• Title/Summary/Keyword: infinite matrix

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Probabilistic Behavior of In-plane Structure due to Multiple Correlated Uncertain Material Constants (상호 상관관계가 있는 다중 재료상수의 불확실성에 의한 평면구조의 확률론적 거동)

  • Noh Hyuk-Chun
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.18 no.3
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    • pp.291-302
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    • 2005
  • Due to the importance of the parameter in structural response, the uncertain elastic modulus was located at the center of stochastic analysis, where the response variability caused by the uncertain system parameters is pursued. However when we analyze the so-called stochastic systems, as many parameters as possible must be included in the analysis if we want to obtain the response variability that can reach a true one, even in an approximate sense. In this paper, a formulation to determine the statistical behavior of in-plane structures due to multiple uncertain material parameters, i.e., elastic modulus and Poisson's ratio, is suggested. To this end, the polynomial expansion on the coefficients of constitutive matrix is employed. In constructing the modified auto-and cross-correlation functions, use is made of the general equation for n-th moment. For the computational purpose, the infinite series of stochastic sub-stiffness matrices is truncated preserving required accuracy. To demons4rate the validity of the proposed formulation, an exemplary example is analyzed and the results are compared with those obtained by means of classical Monte Carlo simulation, which is based on the local averaging scheme.

A Filtered-x Affine Projection Sign Algorithm with Improved Convergence Rate for Active Impulsive Noise Control (능동 충격성 소음 제어를 위한 향상된 수렴 속도를 가지는 Filtered-x 인접 투사 부호 알고리즘)

  • Lee, En Jong;Kim, Jeong Rae;Chung, Ik Joo
    • The Journal of the Acoustical Society of Korea
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    • v.34 no.2
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    • pp.130-137
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    • 2015
  • In this paper, we propose a new Modified Filtered-x Affine Projection Sign Algorithm(MFxAPSA) to improve the convergence speed of the conventional MFxAPSA which has been proposed for active control of impulsive noise. Under the impulsive noise environment, the adaptive algorithms based on the second order moment such as the Filtered-x Least Mean Square(FxLMS) show slow convergence speed or diverge because the noise source tends to have infinite variance. The MFxAPSA is the algorithm derived by applying the Affine Projection Sign Algorithm(APSA) to active noise control. The APSA has an advantage that it does not need the calculation for the inverse matrix, so it may be suitable for the active noise control that requires low computational burden. The proposed MFxAPSA also has APSA's advantage and furthermore, better performance than the conventional MFxAPSA. We carried out a performance comparison of the proposed MFxAPSA with the conventional MFxAPSA. It is shown that the proposed MFxAPSA has the faster convergence speed than the conventional MFxAPSA.

CONSTRUCTION OF TWO- OR THREE-WEIGHT BINARY LINEAR CODES FROM VASIL'EV CODES

  • Hyun, Jong Yoon;Kim, Jaeseon
    • Journal of the Korean Mathematical Society
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    • v.58 no.1
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    • pp.29-44
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    • 2021
  • The set D of column vectors of a generator matrix of a linear code is called a defining set of the linear code. In this paper we consider the problem of constructing few-weight (mainly two- or three-weight) linear codes from defining sets. It can be easily seen that we obtain an one-weight code when we take a defining set to be the nonzero codewords of a linear code. Therefore we have to choose a defining set from a non-linear code to obtain two- or three-weight codes, and we face the problem that the constructed code contains many weights. To overcome this difficulty, we employ the linear codes of the following form: Let D be a subset of ��2n, and W (resp. V ) be a subspace of ��2 (resp. ��2n). We define the linear code ��D(W; V ) with defining set D and restricted to W, V by $${\mathcal{C}}_D(W;V )=\{(s+u{\cdot}x)_{x{\in}D^{\ast}}|s{\in}W,u{\in}V\}$$. We obtain two- or three-weight codes by taking D to be a Vasil'ev code of length n = 2m - 1(m ≥ 3) and a suitable choices of W. We do the same job for D being the complement of a Vasil'ev code. The constructed few-weight codes share some nice properties. Some of them are optimal in the sense that they attain either the Griesmer bound or the Grey-Rankin bound. Most of them are minimal codes which, in turn, have an application in secret sharing schemes. Finally we obtain an infinite family of minimal codes for which the sufficient condition of Ashikhmin and Barg does not hold.

