• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.55-66
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• 2018

By making use of the Riemann-Liouville fractional integrals, we establish further results on Chebyshev inequality. Other Steffensen integral results of the weighted Chebyshev functional are also proved. Some classical results of the paper:[ Steffensen's generalization of Chebyshev inequality. J. Math. Inequal., 9(1), (2015).] can be deduced as some special cases.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.261-266
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• 1999

We present a geometric interpretation of Chebyshev type inequalities. This uses a simple diagram which illustrates the functional bound for the indicator function of the event whose probability we want to assess. We also give a geometric interpretation of the inequalities in terms of volume in a Euclidean space of appropriate dimension. Markov's inequality and Chebyshev's inequality are treated in more detail.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.503-511
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• 2021

In this present work, we obtain certain coefficients of the subclass 𝓗_λ,𝛄(s, b, n) of non-Bazilević functions and estimate the relevant connection to the famous classical Fekete-Szegö inequality of functions belonging to this class.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.47-54
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• 2000

This article is concerned with the algorithm for the Chebyshev estimation with/without linear equality and/or inequality constraints. The algorithm employs a linear scaling transformation scheme to reduce the computational burden which is induced when the data set is quite large. The convergence of the proposed algorithm is proved. And the updating and orthogonal decomposition techniques are considered to improve the computational efficiency and numerical stability.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.33 no.2
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• pp.32-38
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• 2005

In this research, a procedure to improve the feasibility of design space is proposed by an approximation model. The Chebyshev Inequality is used as the criterion of modification of design space. This procedure is applied to the aero-elastic transonic wing design problem and the feasibility of the design space is greatly improved. Also the optimization results are improved by appling this procedure. That is, the probability to satisfy all imposed constraints is increased and the better design points are included in design space after this procedure. And the use of both a second-order response surface model and the Kriging model is investigated and compared in accuracy, efficiency, and robustness as approximation models in this procedure for different sampling methods. As a result, the second-order response surface model is more appropriate for our application than the Kriging model, because it is linear enough to be fitted well by the response surface model.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.647-657
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• 2023

The aim of this paper is to study certain subclass ${\tilde{S^q_{\Sigma}}}({\lambda},\,{\alpha},\,t,\,s,\,p,\,b)$ of analytic and bi-univalent functions which are defined by using symmetric q-derivative operator. We estimate the second and third coefficients of the Taylor-Maclaurin series expansions belonging to the subclass and upper bounds for Feketo-Szegö inequality. Furthermore, some relevant connections of certain special cases of the main results with those in several earlier works are also pointed out.

• ETRI Journal
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• v.30 no.5
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• pp.653-662
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• 2008

Arbitration of tag collision is a significant issue for fast tag identification in RFID systems. A good tag anti-collision algorithm can reduce collisions and increase the efficiency of tag identification. EPCglobal Generation-2 (Gen2) for passive RFID systems uses probabilistic slotted ALOHA with a Q algorithm, which is a kind of dynamic framed slotted ALOHA (DFSA), as the tag anti-collision algorithm. In this paper, we analyze the performance of the Q algorithm used in Gen2, and analyze the methods for estimating the number of slots and tags for DFSA. To increase the efficiency of tag identification, we propose new tag anti-collision algorithms, namely, Chebyshev's inequality, fixed adjustable framed Q, adaptive adjustable framed Q, and hybrid Q. The simulation results show that all the proposed algorithms outperform the conventional Q algorithm used in Gen2. Of all the proposed algorithms, AAFQ provides the best performance in terms of identification time and collision ratio and maximizes throughput and system efficiency. However, there is a tradeoff of complexity and performance between the CHI and AAFQ algorithms.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.8A
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• pp.805-814
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• 2008

Both EPCglobal Generation-2 (Gen2) for passive RFID systems and Intelleflex for semi-passive RFID systems use probabilistic slotted ALOHA with Q algorithm, which is a kind of dynamic framed slotted ALOHA (DFSA), as the tag anti-collision algorithm. A better tag anti-collision algorithm can reduce collisions so as to increase the efficiency of tag identification. In this paper, we introduce and analyze the estimation methods of the number of slots and tags for DFSA. To increase the efficiency of tag identification, we propose two new tag anti-collision algorithms, which are Chebyshev's inequality (CHI) algorithm and hybrid Q algorithm, and compare them with the conventional Q algorithm and adaptive adjustable framed Q (AAFQ) algorithm, which is mentioned in Part I. The simulation results show that AAFQ performs the best in Gen2 scenario. However, in Intelleflex scenario the proposed hybrid Q algorithm is the best. That is, hybrid Q provides the minimum identification time, shows the more consistent collision ratio, and maximizes throughput and system efficiency in Intelleflex scenario.

• International Journal of Reliability and Applications
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• v.3 no.1
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• pp.37-50
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• 2002

Simultaneous estimation of accuracy and probability corresponding to a prediction interval is considered in this study. Traditional application of confidence interval forecasting consists in evaluation of interval limits for a given significance level. The wider is this interval, the higher is probability and the lower is the forecast precision. In this paper a measure of stochastic forecast accuracy is introduced, and a procedure for balanced estimation of both the predicting accuracy and confidence probability is elaborated. Solution can be obtained in an optimizing approach. Suggested method is applied to constructing confidence intervals for parameters estimated by normal and t distributions

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.8 no.2
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• pp.123-133
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• 2010

A statistical evaluation methodology was developed to determine the compliance of candidate waste stream with clearance criteria based upon distribution of radionuclide in a waste stream at a certain confidence level. For the cases where any information on the radionuclide distribution is not available, the relation between arithmetic mean of radioactivity concentration and its acceptable maximum standard deviation was demonstrated by applying widely-known Markov Inequality and One-side Chebyshev Inequality. The relations between arithmetic mean and its acceptable maximum standard deviation were newly derived for normally or lognormally distributed radionuclide in a waste stream, using probability density function, cumulative density function, and other statistical relations. The evaluation methodology was tested for a representative case at 95% of confidence level and 100 Bq/g of clearance level of radioactivity concentration, and then the acceptable range of standard deviation at a given arithmetic mean was quantitatively shown and compared, by varying the type of radionuclide distribution. Furthermore, it was statistically demonstrated that the allowable range of clearance can be expanded, even at the same confidence level, if information on the radionuclide distribution is available.