• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.1039-1048
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• 2018

In this paper we study the dynamics of a general ${\omega}-periodic$ model. Necessary and sufficient conditions for the global stability of zero steady state of the model are given. The conditions under which there exists a unique periodic solutions to the model are determined. We also show that the unique periodic solution is the global attractor of all other positive solutions. Some applications to mathematical models for cancer and tumor growth are given.

• East Asian mathematical journal
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• v.35 no.2
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• pp.217-237
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• 2019

This Modeling is a cyclical process of creating and modifying models of empirical situations to understand them better and improve decisions. The role of modeling and teaching mathematical modeling in school mathematics has received increasing attention as generating authentic learning and revealing the ways of thinking that produced it. In this paper and interactive lecture session, we will review a subset of the related literature, discuss benefits and challenges in teaching and learning mathematical modeling, and share our attempts to improve traditional textbook problems so that they can become more authentic modeling activities and implications for instruction and assessment as well as for research.

• Journal for History of Mathematics
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• v.22 no.3
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• pp.31-44
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• 2009

Anyone wishing to understand cognitive science, a converging science, need to become familiar with three major mathematical landmarks: Turing machines, Neural networks, and $G\ddot{o}del's$ incompleteness theorems. The present paper aims to explore the mathematical foundations of cognitive science, focusing especially on these historical landmarks. We begin by considering cognitive science as a metamathematics. The following parts addresses two mathematical models for cognitive systems; Turing machines as the computer system and Neural networks as the brain system. The last part investigates $G\ddot{o}del's$ achievements in cognitive science and its implications for the future of cognitive science.

• Asian Pacific Journal of Cancer Prevention
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• v.14 no.10
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• pp.6151-6158
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• 2013

Radio frequency ablation (RFA) is an effective means of achieving local control of liver cancer. It is a particularly suitable mode of therapy for small and favorably located tumors. However, local progression rates are substantially higher for large tumors (>3.0 cm). In the current study, we report on a mathematical model based on geometric optimization to treat large liver tumors. A database of mathematical models relevant to the configuration of liver cancer was also established. The specific placement of electrodes and the frequency of ablation were also optimized. In addition, three types of liver cancer lesion were simulated by computer guidance incorporating mathematical models. This approach can be expected to provide a more effective and rationale mechanism for employing RFA in the therapy of hepatic carcinoma.

• Education of Primary School Mathematics
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• v.5 no.2
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• pp.71-94
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• 2001

The purposes of this study were to design small group collaborative learning models for developing the creativity and to analyze the effects on applying the models in mathematics teaching and loaming. The meaning of open education in mathematics learning, the relation of creativity and inquiry learning, the relation of small group collaborative learning and creativity, and the relation of assessment and creativity were reviewed. And to investigate the relation small group collaborative learning and creativity, we developed three types of small group collaborative learning model- inquiry model, situation model, tradition model, and then conducted in elementary school and middle school. As a conclusion, this study suggested; (1) Small group collaborative learning can be conducted when the teacher understands the small group collaborative learning practice in the mathematics classroom and have desirable belief about mathematics instruction. (2) Students' mathematical anxiety can be reduced and students' involvement in mathematics learning can be facilitated, when mathematical tasks are provided through inquiry model and situation model. (3) Students' mathematical creativity can be enhanced when the teacher make classroom culture that students' thinking is valued and teacher's authority is reduced. (4) To develop students' mathematical creativity, the interaction between students in small group should be encouraged, and assessment of creativity development should be conduced systematically and continuously.

• Journal of Welding and Joining
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• v.32 no.1
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• pp.53-60
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• 2014

The automatic arc welding is generally accepted as the preferred joining technique and commonly chosen for assembly of large metal structures such as in areas of automotive, aircraft and shipbuilding due to its joint strength, reliability, and low cost compared to other joint processes. Recently, several mathematical models have been developed and studied for control and monitoring welding quality, productivity, microstructure and weld properties in arc welding processes. This study indicates the prediction of process parameters for the expected welding quality with accordance to the adaptive GTA welding process. Furthermore, the mathematical models is also develop to aid the selection of an optimal welding process as the generation of process controls to predict the bead geometry as a function output parameters in the GTA welding process. The developed models through this study showed comparatively excellent predicted results, and will extend to other welding processes to integrate an optimized system for the robotic welding process.

