• Title/Summary/Keyword: mathematical competition

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RELATIVISTIC INTERPLAY BETWEEN ADAPTIVE MOVEMENT AND MOBILITY ON BIODIVERSITY IN THE ROCK-PAPER-SCISSORS GAME

  • PARK, JUNPYO;JANG, BONGSOO
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.24 no.4
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    • pp.351-362
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    • 2020
  • Adaptive behaviors are one of ubiquitous features in evolutionary dynamics of populations, and certain adaptive behaviors can be witnessed by individuals' movements which are generally affected by local environments. In this paper, by revisiting the previous work, we investigate the sensitivity of species coexistence in the system of cyclic competition where species movement can be affected by local environments. By measuring the extinction probability through Monte-Carlo simulations, we find the relativistic effect of weights of local fitness and exchange rate for adaptive movement on species biodiversity which promotes species coexistence as the relativistic effect is intensified. In addition, by means of basins of initial conditions, we also found that adaptive movement can also affect species biodiversity with respect to the choice of initial conditions. The strong adaptive movement can eventually lead the coexistence as a globally stable state in the spatially extended system regardless of mobility.

Mathematical Models of Competitive Adsorption of Inorganic Anions in Soils

  • Lee, Kyo Suk;Lee, Dong Sung;Lee, Jae Bong;Joo, Rhee Na;Lee, Myong Yun;Chung, Doug Young
    • Korean Journal of Soil Science and Fertilizer
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    • v.48 no.6
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    • pp.666-670
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    • 2015
  • Competition among anion species in solution for same sorption sites and soil surface can be of major significance in determining the effective mobility of any potentially adsorbing species. Major soil anion species include $OH^-$, $F^-$, $Cl^-$, $HCO_3{^-}$, $CO_3{^-}$, $NO_3{^-}$, $SO_4{^{2-}}$, and $PO_4{^{3-}}$. And some micro nutrients such as boron and molybdenum exist as $H_2BO_3{^-}$ and $MoO_4{^{2-}}$, as do some heavy metals such as chrome and arsenic as $CrO_4{^{2-}}$ and $HAsO_4{^{2-}}$. Pesticides such as 2,4,5-T and 2,4-D also exist as anions. Many anion species are retained by more complex mechanisms than the simple electrostatic attractions involved in most cation adsorption reactions. In binary system composed of two anions, the adsorption of one anion is influenced by the other anion due to the competition for the available and limited binding sites in soil constituents. The specifically adsorbed anions may compete more effectively for sorption sites than that of nonspecifically adsorbed anion. In this study, we aim to evaluate the mathematical models to determine the magnitude of concentration variations in adsorption due to competitive interactions between anions introduced to a system in binary mixtures.

An Theoretical Approaches to the Phenomenon of Private Education using the Game Theory (게임 이론을 이용한 사교육 현상에 대한 이론적 접근)

  • Roh, Eun Hwan;Kang, Jeong Gi;Roh, Moon Ghi
    • Journal of the Korean School Mathematics Society
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    • v.16 no.4
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    • pp.771-796
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    • 2013
  • The purpose of the study is to analyze the phenomenon of private education and to get the countermeasures of it. To do this, we approached the phenomenon of private education from the game theory, which is famous in economics. As result, we could make the mathematical model. One is a model consisted of two-person. This is a mathematical model simplifying the competition within the school. The problem of private education can be solved by the disconnection with private education and exam of school in this model. The other is a model consisted of three-person. This is a mathematical model simplifying the interscholastic competition. The problem of private education can not only be solved by the disconnection with private education and exam of school, but can be also solved by the specificity of school education in this model. We will hope that our study can give an aid in deciding an educational policy.

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The Impact of the Internet Channel Introduction Depending on the Ownership of the Internet Channel (도입주체에 따른 인터넷경로의 도입효과)

