• The Pure and Applied Mathematics
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• v.22 no.1
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• pp.75-90
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• 2015

In this paper the existence of global solutions of the parabolic cross-diffusion systems with cooperative reactions is obtained under certain conditions. The uniform boundedness of $W_{1,2}$ norms of the local maximal solution is obtained by using interpolation inequalities and comparison results on differential inequalities.

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.211-227
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• 2008

As a mathematical model proposed to understand the behaviors of interacting species, cross-diffusion systems with functional responses of prey-predator type are considered. In order to obtain $W^{1_2}$-estimates of the solutions, we make use of several forms of calculus inequalities and embedding theorems. We consider the quasilinear parabolic systems with the cross-diffusion terms, and without the self-diffusion terms because of the simplicity of computations. As the main result we derive the uniform $W^{1_2}$-bound of the solutions and obtain the global existence in time.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.2
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• pp.129-138
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• 2013

A spatio-temporal models as systems of ODE which describe two-species Beddington - DeAngelis type predator-prey system living in a habitat of two identical patches linked by migration is investigated. It is assumed in the model that the per capita migration rate of each species is influenced not only by its own but also by the other one's density, i.e. there is cross diffusion present. We show that a standard (self-diffusion) system may be either stable or unstable, a cross-diffusion response can stabilize an unstable standard system and destabilize a stable standard system. For the diffusively stable model, numerical studies show that at a critical value of the bifurcation parameter the system undergoes a Turing bifurcation and the cross migration response is an important factor that should not be ignored when pattern emerges.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.2
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• pp.1064-1079
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• 2019

Information security has become increasingly important with the rapid development of mobile devices and internet. An efficient encryption system is a key to this end. In this paper, we propose an image encryption method based on the cross diffusion of two chaotic maps. We use two chaotic sequences, namely the Logistic map and the Chebyshev map, for key generation which has larger security key space than single one. Moreover, we use these two sequences for further image encryption diffusion which decreases the correlation of neighboring pixels significantly. We conduct extensive experiments on several well-known images like Lena, Baboon, Koala, etc. Experimental results show that our algorithm has the characteristics of large key space, fast, robust to statistic attack, etc.

• Computers and Concrete
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• v.4 no.2
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• pp.157-166
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• 2007

The paper considers a theoretical model to study sulfate ion diffusion in saturated porous media - cement based mineral composites, accounting for simultaneous effects, such as filling micro-capillaries (pores) with ions and chemical products and liquid push out of them. Pore volume change and its effect on the distribution of ion concentration within the specimen are investigated. Relations for the distribution of the capillary relative radius and volume within the composite under consideration are found. The numerical algorithm used is further completed to consider capillary size change and the effects accompanying sulfate ion diffusion. Ion distribution within the cross section and volume of specimens fabricated from mineral composites is numerically studied, accounting for the change of material capillary size and volume. Characteristic cases of 2D and 3D diffusion are analyzed. The results found can be used to both assess the sulfate corrosion in saturated systems and predict changes occurring in the pore structure of the composite as a result of sulfate ion diffusion.

• Journal of KSNVE
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• v.10 no.3
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• pp.430-436
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• 2000

The cross-flow fans have been widely used to constitute the air moving systems in many air-ventilating and air-conditioning units. The cross-flow fan system has many design parameters which have crucial influence on the performance and the noise characteristics of the units. As a result there are many difficulties in the design stage of the system and the general design guide has not been sufficiently established yet. This study presents the experimental results of the parametric investigation of some chosen design parameters which are directly related to the shape of the stabilizer the profile of the scroll casing and the diffusion angle of the flow exit. The results are expressed in terms of the fan performance and the specific sound pressure level characteristics. Some parameters have been found to have crucial effects on the system performance/noise characteristics and should be considered with care in the design stage.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.5C
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• pp.542-549
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• 2007

Recently, many research activities in the image processing area are concentrated on developing new algorithms by finding the solution of the 'diffusion equation'. The diffusion algorithms are expected to be utilized in numerous applications including noise removal and image restoration, edge detection, segmentation, etc. In this paper, at first, it will be shown that the anisotropic diffusion algorithms have the similar structure with the adaptive FIR filters with cross-shaped 5-tap kernel, and this relatively small-sized kernel causes many iterating procedure for satisfactory filtering effects. Moreover, it will also be shown that lots of modifications which are adopted to the conventional Gaussian diffusion method in order to weaken the edge blurring nature of the linear filtering process increases another computational burden. We propose a new Median diffusion scheme by replacing the adaptive linear filters in the diffusion process with the AWM (Adaptive Weighted Median) filters. A diffusion-equation-based adaptation scheme is also proposed. With the proposed scheme, the size of the diffusion kernel can be increased, and thus diffusion speed greatly increases. Simulation results shows that the proposed Median diffusion scheme outperforms in noise removal (especially impulsive noise), and edge preservation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.1416-1422
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• 2000

The cross-flow fans have been widely used to constitute the air moving systems in many air-ventilating and air-conditioning devices. The cross-flow fan system has many design parameters which have crucial influence on the performance and the noise characteristics of the devices. As a result, there are many difficulties in the design stage of the devices and the general design guide has not been sufficiently established yet. This study presents the experimental results of the parametric investigation of some chosen design parameters, which are the shape of the stabilizer, the profile of the scroll casing, and the diffusion angle of the flow exit. The results are expressed as the fan performance and the specific sound pressure level characteristic. These parts have been found to have crucial effects on the system performance/noise characteristics and should be considered with care in the design stage.

• Cross-Cultural Studies
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• v.37
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• pp.7-29
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• 2014

The 'discovery' or 'conquest' of the New World in 1492 was the starting point of world history that irrevocably changed the fate of the Latin American continent. The global stream known as 'Columbian Exchange', which was the widespread inter-continental contacts, inter-civilizational conflicts, or bilateral communication, has rendered multifarious effects throughout many historical periods up to the very contemporary time. The propagation of Catholicism initiated along with this 'discovery' transformed Latin America of nowadays in the region that has the biggest Catholic population in the world. The previous studies in Korea regarding Latin American Catholicism has focused on the spread of Catholicism in relation to the European colonization, rather than analyzing the concrete and detailed ways in which Catholicism exerted tremendous influences in the whole continent. They were less attentive to various historical contexts in which the diffusion of Catholicism differed greatly according to cultural landscapes and political specificities. Thus, this essay attempts to examine the diffusion of Catholicism from the perspective of confrontation between royal authorities and the power of church. The essay points out that the royal communities and institutional authorities which facilitated the intial process of Catholic evangelization maintained antagonistic relationship with ecclesial powers. By delving into the gradual transformation of church systems, it reveals that Catholicism in Latin America became a major field for conquerors in power to attain economic and political dominance. And unlike the initial submission and hospitality, the religious convert of the indigenous people attested to the violent inhumanity and opposition. Therefore, the essay aims to pave a clearer way to the understanding of complicated dynamics and conflicts between Catholicism in Latin America and the establishment of Spanish colonization.

• Korean Journal of Materials Research
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• v.12 no.4
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• pp.254-258
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• 2002

To realize channel cross-connecting in optical communications systems, a high speed optical matrix switch was fabricated using z-cut $LiNbO_3$. For switch fabrication was design bending structure and coupling length and four $2{\times}2$ directional couplers were integrated on one substrate far construction of a $4{\times}4$ switch. Single-mode optical waveguides were formed by Ti-diffusion at a wet $O_2$ atmosphere. Ti-diffusion profile, refractive index variation and waveguide morphology were analyzed by Prism coupler and optical microscopy, respectively.