• Journal of applied mathematics & informatics
• /
• 제14권1_2호
• /
• pp.81-96
• /
• 2004

The level-m scaled circulant factor matrix over the complex number field is introduced. Its diagonalization and spectral decomposition and representation are discussed. An explicit formula for the entries of the inverse of a level-m scaled circulant factor matrix is presented. Finally, an algorithm for finding the inverse of such matrices over the quaternion division algebra is given.

• 대한수학회지
• /
• 제59권3호
• /
• pp.621-634
• /
• 2022

The scaled inverse of a nonzero element a(x) ∈ ℤ[x]/f(x), where f(x) is an irreducible polynomial over ℤ, is the element b(x) ∈ ℤ[x]/f(x) such that a(x)b(x) = c (mod f(x)) for the smallest possible positive integer scale c. In this paper, we investigate the scaled inverse of (xⁱ - x^j) modulo cyclotomic polynomial of the form Φ_p^s (x) or Φ_p^sq^t (x), where p, q are primes with p < q and s, t are positive integers. Our main results are that the coefficient size of the scaled inverse of (xⁱ - x^j) is bounded by p - 1 with the scale p modulo Φ_p^s (x), and is bounded by q - 1 with the scale not greater than q modulo Φ_p^sq^t (x). Previously, the analogous result on cyclotomic polynomials of the form Φ_2ⁿ (x) gave rise to many lattice-based cryptosystems, especially, zero-knowledge proofs. Our result provides more flexible choice of cyclotomic polynomials in such cryptosystems. Along the way of proving the theorems, we also prove several properties of {x^k}_k∈ℤ in ℤ[x]/Φ_pq(x) which might be of independent interest.

• Journal of Magnetics
• /
• 제20권1호
• /
• pp.62-68
• /
• 2015

This paper presents an experimental technique to accurately separate a permanent magnetic field and an induced one from the total magnetic fields generated by a steel ship, through compensating for the Earth's magnetic field. To achieve this, an Earth's magnetic field simulator was constructed at a non-magnetic laboratory, and the field separation technique was developed, which consisted of five stages. The proposed method was tested with a scaled model ship, and its permanent and induced magnetic fields were successfully extracted from the magnetic field created by the ship. Finally, based on the separated permanent magnetic field data, the permanent magnetization distribution on the hull was predicted by solving an inverse problem. Accordingly, the permanent magnetic fields generated by the ship can easily be calculated at any depth of water.

• 로봇학회논문지
• /
• 제12권1호
• /
• pp.42-54
• /
• 2017

Using an inverse of the geometric Jacobian matrix is one of the most popular ways to control robot manipulators, because the Jacobian matrix contains the relationship between joint space velocities and operational space velocities. However, the control algorithm based on Jacobian matrix has algorithmic singularities: The robot manipulator becomes unstable when the Jacobian matrix loses rank. To solve this problem, various methods such as damped and filtered inverse have been proposed, but comparative studies to evaluate the performance of these algorithms are insufficient. Thus, this paper deals with a comparative analysis of six representative singularity avoidance algorithms: Damped Pseudo Inverse, Error Damped Pseudo Inverse, Scaled Jacobian Transpose, Selectively Damped Inverse, Filtered Inverse, and Task Transition Method. Especially, these algorithms are verified through computer simulations with a virtual model of a humanoid robot, THORMANG, in order to evaluate tracking error, computational time, and multiple task performance. With the experimental results, this paper contains a deep discussion about the effectiveness and limitations of each algorithm.

• 전산구조공학
• /
• 제9권4호
• /
• pp.209-217
• /
• 1996

구조물의 손상전후에 나타나는 고유진동수와 모드 형상으로 부터 Inverse Modal Perturbation기법을 이용하여 잔교식 부두나 돌핀과 같은 대규모 항만구조물의 손상도 추정을 위한 모드 기여도 계수를 근사적으로 직접 구하는 방법을 제시하였다. 잔교식 항만구조물의 고유치 해석을 통해 구조물의 강성 변화량과 구조물의 고유진동수와 모드 형상의 변화량과 요소 손상도 계수를 도입하여 Inverse Modal Perturbation의 2차항을 고려한 관계식을 유도하고 손상전후에 구조물의 강성 감소로 나타나는 구조물의 손상도를 추정하여 수렴정도를 고찰하였다.

• Wind and Structures
• /
• 제24권3호
• /
• pp.249-265
• /
• 2017

An efficient and accurate algorithm is proposed to estimate flutter safety factor of suspension bridges satisfying prescribed reliability levels. Uncertainties which arise from the basic wind speed at the bridge deck location, critical flutter velocity, the wind conversion factor from a scaled model to the prototype structure and the gust speed factor are incorporated. The proposed algorithm integrates the concepts of the inverse reliability method and the calculation method of the critical flutter velocity of suspension bridges. The unique feature of the proposed method is that it offers a tool for flutter safety assessment of suspension bridges, when the reliability level is specified as a target to be satisfied by the designer. Accuracy and efficiency of this method with reference to three example suspension bridges is studied and numerical results validate its superiority over conventional deterministic method. Finally, the effects of various parameters on the flutter safety factor of suspension bridges are also investigated.

