• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.899-911
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• 2018

In this paper, we consider the second-order nonlinear differential equation with the nonlocal boundary conditions. We first reformulate this boundary value problem as a fixed point problem for a Fredholm integral equation operator, and then present a result on the existence and uniqueness of the solution by using the contraction mapping theorem. Furthermore, we establish a sufficient condition on the functions ${\mu}$ and $h_i$, i = 1, 2 that guarantee a unique solution for this nonlocal problem in a Hilbert space. Also, accurate analytic solutions in series forms for this boundary value problems are obtained by the Adomian decomposition method (ADM).

• The Journal of Korean Institute of Communications and Information Sciences
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• v.14 no.2
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• pp.95-107
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• 1989

This paper proposes a realization method of multidimensional digital filters that has high modularity, regularity and parallelism enjoying the attributes for efficient VLSI implementation. The method shows that multidimensional transfer functions can be treated as two-dimensional transfer functions modifying the decomposition method of multidimensional transfer functions proposed by Venetsanopoulos etal, and then be displayed by multiplications and additions of one-dimensional transfer functions by applying the griangular decomposition theorem to the coefficient matrices of the two-dimensional transfer functions.

• ETRI Journal
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• v.40 no.5
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• pp.634-642
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• 2018

Projection spectral analysis is investigated and refined in this paper, in order to unify principal component analysis and independent component analysis. Singular value decomposition and spectral theorems are applied to nonsymmetric correlation or covariance matrices with multiplicities or singularities, where projections and nilpotents are obtained. Therefore, the suggested approach not only utilizes a sum-product of orthogonal projection operators and real distinct eigenvalues for squared singular values, but also reduces the dimension of correlation or covariance if there are multiple zero eigenvalues. Moreover, incremental learning strategies of projection spectral analysis are also suggested to improve the performance.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.189-201
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• 2022

The aim of the current work is to investigate the numerical study of a nonlinear Volterra-Fredholm integro-differential equation with initial conditions. Our approximation techniques modified adomian decomposition method (MADM) and variational iteration method (VIM) are based on the product integration methods in conjunction with iterative schemes. The convergence of the proposed methods have been proved. We conclude the paper with numerical examples to illustrate the effectiveness of our methods.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.421-426
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• 2013

We give a series of discrete random variables which converges to a random variable whose distribution function is the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs (RNT) distribution. We show this using the correspondence theorem that if the moments coincide then their corresponding distribution functions also coincide.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.735-740
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• 2015

Tomova [8] gave an upper bound for the distance of a bridge surface for a knot with two different bridge positions in a 3-manifold. In this paper, we show that the result of Tomova [8, Theorem 10.3] can be improved in the case when there are two different bridge spheres for a link in $S^3$.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.321-332
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• 2014

In this article we introduce different types of multiplier I-convergent double sequence spaces. We study their different algebraic and topological properties like solidity, symmetricity, completeness etc. The decomposition theorem is established and some inclusion results are proved.

• Honam Mathematical Journal
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• v.35 no.1
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• pp.1-15
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• 2013

In this paper, we study a sheaf-theoretic analysis of the convolution algebra on quiver varieties. As by-products, we reinterpret the results of H. Nakajima. We also produce a refined form of the BBD decomposition theorem for quiver varieties. Finally, we study a construction of highest weight modules through constructible functions.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.317-325
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• 1994

Suppose X is a complex Banach space and write B(X) for the Banach algebra of bounded linear operators on X, X＊ for the dual space of X, and T＊$\in$ B(X＊) for the dual operator of T. For T $\in$ B(X) write a(T) = dim T$^{-1}$ (0) and $\beta$(T) = codim T(X).(omitted)

• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.6
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• pp.749-753
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• 2003

In this paper we introduce the concepts on retrievability, separability and connectedness of fuzzy submachines, which generalize those of crisp submachines. And also we generalize crisp primary submachines to those with fuzziness, from which we obtain the decomposition theorem of fuzzy submachines.