• 대한수학회논문집
• /
• 제9권3호
• /
• pp.521-529
• /
• 1994

This paper studies the realization of irreducible unitary representations of $GL_2(R)$ and $GL_2(C)$ by Bargmann's classification[1]. Since the representations of general matrix groups can be obtained by the extensions of characters of a special linear group, we shall follow to a large extent the pattern of the results in [5], [6], and [8]. This article is divided into two sections. In the first section we describe the realization of principal series and discrete series and complementary series of $GL_2(R)$. The last section is devoted to the derivation of principal series and complementary series of $GL_2(C).

• 산업경영시스템학회지
• /
• 제37권2호
• /
• pp.27-34
• /
• 2014

In this paper, we investigate the statistical correlation of the time series for temperature measured at the heat box in the automobile drying process. We show, in terms of the sample variance, that a significant non-linear correlation exists in the time series that consist of absolute temperature changes. To investigate further the non-linear correlation, we utilize the volatility, an important concept in the financial market, and induce volatility time series from absolute temperature changes. We analyze the time series of volatilities in terms of the de-trended fluctuation analysis (DFA), a method especially suitable for testing the long-range correlation of non-stationary data, from the correlation perspective. We uncover that the volatility exhibits a long-range correlation regardless of the window size. We also analyze the cross correlation between two (inlet and outlet) volatility time series to characterize any correlation between the two, and disclose the dependence of the correlation strength on the time lag. These results can contribute as important factors to the modeling of forecasting and management of the heat box's temperature.

• 정보처리학회논문지B
• /
• 제9B권4호
• /
• pp.421-428
• /
• 2002

지금까지 삽입(Embedding)백터를 이용한 국소적예측방법은 고차미분방정식으로부터 생성된 카오스 시계열을 예측할 때, 파라메타 $\tau$의 추정이 정확하지 않으면 예측성능은 떨어졌다. 지금까지 지연시간 ($\tau$)의 값을 추정하는 방법은 많이 제안되어있지만 실제로 고차원미분방정식부터 생성되어진 수많은 시계열에 모두 적용 가능한 방법은 아직 없다. 이것을 기울기 백터를 이용한 기울기 선형모델을 도입하는 것에 의해 정확한 지연시간 ($\tau$)의 값을 추정하지 않아도 예측성능에 만족할 수 있는 결과를 표시했다. 이것을 이론뿐이 아니고 경제시계열에도 적용해서 종래의 예측방법과 비교해서 그 유효성을 표시했다.

• 전기의세계
• /
• 제23권2호
• /
• pp.46-54
• /
• 1974

The purposes of this paper are to deal with the design of m-input, m-output linear systems by the state variable feedback, and to extend the design capability of the state variable feedback design. The design requirements are decoupling and the exact realigation of desired transfer functions. Some methods are proposed to insert series compensators in the fixed plant in the cases when series compensators are needed to meet the input-output transfer matrix specification. The method for adding series compensators to the input channels of the fixed plant is shown by examples to lead both to the loss of the ability to decouple the augmented plant by the state variable feedback, and to the loss of desired zeroes. A method which avoids these two hazards is developed in which series compensators are put on the output channels of the fixed plant: it is proved that the augmented plant is F-invariant. By treating each subsystem individually, the designer can apply some of the previous developed knowledge of the state variable design of single-input, single-output systems.

• 상하수도학회지
• /
• 제18권6호
• /
• pp.758-769
• /
• 2004

The trends and seasonalities of most time series have a large variability. The result of the Singular Spectrum Analysis(SSA) processing is a decomposition of the time series into several components, which can often be identified as trends, seasonalities and other oscillatory series, or noise components. Generally, forecasting by the SSA method should be applied to time series governed (may be approximately) by linear recurrent formulae(LRF). This study examined forecasting ability of SSA-LRF model. These methods are applied to daily water demand data. These models indicate that most cases have good ability of forecasting to some extent by considering statistical and visual assessment, in particular forecasting validity shows good results during 15 days.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1998년도 하계학술대회 논문집 G
• /
• pp.2299-2301
• /
• 1998

