• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.11
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• pp.5324-5337
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• 2017

In this paper, we investigate the feasibility of interference alignment(IA) in signal space in the scenario of multiple cell and multiple user cellular networks, as the feasibility issue is closely related to the solvability of a multivariate polynomial system, we give the mathematical analysis to support the constraint condition obtained from the polynomial equations with the tools of algebraic geometry, and a new distribute IA algorithm is also provided to verify the accessibility of the constraint condition for symmetric system in this paper. Simulation results illustrate that the accessibility of the constraint condition is hold if and only if the degree of freedom(DoF) of each user can be divided by both the transmit and receive antenna numbers.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.04a
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• pp.62-69
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• 1995

The differential equations governing both the free vibrations and buckling loads of the beam-columns with constant volumes are derived and solved numerically. The axial load effects are included in the differential equations. The Runge-Kutta method and Regula-Falsi method are used to compute the eigenvalues corresponding to the natural frequencies. and buckling loads. In numerical examples, the simple end constraint is considered.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.559-564
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• 1993

Nonlinear equation of motion of the flexible manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. The resulting equations of motion have a structure which is useful to reduce the number of terms calculated, to check correctness, or to extend the model to high order. A manipulator with a flexible 4 bar link mechanism is a constrained system whose equations are sensitive to numerical integration error. This constrained system is solved using the null space matrix of the constraint Jacobian matrix. Singular value decomposition is a stable algorithm to find the null space matrix.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.680-685
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• 1992

Solar arrays and antennas of the satellite are usually stowed within the dimensions of the launch-vehicle fairing and deployed in the orbit. To solve such multibody dynamic problems, differential equations and algebraic equations are simultaneously solved, and special solution techniques are required. In this paper, Lagrange multipliers associated with the constraints are iteratively computed by monotonically reducing an appropriately defined constraint error vector, and the resulting equation of motion is solved by a well-established ODE technique. Defomable bodies as well as rigid bodies are treated, and applications to satellite solar arrays are explained.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.170.2-170
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• 2001

In this paper, the dynamic system modeling and the state sensitivity analysis of the spin-coater system for the reduction of the vibration are proposed. In the respect of modeling, the spin-coater system is composed of components of servomotor, belt, spindle, and a supported base. Each component is defined and combined modeling is derived to 3dimensional equations. Verification of modeling is verified by experimental values of actual system in the frequency domain. By direct differentiation the constraint equations with respect to kinematic design variables, such as eccentricity of spindle, moment of inertia, torsional stiffness and damping of supported base, sensitivity equations are derived to the verified state equations. Sensitivity of design variables could be used for vibration reduction and natural frequency shift in the frequency domain. Finally, dominant design variables ...

• Journal of the Korean Society for Precision Engineering
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• v.20 no.2
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• pp.209-217
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• 2003

In this paper, the dynamic system modeling and the state sensitivity analysis of the spin-coater system are proposed for the reduction of the vibration. In the respect of modeling, the spin-coater system is considered to be composed of servomotor, spindle, supporting base and so on. Each component of model is combined and derived to 3 dimensional equations. The combined model is verified by experimental values of actual system in the frequency domain. By direct differentiation of the constraint equations with respect to kinematic design variables, such as eccentricity of spindle, moment of inertia, rotational stiffness and damping of supported base, sensitivity equations are derived to the verified state equations. Sensitivity of design variables could be used for vibration reduction and natural frequency shift in the frequency domain. Finally, dominant design variables are selected from the sensitivity analysis.