Sound transmission of multi-layered micro-perforated plates in a cylindrical impedance tube (원통형 임피던스 튜브 내 다중 미세천공 판의 음향투과)

  • Kim, Hyun-Sil;Ma, Pyung-Sik;Kim, Bong-Ki;Lee, Seong-Hyun;Seo, Yun-Ho
    • The Journal of the Acoustical Society of Korea
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    • v.39 no.4
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    • pp.270-278
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    • 2020
  • In this paper, sound transmission of Micro-Perforated Plates (MPPs) installed in an impedance tube with a circular cross-section is described using an analytic method. Vibration of the plates is expressed in terms of an infinite series of modal functions, where modal function in the radial direction is given by the Bessel function. Under the plane wave assumption, a low frequency approximation is derived, and a formula for the sound transmission coefficient of multi-layered MPPs is presented using the transfer matrix method. The Sound Transmission Losses (STLs) of single and double MPPs are computed using the proposed method and compared with those done by the Finite Element Method (FEM), which shows an excellent agreement. As the perforation increases, the STL is degraded, since the STL becomes dominated by the perforation ratio rather than by vibration of the plate. The STL shows dips at natural frequencies as well as at the mass-spring-mass resonance frequency. The proposed model for the STL prediction in this study can be applied to an arbitrary number of MPPs, where each MPP may or may not have a perforation.

Level Set based Topological Shape Optimization of Phononic Crystals (음향결정 구조의 레벨셋 기반 위상 및 형상 최적설계)

  • Kim, Min-Geun;Hashimoto, Hiroshi;Abe, Kazuhisa;Cho, Seonho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.25 no.6
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    • pp.549-558
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    • 2012
  • A topology optimization method for phononic crystals is developed for the design of sound barriers, using the level set approach. Given a frequency and an incident wave to the phononic crystals, an optimal shape of periodic inclusions is found by minimizing the norm of transmittance. In a sound field including scattering bodies, an acoustic wave can be refracted on the obstacle boundaries, which enables to control acoustic performance by taking the shape of inclusions as the design variables. In this research, we consider a layered structure which is composed of inclusions arranged periodically in horizontal direction while finite inclusions are distributed in vertical direction. Due to the periodicity of inclusions, a unit cell can be considered to analyze the wave propagation together with proper boundary conditions which are imposed on the left and right edges of the unit cell using the Bloch theorem. The boundary conditions for the lower and the upper boundaries of unit cell are described by impedance matrices, which represent the transmission of waves between the layered structure and the semi-infinite external media. A level set method is employed to describe the topology and the shape of inclusions. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. Through several numerical examples, the applicability of the proposed method is demonstrated.

Synthesis and Structure of Bis(ethylenediamine) cuprate(II)$\cdot$Dichromate (Bis(ethylenediamine) cuprate(II)$\cdot$Dichromate의 합성 및 결정구조 연구)

  • Kim, Seung-Bin;Namgung, Hae
    • Korean Journal of Crystallography
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    • v.16 no.1
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    • pp.38-42
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    • 2005
  • The crystal structure of Bis(ethylenediamine) cuprate(II)$\cdot$dichromate, $Cu(C_2H_8N_2)_2{\cdot}Cr_2O_7$, has been determined by X-ray crystallography. Crystal data: a=5.682(2), b=8.567(3), c=14.839(3) ${\AA},\;{\alpha}=97.50(2),\;{\beta}=101.06(1),\;{\gamma}=109.38(2)^{\circ}$ Triclinic, P-1 (SG No=2), Z=2, V=653.9(2) ${\AA}^3,\;D_c=2.030gcm^{-3},\;{\mu}=3.273mm^{-1}$. The structure was solved by Patterson method and refined by full matrix least-square methods uslng unit weights. The final R and S values were $R_1=0.0256,\;R_w=0.0708,\;R_{all}=0.0316,\;S=1.151$ for the observed 2291 reflections. The two cupper complex ion has the usual distorted octahedral structure with mean four Cu-N distances of 2.010(3) $\AA$ and the longer mean Cu-O distance of 2.525(2) $\AA$. The Cu-complex and dichromate ions are linked to form infinite chain arranged alternatively along the [111]-direction. The neighboring chains in the (0-11) plane are connected with N1-O5 and N3-O1 hydrogen bonds.

