• Bulletin of the Korean Mathematical Society
• /
• v.52 no.3
• /
• pp.977-986
• /
• 2015

Let G be a graph on the vertex set $V(G)=\{x_1,{\cdots},x_n\}$ with the edge set E(G), and let $R=K[x_1,{\cdots},x_n]$ be the polynomial ring over a field K. Two monomial ideals are associated to G, the edge ideal I(G) generated by all monomials $x_i,x_j$ with $\{x_i,x_j\}{\in}E(G)$, and the vertex cover ideal $I_G$ generated by monomials ${\prod}_{x_i{\in}C}{^{x_i}}$ for all minimal vertex covers C of G. A minimal vertex cover of G is a subset $C{\subset}V(G)$ such that each edge has at least one vertex in C and no proper subset of C has the same property. Indeed, the vertex cover ideal of G is the Alexander dual of the edge ideal of G. In this paper, for an unmixed bipartite graph G we consider the lattice of vertex covers $L_G$ and we explicitly describe the minimal free resolution of the ideal associated to $L_G$ which is exactly the vertex cover ideal of G. Then we compute depth, projective dimension, regularity and extremal Betti numbers of R/I(G) in terms of the associated lattice.

• Nuclear Engineering and Technology
• /
• v.31 no.2
• /
• pp.214-225
• /
• 1999

An accurate method is presented for flexural vibrations of sectorial plates having simply supported-free and free-free radial edges, when the circular edge is either clamped or simply supported. The classical Ritz method is employed with two sets of admissible functions assumed for the transverse vibratory displacements. These sets consist of : (1) mathematically complete algebraic-trigonometric polynomials which gurantee convergence to exact frequencies as sufficient terms are retained, and (2) comer functions which account for the bending moment singularities at re-entrant comer of the radial edges having arbitrary edge conditions. Accurate (at least four significant figures) frequencies and normalized contours of the transverse vibratory displacement are presented for the spectra of corner angles [90$^{\circ}$, 180$^{\circ}$(semi-circular), 270$^{\circ}$, 300$^{\circ}$, 330$^{\circ}$, 350$^{\circ}$, 355$^{\circ}$, 360$^{\circ}$ (complete circular)] causing a re-entrant comer of the radial edges. Future solutions drawn from alternative numerical procedures and finite element techniques may be compared with these accurate results.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.21 no.7
• /
• pp.1814-1819
• /
• 1996

This paper describes a dnw serial interface system which uses comma free code. Typically parallel 25 pin cable and connectors are used to transfer and receive the data between digital systems such as HDVCR, D3VTR and HDTV Receiver.The coaxial cable is more desirable for consumer product applications and also for studio applications where long signal paths and switching are requeired. This serial data trasfer technique is possible the error detection and the self synchronization, also easy edge insertion for PLL control. It is also cost effective because is does not requeire RF PLL, scrambling, and NRZI hardware.

• Structural Engineering and Mechanics
• /
• v.55 no.4
• /
• pp.785-799
• /
• 2015

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of hyperboloidal shells free at the top edge and clamped at the bottom edge like a hyperboloidal cooling tower by the Ritz method based upon the circular cylindrical coordinate system instead of related 3-D shell coordinates which are normal and tangent to the shell midsurface. The Legendre polynomials are used as admissible displacements. Convergence to four-digit exactitude is demonstrated. Natural frequencies from the present 3-D analysis are also compared with those of straight beams with circular cross section, complete (not truncated) conical shells, and circular cylindrical shells as special cases of hyperboloidal shells from the classical beam theory, 2-D thin shell theory, and other 3-D methods.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.18 no.3
• /
• pp.225-240
• /
• 2006

In order to calculate bending moments of rectangular plates with three edges clamped the other free subjected to both a uniform load and a triangular load, a finite difference equation for the non-dimensional governing equation are presented and numerical solutions with different aspect ratios and/or number of grid points are analyzed. The finite difference solutions are obtained by use of grid points up to 11,520 and the optimum grid points according to aspect ratios of the plate are presented as well. The obtained numerical solutions are shown to satisfy the given x moment boundary condition at the free edge, which can not be satisfied in Levy's analytical solutions and peculiar behaviour of the calculated moments is observed around the corners between the free edge and fixed ones. The numerical solutions of bending moments subjected to both a uniform load and a triangular load are compared with the corresponding analytical solutions which are shown in very good agreement on the solution domain except the neighborhood of the free edge.

