• 대한수학회지
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• 제37권3호
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• pp.391-410
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• 2000

In the complex case, we construct a q-analogue of the Riemann zeta function q(s) and a q-analogue of the Dirichlet L-function L(s,X), which interpolate the 1-analogue Bernoulli numbers. Using the properties of p-adic integrals and measures, we show that Kummer type congruences for the q-analogue Bernoulli numbers are the generalizations of the usual Kummer congruences for the ordinary Bernoulli numbers. We also construct a q0analogue of the p-adic L-function Lp(s, X;q) which interpolates the q-analogue Bernoulli numbers at non positive integers.

• 산업경영시스템학회지
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• 제44권3호
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• pp.22-32
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• 2021

To meet rapidly changing market demands, manufacturers strive to increase both of productivity and diversity at the same time. As a part of those effort, they are applying flexible manufacturing systems that produce multiple types and/or options of products at a single production line. This paper studies such flexible manufacturing system with multiple types of products, multiple Bernoulli reliability machines and dedicated buffers between them for each of product types. As one of the prevalent control policies, priority based policy is applied at each machines to select the product to be processed. To analyze such system and its performance measures exactly, Markov chain models are applied. Because it is too complex to define all relative transient and its probabilities for each state, an algorithm to update transient state probability are introduced. Based on the steady state probability, some performance measures such as production rate, WIP-based measures, blocking probability and starvation probability are derived. Some system properties are also addressed. There is a property of non-conservation of flow, which means the product ratio at the input flow is not conserved at the succeeding flows. In addition, it is also found that increased buffer capacity does not guarantee improved production rate in this system.

• Kyungpook Mathematical Journal
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• 제45권4호
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• pp.503-510
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• 2005

Let $\left{K_{\alpha}\right}_{{\alpha}{\in}{\mathbb{R}}}$ be the multifractal spectrums of a perturbed Cantor set K. We find the set of values ${\alpha}$ of nonempty set $K_{\alpha}$ by using the Birkhoff ergodic theorem. And we also show that such $K_{\alpha}$ is a fractal set in the sense of Taylor [12].

• Korean Journal of Mathematics
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• 제29권2호
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• pp.371-386
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• 2021

This paper investigates two discrete time queueing inventory models with positive service time and lead time. Customers arrive according to a Bernoulli process and service time and lead time follow geometric distributions. The first model under discussion based on replenishment of order upto S policy where as the second model is based on order placement by a fixed quantity Q, where Q = S - s, whenever the inventory level falls to s. We analyse this queueing systems using the matrix geometric method and derive an explicit expression for the stability condition. We obtain the steady-state behaviour of these systems and several system performance measures. The influence of various parameters on the systems performance measures and comparison on the cost analysis are also discussed through numerical example.

• Structural Engineering and Mechanics
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• 제72권2호
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• pp.217-227
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• 2019

The methodology known as "shape sensing" allows the reconstruction of the displacement field of a structure starting from strain measurements, with considerable implications for structural monitoring, as well as for the control and implementation of smart structures. An approach to shape sensing is based on the inverse Finite Element Method (iFEM) that uses a variational principle enforcing a least-squares compatibility between measured and analytical strain measures. The structural response is reconstructed without the knowledge of the mechanical properties and load conditions but based only on the relationship between displacements and strains. In order to efficiently apply iFEM to the most common structural typologies of civil engineering, its formulation according to the kinematical assumptions of the Bernoulli-Euler theory is presented. Two beam inverse finite elements are formulated for different loading conditions. Depending on the type of element, the relationship between the minimum number of required measurement stations and the interpolation order is defined. Several examples representing common applications of civil engineering and involving beams and frames are presented. To simulate the experimental strain data at the station points and to verify the accuracy of the displacements obtained with the iFEM shape sensing procedure, a direct FEM analysis of the considered structures is performed using the LUSAS software.

• ETRI Journal
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• 제25권4호
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• pp.238-246
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• 2003

This paper introduces the modeling and analysis of a discrete-time, two-phase queueing system for both exhaustive batch service and gated batch service. Packets arrive at the system according to a Bernoulli process and receive batch service in the first phase and individual services in the second phase. We derive the probability generating function (PGF) of the system size and show that it is decomposed into two PGFs, one of which is the PGF of the system size in the standard discrete-time Geo/G/1 queue without vacations. We also present the PGF of the sojourn time. Based on these PGFs, we present useful performance measures, such as the mean number of packets in the system and the mean sojourn time of a packet.

