• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.551-563
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• 2017

In this paper, by using fixed point theorems in cones, the existence of positive solutions is considered for nonlinear m-point boundary value problem for the following second-order dynamic equations on time scales $$u^{{\Delta}{\nabla}}(t)+a(t)f(t,u(t))=0,\;t{\in}(0,T),\;{\beta}u(0)-{\gamma}u^{\Delta}(0)=0,\;u(T)={\sum_{i=1}^{m-2}}\;a_iu({\xi}_i),\;m{\geq}3$$, where $a(t){\in}C_{ld}((0,T),\;[0,+{\infty}))$, $f{\in}C([0,T]{\times}[0,+{\infty}),\;(-{\infty},+{\infty}))$, the nonlinear term f is allowed to change sign. We obtain several existence theorems of positive solutions for the above boundary value problems. In particular, our criteria generalize and improve some known results [15] and the obtained conditions are different from related literature [14]. As an application, an example to demonstrate our results is given.

• 한국지구과학회:학술대회논문집
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• 2010.04a
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• pp.73-73
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• 2010

The purpose of this study is to analyze illustrations, contents, and experiment in 6 kinds of science textbook from the 9th grade covering the phase change of the Moon (on the phase change of the Moon in six 9th grade science textbook) and to suggest coherent and effective contents and frame of the science textbook. Hence, the researcher decided the study problem. The study problems are as follows; 'Are the illustrations in the science textbook presented to help understand the phase change of the Moon depending on the position of the observer?', 'Does the contents of the book clearly mention the phase change of the Moon?', 'Can students understand the phase change of the Moon through the experiments in the science textbook?', 'Do illustrations, contents, and experiment of the science textbook consistently explain phase change of the Moon?'. 10 persons (9graduate students including the researcher) took part in this study. All things unanimously agreed upon by all participants were reflected in the results. The results are as follows. First, the universe observer's view point is mixed with the earth observer's view in illustration of these science textbook regarding the phase change of the Moon. Moreover, illustrations of some textbooks are presented with such words as 'sunrise', 'midnight' and consequently contain too much contents. Second, the contents of the science textbook concerning the phase change of the Moon is not described clearly. In addition, they don't give clear and detailed explanations for the reason of the phase change of the Moon. Third, all of the textbooks, except one textbook, describe the experiment regarding the phase change of the Moon with the earth observer's view point but don't specifically mention that the view point is that of the earth observer's view point. Fourth, illustrations, contents, and experiments in the science textbook don't coherently explain the phase change of the Moon. In addition, it is confirmed through the process of the result analysis that the described contents in the science curriculum is not well constructed or logical.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.789-798
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• 2000

The mean residual function is the expected remaining life of an item at age x. The problem of trend change in the mean residual life is great interest in the reliability and survival analysis. In this paper, we develop a family of test statistics for testing whether or not the mean residual life changes its trend. The asymptotic normality of the test statistics is established. Monte Carlo simulations are conducted to study the performance of our test statistics.

• Proceedings of the Korean Statistical Society Conference
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• 2005.11a
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• pp.43-48
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• 2005

We consider the problem of testing for parameter changes in time series models based on a cusum test. Although the test procedure is well-established for the mean and variance in time series models, a general parameter case has not been discussed in the literature. Therefore, here we develop a cusum test for parameter change in a more general framework. As an example, we consider the change of the parameters in an RCA(1) model and that of the autocovariances of a linear process. We also consider the variance change test for unstable models with unit roots and GARCH models.

• Communications for Statistical Applications and Methods
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• v.16 no.4
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• pp.587-594
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• 2009

In this paper the change point problem of the error terms in linear regression models is considered. Since fixed or stochastic independent variables and weakly dependent errors are assumed, usual multiple regression models and time series models including ARMA are covered. We use the estimates of probability density function based on residuals in order to test the distribution change of the unobserved errors. Under some mild conditions, the test using the residuals is proved to have the same limiting distribution as the test based on true errors.

• Communications for Statistical Applications and Methods
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• v.12 no.1
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• pp.199-205
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• 2005

In general, simple correspondence analysis has handled mainly correspondence relations between the row and column categories but can not display the trends of their change over the time. For solving this problem, we will propose DSCA(Dynamic Simple Correspondence Analysis) of transition matrix data using supplementary categories in this study, Moreover, DSCA provides its trend of the change for the future by predicting and displaying trend toward the change from a standard point of time to the next.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.517-529
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• 2012

In this paper, the existence theorem of two positive solutions is established for nonlinear m-point boundary value problem by using an inequality for the following third-order differential equations $$({\phi}(u^{\prime\prime}))^{\prime}+a(t)f(t,u(t))=0,\;t{\in}(0,1)$$, $${\phi}(u^{\prime\prime}(0))=\sum^{m-2}_{i=1}a_i{\phi}(u^{\prime\prime}({\xi}_i)),\;u^{\prime}(1)=0,\;u(0)=\sum^{m-2}_{i=1}b_iu({\xi}_i)$$, where ${\phi}:R{\rightarrow}R$ is an increasing homeomorphism and homomorphism and $\phi(0)=0$. The nonlinear term f may change sign, as an application, an example to demonstrate our results is given.

• Journal of the Korean Operations Research and Management Science Society
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• v.12 no.1
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• pp.19-26
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• 1987

In analyzing time series, estimating the level or the current mean of the process plays an important role in understanding its structure and in being able to make forecasts. The studies the class of time series models where the level of the process is assumed to follow a random walk and the deviation from the level follow an ARMA process. The estimation and forecasting problem in a Bayesian framework and uses the Kalman filter to obtain forecasts based on estimates of level. In the analysis of time series, we usually make the assumption that the time series is generated by one model. However, in many situations the time series undergoes a structural change at one point in time. For example there may be a change in the distribution of random variables or in parameter values. Another example occurs when the level of the process changes abruptly at one period. In order to study such problems, the assumption that level follows a random walk process is relaxed to include a major level change at a particular point in time. The major level change is detected by examining the likelihood raio under a null hypothesis of no change and an alternative hypothesis of a major level change. The author proposes a method for estimation the size of the level change by adding one state variable to the state space model of the original Kalman filter. Detailed theoretical and numerical results are obtained for th first order autoregressive process wirth level changes.

• Journal of Power Electronics
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• v.16 no.1
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• pp.142-152
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• 2016

Common mode voltage (CMV) generation is a major problem in switching power converter fed induction motor drive systems. CMV is the zero sequence voltage generated due to the switching action of power converters. Even a small magnitude of CMV with a high rate of change may circulate large bearing currents which may damage a machine's bearings and shorten its life. There are several methods of controlling CMV. This paper presents 3-level sinusoidal pulse width modulation based techniques to control the magnitude and rate of change of CMV in multilevel AC-DC-AC drive systems. Simulation and experimental investigations have been presented to validate the performance of proposed technique to control CMV in 3-level neutral point clamped inverter based AC-DC-AC system.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.553-567
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• 2023

There are real life situations in our lives where the things are changing continuously or from time to time. It is a very important problem for one whether to continue the existing relationship or to form a new one after some occasions. That is, people, companies, cities, countries, etc. may change their opinion or position rapidly. In this work, we think of the problem of changing relationships from a mathematical point of view and think of an answer. In some sense, we comment these changes as power changes. Our number theoretical model will be based on this idea. Using the convolution sum of the restricted divisor function E, we obtain the answer to this problem.