• Journal of applied mathematics & informatics
• /
• v.41 no.3
• /
• pp.603-613
• /
• 2023

In this paper, the concept of geodesic centered tractography is explored for diffusion tensor imaging (DTI). In DTI, where geodesics has been tracked and the inverse of the fourth-order diffusion tensor is inured to determine the diversity. Specifically, we investigated geodesic tractography technique for High Angular Resolution Diffusion Imaging (HARDI). Riemannian geometry can be extended to a direction-dependent metric using Finsler geometry. Euler Lagrange geodesic calculations have been derived by Finsler geometry, which is expressed as HARDI in sixth order tensor.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.17 no.2
• /
• pp.412-434
• /
• 2023

This study discusses the high-order diffusion method in the wavelet domain. It aims to improve the edge protection capability of the high-order diffusion method using wavelet coefficients that can reflect image information. During the first step of the proposed diffusion method, the wavelet packet decomposition is a more refined decomposition method that can extract the texture and structure information of the image at different resolution levels. The high-frequency wavelet coefficients are then used to construct the edge detection function. Subsequently, because accurate wavelet coefficients can more accurately reflect the edges and details of the image information, by introducing the idea of state weight, a scheme for recovering wavelet coefficients is proposed. Finally, the edge detection function is constructed by the module of the wavelet coefficients to guide high-order diffusion, the denoised image is obtained. The experimental results showed that the method presented in this study improves the denoising ability of the high-order diffusion model, and the edge protection index (SSIM) outperforms the main methods, including the block matching and 3D collaborative filtering (BM3D) and the deep learning-based image processing methods. For images with rich textural details, the present method improves the clarity of the obtained images and the completeness of the edges, demonstrating its advantages in denoising and edge protection.

• Journal of applied mathematics & informatics
• /
• v.28 no.1_2
• /
• pp.295-309
• /
• 2010

In this paper, we study delayed high-order Cohen-Grossberg neural networks with reaction-diffusion terms and Neumann boundary conditions. By using inequality techniques and constructing Lyapunov functional method, some sufficient conditions are given to ensure the existence and convergence of the periodic oscillatory solution. Finally, an example is given to verify the theoretical analysis.

• Communications of the Korean Mathematical Society
• /
• v.14 no.4
• /
• pp.815-832
• /
• 1999

High-order weighted difference schemes with uniform meshes are considered for the convection-diffusion problem depending on Reynolds numbers. For small Reynolds numbers, a weighed cen-tral difference scheme is suggested since there is no boundary layer. For large Reynolds numbers, we propose a modified up wind method with an artificial diffusion in order to overcome nonphysical oscilla-tion of central schemes and obtain good accuracy in the boundary later. Existence and corresponding error estimates of the solution for the difference scheme have been shown. Numerical experiments are provided to back up the analysis.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.423-440
• /
• 2016

The bubble stabilization technique of Chebyshev-Legendre high-order element methods for one dimensional advection-diffusion equation is analyzed for the proposed scheme by Canuto and Puppo in [8]. We also analyze the finite element lower-order preconditioner for the proposed stabilized linear system. Further, the numerical results are provided to support the developed theories for the convergence and preconditioning.

• The Bulletin of The Korean Astronomical Society
• /
• v.40 no.2
• /
• pp.38.1-38.1
• /
• 2015

Supernova remnants (SNRs) are one of the most energetic astrophysical events and are thought to be the dominant source of Galactic cosmic rays (CRs). A recent report on observations of gamma rays from the vicinity of SNRs have shown strong evidence that Galactic CR protons are accelerated by the shock waves of the SNRs. The actual gamma-ray emission from pion decay should depend on the diffusion of CRs in the interstellar medium. In order to quantitatively analyze the diffusion of high-energy CRs from acceleration sites, we have performed test particle numerical simulations of CR protons using a three-dimensional magnetohydrodynamics (MHD) simulation of an interstellar medium swept-up by a blast wave. We analyse the CRs diffusion at a length scale of order a few pc, and show the Richtmeyer-Meshkov instability can provide enough turbulence downstream of the shock to make the diffusion coefficient close to the Bohm level for energy larger than 30 TeV for a realistic interstellar medium.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.40 no.4
• /
• pp.107-121
• /
• 2015

