformations, the NMF(Non-negative Matrix Factorization) is one of part-based representation. Therefore, we can extract NMF features with sparsity and improve the vehicle recognition rate by the representation of local features of a car as a basis vector. In this paper, we propose a feature extraction using NMF suitable for the vehicle recognition, and verify the recognition rate with it. Also, we compared the vehicle recognition rate for the occluded area using the SNMF(sparse NMF) which has basis vectors with constraint and LVQ2 neural network. We showed that the feature through the proposed NMF is robust in the urban scene where occlusions are frequently occur.

• Journal of Advanced Marine Engineering and Technology
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• v.31 no.7
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• pp.833-841
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• 2007

The aim of this paper is to analyze the conjugate problems of heat conduction in solid walls coupled with laminar free convection flow adjacent to a vertical flat plate under boundary layer approximation. Using the similarity transformations the governing boundary layer equations for momentum and energy are reduced to a system of partial differential equations and then solved numerically using Finite Difference Method(FDM) known as the Keller-box scheme. Computed solutions to the governing equations are obtained for a wide range of non-dimensional parameters that are present in this problem, namely the coupling parameter P. the Prandtl number Pr and the heat generation parameter Q. The variations of the local heat transfer rate as well as the interface temperature and the friction along the plate and typical velocity and temperature profiles in the boundary layer are shown graphically. Numerical solutions have been consider for the Prandtl number Pr=0.70

• Steel and Composite Structures
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• v.36 no.5
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• pp.603-615
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• 2020

The present manuscript focuses on the flow and heat transfer of the dusty fluid along exponentially stretching cylinder. Enormous attempts are made for fluid flow along cylinder but the study of fluid behavior along exponentially stretching cylinder is discussed lately. Using appropriate transformations, the governing partial differential equations are converted to non-dimensional ordinary differential equations. The transformed equations are solved numerically using Shooting technique with Runge-Kutta method. The influence of the physical parameters on the velocity and temperature profiles as well as the skin fraction coefficient and the local Nusselt number are examined in detail. The essential observations are as the fluid velocity decreases but temperature grows with rise in particle interaction parameter, and both the fluid velocity and temperature fall with increase in mass concentration parameter, Reynold number, Particle interaction parameter for temperature and the Prandtl number.