• Structural Engineering and Mechanics
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• v.57 no.2
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• pp.327-355
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• 2016

A new analytical derivation of the elastodynamic point load solutions for an isotropic multi-layered half-space is presented by means of the precise integration method (PIM) and the approach of dual vector. The time-harmonic external load is prescribed either on the external boundary or in the interior of the solid medium. Starting with the axisymmetric governing motion equations in a cylindrical coordinate system, a second order ordinary differential matrix equation can be gained by making use of the Hankel integral transform. Employing the technique of dual vector, the second order ordinary differential matrix equation can be simplified into a first-order one. The approach of PIM is implemented to obtain the solutions of the ordinary differential matrix equation in the Hankel integral transform domain. The PIM is a highly accurate algorithm to solve sets of first-order ordinary differential equations and any desired accuracy of the dynamic point load solutions can be achieved. The numerical simulation is based on algebraic matrix operation. As a result, the computational effort is reduced to a great extent and the computation is unconditionally stable. Selected numerical trials are given to validate the accuracy and applicability of the proposed approach. More examples are discussed to portray the dependence of the load-displacement response on the isotropic parameters of the multi-layered media, the depth of external load and the frequency of excitation.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.81-93
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• 2013

We consider a distributed optimal flux control problem: finding the potential of which gradient approximates the target vector field under an elliptic constraint. Introducing the Lagrange multiplier and a change of variables the Euler-Lagrange equation turns into a coupled equation of an elliptic equation and a reaction diffusion equation. The change of variables reduces iteration steps dramatically when the Gauss-Seidel iteration is considered as a solution method. For the elliptic equation solver we consider the Cell Boundary Element (CBE) method, which is the finite element type flux preserving methods.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.18 no.2
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• pp.117-123
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• 2018

In this study, we suggest a fast image reconstruction scheme using Poisson equation from image gradient domain. In this approach, using the Poisson equation, a guided vector field is created by employing source and target images within a selected region at the first step. Next, the guided vector is used in generating the result image. We analyze the problem of reconstructing a two-dimensional function that approximates a set of desired gradients and a data term. The joined data and gradients are able to work like modifying the image gradients while staying close to the original image. Starting with this formulation, we have a screened Poisson equation known in physics. This equation leads to an efficient solution to the problem in FFT domain. It represents the spatial filters that solve the two-dimensional screened Poisson model and shows gradient scaling to be a well-defined sharpen filter that generalizes Laplace sharpening. We demonstrate the results using a discrete cosine transformation based this Poisson model.

• The Journal of Korean Institute of Next Generation Computing
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• v.15 no.3
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• pp.25-30
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• 2019

Magnetic sensors have the disadvantage that their vector values differ depending on the direction. In this paper, we propose a magnetic vector calibration method for geomagnetic-based indoor localization estimates. The fingerprinting technique used in geomagnetic-based indoor localization the position by matching the magnetic field map and the magnetic sensor value. However, since the moving direction of the current user may be different from the moving direction of the person who creates the magnetic field map at the collection time, the sampled magnetic vector may have different values from the vector values recorded in the field map. This may substantially lower the positioning accuracy. To avoid this problem, the existing studies use only the magnitude of magnetic vector, but this reduces the uniqueness of the fingerprint, which may also degrade the positioning accuracy. In this paper we propose a vector calibration algorithm which can adjust the sampled magnetic vector values to the vector direction of the magnetic field map by using the parametric equation of a circle. This can minimize the inaccuracy caused by the direction mismatch.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.811-821
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• 2013

We study the initial value problem of the exponential wave equation in $\math{R}^{n+1}$ for small initial data. We shows, in the case of $n=1$, the global existence of solution by applying the formulation of first order quasilinear hyperbolic system which is weakly linearly degenerate. When $n{\geq}2$, a vector field method is applied to show the stability of a trivial solution ${\phi}=0$.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.227-230
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• 1995

Stability of a coupled nonautonomous ordinary differential equation is investigated. Asymptotic convergence to zero of a part of state vector is additionally shown, otherwise only uniform stability could have been concluded by the Lyapunov direct method. Obtained results could be particularly useful in analysis of nonautonomous systems in which the invariance principle does not hold. An illustrating example is given.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.1
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• pp.70-74
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• 2008

In the field of camera motion research, it is widely held that the position (movement) and pose (rotation) of cameras are correlated and cannot be independently separated. A new equation based on inner product is proposed here to independently separate the position and pose. It is proved that the position and pose are not correlated and the equation is applied to estimation of the camera exterior parameters using a real image and 3D data.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.589-598
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• 2023

Magnetic curves are the trajectories of charged particals which are influenced by magnetic fields and they satisfy the Lorentz equation. It is important to find relationships between magnetic curves and other special curves. This paper is a study of magnetic curves and this kind of relationships. We give the relationship between β-magnetic curves and Mannheim, Bertrand, involute-evolute curves and we give some geometric properties about them. Then, we study this subject for γ-magnetic curves. Finally, we give an evaluation of what we did.

• Steel and Composite Structures
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• v.50 no.2
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• pp.123-133
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• 2024

The paper deals with the propagation of Rayleigh waves in a nonlocal thermoelastic isotropic layer which is lying over a nonlocal thermoelastic isotropic half-space under the purview of Green-Lindsay model and Eringen's nonlocal elasticity in the presence of voids. The normal mode analysis is employed to the considered equations to obtain vector matrix differential equation which is then solved by eigenvalue approach. The frequency equation of Rayleigh waves is derived and different particular cases are also deduced. The effects of voids and nonlocality on different characteristics of Rayleigh waves are presented graphically.

• The Journal of the Acoustical Society of Korea
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• v.36 no.3
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• pp.158-164
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• 2017

Typical hydrophones in line array sensors for early detection of covert underwater targets can measure only sound-pressure-magnitude with the limitation of being unable to identify the direction of an incoming wave. In this study, a thickness shear mode vibrator was proposed as the main component of an inertia type vector hydrophone to measure both magnitude and direction of acoustic signals from targets. The equation to analyze the output voltage of the vibrator to an external force was derived, and the validity of the equation was verified through finite element analysis of a PMN-PT single crystal vibrator. The analysis results from this study will be utilized in the future for the design of inertia type vector hydrophones made of thickness shear vibrators.