• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.437-460
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• 2024

In this paper we present the weighted shift operators having the property of moment infinite divisibility. We first review the monotone theory and conditional positive definiteness. Next, we study the infinite divisibility of sequences. A sequence of real numbers γ is said to be infinitely divisible if for any p > 0, the sequence γ^p = {γ^p_n}^∞_n=0 is positive definite. For sequences α = {α_n}^∞_n=0 of positive real numbers, we consider the weighted shift operators W_α. It is also known that W_α is moment infinitely divisible if and only if the sequences {γ_n}^∞_n=0 and {γ_n+1}^∞_n=0 of W_α are infinitely divisible. Here γ is the moment sequence associated with α. We use conditional positive definiteness to establish a new criterion for moment infinite divisibility of W_α, which only requires infinite divisibility of the sequence {γ_n}^∞_n=0. Finally, we consider some examples and properties of weighted shift operators having the property of (k, 0)-CPD; that is, the moment matrix M_γ(n, k) is CPD for any n ≥ 0.

• International Journal of Automotive Technology
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• v.8 no.3
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• pp.299-308
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• 2007

This study proposes a two-layer hierarchical control system that integrates active front wheel steering and four wheel braking torque control to improve vehicle handling performance and stability. The first layer is a robust model matching controller (R-MMC) based on linear matrix inequalities (LMIs), which optimizes an active front steering angle compensation and a desired yaw moment control, and calculates reference wheel slip for the target wheel according to the desired yaw moment. The second layer is a moving sliding mode controller (MSMC) that can track the reference wheel slip in a predetermined time by commanding proper braking torque on the target wheel to achieve the desired yaw moment. Since vehicle sideslip angle measurement is difficult to achieve in practice, a sliding mode observer (SMO) that requires only vehicle yaw rate as the measured input is also developed in this study. The performance and robustness of the SMO and the integrated control system are demonstrated through comprehensive computer simulations. Simulation results reveal the satisfactory tracking ability of the SMO, and the superior improved vehicle handling performance, stability and robustness of the integrated control vehicle.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.9
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• pp.133-144
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• 2000

The dynamic walking planning and the inverse dynamics of the biped robot is investigated in this paper. The biped robot is modeled with 14 degrees of freedom rigid bodies considering the walking pattern and kinematic construction of humanoid. The method of the computer aided multibody dynamics is applied to the dynamic analysis. The equations of motion of biped are initially represented as terms of the Cartesian corrdinates then they are converted to the minimum number of equations of motion in terms of the joint coordinates using the velocity transformation matrix. For the consideration of the relationships between the ground and foot the holonomic constraints are added or deleted on the equations of motion. the number of these constraints can be changed by types of walking patterns with three modes. In order for the dynamic walking to be stabilizable optimized trunk positions are iteratively determined by satisfying the system ZMP(Zero Moment Point) and ground conditions.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.548-555
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• 2000

The dynamic walking and the inverse dynamics of the biped walking robot is investigated in this paper. The biped robot is modeled with 14 degrees of freedom rigid bodies considering the walking pattern and kinematic construction of humanoid. The method of the computer aided multibody dynamics is applied to the dynamic analysis. The equations of motion of biped are initially represented as terms of the Cartesian coordinates, then they are converted to the minimum number of equations of motion in terms of the joint coordinates using the velocity transformation matrix. For the consideration of the relationships between the ground and foot, the holonomic constraints are added or deleted on the equations of motion. The number of these constraints can be changed by types of walking pattern with three modes. In order for the dynamic walking to be stabilizable, optimized trunk positions are iteratively determined by satisfying the system ZMP(Zero Moment Point) and ground conditions.

• Journal of the Korean Data and Information Science Society
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• v.27 no.1
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• pp.265-274
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• 2016

In this paper, we consider a diffusion risk process, in which, its surplus process behaves like a Brownian motion in-between adjacent epochs of claims. We assume that the claims occur following a Poisson process and their sizes are independent and exponentially distributed with the same intensity. Our main goal is to derive the exact formula of the joint moment generating function of the ruin time and the total amount of aggregated claim sizes until ruin in the diffusion risk process. We also provide a method for computing the related first and second moments using the joint moment generating function and the augmented matrix exponential function.

• Bulletin of the Korean Chemical Society
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• v.7 no.4
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• pp.299-304
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• 1986

Master formulas for overlap integrals and the dipole moments involving |4p > atomic orbitals have been derived by the expansion method for spherical harmonics. The radial integrals for the hyperfine interaction have also been derived for |4p > atomic orbitals. The calculated values of the overlap integrals and dipole moment matrix elements by the expansion method for spherical harmonics for a hypothetical NO molecule are exactly in agreement with those of Mulliken's method. The radial integrals for the hyperfine interaction may be used to calculate the chemical shift for |4p > atomic orbitals.

• 한국정보통신설비학회:학술대회논문집
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• 2008.08a
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• pp.418-421
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• 2008

This paper presents the program to analyze an antenna for using the Moment Method. The program contains three different functional steps. In the first stage, the pre-processor is based on the Delaunay Triangulation Algorithm. The next stage, the main-processor, can be considered the core process of the program, which solutions are obtaining the linear matrix for using the Moment Method. The final stages, the name of the post-processor, analyze radiation patterns, which results are same with the S-parameters. The results demonstrate satisfactory agreement with the results for using other numerical packages and measurement data. We can confirm that the results of this program compare with the results of common program to analyze for an antenna.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.4 no.6
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• pp.1253-1272
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• 2010

In this paper, we propose a new affine shape adaptation scheme for the affine invariant feature detector, in which the convergence stability is still an opening problem. This paper examines the relation between the integration scale matrix of next iteration and the current second moment matrix and finds that the convergence stability of the method can be improved by adjusting the relation between the two matrices instead of keeping them always proportional as proposed by previous methods. By estimating and updating the shape of the integration kernel and differentiation kernel in each iteration based on the anisotropy of the current second moment matrix, we propose a coarse-to-fine affine shape adaptation scheme which is able to adjust the pace of convergence and enable the process to converge smoothly. The feature matching experiments demonstrate that the proposed approach obtains an improvement in convergence ratio and repeatability compared with the current schemes with relatively fixed integration kernel.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.3
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• pp.252-261
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• 1988

Employed the new invese scattering scheme based on the moment mehtod, which was presented in the Part I of these companion papers, numerical simulations are performed to investigate the effect of measurement errors and noise contaminating the field scattered from dielectric objects. In order to reduce those effects on the reconstructed permittivity profiles, some techniques such as regularization, iterative matrix inversion, and multiple incidence are applied to this problem.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.04b
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• pp.246-250
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• 1995

This paper presents a method in analyzing the output force/moments transmission form the applied input forces of the paralled manipulator. Like a serial manipulator the Jacobian matrix introduced in the paper plays role in relating the output forces/monents with the input forces. The force/moment manipulability have been investigated by considering the force transmission and momen transmission independently. Sensitivity analysis has been done and an illuatrating example is given.