One Dimensional Heat Flow Equation Incorporated with the Vertical Water Flow in Paddy Soils I. An Analytical Solution and It's Application to Tow Different Paddy Soils with Different Percolation Rates (답토양(沓土壤)에 있어서 물 이동(移動)이 복합(複合)된 일차원(一次元) 열이동방정식(熱移動方程式)에 관(關)하여 I. 분석해(分析解)와 투수속도(透水速度)가 다른 두 답토양(沓土壤)에 대(對)한 적용(適用))

  • Jung, Yeong-Sang;Kim, Lee-Yul;Im, Jeong-Nam
    • Korean Journal of Soil Science and Fertilizer
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    • v.14 no.4
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    • pp.179-184
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    • 1982
  • To describe a mathematical heat transfer model in saturated paddy soils, an analytical solution of the heat flow equation incorporated with the heat transfer by mass flow of water was obtained under the assumptions: 1) the diurnal (or annual) changes in temperature at a depth follow harmonic curves, 2) the temperature at the infinite depth be constant and 3) the temperatures of soil and water at the one depth be identical. The calculation of thermal diffusivities of the soil is possible with the known values of the physical parameters of each component in the soil matrix (heat capacity, density and porosity), percolation rate and the minimum and maximum temperatures at two different depths. The calculated thermal diffusivities using the solution were $9.5cm^2/hr$ for the loam soil with the percolation rate of 0.88cm/day and $13.9cm^2/hr$ for the sandy loam soil with the percolation rate of 2.64 cm/day.

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Metal Matrix Composite(MMC) Layered Armour System (금속복합판재 적용 다층 구조 방호성능 평가)

  • Lee, Minhyung;Park, Sang-Won;Jo, Ilguk
    • Journal of the Korea Institute of Military Science and Technology
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    • v.20 no.6
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    • pp.752-757
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    • 2017
  • Analysis has been performed for the penetration of a long-rod into MMC/Ceramic layered armour system with several shot test and a series of simulations. Two types of MMC plate have been fabricated by a liquid pressing method; A356/45%vol.%SiCp with a uniform distribution of SiC particle and Al7075/45%vol.B4Cp with B4C particle. The mechanical properties were measured with the high-speed split Hopkins bar test, hardness test and compression test. The popular Simplified Johnson-Cook model was adopted to represent the material characteristics for FEM simulations. The performance of the MMC applied armour system has been made by comparing with the semi-infinite mild steel target using the depth of penetration(DOP). The results show that placing ceramic front layer provides a certain gain in protection, and that placing another ductile front layer provides a further gain. The application of MMC is found to be attractive.

A Consideration on Creativity of the Unconscious: Focusing on a Series of Dreams (무의식의 창조성에 관한 하나의 고찰: 일련의 꿈을 중심으로)

  • Dukkyu Kim
    • Sim-seong Yeon-gu
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    • v.38 no.2
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    • pp.239-268
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    • 2023
  • Humanity has faced destruction(chaos) due to catastrophes (Covid-19, war, earthquake) and awaits a new restoration. For civilizations and individuals, creation or creativity is essential to psychic development. Creativity is the driving force that renews an individual when a new stance and attitude of consciousness or a new adaptation to reality is desperately needed in the depth of the human mind. This article is the result of an exploration of the nature and characteristics of creativity presented by a series of four dreams. First, the definition and form of creativity were explored in the context of religion, mythology, and history of Eastern and Western. While Western mythology refers to creation or creativity originating from God, ancient China viewed creativity as expressed through the interaction of yin and yang, the movement of Tao. In East and West, the form of creation is divided into creation from nothing, creation from matter, and creation through dissolution from the matrix, which psychologically suggests that creativity or creation originates from the unconscious, the seedbed of infinite potential and creative power. Next, with insights from the second dream, the characteristics of creativity were discussed. Creativity occurs through transcendent function and 'going beyond the frame of reference,' that is, 'transgressivity.' Third, the nature of creativity was explored as the creativity of the unconscious aims for regeneration and drives the renewal of Self archetypal images within the collective and individuals. Ultimately, the creativity of the unconscious is the goal of the whole psyche and aims for individuation to become the whole. Realizing the creativity of the unconscious is the fate of humans as the second creator.