• Journal of Electrical Engineering and Technology
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• v.13 no.6
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• pp.2220-2226
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• 2018

Electric vehicles (EVs) are significant resources for demand response (DR). Thus, it is essential for EV aggregators to quantitatively evaluate their capability for DR. In this paper, a concept of dynamic equivalent battery (DEB) is proposed as a metric for evaluating the DR performance using EVs. The DEB is the available virtual battery for DR. The capacity of DEB is determined from stochastic calculation while satisfying the charging requirements of each EV, and it varies also with time. Further, a new indicator based on the DEB and time-varying electricity prices, named as value of DEB (VoDEB), is introduced to quantify the value of DEB coupled with the electricity prices. The effectiveness of the DEB and the VoDEB as metrics for the DR performance of EVs is verified with the simulations, where the difference of charging cost reduction between direct charging and optimized bidding methods is used to express the DR performance. The simulation results show that the proposed metrics accord well with the DR performance of an EV fleet. Thus, an EV aggregator may utilize the proposed concepts of DEB and VoDEB for designing an incentive scheme to EV users, who participate in a DR program.

• The Pure and Applied Mathematics
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• v.11 no.4
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• pp.267-274
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• 2004

A related fixed point theorem for set valued mappings on two complete metric spaces is obtained.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.689-701
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• 2021

The purpose of this paper is to optimize the number of source places required for the unique representation of the destination using the tools of graph theory. A subset S of vertices of a graph G is called a rational resolving set of G if for each pair u, v ∈ V - S, there is a vertex s ∈ S such that d(u/s) ≠ d(v/s), where d(x/s) denotes the mean of the distances from the vertex s to all those y ∈ N[x]. A rational resolving set is called minimal rational resolving set if no proper subset of it is a rational resolving set. In this paper we study varieties of minimal rational resolving sets defined on the basis of its complements and compute the minimum and maximum cardinality of such sets, respectively called as lower and upper rational metric dimensions for power of a path P_n analysing various possibilities.

• East Asian mathematical journal
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• v.32 no.5
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• pp.745-765
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• 2016

We propose coupled fixed point theorems for maps satisfying contractive conditions involving a rational expression in the setting of partially ordered metric spaces. We also present a result on the existence and uniqueness of coupled fixed points. In particular, it is shown that the results existing in the literature are extend, generalized, unify and improved by using mixed monotone property. Given to support the useability of our results, and to distinguish them from the known ones.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.391-403
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• 2023

In this work, we establish common fixed point results by utilizing a variant of F-contraction in the framework of C^*-algebra valued metric spaces. We utilize E.A. and C.L.R. property possessed by the mappings to prove common fixed point results in the same metric settings. To validate the applicability of these common fixed point results, we provide illustrative examples too.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.1105-1114
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• 2021

In this paper, we prove a fixed point theorem for G-contractive type non-self mapping in cone metric space endowed with a graph. Our result generalizes many results in the literature and provide a new pavement for solving nonlinear functional equations.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.757-771
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• 2022

In this paper, we present some fixed point theorems for rational type contractive conditions in the setting of a complete metric space via a cyclic (𝛼, 𝛽)-admissible mapping imbedded in simulation function. Our results extend and generalize some previous works from the existing literature. We also give some examples to illustrate the obtained results.

• International Journal of Quality Innovation
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• v.3 no.2
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• pp.113-131
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• 2002

The relationships among multi-dimensional data (such as medical examination data) with ambiguity and variation are difficult to explore. The traditional approach to building a data classification system requires the formulation of rules by which the input data can be analyzed. The formulation of such rules is very difficult with large sets of input data. This paper first describes two classification approaches using back-propagation (BP) neural network and Mahalanobis distance (MD) classifier, and then proposes two classification approaches for multi-dimensional feature selection. The first one proposed is a feature selection procedure from the trained back-propagation (BP) neural network. The basic idea of this procedure is to compare the multiplication weights between input and hidden layer and hidden and output layer. In order to simplify the structure, only the multiplication weights of large absolute values are used. The second approach is Mahalanobis-Taguchi system (MTS) originally suggested by Dr. Taguchi. The MTS performs Taguchi's fractional factorial design based on the Mahalanobis distance as a performance metric. We combine the automatic thresholding with MD: it can deal with a reduced model, which is the focus of this paper In this work, two case studies will be used as examples to compare and discuss the complete and reduced models employing BP neural network and MD classifier. The implementation results show that proposed approaches are effective and powerful for the classification.