  • Yoo, Weon-Sang
    • Journal of Global Scholars of Marketing Science
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    • v.19 no.1
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    • pp.37-46
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    • 2009
  • The Census Bureau of the Department of Commerce announced in May 2008 that U.S. retail e-commerce sales for 2006 reached $ 107 billion, up from $ 87 billion in 2005 - an increase of 22 percent. From 2001 to 2006, retail e-sales increased at an average annual growth rate of 25.4 percent. The explosive growth of E-Commerce has caused profound changes in marketing channel relationships and structures in many industries. Despite the great potential implications for both academicians and practitioners, there still exists a great deal of uncertainty about the impact of the Internet channel introduction on distribution channel management. The purpose of this study is to investigate how the ownership of the new Internet channel affects the existing channel members and consumers. To explore the above research questions, this study conducts well-controlled mathematical experiments to isolate the impact of the Internet channel by comparing before and after the Internet channel entry. The model consists of a monopolist manufacturer selling its product through a channel system including one independent physical store before the entry of an Internet store. The addition of the Internet store to this channel system results in a mixed channel comprised of two different types of channels. The new Internet store can be launched by the independent physical store such as Bestbuy. In this case, the physical retailer coordinates the two types of stores to maximize the joint profits from the two stores. The Internet store also can be introduced by an independent Internet retailer such as Amazon. In this case, a retail level competition occurs between the two types of stores. Although the manufacturer sells only one product, consumers view each product-outlet pair as a unique offering. Thus, the introduction of the Internet channel provides two product offerings for consumers. The channel structures analyzed in this study are illustrated in Fig.1. It is assumed that the manufacturer plays as a Stackelberg leader maximizing its own profits with the foresight of the independent retailer's optimal responses as typically assumed in previous analytical channel studies. As a Stackelberg follower, the independent physical retailer or independent Internet retailer maximizes its own profits, conditional on the manufacturer's wholesale price. The price competition between two the independent retailers is assumed to be a Bertrand Nash game. For simplicity, the marginal cost is set at zero, as typically assumed in this type of study. In order to explore the research questions above, this study develops a game theoretic model that possesses the following three key characteristics. First, the model explicitly captures the fact that an Internet channel and a physical store exist in two independent dimensions (one in physical space and the other in cyber space). This enables this model to demonstrate that the effect of adding an Internet store is different from that of adding another physical store. Second, the model reflects the fact that consumers are heterogeneous in their preferences for using a physical store and for using an Internet channel. Third, the model captures the vertical strategic interactions between an upstream manufacturer and a downstream retailer, making it possible to analyze the channel structure issues discussed in this paper. Although numerous previous models capture this vertical dimension of marketing channels, none simultaneously incorporates the three characteristics reflected in this model. The analysis results are summarized in Table 1. When the new Internet channel is introduced by the existing physical retailer and the retailer coordinates both types of stores to maximize the joint profits from the both stores, retail prices increase due to a combination of the coordination of the retail prices and the wider market coverage. The quantity sold does not significantly increase despite the wider market coverage, because the excessively high retail prices alleviate the market coverage effect to a degree. Interestingly, the coordinated total retail profits are lower than the combined retail profits of two competing independent retailers. This implies that when a physical retailer opens an Internet channel, the retailers could be better off managing the two channels separately rather than coordinating them, unless they have the foresight of the manufacturer's pricing behavior. It is also found that the introduction of an Internet channel affects the power balance of the channel. The retail competition is strong when an independent Internet store joins a channel with an independent physical retailer. This implies that each retailer in this structure has weak channel power. Due to intense retail competition, the manufacturer uses its channel power to increase its wholesale price to extract more profits from the total channel profit. However, the retailers cannot increase retail prices accordingly because of the intense retail level competition, leading to lower channel power. In this case, consumer welfare increases due to the wider market coverage and lower retail prices caused by the retail competition. The model employed for this study is not designed to capture all the characteristics of the Internet channel. The theoretical model in this study can also be applied for any stores that are not geographically constrained such as TV home shopping or catalog sales via mail. The reasons the model in this study is names as "Internet" are as follows: first, the most representative example of the stores that are not geographically constrained is the Internet. Second, catalog sales usually determine the target markets using the pre-specified mailing lists. In this aspect, the model used in this study is closer to the Internet than catalog sales. However, it would be a desirable future research direction to mathematically and theoretically distinguish the core differences among the stores that are not geographically constrained. The model is simplified by a set of assumptions to obtain mathematical traceability. First, this study assumes the price is the only strategic tool for competition. In the real world, however, various marketing variables can be used for competition. Therefore, a more realistic model can be designed if a model incorporates other various marketing variables such as service levels or operation costs. Second, this study assumes the market with one monopoly manufacturer. Therefore, the results from this study should be carefully interpreted considering this limitation. Future research could extend this limitation by introducing manufacturer level competition. Finally, some of the results are drawn from the assumption that the monopoly manufacturer is the Stackelberg leader. Although this is a standard assumption among game theoretic studies of this kind, we could gain deeper understanding and generalize our findings beyond this assumption if the model is analyzed by different game rules.

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The Effects of Mastery Learning and Cooperative, Competitive and Individualistic Learning Environment Organizations on Achievement and Attitudes in Mathematics

  • Guzver Yildiran;Emin Aydin
    • Research in Mathematical Education
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    • v.9 no.1 s.21
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    • pp.69-96
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    • 2005
  • Motivation for learning is important for positive learning outcomes as well as for measured achievement levels. When students come to our classes, they bring with them learning histories in which we as individual teachers, most likely, did not have an input. Our students do not only bring with them different levels of prerequisite leanings but also different levels of affect for what they will be learning. If we leave their final learning at the mercy of these entry characteristics, a test given the first day before the course will have almost isomorphic results with their achievement levels on the last day. The ones who had 'it' on the first day will be the ones who in the future will also have 'it', not too different from what the present situation is all over the world. These circumstances will tend to be the case ad infinitum, unless of course, we want to change the situation. This research clearly shows that effective instructional methodologies coupled with cooperative peer interactions not only have an impact on achievement but also on positive attitudes toward one's learning.