• Wind and Structures
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• v.25 no.5
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• pp.493-506
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• 2017

Wind-induced response behavior of long-span roof structures is very complicated, showing significant contributions of multiple vibration modes. The largest load effects in a huge number of members should be considered for the sake of the equivalent static wind loads (ESWLs). Studies on essential matters and necessary conditions of the universal ESWLs are discussed. An efficient method for universal ESWLs on long-span roof structures is proposed. The generalized resuming forces including both the external wind loads and inertial forces are defined. Then, the universal ESWLs are given by a combination of eigenmodes calculated by proper orthogonal decomposition (POD) analysis. Firstly, the least squares method is applied to a matrix of eigenmodes by using the influence function. Then, the universal ESWLs distribution is obtained which reproduces the largest load effects simultaneously. Secondly, by choosing the eigenmodes of generalized resuming forces as the basic loading distribution vectors, this method becomes efficient. Meanwhile, by using the constraint equations, the universal ESWLs becomes reasonable. Finally, reproduced largest load effects by load-response-correlation (LRC) ESWLs and universal ESWLs are compared with the actual largest load effects obtained by the time domain response analysis for a long-span roof structure. The results demonstrate the feasibility and usefulness of the proposed universal ESWLs method.

• Macromolecular Research
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• v.11 no.6
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• pp.399-409
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• 2003

The first esterification reactor in the continuous polymerization of poly(ethylene terephthalate) has been analyzed by solving the material balances for the two-phase system with respect to the solubility of terephthalic acid. The Newton-Raphson method was used to solve the material balance equations instead of the Simplex method that is frequently used for finding a minimum point of a residual rather than a solution of an equation. A solution for the material balance equations, with the constraint of non-zero liquid phase fraction, could not be obtained with the solubility data of Yamada et al., but could be obtained with solubilities over a minimum value that is larger than their data. Thus, the solubility data of Yamada et al. are considered to be too small. On the other hand, the solubility data of Baranova and Kremer are so large that they gave a solution with the liquid phase only. Based on our results, several typical solubility curves satisfying the constraint of a non-zero liquid phase fraction are suggested in this study; we studied the reaction characteristics of the system using these curves. A higher temperature and a lower pressure are preferred for reducing the content of diethylene glycol.

• Journal of the Optical Society of Korea
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• v.20 no.5
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• pp.614-622
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• 2016

In this paper, we propose a novel differential equation method for designing a total internal reflection (TIR) LED lens with double freeform surfaces. A complete set of simultaneous differential equations for the method is derived from the condition for minimizing the Fresnel loss, illumination models, Snell’s Law of ray propagation, and a new constraint on the incident angle of a ray on the light-exiting surface of the lens. The last constraint is essential to complete the set of simultaneous differential equations. By adopting the TIR structure and applying the condition for minimizing the Fresnel loss, it is expected that the proposed TIR LED lens can have a high luminous flux efficiency, even though its beam-spread angle is narrow. To validate the proposed method, three TIR LED lenses with beam-spread angles of less than 22.6° have been designed, and their performances evaluated by ray tracing. Their luminous flux efficiencies could be obviously increased by at least 35% and 5%, compared to conventional LED lenses with a single freeform surface and with double freeform surfaces, respectively.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.45 no.1
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• pp.1-8
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• 1996

Recently, much attention has been paid to problems which is concerned with voltage instability phenomena and much works on these phenomena have been made. In this paper, by substituting d $P_{k}$ d $e_{k}$ ( $v^{\rarw}$= e +j f) for $P_{k}$ in conventional load flow, direct method for finging the limit of voltage stability is proposed. Here, by using the fact that taylor se- ries expansion in .DELTA. $P_{k}$ and .DELTA. $Q_{k}$ is terminated at the second-order terms, constraint equation (d $P_{k}$ d $e_{k}$ =0) and power flow equations are formulated with new variables .DSLTA. e and .DELTA.f, so partial differentiations for constraint equation are precisely calculated. The fact that iteratively calculated equations are reformulated with new variables .DELTA.e and .DELTA.f means that limit of voltage stability can be traced precisely through recalculation of jacobian matrix at e+.DELTA.e and f+.DELTA.f state. Then, during iterative process divergence may be avoid. Also, as elements of Hessian mat rix are constant, its computations are required only once during iterative process. Results of application of the proposed method to sample systems are presented. (author). 13 refs., 11 figs., 4 tab.