• 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.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.20 no.4
• /
• pp.295-308
• /
• 2016

We propose a projection-based analysis of a new hybridizable discontinuous Gale-rkin method for second order elliptic equations. The method is more advantageous than the standard HDG method in a sense that the new method has higher-order accuracy and lower computational cost, and is more flexible. Notable distinctions of our new method, when compared to the standard HDG emthod, are that our method uses $L^2$-projection and suitable stabilization parameter depending on a mesh size for superconvergence. We show that the error for the solution of the equation converges with order p + 2 when we only use polynomials of degree p + 1 as a finite element space without postprocessing. After establishing the theory, we carry out numerical tests to demonstrate and ensure that the proposed method is effective and accurate in practice.

• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.42 no.1
• /
• pp.57-67
• /
• 2005

Fast scalar multiplication of points on elliptic curve is important for elliptic curve cryptography applications. In order to vary field sizes depending on security situations, the cryptography coprocessors should support variable length finite field arithmetic units. To determine the effective variable length finite field arithmetic architecture, two well-known curve scalar multiplication algorithms were implemented on FPGA. The affine coordinates algorithm must use a hardware division unit, but the projective coordinates algorithm only uses a fast multiplication unit. The former algorithm needs the division hardware. The latter only requires a multiplication hardware, but it need more space to store intermediate results. To make the division unit versatile, we need to add a feedback signal line at every bit position. We proposed a method to mitigate this problem. For multiplication in projective coordinates implementation, we use a widely used digit serial multiplication hardware, which is simpler to be made versatile. We experimented with our implemented ECC coprocessors using variable length finite field arithmetic unit which has the maximum field size 256. On the clock speed 40 MHz, the scalar multiplication time is 6.0 msec for affine implementation while it is 1.15 msec for projective implementation. As a result of the study, we found that the projective coordinates algorithm which does not use the division hardware was faster than the affine coordinate algorithm. In addition, the memory implementation effectiveness relative to logic implementation will have a large influence on the implementation space requirements of the two algorithms.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.24 no.4
• /
• pp.355-364
• /
• 2011

In this study, the details of WSA(wavelet series analysis) have been demonstrated to solve the 4th-order elliptic differential equation. It is clear to solve the 2nd-order elliptic differential equation with the basis function of Hat wavelet series that is used in the previous study existed in $H^1$-space. However, it is difficult to solve the 4th order differential equation with same basis function of Hat wavelet series because of insufficient differentiability and integrability. To overcome this problem, the linear equations in terms of moment and deflection have been formulated and solved sequentially that are similar to extension of Elastic Load Method and Moment Area Method in some senses. Also, the differences and common points between the proposed method and the meshless method are discussed in the procedure of WSA formulation. As we expect, it is easy to ascertain that the more terms of Hat wavelet series are used, the better numerical solutions are improved. Also the solutions obtained by WSA have been compared with the conventional FEM solutions in case of Euler beam problems with stress singularity.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.14 no.9
• /
• pp.2099-2104
• /
• 2010

In this paper, HRV signal which was appeared RR intervals from ECG was analyzed using return-map during anesthesia. We intended to estimate the depth of anesthesia observing the change of autonomic nervous activity(ANS) because HRV showed change of cardio-vascular system of the body according to state of ANS. Return-map analysis is to reconstruct time series of HRV to phase space after calculating delay time and embedded time. After approximating the signal distribution which was reconstructed in phase space in elliptic, we calculated the lengths of major and minor axises of the elliptic and the values was used to estimate the depth of anesthesia. Stages of the anesthesia were 7 levels to evaluate the depth of anesthesia. At induction stage of strong external stimulation, the length of major and minor axis were statistically high and at the operation stage of non-external stimulation, the values were statistically low. Conclusively, the stages of anesthesia were discriminated by HRV signal mapped in the phase space during operation.

• Journal of Plant Biology
• /
• v.26 no.1
• /
• pp.41-51
• /
• 1983

This study was carried out to investigate ontogeny of stomata and aerenchyma tissue in Trapa natans L. var. bispinosa Makino, an aquatic plant. Ontogeny of stomata in this plant was an aperigenous type surrounding with 5 to 8 epidermal cells without subsidiary cells. Stomata were distributed abundantly on the upper surface of leaf, however, no stoma was found on the lower surface of leaf, and on the epidermis of reproductive organ, petiole and stem. Ontogency of aerenchyma tissue was progressed with five steps; 1) formation of angular cells by division of cortex cells, 2) development of small and large globular cells in accompany with schizogenous intercellular space, 3) enlargement of globular cells and more expansion of intercellular space, 4) cell induction of long elliptic and triarmed shape, 5) completion of the largest intercellular space from endodermis toepidermis. During the growth period two types of leaf were appeared at each node of stems; one type was a submerged and early-fallen leaf, the other was a floating leaf on water surface.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.1051-1063
• /
• 2018

The real moment-angle complex (or, more generally, real polyhedral product) and its real toric space have recently attracted much attention in toric topology. The aim of this paper is to give two interesting remarks regarding real polyhedral products and real toric spaces. That is, we first show that Moore's conjecture holds to be true for certain real polyhedral products. In general, real polyhedral products show some drastic difference between the rational and torsion homotopy groups. Our result shows that at least in terms of the homotopy exponent at a prime this is not the case for real polyhedral products associated to a simplicial complex whose minimal missing faces are all k-simplices with $k{\geq}2$. Moreover, we also show a structural theorem for a finite group G acting simplicially on the real toric space. In other words, we show that G always contains an element of order 2, and so the order of G should be even.

• Bulletin of the Korean Mathematical Society
• /
• v.35 no.2
• /
• pp.345-362
• /
• 1998

We introduce and anlyze a naturally parallelizable frequency-domain method for parabolic problems with a Neumann boundary condition. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution of the original problem in the space-time domain. Existence and uniqueness of a solution of the transformed problem corresponding to each frequency is established. Fourier invertibility of the solution in the frequency-domain is also examined. Error estimates for a finite element approximation to solutions fo transformed problems and full error estimates for solving the given problem using a discrete Fourier inverse transform are given.

• Bulletin of the Korean Mathematical Society
• /
• v.39 no.4
• /
• pp.589-606
• /
• 2002

We introduce and analyze a frequency-domain method for parabolic partial differential equations. The method is naturally parallelizable. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we propose to solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution in the space-time domain. Existence and uniqueness as well as error estimates are given. Fourier invertibility is also examined. Numerical experiments are presented.

• Korean Journal of Mathematics
• /
• v.26 no.3
• /
• pp.467-481
• /
• 2018

In this paper we present a postprocessing scheme for the Raviart-Thomas mixed finite element approximation of the second order elliptic eigenvalue problem. This scheme is carried out by solving a primal source problem on a higher order space, and thereby can improve the convergence rate of the eigenfunction and eigenvalue approximations. It is also used to compute a posteriori error estimates which are asymptotically exact for the $L^2$ errors of the eigenfunctions. Some numerical results are provided to confirm the theoretical results.