• Journal of Communications and Networks
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• v.4 no.2
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• pp.81-89
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• 2002

In this paper, we design and implement an efficient fair off-line electronic cash system based on Elliptic Curve Discrete Logarithm Problem (ECDLP), in which the anonymity of coins is revocable by a trustee in case of dispute. To achieve this, we employ the Petersen and Poupard s electronic cash system [1] and extend it by using an elliptic curve over the finite field GF($2^n$). This naturally reduces message size by 85% compared with the original scheme and makes a smart card to store coins easily. Furthermore, we use the Baek et al. s provably secure public key encryption scheme [2] to improve the security of electronic cash system. As an extension, we propose a method to add atomicity into new electronic cash system. To the best of our knowledge, this is the first result to implement a fair off-line electronic cash system based on ECDLP with provable security.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.153-161
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• 2015

In this work, we consider an elliptic system $$\left{\array {-{\Delta}u=au+bv+{\delta}_1u+-{\delta}_2u^-+f_1(x,u,v) && in\;{\Omega},\\-{\Delta}v=bu+cv+{\eta}_1v^+-{\eta}_2v^-+f_2(x,u,v) && in\;{\Omega},\\{\hfill{70}}u=v=0{\hfill{90}}on\;{\partial}{\Omega},}$$, where ${\Omega}{\subset}R^N$ be a bounded domain with smooth boundary. We prove that the system has at least two nontrivial solutions by applying linking theorem.

• Korean Journal of Mathematics
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• v.23 no.2
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• pp.259-267
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• 2015

This paper is devoted to investigate the existence of the solutions for a class of the noncooperative elliptic system involving critical Sobolev exponents. We show the existence of the negative solution for the problem. We show the existence of the unique negative solution for the system of the linear part of the problem under some conditions, which is also the negative solution of the nonlinear problem. We also consider the eigenvalue problem of the matrix.

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.619-630
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• 2015

This paper is devoted to investigate the multiple solutions for a class of the cooperative elliptic system involving subcritical Sobolev exponents on the bounded domain with smooth boundary. We first show the uniqueness and the negativity of the solution for the linear system of the problem via the direct calculation. We next use the variational method and the mountain pass theorem in the critical point theory.

• Korean Journal of Mathematics
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• v.17 no.2
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• pp.197-210
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• 2009

We prove the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the elliptic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}A{\xi}+g_1({\xi}+ 2{\eta})=s{\phi}_1+h\;in\;{\Omega},\\A{\xi}+g_2({\xi}+ 2{\eta})=s{\phi}_1+h\;in\;{\Omega},\end{array}$$ where $lim_{u{\rightarrow}{\infty}}\frac{gj(u)}{u}={\beta}_j$, $lim_{u{\rightarrow}-{\infty}}\frac{gj(u)}{u}={\alpha}_j$ are finite and the nonlinearity $g_1+2g_2$ crosses eigenvalues of A.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.1
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• pp.139-146
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• 2008

We investigate the uniqueness and multiplicity of solutions for the nonlinear elliptic system with Dirichlet boundary condition $$\{-{\Delta}u+g_1(u,v)=f_1(x){\text{ in }}{\Omega},\\-{\Delta}v+g_2(u,v)=f_2(x){\text{ in }}{\Omega},$$ where ${\Omega}$ is a bounded set in $R^n$ with smooth boundary ${\partial}{\Omega}$. Here $g_1$, $g_2$ are nonlinear functions of u, v and $f_1$, $f_2$ are source terms.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.707-720
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• 2014

We get a theorem which shows the existence of at least three solutions for some elliptic system with Dirichlet boundary condition. We obtain this result by using the finite dimensional reduction method which reduces the infinite dimensional problem to the finite dimensional one. We also use the critical point theory on the reduced finite dimensioal subspace.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.1-10
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• 2012

Let ${\Omega}$ be a bounded subset of $\mathbb{R}^n$ with smooth boundary. We investigate the solvability for a class of the system of the nonlinear elliptic equations with Dirichlet boundary condition. Using the mountain pass theorem we prove that the system has at least one nontrivial solution.

• Journal of Mechanical Science and Technology
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• v.20 no.1
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• pp.167-175
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• 2006

A parametric study has been accomplished to figure out the effects of elliptic cylinder thickness, angle of attack, and Reynolds number on the unsteady lift and drag forces exerted on the elliptic cylinder. A two-dimensional incompressible Navier-Stokes flow solver is developed based on the SIMPLER method in the body-intrinsic coordinates system to analyze the unsteady viscous flow over elliptic cylinder. Thickness-to-chord ratios of 0.2, 0.4, and 0.6 elliptic cylinders are simulated at different Reynolds numbers of 400 and 600, and angles of attack of $10^{\circ},\;20^{\circ},\;and\;30^{\circ}$. Through this study, it is observed that the elliptic cylinder thickness, angle of attack, and Reynolds number are very important parameters to decide the lift and drag forces. All these parameters also affect significantly the frequencies of the unsteady force oscillations.

• Korea-Australia Rheology Journal
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• v.17 no.4
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• pp.171-180
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• 2005

We present numerical results for inertialess elliptic particle suspensions in a Newtonian fluid subject to simple shear flow, using the sliding bi-periodic frame concept of Hwang et al. (2004) such that a particulate system with a small number of particles could represent a suspension system containing a large number of particles. We report the motion and configurational change of elliptic particles in simple shear flow and discuss the inter-relationship with the bulk shear stress behaviors through several example problems of a single, two-interacting and ten particle problems in a sliding bi-periodic frame. The main objective is to check the feasibility of the direct simulation method for understanding the relationship between the microstructural evolution and the bulk material behaviors.