• 호남수학학술지
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• 제32권3호
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• pp.389-397
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• 2010

Exton introduced 20 distinct triple hypergeometric functions whose names are Xi (i = 1,$\ldots$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function $\Psi_2$, a Humbert function $\Phi_2$. The object of this paper is to present 25 (presumably new) integral representations of Euler types for the Exton hypergeometric function $X_5$ among his twenty $X_i$ (i = 1,$\ldots$, 20), whose kernels include the Exton function X5 itself, the Exton function $X_6$, the Horn's functions $H_3$ and $H_4$, and the hypergeometric function F = $_2F_1$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.347-354
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• 2010

Exton [Hypergeometric functions of three variables, J. Indian Acad. Math. 4 (1982), 113~119] introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ..., 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_oF_1$, $_1F_1$, a Humbert function ${\Psi}_2$, a Humbert function ${\Phi}_2$. The object of this paper is to present 16 (presumably new) integral representations of Euler type for the Exton hypergeometric function $X_2$ among his twenty $X_i$ (i = 1, ..., 20), whose kernels include the Exton function $X_2$ itself, the Appell function $F_4$, and the Lauricella function $F_C$.

• 대한수학회논문집
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• 제27권2호
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• pp.257-264
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• 2012

Exton introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ${\ldots}$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function ${\Psi}_1$, and a Humbert function ${\Phi}_2$. The object of this paper is to present 18 new integral representations of Euler type for the Exton hypergeometric function $X_8$, whose kernels include the Exton functions ($X_2$, $X_8$) itself, the Horn's function $H_4$, the Gauss hypergeometric function $F$, and Lauricella hypergeometric function $F_C$. We also provide a system of partial differential equations satisfied by $X_8$.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2002년도 ICCAS
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• pp.61.6-61
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• 2002

In these days, Block Pulse functions are used in a variety of fields such as the analysis and controller design of the systems. In applying the Block Pulse function technique to control and systems science, the integral operation of the Block Pulse series plays important roles. This is because differential equations are always involved in the representations of continuous-time models of dynamic systems, and differential operations are always approximated by the corresponding Block Pulse series through integration operational matrices. In order to apply the Block Pulse function technique to the problems of continuous-time dynamic systems more efficiently, it is necessary to find th...

• East Asian mathematical journal
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• 제34권1호
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• pp.29-37
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• 2018

We introduce formal symbols of product type, of zero class, and of minimum type and show that the formal power series representations for $e^p$ and $e^q$ are formal symbols of product type giving the same pseudodifferential operator, where p and q are formal symbols of minimum type and p - q is of zero class.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제18권2호
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• pp.348-369
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• 2024

With the advancement of Industry 4.0 and Industrial Internet of Things (IIoT), manufacturing increasingly seeks automation and intelligence. Temperature and vibration monitoring are essential for machinery health. Traditional abnormal state detection methodologies often overlook the intricate frequency characteristics inherent in vibration time series and are susceptible to erroneously reconstructing temperature abnormalities due to the highly similar waveforms. To address these limitations, we introduce synergistic, end-to-end, unsupervised Frequency-Time Domain Memory-Enhanced Autoencoders (FTD-MAE) capable of identifying abnormalities in both temperature and vibration datasets. This model is adept at accommodating time series with variable frequency complexities and mitigates the risk of overgeneralization. Initially, the frequency domain encoder processes the spectrogram generated through Short-Time Fourier Transform (STFT), while the time domain encoder interprets the raw time series. This results in two disparate sets of latent representations. Subsequently, these are subjected to a memory mechanism and a limiting function, which numerically constrain each memory term. These processed terms are then amalgamated to create two unified, novel representations that the decoder leverages to produce reconstructed samples. Furthermore, the model employs Spectral Entropy to dynamically assess the frequency complexity of the time series, which, in turn, calibrates the weightage attributed to the loss functions of the individual branches, thereby generating definitive abnormal scores. Through extensive experiments, FTD-MAE achieved an average ACC and F1 of 0.9826 and 0.9808 on the CMHS and CWRU datasets, respectively. Compared to the best representative model, the ACC increased by 0.2114 and the F1 by 0.1876.

• 대한수학회보
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• 제57권1호
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• pp.207-218
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• 2020

Some modular representations of reflection groups related to Weyl groups are considered. The rational cohomology of the classifying space of a compact connected Lie group G with a maximal torus T is expressed as the ring of invariants, H*(BG; ℚ) ≅ H*(BT; ℚ)^W(G), which is a polynomial ring. If such Lie groups are locally isomorphic, the rational representations of their Weyl groups are equivalent. However, the integral representations need not be equivalent. Under the mod p reductions, we consider the structure of the rings, particularly for the Weyl group of symplectic groups Sp(n) and for the alternating groups A_n as the subgroup of W(SU(n)). We will ask if such rings of invariants are polynomial rings, and if each of them can be realized as the mod p cohomology of a space. For n = 3, 4, the rings under a conjugate of W(Sp(n)) are shown to be polynomial, and for n = 6, 8, they are non-polynomial. The structures of H*(BT^n-1; 𝔽_p)^A_n will be also discussed for n = 3, 4.

• 응용통계연구
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• 제31권6호
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• pp.707-719
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• 2018

시계열 데이터의 분류와 군집화를 효율적으로 수행하기 위해 다양한 시계열 표현 방법들이 제안되었다. 본 연구는 Lin 등 (2007)이 제안한 국소 평균 근사를 이용하여 시계열의 차원을 축소한 후 심볼릭 자료로 이산화하는 symbolic aggregate approximation (SAX) 방법의 개선에 대해서 연구하였다. SAX는 국소 평균 근사를 할 때 등간격으로 임의의 개수의 세그먼트로 나누어 평균을 계산하여 세그먼트의 개수에 그 성능이 크게 좌우된다. 따라서 본 논문은 불균형 Haar 웨이블릿 변환을 통해 국소 평균 수준을 등간격이 아니라 자료의 특성을 반영하여 자료 의존적으로 선택하게 함으로써 시계열의 차원을 효과적으로 축소함과 동시에 정보의 손실을 줄이는 방법에 대해서 제안한다. 제안한 방법은 실증 자료 분석을 통해 SAX 방법을 개선시킴을 확인하였다.

• Journal of the Korean Data and Information Science Society
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• 제18권3호
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• pp.697-704
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• 2007

It is common in financial time series that volatility(conditional variance) as a measure of risk exhibits asymmetry in such a manner that positive and negative values of return rates of the series tend to provide different contributions to the volatility. We are concerned with asymmetric conditional variances for Korean financial time series especially during the time span of 2000-2001. Notice that these periods suffer from 9-11 disaster in US and collapses of stock prices of dot-companies in Korea. Threshold-ARCH models are considered and a Wald test of asymmetry is suggested. News impact curves are illustrated for graphical representations of leverage effects inherent in various Korean financial time series.

• 호남수학학술지
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• 제33권4호
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• pp.441-452
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• 2011

The enormous success of the theory of hypergeometric series in a single variable has stimulated the development of a corresponding theory in two and more variables. A wide variety of investigations in the theory of several variable hypergeometric functions have been essentially motivated by the fact that solutions of many applied problems involving partial differential equations are obtainable with the help of such hypergeometric functions. Here, in this trend, we aim at presenting further decomposition formulas for Saran function $F_E$, which are used to give some integral representations of the function $F_E$. We also present a system of partial differential equations for the Saran function $F_E$.