• International Journal of Computer Science & Network Security
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• 제21권7호
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• pp.350-358
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• 2021

In modern years, the performance of the students is analysed with lot of difficulties, which is a very important problem in all the academic institutions. The main idea of this paper is to analyze and evaluate the academic performance of the college students with bipolar disorder by applying data mining classification algorithms using Jupiter Notebook, python tool. This tool has been generally used as a decision-making tool in terms of academic performance of the students. The various classifiers could be logistic regression, random forest classifier gini, random forest classifier entropy, decision tree classifier, K-Neighbours classifier, Ada Boost classifier, Extra Tree Classifier, GaussianNB, BernoulliNB are used. The results of such classification model deals with 13 measures like Accuracy, Precision, Recall, F1 Measure, Sensitivity, Specificity, R Squared, Mean Absolute Error, Mean Squared Error, Root Mean Squared Error, TPR, TNR, FPR and FNR. Therefore, conclusion could be reached that the Decision Tree Classifier is better than that of different algorithms.

• 대한의용생체공학회:의공학회지
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• 제25권5호
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• pp.351-359
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• 2004

속도계측형 호흡기류센서는 베르누이 원리에 의해 기류속도를 동압력으로 변환하여 호흡기류를 측정하는 센서로써 다수의 샘플링 구멍을 기류통과면 상에 설치해야 한다. 본 연구에서는 속도 샘플 구명들을 비균등하게 배치시킴으로써 단순하게 균등 배치하는 것보다 훨씬 정확한 기류 계측이 가능함을 이론적으로 입증하였다 컴퓨터 시뮬레이션 결과 기류통과면을 다수의 등면적 링으로 분한하고 각각의 링의 면적을 다시 2등분하는 위치에서 속도를 샘플링함으로써 균등 배치할 경우에 비해 계측오차가 약 1/5로 감소하였다. 또한 충 샘플개수가 4개 이상이면 상대오차 1％ 이내의 매우 정확한 기류계측이 가능하였다. 기류 속도분포의 변화에 따른 영향을 비교한 결과 균등 샘플링에 비해 1/2 이하로 둔감하였다. 따라서 본 인구에서 제안하는 비균등 속도샘플링 기법은 속도 계측형 호흡기류센서의 설계시 매우 유용하게 적용될 것으로 판단된다.

• 한국산업정보학회논문지
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• 제23권2호
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• pp.29-39
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• 2018

본 논문에서는 일량제어정책과 복수휴가정책이 혼합된 서버제어정책 하에서 운영되는 이산시간 대기행렬시스템을 다룬다. 고객들은 베르누이 도착과정으로 시스템에 도착하고, 서버는 한대가 운영되며 시스템 내 서비스할 고객이 없으면 유휴기간을 갖는 서버가 이산 확률변수 V만큼의 휴가를 떠났다가 돌아와서 대기 중인 고객들의 총 일량이 임계값 D를 넘길 때까지 휴가를 반복한다. 본 논문에서는 이산시간 시스템을 대상으로 하여 보다 현실적이며 유연한 혼합제어 정책 하에서 운영되는 대기행렬시스템의 안정상태 일량분포를 유도하고 평균일량을 계산하였다. 이는 시스템 내 고객수, 대기시간, 체재시간과 같은 시스템의 여러 성능척도를 분석하는데 기본이 된다.

• 천문학회지
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• 제46권3호
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• pp.125-131
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• 2013

We present the relation between the genus in cosmology and the Betti numbers for excursion sets of three- and two-dimensional smooth Gaussian random fields, and numerically investigate the Betti numbers as a function of threshold level. Betti numbers are topological invariants of figures that can be used to distinguish topological spaces. In the case of the excursion sets of a three-dimensional field there are three possibly non-zero Betti numbers; ${\beta}_0$ is the number of connected regions, ${\beta}_1$ is the number of circular holes (i.e., complement of solid tori), and ${\beta}_2$ is the number of three-dimensional voids (i.e., complement of three-dimensional excursion regions). Their sum with alternating signs is the genus of the surface of excursion regions. It is found that each Betti number has a dominant contribution to the genus in a specific threshold range. ${\beta}_0$ dominates the high-threshold part of the genus curve measuring the abundance of high density regions (clusters). ${\beta}_1$ dominates the genus near the median thresholds which measures the topology of negatively curved iso-density surfaces, and ${\beta}_2$ corresponds to the low-threshold part measuring the void abundance. We average the Betti number curves (the Betti numbers as a function of the threshold level) over many realizations of Gaussian fields and find that both the amplitude and shape of the Betti number curves depend on the slope of the power spectrum n in such a way that their shape becomes broader and their amplitude drops less steeply than the genus as n decreases. This behaviour contrasts with the fact that the shape of the genus curve is fixed for all Gaussian fields regardless of the power spectrum. Even though the Gaussian Betti number curves should be calculated for each given power spectrum, we propose to use the Betti numbers for better specification of the topology of large scale structures in the universe.