• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.5
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• pp.2792-2810
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• 2017

Forward-secure signature is a specific type of signature, which can mitigate the damage caused by the signing key exposure. Most of the existing forward-secure (identity-based) signature schemes can update users' secret keys at each time period, achieve the existential unforgeability, and resist against classical computer attacks. In this paper, we first revisit the framework of forward-secure identity-based signatures, and aim at supporting flexible key update at multi time period. Then we propose a post-quantum forward-secure identity-based signature scheme from lattices and use the basis delegation technique to provide flexible key update. Finally, we prove that the proposed scheme is strongly unforgeable under the short integer solution (SIS) hardness assumption in the random oracle model.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.10a
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• pp.349-352
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• 2004

In this paper, we propose a newly energy-efficient routing protocol, which is called Maximum Utility Routing(MUR), in mobile ad hoc networks (MANETs) so as to investigate the minimum energy and maximum lifetimes issues together. We present a utility-based framework so as to meet various incompatible constraints simultaneously and fairly. To explore this issue, we use the concepts and mathematics of microeconomics and game theory. Though simulation results, we show that our routing scheme has much better performance especially in terms of network efficiency, network lifetime, and average power consumption.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.533-546
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• 2018

The object of this work is to study the existence of solutions for a class of p(x)-Kirchhoff type problem under no-flux boundary conditions with dependence on the gradient. We establish our results by using the degree theory for operators of ($S_+$) type in the framework of variable exponent Sobolev spaces.

• Publications of The Korean Astronomical Society
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• v.30 no.2
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• pp.385-387
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• 2015

Stellar mass is an important parameter of galaxies. We estimate the dynamical mass of an elliptical galaxy by its velocity dispersion and effective radius using the Hernquist model in the framework of MOdified Newtonian Dynamics (MOND). MOND is an alternative theory to the dark matter paradigm. In MOND the dynamical mass is the same as the baryonic mass or luminous mass, and in elliptical galaxies most of the baryons reside in stars. We select elliptical galaxies between redshift 0.05 and 0.5 from the main galaxy sample and the luminous red galaxy sample in the Sloan Digital Sky Survey. We find that the stellar mass-to-light ratio at different redshift epochs can be fitted by a gamma distribution, and its mean is smaller at smaller redshifts.

• Industrial Engineering and Management Systems
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• v.11 no.1
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• pp.18-25
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• 2012

IChinese postman problem is one of the classical combinatorial optimization problems with many applications. However, in application, some uncertain factors are frequently encountered. This paper employs uncertain programming to deal with Chinese postman problem with uncertain weight Within the framework of uncertainty theory, the concepts of expected shortest route, ${\alpha}$-shortest route, and distribution shortest route are proposed. After that, expected shortest model, and ${\alpha}$-shortest model are constructed. Taking advantage of properties of uncertainty theory, these models can be transf-ormed into their corresponding deterministic forms, which can be solved by classical algorithm..

• Communications for Statistical Applications and Methods
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• v.22 no.4
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• pp.321-331
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• 2015

The K-means clustering algorithm is a popular and widely used method for clustering. For covariance matrices, we consider a geodesic clustering algorithm based on the K-means clustering framework in consideration of symmetric positive definite matrices as a Riemannian (non-Euclidean) manifold. This paper considers a geodesic clustering algorithm for data consisting of symmetric positive definite (SPD) matrices, utilizing the Riemannian geometric structure for SPD matrices and the idea of a K-means clustering algorithm. A K-means clustering algorithm is divided into two main steps for which we need a dissimilarity measure between two matrix data points and a way of computing centroids for observations in clusters. In order to use the Riemannian structure, we adopt the geodesic distance and the intrinsic mean for symmetric positive definite matrices. We demonstrate our proposed method through simulations as well as application to real financial data.

• The Mathematical Education
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• v.46 no.4
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• pp.423-443
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• 2007

Based on the framework of Huffered-Ackles, Fuson and Sherin(2004), data were analyzed in terms of 3 components: explaining(E), questioning(Q) and justifying(J) of students' mathematical concepts and problem solving in a math classroom. The students used varied presentations to explain and justify their mathematical concepts and ideas. They corrected their mathematical errors or misconceptions through discourses. In addition, they constructed and clarified their concepts and thinking while they were interacted. We were able to recognize there was a special feature in discourses that encouraged the students to construct and develop their mathematical concepts. As they participated in math class and received feedback on their learning, the whole class worked cooperatively in a positive way. Their discourse was improved from the level of the actual development to the level of the potential development and the pattern of interaction moved from ERE(Elicitaion-Response-Elaboration to PD(Proposition Discussion).

• The Mathematical Education
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• v.52 no.1
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• pp.111-128
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• 2013

The purpose of this study was to examine and analyze the cognitive demand of the mathematical tasks suggested in the middle school textbooks. In particular, it aimed to reveal the overall picture of the level of cognitive demand of the mathematical tasks in the strand of geometry in the textbooks. We adopted the framework for mathematical task analysis suggested by Stein & Smith(1998) and analyzed the mathematical tasks accordingly. The findings from the analysis showed that 95 percent of the mathematical tasks were at high level and the rest at low level in terms of cognitive demand. Most of the mathematical tasks in the textbooks were algorithmic and focused on producing correct answers by using procedures. In particular, the high level tasks were presented at the end of each chapter or unit for wrap up rather than as key resources.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.163-169
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• 2011

Recently, Kazmi and Khan [7] introduced a kind of equilibrium problem called generalized system (GS) with a single-valued bi-operator F. In this note, we aim at an extension of (GS) due to Kazmi and Khan [7] into a multi-valued circumstance. We consider a fairly general problem called the multi-valued quasi-generalized system (in short, MQGS). Based on the existence of 1-person game by Ding, Kim and Tan [5], we give a generalization of (GS) in the name of (MQGS) within the framework of Hausdorff topological vector spaces. As an application, we derive an existence result of the generalized vector quasi-variational inequality problem. This result leads to a multi-valued vector quasi-variational inequality extension of the strong vector variational inequality (SVVI) due to Fang and Huang [6] in a general Hausdorff topological vector space.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.19-34
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• 2019

The article is written with a view to introducing the new idea of an F-contraction on a closed ball and have new ${\acute{C}}iri{\acute{c}}$ type fixed point theorems in the framework of a complete metric space. That is why this outcome becomes useful for the contraction of the mapping on a closed ball instead of the whole space. At the same time, some comparative examples are constructed which establish the superiority of our results. It can be stated that the results that have come into being give proof of extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature.