• 제목/요약/키워드: convex functions

Search Result 356, Processing Time 0.025 seconds

A Study of Disk-Shaped Bronze Implements (부록 1. 원개형동기의 앞뒷면 - 그 사용법에 관하여 -)

  • Shimizu, Yasuji
    • Korean Journal of Heritage: History & Science
    • /
    • v.39
    • /
    • pp.281-314
    • /
    • 2006
  • Several explanations exist about the usage of disk-shaped bronze implements in the ancient society. Some argue that they were used as mirrors, others suggest percussion instruments, and still others bronze ornaments. Differences between disk-shaped bronze implements and mirrors with multiple knobs are that the former have no visible design, only one handle, and a sharp curvature unlike the latter with smooth curvature. The question is whether disk-shaped bronze implements excavated from Korean peninsula have any light reflecting function. To answer this question, I carefully studied the concave surfaces of disk-shaped bronze implements excavated from Goejeong-dong, Tongso-ri and Hapsong-ri sites. The main findings are as follows: (1) The concave sides of the disk-shaped bronze implements excavated from Goejeong-dong and Tongso-ri sites were highly polished, and they were as reflective as bronze mirrors. (2) The concave side of the disk-shaped bronze implement from Hapsong-ri site was unpolished, and it was different from bronze mirrors. (3) As for the convex sides of the disk-shaped bronze implements, they did not appear to have been polished with care. Considering the above findings, the disk-shaped bronze implements excavated from Goejeong-dong and Tongso-ri sites belong to the stage where they could act as both mirrors and instruments. On the contrary, the disk-shaped bronze implement from Hapsong-ri site can belong to the stage where it lost the function of being a mirror as the result of maintaining only its function as an instrument. Even though disk-shaped implements had two functions, it can be considered that the light reflecting function expanded the role of a mirror with multiple knobs and the sound function helped the engraved round bronze implement to be converted into an eight-armed bronze rattle. Since it has been reported that shamans used bronze mirrors as percussion instruments in their performances in Korean peninsula and Siberia, I propose a reconsideration of the usage of mirrors in the ancient East Asia. Although the essential function of a mirror is to reflect light, other possible usages involving important functions need to be further investigated.

Nonlinear Controller Design of Active Magnetic Bearing Systems Based on Polytopic Quasi-LPV Models (Polytopic Quasi-LPV 모델 기반 능동자기베어링의 비선형제어기 설계)

  • Lee, Dong-Hwan;Park, Jin-Bae;Jeong, Hyun-Suk;Joo, Young-Hoon
    • The Transactions of The Korean Institute of Electrical Engineers
    • /
    • v.59 no.4
    • /
    • pp.797-802
    • /
    • 2010
  • In this paper, a systematic procedure to design a nonlinear controller for nonlinear active magnetic bearing (AMB) systems is presented. To do this, we effectively convert the AMB system into a polytopic quasi-linear parameter varying (LPV) system, which is a representation of nonlinear state-space models and is described by the convex combination of a set of precisely known vertices. Unlike the existing quasi-LPV systems, the nonlinear weighting functions, which construct the polytopic quasi-LPV model of the AMB system by connecting the vertices, include not only state variables but also the input ones. This allows us to treat the input nonlinearity effectively. By means of the derived polytopic quasi-LPV model and linear matrix inequality (LMI) conditions, nonlinear controller that stabilizes the AMB system is obtained. The effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations.

A Study on the Control Method for the Tool Path of Aspherical Surface Grinding and Polishing (비구면 연삭 및 연마를 위한 공구 경로 제어에 관한 연구)

  • Kim, Hyung-Tae;Yang, Hae-Jeong;Kim, Sung-Chul
    • Journal of the Korean Society for Precision Engineering
    • /
    • v.23 no.1 s.178
    • /
    • pp.113-120
    • /
    • 2006
  • This paper proposed the control algorithm fur aspheric surface grinding and was verified by the experiment. The functions of the algorithm were simultaneous control of the position and interpolation of the aspheric curve. The non-linear formula of the tool position was derived from the aspheric equations and the shape of the tool. The function was partitioned by an certain interval and the control parameters were calculated at each control section. The movement in a session was interpolated with acceleration and velocity. The position error was feed-backed by rotary encorder. The concept of feedback algorithm was correcting position error by increasing or decreasing the speed. In the experiment, two-axis machine was controlled to track the aspheric surface by the proposed algorithm. The effect of the control and process parameters was monitored. The result showed that the maximum tracking error was under sub-micro level for the concave and convex surfaces.

A study on the flow characteristics in a plug valve with various port shapes (플러그 밸브의 포트형상 변화에 따른 유동특성 연구)

  • Choi, G.-W.;Park, G.-J.;Kim, Youn J.
    • 유체기계공업학회:학술대회논문집
    • /
    • 2000.12a
    • /
    • pp.259-264
    • /
    • 2000
  • The functions of the plug valve are the control of flow rate as well closing and opening pipe lines. Analyses on the flow characteristics in plug valve port are required to improve the performance and safety at severe operating conditions such as high-pressure and high-temperature. In this study, numerical analyses are carried out with varying the opening rate (fraction of the full open to close) of the valve and the shapes of valve Uk: straight, convex, concave and mixed shapes. The parameters influencing the flow characteristics in the valve are the discharge coefficient( $C_v$) and the resistance coefficient( K). Therefore, the distributions of static pressure, velocity vector and stream lines are investigated, and $C_v$ and K are calculated in each opening rate and shape. In case of full open, the static pressure passed through the valve port has almost been recovered. However, in case of other opening rates, the pressure does not permanently regained due to pressure drop leading to loss. This phenomenon in each shape of the valve shows the different behaviors. Calculation results show that the mixed shape has the best flow attribute.

  • PDF

Some Theoretical Foundations on the Necessities and Functions of Global Electronic Transactions Act (전자무역 활성화를 위한 글로벌 전자무역거래법의 요건과 역할기능의 이론적 기초)

  • Kim, Ki-Sun
    • THE INTERNATIONAL COMMERCE & LAW REVIEW
    • /
    • v.17
    • /
    • pp.129-146
    • /
    • 2002
  • The electronic technology development have occurred in the face of existing legal barriers to legal efficacy of computer information goods, and the liberating promise of electronic transactions cannot fully realized unless there is predictability in the legal rules that govern such transactions. This study analyzes some theoretical fundamentals of the Act. First, it proposes that the Act clarify and set forth uniform legal principles applicable to computer information transactions. Secondly, it suggests that if the individual is risk averse, the acceptance set for electronic transactions will be a convex set, and that the application of the Act will make the acceptance set more expanded by lowering the probability of conflicts and by downsizing the risk averness. Thirdly, it also suggest that through the mothod of contingent commodities analysis, the application of the Act by means of its restricted regulations will give more expected utility than the absence of the Act. Fourthly, it derives some implications that the degree of legitimate restriction will be affected by the objective risk inherent to the electronic transactions, and the individual's subjective risk-averseness. Finally, it concludes that harmonization of restriction and protection of individual's rights in electronic transaction process will be a necessary condition for more efficient body of law from the law-economic perspectives.

  • PDF

Vibration-mode-based story damage and global damage of reinforced concrete frames

  • Guo, Xiang;He, Zheng
    • Earthquakes and Structures
    • /
    • v.14 no.6
    • /
    • pp.589-598
    • /
    • 2018
  • An attempt is conducted to explore the relationship between the macroscopic global damage and the local damage of shear-type RC frames. A story damage index, which can be expressed as multi-variate functions of modal parameters, is deduced based on the tridiagonal matrix of the shear-type frame. The global damage model is also originated from structural modal parameters. Due to the connection of modal damage indexes, the relationship between the macroscopic global damage and the local story damage is reasonably established. In order to validate the derivation, a case study is carried out via an 8-story shear-type frame. The sensitivities of modal damage indexes to the location and severity of local story damages are studied. The evolution of the global damage is investigated as well. Results show that the global damage is sensitive to the degree of story damage, but it's not sensitive to its location. As the number of the damaged stories increases, more and more modes will be involved. Meanwhile, the global damage evolution curve changes from the concave shape to the S-type and then finally transforms into the convex shape. Through the proposed story damage, modal damage and global damage model, a multi-level damage assessment method is established.

Direct Position Determination of Coherently Distributed Sources based on Compressed Sensing with a Moving Nested Array

  • Yankui, Zhang;Haiyun, Xu;Bin, Ba;Rong, Zong;Daming, Wang;Xiangzhi, Li
    • KSII Transactions on Internet and Information Systems (TIIS)
    • /
    • v.13 no.5
    • /
    • pp.2454-2468
    • /
    • 2019
  • The existing direct position determinations(DPD) for coherently distributed(CD) sources are mostly applicable for uniform linear array(ULA), which result in a low degree of freedom(DOF), and it is difficult for them to realize the effective positioning in underdetermined condition. In this paper, a novel DPD algorithm for coherently distributed sources based on compressed sensing with a moving nested array is present. In this algorithm, the nested array is introduced to DPD firstly, and a positioning model of signal moving station based on nested array is constructed. Owing to the features of coherently distributed sources, the cost function of compressed sensing is established based on vectorization. For the sake of convenience, unconstrained transformation and convex transformation of cost functions are carried out. Finally, the position coordinates of the distribution source signals are obtained according to the theory of optimization. At the same time, the complexity is analyzed, and the simulation results show that, in comparison with two-step positioning algorithms and subspace-based algorithms, the proposed algorithm effectively solves the positioning problem in underdetermined condition with the same physical element number.

Blast Fragility and Sensitivity Analyses of Steel Moment Frames with Plan Irregularities

  • Kumar, Anil;Matsagar, Vasant
    • International journal of steel structures
    • /
    • v.18 no.5
    • /
    • pp.1684-1698
    • /
    • 2018
  • Fragility functions are determined for braced steel moment frames (SMFs) with plans such as square-, T-, L-, U-, trapezoidal-, and semicircular-shaped, subjected to blast. The frames are designed for gravity and seismic loads, but not necessarily for the blast loads. The blast load is computed for a wide range of scenarios involving different parameters, viz. charge weight, standoff distance, and blast location relative to plan of the structure followed by nonlinear dynamic analysis of the frames. The members failing in rotation lead to partial collapse due to plastic mechanism formation. The probabilities of partial collapse of the SMFs, with and without bracing system, due to the blast loading are computed to plot fragility curves. The charge weight and standoff distance are taken as Gaussian random input variables. The extent of propagation of the uncertainties in the input parameters onto the response quantities and fragility of the SMFs is assessed by computing Sobol sensitivity indices. The probabilistic analysis is conducted using Monte Carlo simulations. The frames have least failure probability for blasts occurring in front of their corners or convex face. Further, the unbraced frames are observed to have higher fragility as compared to counterpart braced frames for far-off detonations.

A semi-analytical procedure for cross section effect on the buckling and dynamic stability of composite imperfect truncated conical microbeam

  • Zhang, Peng;Gao, Yanan;Moradi, Zohre;Ali, Yasar Ameer;Khadimallah, Mohamed Amine
    • Steel and Composite Structures
    • /
    • v.44 no.3
    • /
    • pp.371-388
    • /
    • 2022
  • The present study tackles the problem of forced vibration of imperfect axially functionally graded shell structure with truncated conical geometry. The linear and nonlinear large-deflection of the structure are considered in the mathematical formulation using von-Kármán models. Modified coupled stress method and principle of minimum virtual work are employed in the modeling to obtain the final governing equations. In addition, formulations of classical elasticity theory are also presented. Different functions, including the linear, convex, and exponential cross-section shapes, are considered in the grading material modeling along the thickness direction. The grading properties of the material are a direct result of the porosity change in the thickness direction. Vibration responses of the structure are calculated using the semi-analytical method of a couple of homotopy perturbation methods (HPM) and the generalized differential quadrature method (GDQM). Contradicting effects of small-scale, porosity, and volume fraction parameters on the nonlinear amplitude, frequency ratio, dynamic deflection, resonance frequency, and natural frequency are observed for shell structure under various boundary conditions.

ADMM algorithms in statistics and machine learning (통계적 기계학습에서의 ADMM 알고리즘의 활용)

  • Choi, Hosik;Choi, Hyunjip;Park, Sangun
    • Journal of the Korean Data and Information Science Society
    • /
    • v.28 no.6
    • /
    • pp.1229-1244
    • /
    • 2017
  • In recent years, as demand for data-based analytical methodologies increases in various fields, optimization methods have been developed to handle them. In particular, various constraints required for problems in statistics and machine learning can be solved by convex optimization. Alternating direction method of multipliers (ADMM) can effectively deal with linear constraints, and it can be effectively used as a parallel optimization algorithm. ADMM is an approximation algorithm that solves complex original problems by dividing and combining the partial problems that are easier to optimize than original problems. It is useful for optimizing non-smooth or composite objective functions. It is widely used in statistical and machine learning because it can systematically construct algorithms based on dual theory and proximal operator. In this paper, we will examine applications of ADMM algorithm in various fields related to statistics, and focus on two major points: (1) splitting strategy of objective function, and (2) role of the proximal operator in explaining the Lagrangian method and its dual problem. In this case, we introduce methodologies that utilize regularization. Simulation results are presented to demonstrate effectiveness of the lasso.