• Journal of the Institute of Electronics Engineers of Korea SC
• /
• v.43 no.5 s.311
• /
• pp.36-43
• /
• 2006

In this paper we present a new high-speed parallel multiplier for Performing the bit-parallel multiplication of two polynomials in the finite fields $GF(2^m)$. Prior to construct the multiplier circuits, we consist of the MOD operation part to generate the result of bit-parallel multiplication with one coefficient of a multiplicative polynomial after performing the parallel multiplication of a multiplicand polynomial with a irreducible polynomial. The basic cells of MOD operation part have two AND gates and two XOR gates. Using these MOD operation parts, we can obtain the multiplication results performing the bit-parallel multiplication of two polynomials. Extending this process, we show the design of the generalized circuits for degree m and a simple example of constructing the multiplier circuit over finite fields $GF(2^4)$. Also, the presented multiplier is simulated by PSpice. The multiplier presented in this paper use the MOD operation parts with the basic cells repeatedly, and is easy to extend the multiplication of two polynomials in the finite fields with very large degree m, and is suitable to VLSI. Also, since this circuit has a low propagation delay time generated by the gates during operating process because of not use the memory elements in the inside of multiplier circuit, this multiplier circuit realizes a high-speed operation.

• Korean Journal of Computational Design and Engineering
• /
• v.19 no.4
• /
• pp.356-367
• /
• 2014

A robotic sapatial augmented reality (RSAR) system, which combines robotic components with projector-based AR technique, is unique in its ability to expand the user interaction area by dynamically changing the position and orientation of a projector-camera unit (PCU). For a moving PCU mounted on a conventional robotic device, we can compute its extrinsic parameters using a robot kinematics method assuming a link and joint geometry is available. In a RSAR system based on user-created robot (UCR), however, it is difficult to calibrate or measure the geometric configuration, which limits to apply a conventional kinematics method. In this paper, we propose a data-driven kinematics control method for a UCR-based RSAR system. The proposed method utilized a pre-sampled data set of camera calibration acquired at sufficient instances of kinematics configurations in fixed joint domains. Then, the sampled set is compactly represented as a set of B-spline surfaces. The proposed method have merits in two folds. First, it does not require any kinematics model such as a link length or joint orientation. Secondly, the computation is simple since it just evaluates a several polynomials rather than relying on Jacobian computation. We describe the proposed method and demonstrates the results for an experimental RSAR system with a PCU on a simple pan-tilt arm.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.32 no.5
• /
• pp.273-278
• /
• 2019

In this study, a new simple method for the estimation of hyperelastic material properties by indentation tests is proposed. Among hyperelastic material models, the Yeoh model with three material properties ($C_{10}$, $C_{20}$, $C_{30}$) is adopted to describe the strain energy density in terms of strain invariants. Finite element simulations of the spherical indentation of hyperelastic materials of the Yeoh model with different material properties are performed to establish a database of indentation force-displacement curves. The indentation force-displacement curves are fitted by cubic polynomials, which are approximated as a product of third-order polynomials of ($C_{10}$, $C_{20}$, $C_{30}$). A regression analysis is conducted to determine the coefficients of the equations for the indentation force-displacement curve approximations. A regression equation is used to estimate the hyperelastic material properties. The present method is verified by comparing the estimated material properties with true values.

• Nuclear Engineering and Technology
• /
• v.52 no.6
• /
• pp.1137-1147
• /
• 2020

The discrete ordinates method (S_N) is one of the major shielding calculation method, which is suitable for solving deep-penetration transport problems. Our objective is to explore the available quadrature sets and to improve the accuracy in shielding problems involving strong anisotropy. The linear discontinuous finite-element (LDFE) quadrature sets based on the icosahedron (in short, ICLDFE quadrature sets) are developed by defining projected points on the surfaces of the icosahedron. Weights are then introduced in the integration of the discontinuous finite-element basis functions in the relevant angular regions. The multivariate secant method is used to optimize the discrete directions and their corresponding weights. The numerical integration of polynomials in the direction cosines and the Kobayashi benchmark are used to analyze and verify the properties of these new quadrature sets. Results show that the ICLDFE quadrature sets can exactly integrate the zero-order and first-order of the spherical harmonic functions over one-twentieth of the spherical surface. As for the Kobayashi benchmark problem, the maximum relative error between the fifth-order ICLDFE quadrature sets and references is only -0.55%. The ICLDFE quadrature sets provide better integration precision of the spherical harmonic functions in local discrete angle domains and higher accuracy for simple shielding problems.

