• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.127-133
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• 2012

In this paper we give a necessary and sufficient condition for characterizing $h$-stability for linear dynamic systems on time scales by using Lyapunov functions.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.495-502
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• 2014

In this paper, we show the ${\psi}$-uniform stability for linear impulsive differential equations and their perturbations by using the impulsive Gronwall's inequalities.

• Journal of the Korean Statistical Society
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• v.34 no.4
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• pp.281-295
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• 2005

We investigate the rate of convergence of the distribution of the maximum likelihood estimator (MLE) of an unknown parameter in the drift coefficient of a stochastic process described by a linear stochastic differential equation driven by a fractional Brownian motion (fBm). As a special case, we obtain the rate of convergence for the case of the fractional Ornstein- Uhlenbeck type process studied recently by Kleptsyna and Le Breton (2002).

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.579-594
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• 2005

In this paper, we will establish some new oscillation criteria for the second-order half-linear delay difference equation $${\Delta}(Pn ({\Delta}Xn)^{\gamma})+q_nx_\array{{\gamma}\\n-{\sigma}}=0,\;n{\geq}n_0$$, where ${\gamma}>0$ is a quotient of odd positive integers. Our results in this paper are sharp and improve some of the well known oscillation results in the literature. Some examples are considered to illustrate our main results.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• v.3B no.4
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• pp.159-164
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• 2003

In this paper, a three-dimensional finite element method and construction of equivalent-circuit for a linear ultrasonic motor are presented. The validity of three-dimensional finite element routine in this paper is experimentally confirmed by analyzing impedance of a piezoelectric transducer. Using this confirmed finite element routine, impedance and vibration mode of a linear ultrasonic motor are calculated. Elliptical motion of contact point between vibrator and rail of the linear ultrasonic motor is shown for determination of contact points. By using the finite element method and analytic equations, characteristics of the linear ultrasonic motor, such as thrust force, speed, losses, powers and efficiency, are calculated. The results are confirmed by experiment. Finally, equivalent circuit parameters of the linear ultrasonic motor are obtained using the three-dimensional finite element method and analytic equations.

• Advances in nano research
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• v.12 no.1
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• pp.37-47
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• 2022

In this paper, the non-linear static analysis of Timoshenko nanobeams consisting of bi-directional functionally graded material (BFGM) with immovable ends is investigated. The scratching in the FG nanobeam mid-plane, is the source of nonlinearity of the bending problems. The nonlocal theory is used to investigate the non-linear static deflection of nanobeam. In order to simplify the formulation, the problem formulas is derived according to the physical middle surface. The Hamilton principle is employed to determine governing partial differential equations as well as boundary conditions. Moreover, the differential quadrature method (DQM) and direct iterative method are applied to solve governing equations. Present results for non-linear static deflection were compared with previously published results in order to validate the present formulation. The impacts of the nonlocal factors, beam length and material property gradient on the non-linear static deflection of BFG nanobeams are investigated. It is observed that these parameters are vital in the value of the non-linear static deflection of the BFG nanobeam.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.865-876
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• 2023

This paper presents properties of the cocycle equations via cochains on a semigroup. And then we offer hyperstability results of related functional equations using the properties of cocycle equations via cochains. These results generalize hyperstability results of a class of linear functional equation by Maksa and Páles. The obtained results can be applied to obtain hyperstability of various functional equations such as Euler-Lagrange type quadratic equations.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.3
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• pp.243-291
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• 2020

In this paper, multi-block generalized backward differentiation methods for numerical solutions of ordinary differential and differential algebraic equations are introduced. This class of linear multi-block methods is implemented as multi-block boundary value methods (MB₂ VMs). The root distribution of the stability polynomial of the new class of methods are determined using the Wiener-Hopf factorization of a matrix polynomial for the purpose of their correct implementation. Numerical tests, showing the potential of such methods for output of multi-block of solutions of the ordinary differential equations in the new approach are also reported herein. The methods which output multi-block of solutions of the ordinary differential equations on application, are unlike the conventional linear multistep methods which output a solution at a point or the conventional boundary value methods and multi-block methods which output only a block of solutions per step. The MB₂ VMs introduced herein is a novel approach at developing very large scale integration methods (VLSIM) in the numerical solution of differential equations.

• Journal of KSNVE
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• v.7 no.3
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• pp.387-392
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• 1997

This paper concerns a SCARA robot with the flexible forearm linked to the rigid upper arm. The equations of motion are derived by the Lagrangian mechanics. For controller design, the perturbation approach is taken to separate the original equations of motion into linear equations describing small perturbed motions and nonlinear equations describing purely rigid motion of the robot. To effect the desired payload motion, open loop control inputs are determined based on the inverse dynamics of the latter. In order to reduce the positional error during maneuver, an active vibration suppression is done. To this end, a feedback control is designed for robustness against disturbance on the basis of the linear equations and the LQR theory modified to have a prescribed degree of stability. The proposed control scheme shows satisfactory performances in experiments as well as in numerical simulations.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.225-228
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• 1996

This paper concerns a SCARA type robot with the second arm flexible. Its equations of motion are derived by the Lagrangian mechanics. For controller design, the perturbation approach is taken to separate the original equations of motion into linear equations describing small perturbed motions and nonlinear equations describing purely rigid motion of the robot. To effect the desired payload motion, open loop control inputs are first determined based on the inverse dynamics of the latter. Next, in order to reduce the positional error during maneuver, an active vibration suppression is done. To this end, a feedback control is designed for robustness against disturbance on the basis of the linear equations and the LQR theory modified with a prescribed degree of stability. The numerical simulations results show the satisfactory control performance.