• Asian Journal of Business Environment
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• v.14 no.1
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• pp.23-30
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• 2024

Purpose: The purpose of this research is to explore the macroeconomic model through both static and dynamic equations. The primary objective of this study is to investigate the variations in the elasticity of substitution across changing economic variables within the framework of the Allen-Uzawa production functions. Research, design, data and methodology: The data were drawn from the World Bank's annual central statistical office database from 2010 to 2021 in the United States of America. The level of expenditures and of the public finance sector, macroeconomic data like output, inflation rates, and labor are examined. Results: This study demonstrates the interaction of two equations, clarifying that the macroeconomic model is practical to determining the stability of both static and dynamic equation systems analytically. The Allen-Uzawa equations allow for the verification of macroeconomic model properties, and study results demonstrate an increase in the range of capital uses as a form of mechanization. A constant elasticity of substitution function is derived from the macroeconomic variables. Conclusion: The macroeconomic model, though the analysis of the static and dynamic Allen - Uzawa model, not only facilitates the examination of long-term trends in crucial endogenous variables but also overcomes challenges commonly associated with other mathematical methods. Overall, the analysis promotes economic growth, investment, and employment. The levels of expenditures and the public finance sector, along with macroeconomic data such as output, inflation rates, and labor, are examined.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.300-306
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• 2004

This paper is concerned with the application of perturbation method to the dynamic analysis of free-free beam. In general, the rigid-body motions and elastic vibrations are analyzed separately. However, the rigid-body motions cause vibrations and elastic vibrations also affect rigid-body motions in turn, which indicates that the rigid-body motions and elastic vibrations are coupled in nature. The resulting equations of motion are hybrid and nonlinear. We can discretize the equations of motion by means of admissible functions but still we have to cope with nonlinear equations. In this paper, we propose the use of .perturbation method to the coupled equations of motion. The resulting equations consist of zero-order equations of motion which depict the rigid-body motions and first-order equations of motion which depict the perturbed rigid-body motions and elastic vibrations. Numerical results show the efficacy of the proposed method.

• The Journal of Industrial Distribution & Business
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• v.6 no.4
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• pp.27-37
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• 2015

Purpose - This study first explores the possible dynamic relationship between ownership structure and firm performance using a panel of 4,900 Chinese-listed small- and medium-sized enterprises (SMEs) from 1999 to 2012. Research design, data, and methodology - We address this issue through a dynamic panel model using a method of moments (GMM) technique and dynamic simultaneous equations to alleviate the potential endogenous problem: unobserved heterogeneity, simultaneity, and dynamic endogeneity. Results - Under the framework of dynamic endogeneity, firm performance has a significantly positive influence on ownership, but not vice versa. Ownership and performance can be explained by their owned lagged values, respectively. Moreover, intertemporal endogeneity exists among ownership, investment, and performance through the application of system dynamic equations, which implies that the relationship among ownership structure, investment, and firm performance is dynamic by nature. Conclusions - This study also significantly contributes to a better understanding of dynamic corporate governance by providing further empirical evidence from the largest capital market in the Asian region.

• Journal of KSNVE
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• v.9 no.4
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• pp.806-812
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• 1999

Dynamic behaviors are analyzed for a flexble spinning disk with angular acceleration, considering geometric nonlinearity. Based upon the Kirchhoff plate theory and the von Karman strain theory, the nonlinear governing equations are derived which are coupled equations with the in-plane and out-of-planedisplacements. The governing equations are discretized by using the Galerkin approximation. With the discretized nonlinear equations, the time responses are computed by using the generalized-$\alpha$ method and the Newton-Raphson method. The analysis shows that the existence of angular acceleration increases the displacements of the spinning disk and makes the disk unstable.

• Proceedings of the KIEE Conference
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• 2007.10c
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• pp.47-49
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• 2007

This paper deals with the generating characteristic analysis of permanent magnet (PM) machines with multi-pole rotor and 3-phase stator windings considering losses such as copper loss, iron loss and mechanical loss. First, using d-q transformation, dynamic equations of PM machines are established. And then, characteristic equations for losses, power and efficiency are also derived. On the basis of d-q dynamic equations and characteristic equations, dynamic simulation algorithm is achieved by the MATLAB/SIMULINK. The simulation results are validated extensively by finite element (FE) analyses.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1285-1304
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• 2010