In this paper, a modified RBF (Radial Basis Function) neural network structure is suggested for the prediction of time series with non-linear, non-stationary characteristics. Conventional RBF neural network predicting time series by using past outputs is for sensing the trajectory of the time series and for reacting when there exists strong relation between input and hidden neuron's RBF center. But this response is highly sensitive to level and trend of time serieses. In order to overcome such dependencies, hidden neurons are modified to react to the increments of input variable and multiplied by increments(or decrements) of out puts for prediction. When the suggested structure is applied to prediction of Lorenz equation, and Rossler equation, improved performances are obtainable.

• 한국정밀공학회지
• /
• 제16권7호
• /
• pp.178-187
• /
• 1999

In order to identify a transfer function model with noise, penalty function method has been widely used. In this method, estimation process for possible model parameters from low to higher order proceeds the model identification process. In this study, based on linear estimation method, a new approach unifying the estimation and the identification of ARMAX model is proposed. For the parameter estimation of a transfer function model with noise, linear estimation method by noise separation is suggested instead of nonlinear estimation method. The feasibility of the proposed model identification and estimation method is verified through simulations, namely by applying the method to time series model. In the case of time series model with noise, the proposed method successfully identifies the transfer function model with noise without going through model parameter identification process in advance. A new algorithm effectively achieving model identification and parameter estimation in unified frame has been proposed. This approach is different from the conventional method used for identification of ARMAX model which needs separate parameter estimation and model identification processes. The consistency and the accuracy of the proposed method has been verified through simulations.

• 충청수학회지
• /
• 제29권1호
• /
• pp.73-82
• /
• 2016

The utility of exponential generating functions is that they are relevant for combinatorial problems involving sets and subsets. Sequences of polynomials play a fundamental role in applied mathematics, such sequences can be described using the exponential generating functions. The actuarial polynomials ${\alpha}^{({\beta})}_n(x)$, n = 0, 1, 2, ${\cdots}$, which was suggested by Toscano, have the following exponential generating function: $${\limits\sum^{\infty}_{n=0}}{\frac{{\alpha}^{({\beta})}_n(x)}{n!}}t^n={\exp}({\beta}t+x(1-e^t))$$. A linear functional on polynomial space can be identified with a formal power series. The set of formal power series is usually given the structure of an algebra under formal addition and multiplication. This algebra structure, the additive part of which agree with the vector space structure on the space of linear functionals, which is transferred from the space of the linear functionals. The algebra so obtained is called the umbral algebra, and the umbral calculus is the study of this algebra. In this paper, we investigate some umbral representations in the actuarial polynomials.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1985년도 하계학술회의논문집
• /
• pp.61-62
• /
• 1985

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2004년도 ICCAS
• /
• pp.631-634
• /
• 2004

In this paper, the Bayesian recurrent neural network (BRNN) is proposed to predict time series data. Among the various traditional prediction methodologies, a neural network method is considered to be more effective in case of non-linear and non-stationary time series data. A neural network predictor requests proper learning strategy to adjust the network weights, and one need to prepare for non-linear and non-stationary evolution of network weights. The Bayesian neural network in this paper estimates not the single set of weights but the probability distributions of weights. In other words, we sets the weight vector as a state vector of state space method, and estimates its probability distributions in accordance with the Bayesian inference. This approach makes it possible to obtain more exact estimation of the weights. Moreover, in the aspect of network architecture, it is known that the recurrent feedback structure is superior to the feedforward structure for the problem of time series prediction. Therefore, the recurrent network with Bayesian inference, what we call BRNN, is expected to show higher performance than the normal neural network. To verify the performance of the proposed method, the time series data are numerically generated and a neural network predictor is applied on it. As a result, BRNN is proved to show better prediction result than common feedforward Bayesian neural network.