• Korean Journal of Mathematics
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• v.5 no.2
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• pp.195-198
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• 1997

In this paper, we have some characterizations of Pettis integrability of bounded weakly measurable function $f:{\Omega}{\rightarrow}X^*$ determined by separable subspace of $X^*$.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.12 no.1
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• pp.65-74
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• 2012

In this paper, we explore the application of 2-D dual-tree discrete wavelet transform (DDWT), which is a directional and redundant transform, for image coding. DDWT introduces limited redundancy and allows the transform to provide approximate shift invariance and directionally selective filters while preserving the usual properties of perfect reconstruction and computational efficiency with good well-balanced frequency responses. Also, quincunx lattice yields a non separable 2D-wavelet transform, which is also symmetric in both horizontal and vertical direction. And non-separable wavelet transformation can generate sub-images of multiple degrees rotated versions. The proposed 2-D non-separable DDWT can provide efficient approximation for directional features of images schemes, such as edges and contours in images that are not aligned with the horizontal or vertical direction. Finally, non-separable image processing using DDWT services good performance.

• Journal of KIISE:Software and Applications
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• v.31 no.5
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• pp.658-666
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• 2004

Separable systems are defined in term rewriting systems, respecting the notion of separability in the λ-calculus. In this research, we generalize separable systems of term rewriting systems, which was studied in restrictive systems such as constructive systems. We also associate separability with index-transitivity and with forward branching Separability is identified with forward branching, and strong sequentiality with index-transitivity satisfies separability. These are such good properties that enable us to describe the procedure of pattern-matching as an index tree, which is a sort of automata, and to transform separable systems into a constructor system with a simple pattern. Separable systems, in particular, can be translated into the λ-calculus. This research can serve a theoretical basis which allows functional languages to be explained by the λ-calculus, since functional languages such as ML and Haskell belong to a subclass of separable systems.

• Journal of the Korea Computer Industry Society
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• v.3 no.3
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• pp.321-330
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• 2002

A 2-D median filter has many applications in various image and video signal processing areas. The rapid development in VLSI technology makes it possible to implement a real-time or near real-time 2-D median filter with reasonable cost. For the efficient VLSI implementation, the algorithm should have characteristics such as small memory requirements, regular computations, and local data transfers. This paper presents an architecture of the real-time two-dimensional separable median filter which has appropriate characteristics for the VLSI implementation. For the efficient two-dimensional median filter, a separable two-dimensional median filtering structure and a bit-sliced pipelined median searching algorithm are used. A behavioral simulator is implemented with C language and used for the analysis of the presented architecture.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.547-556
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• 2013

We investigate complemented Banach sublattices of the Banach envelope of $WeakL^1$. In particular, the Banach envelope of $WeakL^1$ contains a complemented Banach sublattice that is isometrically isomorphic to a separable reflexive Banach lattice.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.16 no.6
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• pp.1273-1278
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• 2012

In this paper, we introduce modified integer transforms for lossless image compression and evaluate their performances for two-dimensional transforms. The two-dimensional extensions of the modified integer transforms show different performances in terms of coding efficiency and computational complexity. Thus, we measure performances for two-dimensional separable transforms and a two-dimensional non-separable transform. The separable modified integer transform used in H.264, the modified integer transform using the lifting scheme, and the non-separable transform in JPEG XR are evaluated in this paper. Also, experiments and their results are given. The experimental results indicate that the modified integer transform using the lifting scheme shows the best performance in terms of compression efficiency.

• Journal of Korean Society of Transportation
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• v.24 no.7 s.93
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• pp.139-148
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• 2006

In order to incorporate substitution effects between different transport modes in optimal road Pricing, relating economic theories and models have been reviewed. It includes unconstrained optimization problem of maximizing separable and non-separable social net benefit functions of different substitutable urban transport modes. In doing that, the problem and limitations such as path-independent conditions with the asymmetric Jacobian of the objective function have been reviewed. Consequently, a plausible way of deriving optimal road price under interdependent market conditions has been suggested so that the idea can help identifying desirable and acceptable urban transport policy alternatives in a more comprehensive way.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.535-539
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• 2007

Given operators X and Y acting on a separable complex Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that AX=Y. In this article, we show the following: Let $Alg\mathcal{L}$ be a tridiagonal algebra on a separable complex Hilbert space $\mathcal{H}$ and let $X=(x_{ij})\;and\;Y=(y_{ij})$ be operators in $\mathcal{H}$. Then the following are equivalent: (1) There exists a normal operator $A=(a_{ij})\;in\;Alg\mathcal{L}$ such that AX=Y. (2) There is a bounded sequence $\{\alpha_n\}\;in\;\mathbb{C}$ such that $y_{ij}=\alpha_jx_{ij}\;for\;i,\;j\;{\in}\;\mathbb{N}$. Given vectors x and y in a separable complex Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that Ax=y. We show the following: Let $Alg\mathcal{L}$ be a tridiagonal algebra on a separable complex Hilbert space $\mathcal{H}$ and let $x=(x_i)\;and\;y=(y_i)$ be vectors in $\mathcal{H}$. Then the following are equivalent: (1) There exists a normal operator $A=(a_{ij})\;in\;Alg\mathcal{L}$ such that Ax=y. (2) There is a bounded sequence $\{\alpha_n\}$ in $\mathbb{C}$ such that $y_i=\alpha_ix_i\;for\;i{\in}\mathbb{N}$.

• Journal of Korea Society of Digital Industry and Information Management
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• v.7 no.4
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• pp.119-131
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• 2011

In this paper, we explore the application of 2-D dual-tree discrete wavelet transform (DDWT), which is a directional and redundant transform, for image coding. DDWT main property is a more computationally efficient approach to shift invariance. Also, the DDWT gives much better directional selectivity when filtering multidimensional signals. The dual-tree DWT of a signal is implemented using two critically-sampled DWTs in parallel on the same data. The transform is 2-times expansive because for an N-point signal it gives 2N DWT coefficients. If the filters are designed is a specific way, then the sub-band signals of the upper DWT can be interpreted as the real part of a complex wavelet transform, and sub-band signals of the lower DWT can be interpreted as the imaginary part. The quincunx lattice is a sampling method in image processing. It treats the different directions more homogeneously than the separable two dimensional schemes. Quincunx lattice yields a non separable 2D-wavelet transform, which is also symmetric in both horizontal and vertical direction. And non-separable wavelet transformation can generate sub-images of multiple degrees rotated versions. Therefore, non-separable image processing using DDWT services good performance.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.5C
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• pp.461-467
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• 2003

We propose an efficient method for separable symmetric linear filtering in the DCT domain. First, separable 2-D linear filtering is decomposed into the cascade of 1-D filtering in the DCT domain. We investigate special characteristics of DCT domain filtering matrices when the filter coefficients are symmetric. Then we present the DCT domain 2-D filtering method using these characteristics. The proposed method requires smaller number of multiplications including typical sparseness of DCT coefficients compared to previous DCT domain linear filtering methods. Also, the proposed method is composed of simple and regular operations, which would be appropriate for efficient VLSI implementation.