• 대한수학회보
• /
• 제55권3호
• /
• pp.899-911
• /
• 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).

• 한국통신학회논문지
• /
• 제14권2호
• /
• pp.95-107
• /
• 1989

본 논문에서는 효과적으로 VLSI화 하는데 적합한 모듈성, 규칙성, 병렬성 등을 가진 다차원 디지털 필터의 한 실현방법을 제안하였다. 이 방법은 Venetsanopoulos 등$^(10)$이 제안한 다차원 전달함수의 분해방법에 근거를 두어 다차원 다항식을 등가적인 2차원 다항식으로 취급할 수 있도록 하였으며, 변환된 2차원 다항식의 계수행렬을 삼각분해하여 다차원 전달함수를 1차원 전달함수들만의 곱 및 합으로 나타낼 수 있도록 하였다.

• ETRI Journal
• /
• 제40권5호
• /
• pp.634-642
• /
• 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
• /
• 제27권1호
• /
• pp.189-201
• /
• 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.

• 충청수학회지
• /
• 제26권2호
• /
• pp.421-426
• /
• 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.

• 대한수학회보
• /
• 제52권3호
• /
• pp.735-740
• /
• 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
• /
• 제54권2호
• /
• pp.321-332
• /
• 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.

• 호남수학학술지
• /
• 제35권1호
• /
• pp.1-15
• /
• 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.

• 대한수학회논문집
• /
• 제9권2호
• /
• pp.317-325
• /
• 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)

• 한국지능시스템학회논문지
• /
• 제13권6호
• /
• pp.749-753
• /
• 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.