Diffusion of innovation is the process in which an innovation is communicated through certain channels over time among the members of a social system. The literatures have emphasized the importance of interpersonal network influences on individuals in convincing them to adopt innovations and thereby promoting its diffusion. In particular, the behavior of opinion leaders who lead in influencing others' opinion is important in determining the rate of adoption of innovation in a system. Centrality has been recognized as a good indicator that quantifies a node's influences on others in a given network. However, recent studies have questioned its relevance on various different types of diffusion processes. In this regard, this study aims at examining the effect of a node exhibiting high centrality on expediting diffusion of innovations. In particular, we considered the situation where two innovations compete with each other to be adopted by potential adopters who are personally connected with each other. In order to analyze this competitive diffusion process, we developed a simulation model and conducted regression analyses on the outcomes of the simulations performed. The results suggest that the effect of a node with high centrality can be substantially reduced depending upon the type of a network structure or the adoption thresholds of potential adopters in a network.

• Journal of the Korean Society of Costume
• /
• v.65 no.6
• /
• pp.25-35
• /
• 2015

The purpose of this study is to investigate the characteristics of members and communities that have significant influence in the online fashion community through their word-of-mouth activities. In order to identify the influence and the diffusion of word-of-mouth in fashion community, the study selected one online fashion community. Then, the study sorted the online posts and comments made on fashion information and put them into the matrix form to perform social network analysis. The result of the analysis is as follows: First, the fashion community network used in the study has many active members that relay information very quickly. Average time for information diffusion is very short, taking only one or two days in most cases. Second, the influence of word-of-mouth is led by key information produced from only a few members. The number of influential members account for less than 20% of the total number of community members, which indicate high level of degree centrality. The diffusion of word-of-mouth is led by even fewer members, which represent high level of betweenness centrality, compared to the case of degree centrality. Third, component characteristic shares similar information with about 70% of all members being linked to maximize information influence and diffusion. Fourth, a node with high degree centrality and betweenness centrality shares similar interests, presenting strain effect to particular information. Specially, members with high betweenness centrality show similar interests with members of high degree centrality. The members with high betweenness centrality also help expansion of related information by actively commenting on posts. The result of this research emphasizes the necessity of creation and management of network to efficiently convey fashion information by identifying key members with high level of information influence and diffusion to enhance the outcome of online word-of-mouth.

• Nuclear Engineering and Technology
• /
• v.55 no.11
• /
• pp.3983-3995
• /
• 2023

In fast reactors, restructuring of the fuel micro-structure driven by high temperature and high temperature gradient can cause the formation of columnar grains. The non-spheroidal shape and the non-uniform temperature field in such columnar grains implies that standard models for fission gas diffusion can not be applied. To tackle this issue, we present a reduced order model for the fission gas diffusion process which is applicable in different geometries and with non-uniform temperature fields, maintaining a computational requirement in line with its application in fuel performance codes. This innovative application of reduced order models as meso-scale tools within fuel performance codes represents a first-of-a-kind achievement that can be extended beyond fission gas behaviour.

• Proceedings of the KSME Conference
• /
• 2001.11b
• /
• pp.112-117
• /
• 2001

An experiment using high preheated and swirled air in the coaxial diffusion flame burner was carried out in order to decrease NOx emission and improve the thermal efficiency. $N_2$ gas was used for diluent and propane was utilized for fuel. Combustion using high preheated air has two remarkable characteristics ; (1) low NOx emission with increasing dilution level, (2) high thermal efficiency in the furnace. Also, swirled air can mix fuel and oxidizer well in condition of diffusion flme and maintain the stable combustion. The color of flame changes from yellow to blue green according to increasing the dilution level of mixture gas. NO emission decreased with increasing dilution level and the swirl number.