• Research in Mathematical Education
• /
• v.8 no.2
• /
• pp.107-114
• /
• 2004

University teachers of linear algebra often feel annoyed and disarmed when faced with the inability of their students to cope with concepts that they consider to be very simple. Usually, they lay the blame on the impossibility for the students to use geometrical intuition or the lack of practice in basic logic and set theory. J.-L. Dorier [(2002): Teaching Linear Algebra at University. In: T. Li (Ed.), Proceedings of the International Congress of Mathematicians (Beijing: August 20-28, 2002), Vol. III: Invited Lectures (pp. 875-884). Beijing: Higher Education Press] mentioned that the situation could not be improved substantially with the teaching of Cartesian geometry or/and logic and set theory prior to the linear algebra. In East Asian countries, science-orientated mathematics curricula of the high schools consist of calculus with many other materials. To understand differential and integral calculus efficiently or for other reasons, students have to learn a lot of content (and concepts) in linear algebra, such as ordered pairs, n-tuple numbers, planar and spatial coordinates, vectors, polynomials, matrices, etc., from an early age. The content of linear algebra is spread out from grades 7 to 12. When the high school teachers teach the content of linear algebra, however, they do not concern much about the concepts of content. With small effort, teachers can help the students to build concepts of vocabularies and languages of linear algebra.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.17 no.2
• /
• pp.29-36
• /
• 1980

This paper presents a method for constructing multiple- valued switching functions based on Galois fields. First the constructing Inethod for single- variable switching functions is developers and the results are extended to multiple- variable functions. The fundalnental Inathelnatical properties used in this paper are. (1) The sum of all elements over CF of is zero. (2) The Product of nonzero elements over GF(N) is equal to e1 for Neven, and e1( ) for N odd. With these properties, a relatlvely simple constructing method is developed, and a process for determining the coefficients of the expanded forms of switching functions is also obtained without successive multiplication of the polynomials. Some examples are given to illustrate the method.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.10 no.2
• /
• pp.207-217
• /
• 1999

When the feed of an offset reflector antenna is displaced from the focal point, the phase distortion results in the aperture field distribution, which in turn gives rise to a deviation of maximum beam, a decrease in gain, and an increase in sidelobes. In order to study these scan characteristics, an offset reflector antenna with the defocused feed is analyzed by a series expansion method using the Zernike polynomials, which can be used to calculate radiation pattern fast and exactly. And from the analyzed results, scan loss data in terms of reflector geometry are presented. And also, the BDF (beam deviation factor) expression is derived with offset reflector configuration analytically, and calculated results and simple formula of BDF are presented for determining beam deviation characteristics.

• Journal of Advanced Marine Engineering and Technology
• /
• v.18 no.4
• /
• pp.102-111
• /
• 1994

This article deals with the problem of designing a robust algorithm for the motion control of robot manipulator whose nonlinear dynamics contain various uncertainties. To ensure high performance of control system, a model-based feedforward compensation with continuous robust control has been developed. The control structure based on the deterministic approach consists of two parts : the nominal control law is first introduced to stabilize the system without uncertainties, then a robust nonlinear control law is adopted to compensate for both the resulting errors(or structured uncertainties) and unstructured uncertainties. The uncertainties assumed in this study are bounded by polynomials in the Euclidean norms of system states with known bounding coefficients. The presented control scheme is relatively simple as well as computationally efficient. With a feasible class of desired trajectories, the proposed control law provides sufficient criteria which guarantee that all possible responses of the closed-loop system are uniformly ultimately bounded in the presence of uncertainties. Therefore, the control algorithm proposed is shown to be robust with respect to the involved uncertainties.

• Journal of the Korea Institute of Military Science and Technology
• /
• v.19 no.2
• /
• pp.227-235
• /
• 2016

Heavy-weight high speed underwater vehicle(HSUV) is launched from the submerged mother ship. For the safety point of view, it is important to confirm whether the HSUV would touch the launching mother ship. In this paper, the hydrodynamic force and moment were modeled by the polynomials of motion variables and the simple lift and drag acting on a plate and cylinder which consist of the HSUV's several parts. The mother ship was assumed as the Rankine half body to consider the flow field near the moving ship. Such hydrodynamic force and moment were included in the 6 DOF equations of motion of the HSUV and the dynamic simulations for the various conditions of the HSUV until the propeller activation were performed. Developed simulation program is expected to reduce the number of expensive sea trial test to develop safety logic of the HSUV at the initial firing stage.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.22 no.2
• /
• pp.173-183
• /
• 1998

An optimization procedure to find the inlet concentration profile that yields the most uniform deposition rate in a cylindrical CVD chamber has been developed. Assuming that the chemical reaction time is negligibly small, a SIMPLE based finite-volume method is adopted to solve the fully elliptic equations for momentum, temperature, and concentration. The inlet concentration profile is expressed by a linear combination of Chebyshev polynomials and the coefficients of which are determined by the local random search technique. It is shown that the present method is very effective in improving the uniformity of the deposition rate, especially when Re is high and/or the wafer is placed close to the inlet. The optimal profiles have been obtained for various Re, Gr, and geometry combinations.