• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.12 no.2
• /
• pp.3-10
• /
• 2002

For efficient implementation of scalar multiplication in Kobliz elliptic curves, Frobenius endomorphism is useful. Instead of binary expansion of scalar, using Frobenius expansion of scalar we can speed up scalar multiplication and so fast scalar multiplication is closely related to the expansion length of integral multipliers. In this paper we propose a new idea to reduce the length of Frobenius expansion of integral multipliers of scalar multiplication, which makes speed up scalar multiplication. By using the element whose norm is equal to a prime instead of that whose norm is equal to the order of a given elliptic curve we optimize the length of the Frobenius expansion. It can reduce more the length of the Frobenius expansion than that of Solinas, Smart.

• Korean Journal of Mathematics
• /
• v.18 no.4
• /
• pp.425-440
• /
• 2010

Using Green's theorem, elliptic boundary value problems can be converted to boundary integral equations. A numerical methods for boundary integral equations are boundary elementary method(BEM). BEM has advantages over finite element method(FEM) whenever the fundamental solutions are known. Helmholtz type equations arise naturally in many physical applications. In a boundary integral formulation for the exterior Neumann there occurs a hypersingular operator which exhibits a strong singularity like $\frac{1}{|x-y|^3}$ and hence is not an integrable function. In this paper we are going to remove this hypersingularity by reducing the regularity of test functions.

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

• Journal of the Korean Mathematical Society
• /
• v.6 no.2
• /
• pp.55-73
• /
• 1969

• Journal of the Korean Mathematical Society
• /
• v.7 no.1
• /
• pp.1-5
• /
• 1970

• Communications of the Korean Mathematical Society
• /
• v.17 no.2
• /
• pp.349-361
• /
• 2002

The ill-posed elliptic wave propagation problems can be transformed into well-posed initial value problems of the reflection and transmission operators characterizing the material structure of the given model by the combination of wave field splitting and invariant imbedding methods. In general, the derived scattering operator equations are of first-order in range, nonlinear, nonlocal, and stiff and oscillatory with a subtle fixed and movable singularity structure. The phase space and path integral analysis reveals that construction and reconstruction algorithms depend crucially on a detailed symbol analysis of the scattering operators. Some information about the singularity structure of the scattering operator symbols is presented and analyzed in the transversely homogeneous limit.

• Structural Engineering and Mechanics
• /
• v.22 no.4
• /
• pp.433-447
• /
• 2006

The problem of very large deflection of a circular cantilever arc device subjected to inward or outward polar force is studied. An exact elliptic integral solution is derived for the two cases and the results are checked using large displacement finite element analysis via the ANSYS package by performing a new novel modeling simulation technique for this problem. Excellent agreements have been obtained between the exact analytical solution and the numerical approach. From this study, a design chart for engineers is developed to predict the required value for the inward polar force for the device to switch on for a given angle forming the circular arc (${\theta}_o$). This study has several interesting applications in mechanical engineering, integrated circuit technology, nanotechnology and especially in microelectromechanical systems (MEMs) such as a MEM circular device switch subjected to attractive or repulsive magnetic forces due to the attachments of two magnetic poles at the fixed and at the free end of the circular cantilever arc switch device.

• The Proceeding of the Korean Institute of Electromagnetic Engineering and Science
• /
• v.2 no.3
• /
• pp.26-31
• /
• 1991

The scattering property of TMz illuminated a elliptic dielectric cylinders with arbitrary cross section are analyzed by the boundary element techniques. The boundary element equations are for- mulated via Maxwell's equations, weighted residual of Green's theorem, and the boundary conditions. The unknown surface fields on the boundaries are then calculated by the boundary element integral equations. Once the surface fields are found, the scattered fields in far-zone and scattering widths (SW) are readily determined. To show the validity and usefulness of this formulation, computations are compared with those obtained using analytical method and one layer circular cylinder. As exten- sion to arbitrary cross-sectioned cylinders, plane wave scattering from a elliptic dielectric cylinders are numerically analyzed. A general computer program has been developed using the quadratic ele- ments(Higher order borndary elements) and the Gaussian quadrature.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.11 no.6
• /
• pp.105-113
• /
• 2001

Recently, Gallant, Lambert arid Vanstone introduced a method for speeding up the scalar multiplication on a family of elliptic curves over prime fields that have efficiently-computable endomorphisms. It really depends on decomposing an integral scalar in terms of an integer eigenvalue of the characteristic polynomial of such an endomorphism. In this paper, by using an element in the endomorphism ring of such an elliptic curve, we present an alternate method for decomposing a scalar. The proposed algorithm is more efficient than that of Gallant\`s and an upper bound on the lengths of the components is explicitly given.

• Honam Mathematical Journal
• /
• v.24 no.1
• /
• pp.25-33
• /
• 2002

In this paper we have shown conditions of R for the existence of the solution to the problem of the type $-u''=ue^{{\varepsilon}u}$ on the interval (0, R) with boundary and other conditions as in $(1-{\varepsilon})-(4)$ for various ${\varepsilon}$.