• Bulletin of the Korean Mathematical Society
• /
• v.49 no.3
• /
• pp.621-633
• /
• 2012

By establishing a new summation formula for the series $_3F_2(\frac{1}{2})$, recently Rathie and Pogany have obtained an interesting result known as Kummer type II transformation for the generalized hypergeometric function $_2F_2$. Here we aim at deriving their result by using a very elementary method and presenting two elegant results for certain terminating series $_3F_2(2)$. Furthermore two interesting applications of our new results are demonstrated.

• Journal of the Korean Mathematical Society
• /
• v.55 no.5
• /
• pp.1103-1129
• /
• 2018

In this paper, we show several vanishing type theorems for p-harmonic ${\ell}$-forms on Riemannian manifolds ($p{\geq}2$). First of all, we consider complete non-compact immersed submanifolds $M^n$ of $N^{n+m}$ with flat normal bundle, we prove that any p-harmonic ${\ell}$-form on M is trivial if N has pure curvature tensor and M satisfies some geometric conditions. Then, we obtain a vanishing theorem on Riemannian manifolds with a weighted $Poincar{\acute{e}}$ inequality. Final, we investigate complete simply connected, locally conformally flat Riemannian manifolds M and point out that there is no nontrivial p-harmonic ${\ell}$-form on M provided that the Ricci curvature has suitable bound.

• Journal of the Korean Data and Information Science Society
• /
• v.16 no.3
• /
• pp.665-682
• /
• 2005

The sample reuse bootstrap technique has been successful to attract both applied and theoretical statisticians since its origination. In recent years a good deal of attention has been focused on the applications of bootstrap methods in regression analysis. It is easier but more accurate computation methods heavily depend on high-speed computers and warrant tough mathematical justification for their validity. It is now evident that the presence of multiple unusual observations could make a great deal of damage to the inferential procedure. We suspect that bootstrap methods may not be free from this problem. We at first present few examples in favour of our suspicion and propose a new method diagnostic-before-bootstrap method for regression purpose. The usefulness of our newly proposed method is investigated through few well-known examples and a Monte Carlo simulation under a variety of error and leverage structures.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.19 no.2
• /
• pp.57-73
• /
• 1994

KADS is currently a best known methodology for expert system development is Europe. KADS world sees the expert system development as a modeling activity and uses models to control complexity of the development process. Four layers KADS expertise model is used to describe expert knowledge. But this expertise model in high abstraction level is conceptual and not formalized. This paper has formalized KADS expertise model using set theory and mathematical semantics combined in order to reduce the ambiguity of informal models of expertise, provide a precise means of communication about the model of expertise and point out incompleteness and inconsistency of the model of expertise. Instead of first order predicate calculs, set theory and mathematical semantics are used because they are a more general and have compositive quality.

• Journal of the Korean Mathematical Society
• /
• v.50 no.1
• /
• pp.111-125
• /
• 2013

In this paper, we consider a continuous time risk model involving two types of dependent claims, namely main claims and by-claims. The by-claim is induced by the main claim and the occurrence of by-claim may be delayed depending on associated main claim amount. Using Rouch$\acute{e}$'s theorem, we first derive the closed-form solution for the Laplace transform of the survival probability in the dependent risk model from an integro-differential equations system. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival probability. For the exponential claim sizes, we present the explicit formula for the survival probability. We also illustrate the influence of the model parameters in the dependent risk model on the survival probability by numerical examples.

• Journal of the Korean Mathematical Society
• /
• v.56 no.5
• /
• pp.1159-1172
• /
• 2019

A semigroup S is called a weakly abundant semigroup if its every $\tilde{\mathcal{L}}$-class and every $\tilde{\mathcal{R}}$-class contains an idempotent. Our purpose is to study an analogue of orthodox semigroups in the class of weakly abundant semigroups. Such an analogue is called a left quasi-abundant semigroup, which is a weakly abundant semigroup with a left quasi-normal band of idempotents and having the congruence condition (C). To build our main structure theorem for left quasi-abundant semigroups, we first give a sufficient and necessary condition of the idempotent set E(S) of a weakly abundant semigroup S being a left quasi-normal band. And then we construct a left quasi-abundant semigroup in terms of weak spined products. Such a result is a generalisation of that of Guo and Shum for left semi-perfect abundant semigroups. In addition, we consider a type Q semigroup which is a left quasi-abundant semigroup having the PC condition.

• Management Science and Financial Engineering
• /
• v.10 no.2
• /
• pp.53-71
• /
• 2004

In this study, a mathematical model that shows the optimal payout policy is developed. The model is new and unique in the sense that not only continuous-time framework is used, but also both partial differential equation (PDE) and real-option approach are utilized in the derivation of optimal payouts for the first time. In the model building, non-linear demand curve for dividend payouts in the competitive capital markets is assumed. From the sensitivity analysis using traditional comparative static analysis, some useful managerial implications which are consistent with famous previous studies are derived under realistic conditions. All results in this study, however, are valid under the assumption that the opportunity costs follow geometric Brownian motion, which is widely used in economic science and finance literature.

• The Pure and Applied Mathematics
• /
• v.26 no.3
• /
• pp.177-188
• /
• 2019

Suppose G is a molecular graph with edge set E(G). The hyper-Zagreb index of G is defined as $HM(G)={\sum}_{uv{\in}E(G)}[deg_G(u)+deg_G(v)]^2$, where $deg_G(u)$ is the degree of a vertex u in G. In this paper, all chemical trees of order $n{\geq}12$ with the first twenty smallest hyper-Zagreb index are characterized.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.14 no.11
• /
• pp.4573-4594
• /
• 2020

Announcement protocol in Internet of Vehicles (IoV) is an intelligent application to enhance public safety, alleviate traffic jams and improve transportation quality. It requires communication between vehicles, roadside units and pedestrian to disseminate safety-related messages. However, as vehicles connected to internet, it makes them accessible globally to a potential adversary. Safety-related application requires a message to be reliable, however it may intrude the privacy of a vehicle. Contrarily, if some misbehaviour emerges, the malicious vehicles must be able to traceable and revoke from the network. This is a contradiction between privacy and accountability since the privacy of a user should be preserved. For a secure communication among intelligent entities, we propose a novel announcement protocol in IoV using group signature. To the best of our knowledge, our work is the first comprehensive construction of an announcement protocol in IoV that deploys group signature. We show that our protocol efficiently solves these conflicting security requirements of message reliability, privacy and accountability using 5G communication channel. The performance analysis and simulation results signify our work achieves performance efficiency in IoV communication.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.17 no.5
• /
• pp.1450-1470
• /
• 2023

In a Vehicular Cloud (VC) network, an announcement protocol plays a critical role in promoting safety and efficiency by enabling vehicles to disseminate safety-related messages. The reliability of message exchange is essential for improving traffic safety and road conditions. However, verifying the message authenticity could lead to the potential compromise of vehicle privacy, presenting a significant security challenge in the VC network. In contrast, if any misbehavior occurs, the accountable vehicle must be identifiable and removed from the network to ensure public safety. Addressing this conflict between message reliability and privacy requires a secure protocol that satisfies accountability properties while preserving user privacy. This paper presents a novel announcement protocol for secure communication in VC networks that utilizes group signature to achieve seemingly contradictory goals of reliability, privacy, and accountability. We have developed the first comprehensive announcement protocol for VC using group signature, which has been shown to improve the performance efficiency and feasibility of the VC network through performance analysis and simulation results.