• Computers and Concrete
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• v.4 no.1
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• pp.1-18
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• 2007

Over the past decades, an enormous amount of effort has been expended in laboratory and field studies on concrete durability estimation. The results of this research are still either widely scattered in the journal literature or mentioned briefly in the standard textbooks. Moreover, the theoretical approaches of deterioration mechanisms with a predictive character are limited to some complicated mathematical models not widespread in practice. A significant step forward could be the development of appropriate software for computer-based estimation of concrete service life, including reliable mathematical models and adequate experimental data. In the present work, the basis for the development of a computer estimation of the concrete service life is presented. After the definition of concrete mix design and structure characteristics, as well as the consideration regarding the environmental conditions where the structure will be found, the concrete service life can be reliably predicted using fundamental mathematical models that simulate the deterioration mechanisms. The prediction is focused on the basic deterioration phenomena of reinforced concrete, such as carbonation and chloride penetration, that initiate the reinforcing bars corrosion. Aspects on concrete strength and the production cost are also considered. Field observations and data collection from existing structures are compared with predictions of service life using the above model. A first attempt to develop a database of service lives of different types of reinforced concrete structure exposed to varying environments is finally included.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.779-794
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• 2012

In this paper, we study the global stability of two mathematical models for human immunodeficiency virus (HIV) infection with intra-cellular delays. The first model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells, $CD4^+$ T cells and macrophages taking into account the saturation infection rate. The second model generalizes the first one by assuming that the infection rate is given by Beddington-DeAngelis functional response. Two time delays are used to describe the time periods between viral entry the two classes of target cells and the production of new virus particles. Lyapunov functionals are constructed and LaSalle-type theorem for delay differential equation is used to establish the global asymptotic stability of the uninfected and infected steady states of the HIV infection models. We have proven that if the basic reproduction number $R_0$ is less than unity, then the uninfected steady state is globally asymptotically stable, and if the infected steady state exists, then it is globally asymptotically stable for all time delays.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.12
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• pp.4275-4291
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• 2021

With the unprecedented growth of textual information on the Internet, an efficient automatic summarization system has become an urgent need. Recently, the neural network models based on the encoder-decoder with an attention mechanism have demonstrated powerful capabilities in the sentence summarization task. However, for paragraphs or longer document summarization, these models fail to mine the core information in the input text, which leads to information loss and repetitions. In this paper, we propose an abstractive document summarization method by applying guidance signals of key sentences to the encoder based on the hierarchical encoder-decoder architecture, denoted as KI-HABS. Specifically, we first train an extractor to extract key sentences in the input document by the hierarchical bidirectional GRU. Then, we encode the key sentences to the key information representation in the sentence level. Finally, we adopt key information representation guided selective encoding strategies to filter source information, which establishes a connection between the key sentences and the document. We use the CNN/Daily Mail and Gigaword datasets to evaluate our model. The experimental results demonstrate that our method generates more informative and concise summaries, achieving better performance than the competitive models.

• IE interfaces
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• v.21 no.1
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• pp.1-7
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• 2008

In this paper we study the Minimum Edge Addition Problem(MEAP) to decrease the diameter of a graph. MEAP can be used for improving the serviceability of telecommunication networks with a minimum investment. MEAP is an NP-hard optimization problem. We present two mathematical programming models : One is a multi-commodity flow formulation and the other is a path partition formulation. We propose a branch-and-price algorithm to solve the path partition formulation to the optimality. We develop a polynomial time column generation sub-routine conserving the mathematical structure of a sub problem for the path partition formulation. Computational experiments show that the path partition formulation is better than the multi-commodity flow formulation. The branch-and-price algorithm can find the optimal solutions for the immediate size graphs within reasonable time.