• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.113-126
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• 2007

Let A and E be $m{\times}n$ matrices and W an $n{\times}m$ matrix, and let $A_{d,w}$ denote the W-weighted Drazin inverse of A. In this paper, a new representation of the W-weighted Drazin inverse of A is given. Some new properties for the W-weighted Drazin inverse $A_{d,w}\;and\;B_{d,w}$ are investigated, where B=A+E. In addition, the Banach-type perturbation theorem for the W-weighted Drazin inverse of A and B are established, and the perturbation bounds for ${\parallel}B_{d,w}{\parallel}\;and\;{\parallel}B_{d,w}-A_{d,w}{\parallel}/{\parallel}A_{d,w}{\parallel}$ are also presented. When A and B are square matrices and W is identity matrix, some known results in the literature related to the Drazin inverse and the group inverse are directly reduced by the results in this paper as special cases.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1323-1329
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• 2010

In this paper, a new fixed point theorem in cone is applied to obtain the existence of at least one positive pseudo-symmetric solution for the second order three-point boundary value problem {x" + f(t, x, x')=0, t $\in$ (0, 1), x(0)=0, x(1)=x($\eta$), where f is nonnegative continuous function; ${\eta}\;{\in}$ (0, 1) and f(t, u, v) = f(1+$\eta$-t, u, -v).

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1249-1262
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• 2010

An approximate alternating linearization decomposition method, for minimizing the sum of two convex functions with some separable structures, is presented in this paper. It can be viewed as an extension of the method with exact solutions proposed by Kiwiel, Rosa and Ruszczynski(1999). In this paper we use inexact optimal solutions instead of the exact ones that are not easily computed to construct the linear models and get the inexact solutions of both subproblems, and also we prove that the inexact optimal solution tends to proximal point, i.e., the inexact optimal solution tends to optimal solution.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.311-327
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• 2016

In this paper, we propose an error embedded Runge-Kutta method to improve the traditional embedded Runge-Kutta method. The proposed scheme can be applied into most explicit embedded Runge-Kutta methods. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. These solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, the van der Pol equation and another one having a difficulty for the global error control are numerically solved. Finally, a two-body Kepler problem is also used to assess the efficiency of the proposed algorithm.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.805-811
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• 2021

Currently, batteries use commonly as energy sources for mobile electric devices. Due to the high density of energy, the energy storage state of a battery is very important information. To know the battery's energy storage state, it is necessary to find out the open state voltage of the battery. The open state voltage calculates with a mathematical model, but the computation of the real time state is complicated and requires many calculations. Therefore, the state observer designs to estimate in real time the battery open-circuit voltage as disturbance including model error. Using the estimated open voltage and applying it to the state estimation algorithm, we can estimate the charge. In this study, we first estimate the open-circuit voltage and design an estimation algorithm for estimating the state of battery charge. This includes errors in the system model and has a robust characteristic to noise. It is possible to increase the precision of the charge state estimation.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.851-858
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• 2021

In general, secondary batteries are widely used as an electric energy source. Among them, the state of energy storage of mobile devices is very important information. As a method of estimating a state, there is a method of estimating the state by integrating the current according to an energy storage state of a battery, and a method of designing a state estimator by measuring a voltage and estimating a charge amount based on a battery model. In this study, we designed the state estimator using an extended Kalman filter to increase the precision of the state estimation of the charge amount by including the error of the system model and having the robustness to the noise.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.487-496
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• 2021

In this paper we show that if A ∈ L(X) and B ∈ L(Y), X and Y complex Banach spaces, then A ⊕ B ∈ L(X ⊕ Y) is subscalar if and only if both A and B are subscalar. We also prove that if A, Q ∈ L(X) satisfies AQ = QA and Q^p = 0 for some nonnegative integer p, then A has property (C) (resp. property (𝛽)) if and only if so does A + Q (resp. property (𝛽)). Finally, we show that A ∈ L(X, Y) and B, C ∈ L(Y, X) satisfying operator equation ABA = ACA and BA ∈ L(X) is subscalar with property (𝛿) then both Lat(BA) and Lat(AC) are non-trivial.

• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.835-847
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• 2021

We study behavior of numerical solutions for a nonlinear eigenvalue problem on ℝⁿ that is reduced from a dispersion managed nonlinear Schrödinger equation. The solution operator of the free Schrödinger equation in the eigenvalue problem is implemented via the finite difference scheme, and the primary nonlinear eigenvalue problem is numerically solved via Picard iteration. Through numerical simulations, the results known only theoretically, for example the number of eigenpairs for one dimensional problem, are verified. Furthermore several new characteristics of the eigenpairs, including the existence of eigenpairs inherent in zero average dispersion two dimensional problem, are observed and analyzed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.2
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• pp.26-38
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• 2021

Image coloration refers to adding plausible colors to a grayscale image or video. Image coloration has been used in many modern fields, including restoring old photographs, as well as reducing the time spent painting cartoons. In this paper, a method is proposed for colorizing grayscale images using a convolutional neural network. We propose an encoder-decoder model, adapting FusionNet to our purpose. A proper loss function is defined instead of the MSE loss function to suit the purpose of coloring. The proposed model was verified using the ImageNet dataset. We quantitatively compared several colorization models with ours, using the peak signal-to-noise ratio (PSNR) metric. In addition, to qualitatively evaluate the results, our model was applied to images in the test dataset and compared to images applied to various other models. Finally, we applied our model to a selection of old black and white photographs.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.813-830
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• 2022

The generating functions of the divisor function σ_s(n) = Σ_0<d|n d^s are quasimodular forms. In this paper, we find the basis of the space of quasimodular forms of weight 6 on Γ₀(10) consisting of Eisenstein series and η-quotients. Then we evaluate the convolution sum Σ_ak+bl+cm=n σ(k)σ(l)σ(m) with lcm(a, b, c) = 10 and Σ_al+bm=n lσ(l)σ(m) and Σ_al+bm=n σ₃(l)σ(m) with lcm(a, b) = 10.