• Journal of the Korean Data and Information Science Society
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• v.20 no.1
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• pp.211-217
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• 2009

In this paper, we are studying the property for permanence of a three species food chain system with impulsive perturbations and Holling type II functional response, species which is important concept or property in ecological systems. Specially, we give the conditions for the permanence of this system. To do it, we consider the comparison method which is typical skill happened in impulsive differential inequalities. In addition, we reaffirm our results by using a numerical example.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.955-967
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• 2011

In this paper we have considered a nonautonomous predator-prey model with discrete time delay due to gestation, in which there are two prey habitats linked by isotropic migration. One prey habitat contains a predator and the other (a refuge) does not. Here, we have established some sufficient conditions on the permanence of the system by using in-equality analytical technique. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. We have observed that the per capita migration rate among two prey habitats and the time delay has no effect on the permanence of the system but it has an effect on the global asymptotic stability of this model. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness.

• Journal for History of Mathematics
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• v.16 no.1
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• pp.25-44
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• 2003

In this paper, we deal with the ‘dearithmetization’ of algebra. Historically, the origin of algebra comes from arithmetic. Also school algebra is related to arithmetic in general. However, we have many difficulties in teaching school algebra, and there is many problems for students to learn algebra from elementary arithmetic knowledges. This paper supposed that the solution of these problem may be founded in the ‘dearithmetization’ of algebra. And we supposed that the ‘dearithmetization’ of algebra may be developed by three historical achievements - the completion of symbolic algebra, the principle of permanence of form, and the expansion of number concepts. In order to justify these supposition, we investigate Peacock's ideas, i.e. ‘symbolic algebra’, ‘the principle of permanence of form’, and consider how the integer is introduced in modern mathematics. And we analyze various textbooks, and investigate the ‘dearithmetization’ of school algebra which has been progressed in the three fields - symbolic algebra, the principle of permanence of form, and the expansion of number concepts.

• Korean Journal of Child Studies
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• v.2
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• pp.1-16
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• 1981

This study had two purposes. First, to examine the stages and developmental order of object permanence based on Piaget's theory. Second, to assess the effects of delay, attentiveness, and direction of gaze. Two experiments were conducted to examine the object permanence development in infants. The subjects for the 2 experiments were randomly drawn from a well-baby clinic. The subjects for Experiment 1 were 72 infants, 12 each in 6 age levels : 6, 9, 12, 15, 18, and 21 months old. Experiment 1 was designed to examine the stages and developmental order of object concept development, ana infants received 5 tasks as follows : (1) finding an object partially hidden under one box (2) finding an object completely hidden under one box (3) finding an object after successive visible displacements (4) finding an object after one invisible displacement (5) finding an object after successive invisible displacements. The subjects for Experiment 2 were 24 9-month-olds. Experiment 2 was designed to assess the effects of delay, attentiveness, and direction of gaze for Stage IV of object concept development. Subjects were equally assigned into one of two delay groups: 0-sec delay and 3-sec delay. Attentiveness was rated in terms of a three-point scale, and then divided into high and low attentive groups. Direction of gaze was judged into two directions. In two experiments, infants received three trials of task, and received a score of 0, 1, 2 for each trials. Data were analyzed by ANOVA, Tukey test, and t-test for task performance, and direction of gaze was analyzed by chi-square. The results obtained from two experiments were as follows : 1. In object permanence test, subjects obtained significantly higher scores with age, and 6, 9, 12, 18 months were classified into different developmental stages. 2. In object permanence development, subjects received significantly different scores with task and a developmental order of tasks was found. First of all, infants mastered finding an object partially hidden under one box, and then mastered finding an object completely hidden under one box. Contrary to Piagetian theory, in this study, the development of finding an object after successive visible displacements and finding an object after one invisible displacement were sometimes reversed. Finally, finding an object after successive invisible displacements was mastered, and the concept of object permanence was completed. 3. In Stage IV of object concept development, a 3-sec delay did not significantly affect the performance of tasks. The O-sec delay group didn't perform significantly better than the 3-sec delay group. 4. In Stage IV of object concept development, attentiveness of infants significantly affected the performance of task. So the highly attentive infants obtained better performance scores than the low attentive infants. 5. In Stage IV of object concept development, direction of gaze significantly affected the performance of task. That is, infants who gazed at the box which contained the object showed a higher rate of success than infants who gazed at the box which had already displaced the object.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1089-1099
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• 2010

An SIR epidemic model with pulse vaccination and time delay describing infection period is investigated. The global attractiveness of the infection-free periodic solution is discussed, and sufficient condition is obtained for the permanence of the system. Our results indicate that a large vaccination rate or a short period of pulsing leads to the eradication of the disease.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1359-1378
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• 2010

The effect of impulse in the ecological models makes them more realistic. Recently, the eco-epidemiological models have become an important field of study from the both mathematical and ecological view points. In this article, we consider some eco-epidemiological systems under the influence of impulsive force. A set of sufficient conditions for the permanence of the system are derived. Stability of the trivial solution and at least one strictly positive periodic solution are obtained. Numerical examples are given in support to our analytical findings. Finally, a short discussion concludes the paper.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.193-207
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• 2010

In this paper, a predator-prey model with stage structure and distributed delay is investigated. Mathematical analyses of the model equation with regard to boundedness of solutions, nature of equilibria, permanence, extinction and stability are performed. By the comparison theorem, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. Taking the product of the per-capita rate of predation and the rate of conversing prey into predator as the bifurcating parameter, we prove that there exists a threshold value beyond which the positive equilibrium bifurcates towards a periodic solution.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.781-802
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• 2011

Of concern in the paper is a Holling-Tanner predator-prey model with modified version of the Leslie-Gower functional response. Dynamical behaviours such as stability, permanence and Hopf bifurcation have been carried out deterministically. Using the normal form theory and center manifold theorem, the explicit formulae determining the stability and direction of Hopf bifurcation have been derived. The deterministic model is extended to a stochastic one by perturbing the growth equation of prey and predator by white and colored noises and finally the mean square stability of the stochastic model systems is investigated analytically. An extensive quantitative analysis has been performed based on numerical computation so as to validate the applicability of the proposed mathematical model.

• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.48-53
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• 2007

A new way to integrate various geophysical information for evaluation of RQD was developed. In this study, we did not directly define the RQD value where borehole data are not sampled. Instead, we infer the probability of RQD values with prior probability from borehole direct data, and secondary supporting probability from resistivity and seismic tomography data. For the integration, we applied the geostatstical indicator kriging to get prior probability of RQD value, and indicator kriging with soft data to get the supporting probability from resistivity and seismic data. And we finally use the permanence ratio rule to integrate these information. The finally obtained result was also analyzed to fully utilize the probabilistic features. We show the probability of wrongly classifying the RQD evaluation and vice versa. This result may be used for decision making process based on the geophysical exploration.

• Journal of the Korean Society of Safety
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• v.17 no.4
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• pp.146-152
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• 2002

The steel shows plastic deformation after the yield point exceeds. Because of overloads, the plastic deformation occurs at the interior support of a continuous bridge. The plastic deformation is concentrated at the interior support, and the permanence deformation at the interior support remains after loads pass. Because local yielding causes the positive moment at the interior support, it is called "auto moment". Auto moment redistributes the elastic moment. Because of redistribution, auto moment decreases the negative moment at the interior support of a continuous bridge. In this paper, the moment-rotation curve from Schalling is used. The Plastic rotation is computed by using Beam-line method, and auto moment is calculated based on the experiment curve. The design example is presented using limit state criterion.