• 한국재료학회:학술대회논문집
• /
• 한국재료학회 2011년도 춘계학술발표대회
• /
• pp.37.1-37.1
• /
• 2011

Miniaturization of lenses has been widely researched by various scientific and engineering techniques. As a result, micro scaled lens structure could be easily achieved from various fabrication techniques; nevertheless it is still challenging to make nano scaled lenses. This paper reports a novel fabrication method of silicon nanotemplate for nanolens array. The inverse structure of nanolens array was fabricated on silicon substrate by reactive ion etching (RIE) process. This technique has a flexibility to produce different tip shapes using different pattern masks. Once the silicon nano-tip array structure is well-defined using an optimized recipe, it is followed by polymer molding to duplicate nanolens array from the template. Finally, the nanostructures formed on silicon nanotemplate and polymer replica were investigated using FE-SEM and AFM measurements. The nano scaled lens can be manufactured from the same template, also using other replication techniques such as imprinting, injection molding and so on.

• 한국컴퓨터그래픽스학회논문지
• /
• 제17권1호
• /
• pp.39-44
• /
• 2011

영상이나 동영상을 저장하거나 전송할 때 저장 공간의 크기나 네트워크 대역폭을 고려하여 고해상도 윈본 영상을 축소하여 저장, 전송하고 최종적으로 영상을 디스플레이 하는 과정에서 영상을 확대하는 경우가 실제 응용에서 빈번히 나타난다. 기존 연구들에서는 이런 경우 확대 영상의 화질을 개선하기 위해 영상 확대 과정을 개선하기 위한 연구가 많이 진행되었다. 본 논문에서는 이런 상황에서는 고해상도 원본 영상이 존재한다는 점에 착안하여 영상 확대 과정 대신 영상을 축소하는 과정을 개선함으로써 최종 확대 영상의 화질을 개선하기 위한 방법을 제안한다. 특히 실제 하드웨어나 소프트웨어에서 널리 적용되는 선행 보간법, 삼차 보간법 등에서 확대 영상의 화소가 작은 영상의 화소값들의 선형 조합으로 나타난다는 점에 착안하여 영상 확대 과정을 선형 변환으로 모델링하고 최적 축소 영상을 만틀기 위한 역변환을 얻는 방법을 제안한다. 또한 역변환 과정의 계산량을 줄이기 위해 역변환과정을 간단한 필터 커널로 근사하는 방법을 제안한다. 결과적으로 본 논문에서 제안하는 방법으로 축소한 영상을 확대 복원하였을 때 기존에 사용되던 방법에 비해 상당한 화질 개선 효과가 있는 것을 실험적으로 확인하였다.

• 한국통신학회논문지
• /
• 제32권12C호
• /
• pp.1142-1148
• /
• 2007

본 논문에서는 OFDM (Orthogonal Frequency Division Multiplexing) 시스템에서 전송 신호의 PAPR(Peak-to-Average Power Ratio)을 효과적으로 감소시키기 위한 피크 신호 관찰 기반의 적응적 SLM (Adaptive Selective Mapping; ASLM) 기법을 제안한다. 제안 기법은 기존 SLM 방법에서의 복잡도 문제를 개선하기 위해, 매 OFDM 심벌마다 IFFT (Inverse Fast Fourier Transform) 결과에 대한 피크 신호 조정, 피크 조정된 신호의 FFT 결과와 원래 OFDM 심벌간의 부반송파별 전력차 비교를 통한 직교 부호 선택, 선택된 직교 부호만을 이용한 전형적인 SLM 과정의 3단계로 구성된다. 모의실험 결과, 제안된 ASLM 기법은 우수한 PAPR 감소 성능을 유지하면서도 기존 SLM 방법에 비해 훨씬 적은 IFFT 연산 및 PAPR 계산 횟수를 요구함을 확인하였다.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2005년도 ICCAS
• /
• pp.2126-2131
• /
• 2005

Interactions of a humanoid with a human are important, when the humanoid is requested to provide people with human-friendly services in unknown or uncertain environment. Such interactions may require more complicated and human-like behaviors from the humanoid. In this work the arm motions of a human are discussed as the early stage of human motion imitation by a humanoid. A motion capture system is used to obtain human-friendly arm motions as references. However the captured motions may not be applied directly to the humanoid, since the differences in geometric or dynamics aspects as length, mass, degrees of freedom, and kinematics and dynamics capabilities exist between the humanoid and the human. To overcome this difficulty a method to adapt captured motions to a humanoid is developed. The geometric difference in the arm length is resolved by scaling the arm length of the humanoid with a constant. Using the scaled geometry of the humanoid the imitation of actor's arm motions is achieved by solving an inverse kinematics problem formulated using optimization. The errors between the captured trajectories of actor arms and the approximated trajectories of humanoid arms are minimized. Such dynamics capabilities of the joint motors as limits of joint position, velocity and acceleration are also imposed on the optimization problem. Two motions of one hand waiving and performing a statement in sign language are imitated by a humanoid through dynamics simulation.