• Journal of Korea Multimedia Society
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• v.22 no.9
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• pp.1029-1035
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• 2019

In this paper, a tentative Kth order Goldschmidt floating point number Nth root algorithm for K order convergence rate in one iteration is proposed by applying Taylor series to the Goldschmidt square root algorithm. Using the proposed algorithm, Nth root and Nth inverse root can be computed from iterative multiplications without division. It also predicts the error of the algorithm iteration. It iterates until the predicted error becomes smaller than the specified value. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a floating point number Nth root unit.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.655-676
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• 2021

A parameter uniform numerical scheme is proposed for solving singularly perturbed parabolic partial differential-difference convection-diffusion equations with a small delay and advance parameters in reaction terms and spatial variable. Taylor's series expansion is applied to approximate problems with the delay and advance terms. The resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for the temporal discretization and finite difference method for the spatial discretization on a uniform mesh. The proposed numerical scheme is shown to be an ε-uniformly convergent accurate of the first order in time and second-order in space directions. The efficiency of the scheme is proved by some numerical experiments and by comparing the results with other results. It has been found that the proposed numerical scheme gives a more accurate approximate solution than some available numerical methods in the literature.

• East Asian mathematical journal
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• v.37 no.3
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• pp.319-331
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• 2021

In this paper, we aim to introduce two new families of analytic and bi-univalent functions associated with the Attiya's operator, which is defined by the Hadamard product of a generalized Mittag-Leffler function and analytic functions on the open unit disk. Then we estimate the second and third coefficients of the Taylor-Maclaurin series expansions of functions belonging to these families. Also, we investigate Fekete-Szegö problem for these families. Some relevant connections of certain special cases of the main results with those in several earlier works are also pointed out. Two naturally-arisen problems are given for further investigation.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.11
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• pp.4413-4425
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• 2020

In order to completely record all the information of realistic scenes, high dynamic range (HDR) images have been widely used in virtual reality, photography and computer graphics. A simple yet effective tone mapping method based on total variation is proposed so as to reproduce realistic scenes on low dynamic range (LDR) display devices. The structural component and texture component are obtained using total variation model in logarithmic domain. Then, the dynamic range of the structural component is compressed with an adaptive arcsine function. The texture component is processed by Taylor series. Finally, we adjust the saturation component using sigmoid function and restore the color information. Experimental results demonstrate that our method outperforms existing methods in terms of quality and speed.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.17 no.9
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• pp.2348-2360
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• 2023

As science and technology evolve, object detection of moving objects has been widely used in the context of machine learning and artificial intelligence. Traditional moving object detection algorithms, however, are characterized by relatively poor real-time performance and low accuracy in detecting moving objects. To tackle this issue, this manuscript proposes a modified Kalman filter algorithm, which aims to expand the equations of the system with the Taylor series first, ignoring the higher order terms of the second order and above, when the nonlinear system is close to the linear form, then it uses standard Kalman filter algorithms to measure the situation of the system. which can not only detect moving objects accurately but also has better real-time performance and can be employed to predict the trajectory of moving objects. Meanwhile, the accuracy and real-time performance of the algorithm were experimentally verified.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.11C
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• pp.702-711
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• 2011

In this paper, we derived a closed-form equation of a Best Linear Unbiased Estimator (BLUE) and its Crammer-Rao Lower Bound (CRLB) for the estimation of the position of the emitter based on the Time Difference of Arrival (TDOA) teclmique. The BLUE and CRLB were derived for the case of estimating 2 dimensional position of the emitter with 3 base stations or sensors, and for this purpose, we nsed an approximated equation of the TDOA hyperbola equation obtained from the first order Taylor-series after setting the reference points of the position. The derived equation can be used for any kind of noises which are uncorrelated in each other in the TOA measurement noises and for a white Gaussian noise also.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.1
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• pp.39-46
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• 1993

The need to develop method which can improve the shape design efficiency using high quality approximation is being brought up. In this study, to perform shape optimal design of three-dimensional continuum structures an efficient approximation method for stress constraints is proposed, based on expanding the nodal forces in Taylor series with respect to shape variables. Numerical examples are performed using the 3-D cantilever beam and fixed-fixed beam and compared with other method to demonstrate the efficiency and convergence rate of the Force Approximation method. It is shown that by taking advantage of this high quality approximation, the total number of finite element analysis required for shape optimization of 3-D continuum structures can be reduced significantly, resulting to the same level of efficiency achieved previously in sizing optimization problems. Also, shape representation by super curve technique applied to obtain optimal shape finds useful method.

• Journal of Korean Society of Steel Construction
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• v.26 no.3
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• pp.143-154
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• 2014

An improved method for evaluating effective buckling length of semi-rigid frame with inelastic behavior is newly proposed. Also, generalized exact tangential stiffness matrix with rotationally semi-rigid connections is adopted in previous studies. Therefore, the system buckling load of structure with inelastic behaviors can be exactly obtained by only one element per one straight member for inelastic problems. And the linearized elastic stiffness matrix and the geometric stiffness matrix of semi-rigid frame are utilized by taking into account 4th terms of taylor series from the exact tangent stiffness matrix. On the other hands, two inelastic analysis programs(M1, M2) are newly formulated. Where, M1 based on exact tangent stiffness matrix is programmed by iterative determinant search method and M2 is using linear algorithm with elastic and geometric matrices. Finally, in order to verify this present theory, various numerical examples are introduced and the effective buckling length of semi-rigid frames with inelastic materials are investigated.

• Journal of the Korean Society for Advanced Composite Structures
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• v.1 no.2
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• pp.29-35
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• 2010

In addition to the Young's modulus, the Poisson's ratio is also at the center of attention in the field stochastic finite element analysis since the parameters play an important role in determining structural behavior. Accordingly, the sole effect of this parameter on the response variability is of importance from the perspective of estimation of uncertain response. To this end, a formulation to determine the response variability in laminate composite plates due to the spatial randomness of Poisson's ratio is suggested. The independent contributions of random Poisson's ratiocan be captured in terms of sub-matrices which include the effect of the random parameter in the same order, which can be attained by using the Taylor's series expansion about the mean of the parameter. In order to validate the adequacy of the proposed formulation, several example analyses are performed, and then the results are compared with Monte Carlo simulation (MCS). A good agreement between the suggested scheme and MCS is observed showing the adequacy of the scheme.

• Journal of the Korea Concrete Institute
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• v.16 no.2 s.80
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• pp.155-162
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• 2004

An analytical method to predict the time dependent flexural behavior of composite girder is presented based on sectional analysis. The time dependent constitutive relation accounting for the early-age concrete properties including maturing of elastic modulus, creep and shrinkage is derived in an incremental format by the first order Taylor series expansion. The sectional analysis calculates the axial and curvature strains based on the force and moment equilibriums. The deflection curve of the girder approximated by the quadratic polynomial function is calculated by applying to the proper boundary conditions in the consecutive segments. Numerical applications are made for the 3-span double composite steel box girder which is a composite bridge girder filled with concrete at the bottom of the steel box in the negative moment region. The calculated results are compared with those by finite element analysis results. Close agreement is observed between the two approaches.