• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.3
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• pp.161-169
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• 2008

We investigate the existence of solutions u(x, t) for perturbations of the elliptic system with Dirichlet boundary condition $$\array {L{\xi}+{\mu}g({\xi}+2{\eta})=f\;in\;{\Omega}}\\{L{\eta}+{\nu}g({\xi}+2{\eta})=f\;in\;{\Omega}}$$ (0.1) where $g(u)=Bu^+-Au^-$, $u^+=max\{u,\;0\}$, $u^-=max\{-u,\;0\}$, ${\mu}$, ${\nu}$ are nonzero constants and the nonlinearity $({\mu}+2{\nu})g(u)$ crosses the eigenvalues of the elliptic operator L.

• Transactions of Materials Processing
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• v.9 no.3
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• pp.304-312
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• 2000

An inverse finite element approach is employed to efficiently design the optimum blank shape and intermediate shapes from the desired final shape in multi-stage elliptic cup drawing processes. The multi-stage deep-drawing process is difficult to design with the conventional finite element analysis since the process is very complicate with the conventional finite element analysis since the process is very complicated with intermediate shapes and the numerical analysis undergoes the convergence problem even with tremendous computing time. The elliptic cup drawing process needs much effort to design sine it requires full three-dimensional analysis. The inverse analysis is able to omit all complicated and tedious analysis procedures for the optimum process design. In this paper, the finite element inverse analysis provides the thickness strain distribution of each intermediate shape through the multi-stage analysis. The multi-stage analysis deals with the convergence among intermediate shapes and the corresponding sliding constraint surfaces that are described by the analytic function of merged-arc type surfaces.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2000.04a
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• pp.21-25
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• 2000

An inverse finite element approach is employed for more capability to design the optimum blank shape from the desired final shape with small amount of expense and computation time For multi-stage sheet metal forming processes numerical analysis is expense difficult to carry out the to its complexities and convergence problem. It also requires lots of computation time. For the analysis of elliptic cup with large aspect ratio intermediate sliding constraint surfaces are difficult to describe. in this paper multi-stage finite element inverse analysis is applied to multi-stage elliptic cup drawing processes to calculate intermediate blank shapes and strain distributions in each stages. To describe intermediate sliding constraint surfaces an analytic scheme is introduced to deal with merged-arc type sliding surfaces.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.239-263
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• 2019

The $Calder{\acute{o}}n$-Zygmund type estimate is proved for elliptic obstacle problems in bounded non-smooth domains. The problems are related to divergence form nonlinear elliptic equation with measurable nonlinearities. Precisely, nonlinearity $a({\xi},x_1,x^{\prime})$ is assumed to be only measurable in one spatial variable $x_1$ and has locally small BMO semi-norm in the other spatial variables x', uniformly in ${\xi}$ variable. Regarding non-smooth domains, we assume that the boundaries are locally flat in the sense of Reifenberg. We also investigate global regularity in the settings of weighted Orlicz spaces for the weak solutions to the problems considered here.

• International Journal of Computer Science & Network Security
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• v.21 no.3
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• pp.60-70
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• 2021

In this paper we study the problem of implementation of security issues of blue tooth, especially secure simple pairing, with the help of an efficient four user authenticated key (4UAK) for an elliptic curve cryptography (ECC). This paper also deals with the design, implement and performance evaluation of secure simple pairing (SSP) using an elliptic curve cryptography, such as Diffie Hellman protocol when four users are involved. Here, we also compute the best, worst and average case step counts (time complexities). This work puts forth an efficient way of providing security in blue tooth. The time complexity of O(n⁴) is achieved using Rabin Miller Primality methodology. The method also reduces the calculation price and light communication loads.

• The Journal of the Korea institute of electronic communication sciences
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• v.11 no.7
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• pp.693-700
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• 2016

It is important that we can calculate the order of non-supersingular elliptic curves with large prime factors over the finite field GF(q) to guarantee the security of public key cryptosystems based on discrete logarithm problem(DLP). Schoof algorithm, however, which is used to calculate the order of the non-supersingular elliptic curves currently is so complicated that many papers are appeared recently to update the algorithm. To avoid Schoof algorithm, in this paper, we propose an algorithm to calculate orders of elliptic curves over finite composite fields of the forms $GF(2^m)=GF(2^{rs})=GF((2^r)^s)$ using Weil's theorem. Implementing the program based on the proposed algorithm, we find a efficient non-supersingular elliptic curve over the finite composite field $GF(2^5)^{31})$ of the order larger than $10^{40}$ with prime factor larger than $10^{40}$ using the elliptic curve $E(GF(2^5))$ of the order 36.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.4
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• pp.729-739
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• 2017

The objective of this study was to optimize minimum-energy impulsive spacecraft intercept using genetic algorithms. A mathematical model was established on two-body system based on f and g solution and universal variable to address spacecraft intercept problem for non-coplanar elliptical orbits. This nonlinear problem includes many local optima due to discontinuity and strong nonlinearity. In addition, since it does not provide a closed-form solution, it must be solved using a numerical method. Therefore, the initial guess is that a very sensitive factor is needed to obtain globally optimal values. Genetic algorithms are effective for solving these kinds of optimization problems due to inherent properties of random search algorithms. The main goal of this paper was to find minimum energy solution for orbit transfer problem. The numerical solution using initial values evaluated by the genetic algorithm matched with results of Hohmann transfer. Such optimal solution for unrestricted arbitrary elliptic orbits using universal variables provides flexibility to solve orbit transfer problems.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1169-1182
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• 2011

In this paper we study the existence of non-trivial weak solutions of the Neumann problem for quasilinear elliptic equations in the form $$-div(h(x){\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+b(x){\mid}u{\mid}^{p-2}u=f(x,\;u),\;p{\geq}2$$ in an unbounded domain ${\Omega}{\subset}\mathbb{R}^N$, $N{\geq}3$, with sufficiently smooth bounded boundary ${\partial}{\Omega}$, where $h(x){\in}L_{loc}^1(\overline{\Omega})$, $\overline{\Omega}={\Omega}{\cup}{\partial}{\Omega}$, $h(x){\geq}1$ for all $x{\in}{\Omega}$. The proof of main results rely essentially on the arguments of variational method.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.29-37
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• 2010

We establish the existence of weak solutions in an infinite subsonic channel in the self-similar plane to the two-dimensional Burgers system. We consider a boundary value problem in a fixed domain such that a part of the domain is degenerate, and the system becomes a second order elliptic equation in the channel. The problem is motivated by the study of the weak shock reflection problem and 2-D Riemann problems. The two-dimensional Burgers system is obtained through an asymptotic reduction of the 2-D full Euler equations to study weak shock reflection by a ramp.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1035-1054
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• 2010

We consider a mixed type singularly perturbed one dimensional elliptic problem with discontinuous source term. The domain under consideration is partitioned into two subdomains. A convection-diffusion and a reaction-diffusion type equations are posed on the first and second subdomains respectively. Two hybrid difference schemes on Shishkin mesh are constructed and we prove that the schemes are almost second order convergence in the maximum norm independent of the diffusion parameter. Error bounds for the numerical solution and its numerical derivative are established. Numerical results are presented which support the theoretical results.