• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.51-62
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• 2021

Variational method has played an important role in solving problems of uniqueness and existence of the nonlinear works as well as analysis. It will also be extremely useful for researchers in all branches of natural sciences and engineers working with non-linear equations economy, optimization, game theory and medicine. Recently, the existence of infinitely many weak solutions for some non-local problems of Kirchhoff type with Dirichlet boundary condition are studied [14]. Here, a suitable method is presented to treat the elliptic partial derivative equations, especially (p(x), q(x))-Laplacian-like systems. This kind of equations are used in the study of fluid flow, diffusive transport akin to diffusion, rheology, probability, electrical networks, etc. Here, the existence of infinitely many weak solutions for some boundary value problems involving the (p(x), q(x))-Laplacian-like operators is proved. The method is based on variational methods and critical point theory.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.1
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• pp.1-15
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• 2021

In the recent papers, S'anchez-Reyes [Appl. Math. Model. 40 (2016), 1676-1682] described the method for finding a minimal surface through a geodesic, and Li et al. [Appl. Math. Model. 37 (2013), 6415-6424] studied the approximation of minimal surfaces with a geodesic from Dirichlet function. In the present article, we consider an isoparametric surface generated by Frenet frame of a curve introduced by Wang et al. [Comput. Aided Des. 36 (2004), 447-459], and give the necessary and sufficient condition to satisfy both geodesic of the curve and minimality of the surface. From this, we construct minimal surfaces in terms of constant curvature and torsion of the curve. As a result, we present a new approach for constructions of the minimal surfaces from a prescribed closed geodesic and unclosed geodesic, and show some new examples of minimal surfaces with a circle and a helix as a geodesic. Our approach can be used in design of minimal surfaces from geodesics.

• Honam Mathematical Journal
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• v.44 no.2
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• pp.281-295
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• 2022

This paper deals with the long - time behavior of global bounded solutions for a non-autonomous dispersive-dissipative equation with time-dependent nonlinear damping terms under the null Dirichlet boundary condition. By a new Lyapunov functional and Łojasiewicz-Simon inequality, we show that any global bounded solution converges to a steady state and get the rate of convergence as well, which depends on the decay of the non-autonomous term g(x, t), when damping coefficients are integral positive and positive-negative, respectively.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.679-689
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• 2022

In this paper, we establish sufficient conditions for the existence and uniqueness of solution for a class of initial boundary value problems with Dirichlet condition in regard to a category of fractional-order partial differential equations. The results are established by a method based on the theorem of Lax Milligram.

• Journal of the Korea Computer Graphics Society
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• v.20 no.4
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• pp.9-16
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• 2014

This paper proposes a novel method that couples fluid and deformation/fracture. Our method considers two interaction types: fluid-object interaction and fluid-fluid interaction. In fluid-fluid interaction, we simulate water and smoke separately and blend their velocities in the intersecting region depend on their densities. Our method separates projection process into two steps for each of water and smoke. This reduces the number of grid cells required for projection in order to optimize the number of iterations for convergence and improve stability of the simulation. In water projection step, smoke region regarded as the cells with Dirichlet boundary condition. The smoke projection step solves water region with Neumann boundary condition. To take care of fluid-object interaction, we make use of the fluid pressure to update velocities of the each of the mass points so that the object can deform or fracture. Although our method doesn't provide physically accurate results, the various examples show that our method generate appealing visuals with good performance.

• Journal of Intelligence and Information Systems
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• v.25 no.1
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• pp.21-41
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• 2019

Thanks to the rapid development of information technologies, the data available on Internet have grown rapidly. In this era of big data, many studies have attempted to offer insights and express the effects of data analysis. In the tourism and hospitality industry, many firms and studies in the era of big data have paid attention to online reviews on social media because of their large influence over customers. As tourism is an information-intensive industry, the effect of these information networks on social media platforms is more remarkable compared to any other types of media. However, there are some limitations to the improvements in service quality that can be made based on opinions on social media platforms. Users on social media platforms represent their opinions as text, images, and so on. Raw data sets from these reviews are unstructured. Moreover, these data sets are too big to extract new information and hidden knowledge by human competences. To use them for business intelligence and analytics applications, proper big data techniques like Natural Language Processing and data mining techniques are needed. This study suggests an analytical approach to directly yield insights from these reviews to improve the service quality of hotels. Our proposed approach consists of topic mining to extract topics contained in the reviews and the decision tree modeling to explain the relationship between topics and ratings. Topic mining refers to a method for finding a group of words from a collection of documents that represents a document. Among several topic mining methods, we adopted the Latent Dirichlet Allocation algorithm, which is considered as the most universal algorithm. However, LDA is not enough to find insights that can improve service quality because it cannot find the relationship between topics and ratings. To overcome this limitation, we also use the Classification and Regression Tree method, which is a kind of decision tree technique. Through the CART method, we can find what topics are related to positive or negative ratings of a hotel and visualize the results. Therefore, this study aims to investigate the representation of an analytical approach for the improvement of hotel service quality from unstructured review data sets. Through experiments for four hotels in Hong Kong, we can find the strengths and weaknesses of services for each hotel and suggest improvements to aid in customer satisfaction. Especially from positive reviews, we find what these hotels should maintain for service quality. For example, compared with the other hotels, a hotel has a good location and room condition which are extracted from positive reviews for it. In contrast, we also find what they should modify in their services from negative reviews. For example, a hotel should improve room condition related to soundproof. These results mean that our approach is useful in finding some insights for the service quality of hotels. That is, from the enormous size of review data, our approach can provide practical suggestions for hotel managers to improve their service quality. In the past, studies for improving service quality relied on surveys or interviews of customers. However, these methods are often costly and time consuming and the results may be biased by biased sampling or untrustworthy answers. The proposed approach directly obtains honest feedback from customers' online reviews and draws some insights through a type of big data analysis. So it will be a more useful tool to overcome the limitations of surveys or interviews. Moreover, our approach easily obtains the service quality information of other hotels or services in the tourism industry because it needs only open online reviews and ratings as input data. Furthermore, the performance of our approach will be better if other structured and unstructured data sources are added.