• 응용통계연구
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• 제35권5호
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• pp.645-655
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• 2022

본 논문에서는 R에서 시계열 자료 예측을 위한 자동화 함수에 대하여 고찰하고 그 예측 성능을 비교합니다. 대표적인 시계열 예측 방법인 지수 평활 모형과 ARIMA (autoregressive integrated moving average) 모형을 대상으로 하였으며, 이들의 모형화 및 예측 자동화를 가능하게 하는 R의 4가지 자동화 함수인 forecast::ets(), forecast::auto.arima(), smooth::es()와 smooth::auto.ssarima()를 대상으로 하였습니다. 이들의 예측 성능을 비교하기 위하여 3,003가지의 시계열로 구성되어 있는 M3-Competition자료와 3가지의 정확성 척도를 사용하였습니다. 4가지 자동화 함수는 모형화의 다양성 및 편리성, 예측 정확도 및 실행 시간 등에서 각자 장단점이 있음을 확인하였습니다.

• 호남수학학술지
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• 제43권4호
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• pp.741-749
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• 2021

A variant of up-down posets described below and the number of their linear extensions were studied. We obtained the exponential generating functions which showed that how they are related to the Euler's up-down numbers.

• 대한수학회보
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• 제51권6호
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• pp.1805-1827
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• 2014

Let $\mathcal{K}^{\prime}_M$ be the generalized tempered distributions of $e^{M(t)}$-growth, where the function M(t) grows faster than any linear functions as ${\mid}t{\mid}{\rightarrow}{\infty}$, and let $K^{\prime}_M$ be the Fourier transform spaces of $\mathcal{K}^{\prime}_M$. We obtain the relationship between certain classes of analytic functions in tubes, $\mathcal{K}^{\prime}_M$ and $K^{\prime}_M$.

• 정보보호학회논문지
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• 제33권5호
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• pp.761-773
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• 2023

본 논문에서는 딥러닝 분야에서 사용되는 신경망 모델, 그중에서도 다중 계층 퍼셉트론 모델에 사용되는 지수함수 기반의 활성화 함수를 근사 함수로 대체하고, 근사 함수에 마스킹을 적용함으로써 신경망 모델의 추론 과정의 전력 분석 저항성을 높이는 방법을 제안한다. 이미 학습된 값을 사용하여 연산하는 인공 신경망의 추론 과정은 그 특성상 가중치나 편향 등의 내부 정보가 부채널 공격에 노출될 위험성이 있다. 다만 신경망 모델의 활성화 함수 계층에서는 매우 다양한 함수를 사용하고, 특히 지수함수 기반의 활성화 함수에는 마스킹 기법 등 통상적인 부채널 대응기법을 적용하기가 어렵다. 따라서 본 연구에서는 지수함수 기반의 활성화 함수를 단순한 형태로 근사하여도 모델의 치명적인 성능 저하가 일어나지 않음을 보이고, 근사 함수에 마스킹을 적용함으로써 전력 분석으로부터 안전한 순방향 신경망 모델을 제안하고자 한다.

• 대한수학회지
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• 제48권4호
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• pp.727-747
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• 2011

By employing coincidence degree theory and using Halanay-type inequality technique, a sufficient condition is given to guarantee the existence and global exponential stability of periodic solutions for the two-dimensional discrete-time Cohen-Grossberg BAM neural networks. Compared with the results in existing papers, in our result on the existence of periodic solution, the boundedness conditions on the activation are replaced with global Lipschitz conditions. In our result on the existence and global exponential stability of periodic solution, the assumptions in existing papers that the value of activation functions at zero is zero are removed.

• 대한수학회논문집
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• 제35권2호
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• pp.533-546
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• 2020

Since Sheffer introduced the so-called Sheffer polynomials in 1939, the polynomials have been extensively investigated, applied and classified. In this paper, by using matrix algebra, specifically, some properties of Pascal and Wronskian matrices, we aim to present certain interesting identities involving the 2-variable truncated exponential based Sheffer polynomial sequences. Also, we use the main results to give some interesting identities involving so-called 2-variable truncated exponential based Miller-Lee type polynomials. Further, we remark that a number of different identities involving the above polynomial sequences can be derived by applying the method here to other combined generating functions.

• International Journal of Reliability and Applications
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• 제4권3호
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• pp.97-111
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• 2003

By applying Theorem 2.6.4 (Fang and Zhang, 1990, p.66) the dispersion matrix of a multivariate power exponential (MPE) distribution is derived. It is shown that the MPE and the gamma distributions are related and thus the MPE and chi-square distributions are related. By extending Fang and Xu's Theorem (1987) from the normal distribution to the Univariate Power Exponential (UPE) distribution an explicit expression is derived for calculating the probability of an UPE random variable over an interval. A representation of the characteristic function (c.f.) for an UPE distribution is given. Based on the MPE distribution the probability density functions of the generalized non-central chi-square, the generalized non-central t, and the generalized non-central F distributions are derived.

• Journal of Mechanical Science and Technology
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• 제16권1호
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• pp.46-59
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• 2002

The main purpose of this study is to investigate the variation of tool electrode edge wear and machining performance outputs, namely, the machining rate (workpiece removal rate), tool wear rate and the relative wear, with the varying machining parameters (pulse time, discharge current and dielectric flushing pressure) in EDM die sinking. The edge wear profiles obtained are modeled by using the circular arcs, exponential and poller functions. The variation of radii of the circular arcs with machining parameters is given. It is observed that the exponential function models the edge wear profiles of the electrodes, very accurately. The variation of exponential model parameters with machining parameters is presented.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.211-225
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• 2011

In this paper, a class of bi-directional associative memory (BAM) fuzzy cellular neural networks with distributed delays and impulses is formulated and investigated. By employing an integro-differential inequality with impulsive initial conditions and the topological degree theory, some sufficient conditions ensuring the existence and global exponential stability of equilibrium point for impulsive BAM fuzzy cellular neural networks with distributed delays are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on the delay kernel functions and system parameters. It is believed that these results are significant and useful for the design and applications of BAM fuzzy cellular neural networks. An example is given to show the effectiveness of the results obtained here.

• 대한수학회지
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• 제57권4호
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• pp.845-871
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• 2020

We consider generalized Dedekind sums in dimension n, defined as sum of products of values of periodic Bernoulli functions. For the generalized Dedekind sums, we associate a Laurent polynomial. Using this, we associate an exponential sum of a Laurent polynomial to the generalized Dedekind sums and show that this exponential sum has a nontrivial bound that is sufficient to fulfill the equidistribution criterion of Weyl and thus the fractional part of the generalized Dedekind sums are equidistributed in ℝ/ℤ.