• Journal of Welding and Joining
• /
• v.18 no.1
• /
• pp.104-109
• /
• 2000

Based on the principle of complementary energy, an analytical method is developed which focused on the end effects for determining thermal stress distributions in the clad beam. This method gives the stress distributions which completely satisfy the stress-free boundary condition at the edge. Numerical results shows that shear and peeling stress at the interface between the substrate and clad are significant near the edge and become negligible in the interior region. Even thought the relative location where the maximum or minimum stresses take place moves to interior as the length of the beam becomes smaller, the absolute location from the free end and the value of these stresses are the same in spite of the variation of the length of beam.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.16 no.7
• /
• pp.1278-1284
• /
• 1992

In plate rolling, it is desired to reduce the trimming loss by controlling the formation of defective end shapes. For this reason, edge rolling is frequently performed in the plate mill. In this paper, the effect of various process variables on the deformation of plate ends in edge rolling is examined by conducting experiments and finite element computer simulation. A focus is given to investigating the effect of edging on the width of the deformed plate trimming-free plate rolling.

• Proceedings of the KWS Conference
• /
• 1999.10a
• /
• pp.306-309
• /
• 1999

Based on the principle of complementary energy, an analytical method is developed which focused on the end effects for determining thermal stress distributions in the claded beam. This method gives the stress distributions which completely satisfy the stress-free boundary condition at the edge. Numerical result shows that shear stress and peeling stress at the interface between the substrate and clad are significant near the edge and become negligible in the interior region. Even though the relative location where the maximum or minimum stresses take place moves to interior as the length of the beam become smaller, the absolute location from the free end and the value of these stresses are the same in spite of the variation of the length of beam.

• Structural Engineering and Mechanics
• /
• v.5 no.1
• /
• pp.85-104
• /
• 1997

The paper investigates the influence of lateral restraint on the buckling behaviour of plate under non-uniform compression. The unloaded edges are assumed to be partially restrained against translation in the plane of the plate and the distributions of the resulting forces acting on the plate are shown. The stability analysis is done numerically using the Galerkin method and various strategies the economize the numerical implementation are presented. Results are obtained showing the variation of the buckling load, from free edge translation to fully restrained, with unloaded edges simply supported, clamped and partially restrained against rotation for various plate aspect ratios and stress gradient coefficients. An apparent decrease in the buckling load is observed due to these destabilizing forces acting in the plate and changes in the buckling modes are observed by increasing the intensity of the lateral restraint. A comparison is made between the budding loads predicted from various formulas in stability standards based on free edge translation and the values derived from the present investigation. A difference of about 34% in the predicted buckling load and different buckling mode were found.

• Journal of Sensor Science and Technology
• /
• v.29 no.3
• /
• pp.180-186
• /
• 2020

In this study, we applied edge-pulse modulation to prevent the flicker of light-emitting diode (LED) light in a visible light identification system. In the visible light transmitter, positive pulses were transmitted at the edges of the low-to-high transition points, and negative pulses were transmitted at the edges of the high-to-low transition points of the non-return-to-zero (NRZ) data waveforms. In the visible light receiver, the NRZ waveforms were regenerated by making low-to-high and high-to-low transitions at the point of the positive and negative pulses, respectively. This method has two advantages. First, it ensures that the LED light is flicker-free because the average optical power of the LED was kept constant during data transmission in the transmitter. Second, the 120 Hz optical noise from the adjacent lighting lamps was easily cut off using a simple RC-high pass filter in the receiver.