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An Investigation of the Selection Process of Mathematically Gifted Students

  • Lee, Kyung-Hwa;Park, Kyung-Mee;Yim, Jae-Hoon
    • Research in Mathematical Education
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    • v.7 no.3
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    • pp.139-150
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    • 2003
  • The purpose of this paper is to review the gifted education from a reflective perspective. Especially, this research touches upon the issues of selection process from a critical point of view. Most of the problems presented in the mathematics competition or in the programs for preparing such competitions share the similar characteristic: the circumstances that are given for questions are too artificial and complicated; problem solving processes are superficially and fragmentally related to mathematical knowledge; and the previous experience with the problem very much decides whether a student can solve the problem and the speed of problem solving. In contrast, the problems for selecting students for Gifted Education Center clearly show what the related mathematical knowledge is and what kind of mathematical thinking ability these problems intend to assess. Accordingly, the process of solving these problems can be considered an important criterion of a student's mathematical ability. In addition, these kinds of problems can encourage students to keep further interest, and can be used as tasks for mathematical investigation later. We hope that this paper will initiate further discussions on issues derived from the mathematically gifted student selection process.

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A Study of Job Shop Scheduling for Minimizing Tardiness with Alternative Machines (대체기계가 존재하는 Job Shop 일정계획 환경에서 납기지연을 최소화하는 방법에 관한 연구)

  • Kim, Ki-Dong;Kim, Jae-Hong
    • Journal of Industrial Technology
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    • v.28 no.A
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    • pp.51-61
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    • 2008
  • In these days, domestic manufacturers are faced with managerial difficulties such as the increasing competition in their industry and the increasing power of customers. In this situation, they have to satisfy their customers with high quality of their products and meeting due date of their orders. Production of the order within due date is an important factor for improving enterprise competitiveness. The causes of occurrence of tardiness may be wrong product scheduling, unexpected events in field and so on, a way to minimize tardiness is use of alternative machines, overwork, outsourcing and etc.. In this study, we deal with a scheduling problem that can minimize tardiness using alternative machines. This paper provides a mathematical program and a heuristic method for job shop scheduling for minimizing tardiness with alternative machines. And a proposed heuristic method is verified comparing with optimal solution obtained by ILOG CPLEX.

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Development of The New Shape Control Algorithm with The Strip Thickness Decoupling in Hot Strip Mill

  • Dukbum Shin;Kim, Jongcheol;Sangchul Won
    • 제어로봇시스템학회:학술대회논문집
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    • 2001.10a
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    • pp.175.2-175
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    • 2001
  • The strip profile and shape control is one of the most important technologies in Hot Rolling Mill System. Because the unbalance of strip´s shape and wave appearance between stands has a bad effect on Hot Rolling Mill System by making the inferior thickness, strip´s damage and so forth in factories. Many competition Plate Mill introduced shape control system, for example, pair cross-mill, work roll bender, which includes shape measuring instruments and shape control mathematical models. Shape meter, which is equipped for flatness, only does feedback control at the top of coil. And, for crown, we depend on initial setup value and there is no feedback control. Therefore we predict the shape of strip using rolling pressure, bender force and tension of inter-stand in ...

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Prediction for Rolling Force in Hot-rolling Mill Using On-line learning Neural Network (On-line 학습 신경회로망을 이용한 열간 압연하중 예측)

  • Son Joon-Sik;Lee Duk-Man;Kim Ill-Soo;Choi Seung-Gap
    • Transactions of the Korean Society of Machine Tool Engineers
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    • v.14 no.1
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    • pp.52-57
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    • 2005
  • In the foe of global competition, the requirements for the continuously increasing productivity, flexibility and quality(dimensional accuracy, mechanical properties and surface properties) have imposed a mai or change on steel manufacturing industries. Indeed, one of the keys to achieve this goal is the automation of the steel-making process using AI(Artificial Intelligence) techniques. The automation of hot rolling process requires the developments of several mathematical models for simulation and quantitative description of the industrial operations involved. In this paper, an on-line training neural network for both long-term teaming and short-term teaming was developed in order to improve the prediction of rolling force in hot rolling mill. This analysis shows that the predicted rolling force is very closed to the actual rolling force, and the thickness error of the strip is considerably reduced.

Analysis on learning curves of end-use appliances for the establishment of price-sensitivity load model in competitive electricity market (전력산업 경쟁 환경에서의 요금부하모델 수립을 위한 부하기기의 학습곡선 분석)

  • Hwang, Sung-Wook;Kim, Jung-Hoon;Song, Kyung-Bin;Choi, Joon-Young
    • Proceedings of the KIEE Conference
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    • 2001.07a
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    • pp.386-388
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    • 2001
  • The change of the electricity charge from cost base to price base due to the introduction of the electricity market competition causes consumer to choose a variety of charge schemes and a portion of loads to be affected by this change. Besides, it is required the index that consolidate the price volatility experienced on the power exchange with gaming and strategic bidding by suppliers to increase profits. Therefore, in order to find a mathematical model of the sensitively-responding-to-price loads, the price-sensitive load model is needed. And the development of state-of-the-art technologies affects the electricity price, so the diffusion of high-efficient end-uses and these price affect load patterns. This paper shows the analysis on learning curves algorithms which is used to investigate the correlation of the end-uses' price and load patterns.

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