The purpose of this paper is to establish some sufficient conditions for oscillation of solutions of the second-order functional dynamic equation of Emden-Fowler type $\[a(t)x^{\Delta}(t)\]^{\Delta}+p(t)|x^{\gamma}(\tau(t))|\|x^{\Delta}(t)\|^{1-\gamma}$ $sgnx(\tau(t))=0$, $t\;{\geq}\;t_0$, on a time scale $\mathbb{T}$, where ${\gamma}\;{\in}\;(0,\;1]$, a, p and $\tau$ are positive rd-continuous functions defined on $\mathbb{T}$, and $lim_{t{\rightarrow}{\infty}}\;{\tau}(t)\;=\;\infty$. Our results include some previously obtained results for differential equations when $\mathbb{T}=\mathbb{R}$. When $\mathbb{T}=\mathbb{N}$ and $\mathbb{T}=q^{\mathbb{N}_0}=\{q^t\;:\;t\;{\in}\;\mathbb{N}_0\}$ where q > 1, the results are essentially new for difference and q-difference equations and can be applied on different types of time scales. Some examples are worked out to demonstrate the main results.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.11a
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• pp.394-400
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• 2008

This paper presents an analytical method to investigate the stability of FDBs (fluid dynamic bearings) considering the tilting motion. The perturbed equations of motion are derived with respect to translational and tilting motion for the general rotor-bearing system with five degrees of freedom. The Reynolds equations and their perturbed equations are solved by using the FEM in order to calculate the pressure, load capacity, and the stiffness and damping coefficients. This research introduces the radius of gyration to the equations of notion in order to express the mass moment of interia with respect to the critical mass. Then the critical mass of FDBs is determined by solving the eigenvalue problem of the linear equations of motion. This research is numerically validated by comparing the stability chart of FDBs with the time response of the whirl radius obtained from the direct integration of the equations of motion. This research shows that the tilting motion is one of the major design considerations to determine the stability of rotating system. It also shows that the stability of FDBs considering only translation is overestimated in comparison with the stability of FDBs considering both translational and tilting motion.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.12
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• pp.1354-1359
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• 2004

This paper is concerned with the application of perturbation method to the dynamic analysis of floating flexible body. In dealing with the dynamics of free-floating body, the rigid-body motions and elastic vibrations are analyzed separately. However, the rigid-body motions cause vibrations and elastic vibrations also affect rigid-body motions in turn, which indicates that the rigid-body motions and elastic vibrations are coupled in nature. The resulting equations of motion are hybrid and nonlinear. We can discretize the equations of motion by means of admissible functions but still we have to cope with nonlinear equations. In the previous paper, we proposed the use of perturbation method to the coupled equations of motion and derived zero-order and first-order equations of motion. The derivation process was lengthy and tedious. Hence, in this paper, we propose a new approach to the same problem by applying the perturbation method to the Lagrange's equations, thus providing a systematic approach to the addressed problem. Theoretical derivations show the efficacy of the proposed method.

• Proceedings of the Korean Geotechical Society Conference
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• 2006.03a
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• pp.1326-1333
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• 2006

Purpose of this research is a development for the curve fitted equations that can improve practical calculation and work application when seismic performance has been evaluated and this work has been made a study of the dynamic response under various boundary conditions of buried pipelines to compare the dynamic behavior of concrete pipe and steel pipe, FRP pipe. This research have been developed curve fitted equations that can be improving efficiency and practicality. Using a nonlinear least square method, and after testing several different exponential equations, Proposed the curve fitted equations to give the best result and constant value by the propagation velocities. With these results, dynamic response analysis and seismic performance evaluation have been achieved on concrete pipe, steel pipe and FRP pipe that have a various boundary conditions. Degree of a polynomial expression and coefficient value by propagation velocity have been calculated when using the curve fitting equations.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.7
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• pp.1138-1145
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• 2003

In this paper, a study on the dynamic behavior and lubrication characteristics of a reciprocating compression mechanism used in small refrigeration compressor is performed. In the problem formulation of the compressor dynamics, the viscous frictional force between piston and cylinder wall is considered in order to determine the coupled dynamic behaviors of piston and crankshaft. The solutions of the equations of motion of the reciprocating mechanism along with the time dependent Reynolds equations for the lubricating film between piston and cylinder wall and oil films of the journal bearings are obtained simultaneously. The hydrodynamic forces of journal bearings are calculated using finite bearing model and Gumbel boundary condition. And, a Newton-Raphson procedure was employed in solving the nonlinear equations of piston and crankshaft. The results explored the effects of design parameters on the stability and lubrication characteristics of the compression mechanism.