• 대한수학회보
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• 제31권1호
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• pp.61-72
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• 1994

Every irreducible block-finite orthomodular lattice is simple [9] and every irreducible orthomodular alttice such that no proper p-ideal of L contains infinitely many commutators is simple [5]. Every finite (height) OML L which does not belong to the varitety generated by MO2 has one of the OML MO3, 2$^{3}$.2$^{2}$, D$_{16}$ OMLHOUSE as the homomorpyhic image of a subalgebra of L [3]. In this paper, we extend these results.s.

• 대한수학회논문집
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• 제15권3호
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• pp.511-519
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• 2000

If G is a strict generalized orthomodular lattice and H={I｜I=[0, $\chi$, $\chi$$\in$G}, then H is prime ideal of the Janowitz's hull J(G) of G. If f is the janowitz's embedding, then the set of all commutatiors of f(G) equals the set of all commutators of the Janowitz's hull J(G) of G. Let L be an OML. Then L J(G) for a strict GOML G if and only if ther exists a proper nonprincipal prime ideal G in L.

• 대한수학회보
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• 제59권3호
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• pp.547-566
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• 2022

Let T be a bilinear Calderón-Zygmund operator, $b{\in}U_q>_1L^q_{loc}(G)$. We firstly obtain a constructive proof of the weak factorisation of Hardy spaces. Then we establish the characterization of BMO spaces by the boundedness of the commutator [b, T]_j in variable Lebesgue spaces.

• 대한수학회보
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• 제60권2호
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• pp.541-560
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• 2023

Let T be an m-linear Calderón-Zygmund operator. $T_{{\vec{b}S}}$ is the generalized commutator of T with a class of measurable functions {b_i}^∞_i=1. In this paper, we will give some new estimates for $T_{{\vec{b}S}}$ when {b_i}^∞_i=1 belongs to Orlicz-type space and Lipschitz space, respectively.

• 대한수학회보
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• 제60권6호
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• pp.1439-1451
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• 2023

This paper provides a constructive proof of the weak factorizations of the classical Hardy space H¹(ℝⁿ) in terms of multilinear fractional integral operator on the variable Lebesgue spaces, which the result is new even in the linear case. As a direct application, we obtain a new proof of the characterization of BMO(ℝⁿ) via the boundedness of commutators of the multilinear fractional integral operator on the variable Lebesgue spaces.

• 대한수학회보
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• 제53권4호
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• pp.1071-1085
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• 2016

For $b{\in}L^1_{loc}({\mathbb{R}}^n)$, let ${\mathcal{I}}_{\alpha}$ be the bilinear fractional integral operator, and $[b,{\mathcal{I}}_{\alpha}]_i$ be the commutator of ${\mathcal{I}}_{\alpha}$ with pointwise multiplication b (i = 1, 2). This paper shows that if the commutator $[b,{\mathcal{I}}_{\alpha}]_i$ for i = 1 or 2 is bounded from the product Morrey spaces $L^{p_1,{\lambda}_1}({\mathbb{R}}^n){\times}L^{p_2,{\lambda}_2}({\mathbb{R}}^n)$ to the Morrey space $L^{q,{\lambda}}({\mathbb{R}}^n)$ for some suitable indexes ${\lambda}$, ${\lambda}_1$, ${\lambda}_2$ and $p_1$, $p_2$, q, then $b{\in}BMO({\mathbb{R}}^n)$, as well as that the compactness of $[b,{\mathcal{I}}_{\alpha}]_i$ for i = 1 or 2 from $L^{p_1,{\lambda}_1}({\mathbb{R}}^n){\times}L^{p_2,{\lambda}_2}({\mathbb{R}}^n)$ to $L^{q,{\lambda}}({\mathbb{R}}^n)$ implies that $b{\in}CMO({\mathbb{R}}^n)$ (the closure in $BMO({\mathbb{R}}^n)$of the space of $C^{\infty}({\mathbb{R}}^n)$ functions with compact support). These results together with some previous ones give a new characterization of $BMO({\mathbb{R}}^n)$ functions or $CMO({\mathbb{R}}^n)$ functions in essential ways.

• ETRI Journal
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• 제30권3호
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• pp.451-460
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• 2008

Recently, the power consumption of integrated circuits has been attracting increasing attention. Many techniques have been studied to improve the power efficiency of digital signal processing units such as fast Fourier transform (FFT) processors, which are popularly employed in both traditional research fields, such as satellite communications, and thriving consumer electronics, such as wireless communications. This paper presents solutions based on parallel architectures for high throughput and power efficient FFT cores. Different combinations of hybrid low-power techniques are exploited to reduce power consumption, such as multiplierless units which replace the complex multipliers in FFTs, low-power commutators based on an advanced interconnection, and parallel-pipelined architectures. A number of FFT cores are implemented and evaluated for their power/area performance. The results show that up to 38% and 55% power savings can be achieved by the proposed pipelined FFTs and parallel-pipelined FFTs respectively, compared to the conventional pipelined FFT processor architectures.

• 한국수학사학회지
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• 제15권3호
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• pp.17-24
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• 2002

It will be described the discovery of fundamental algebras such as complex numbers and the quaternions. Cardano(1539) was the first to introduce special types of complex numbers such as 5$\pm$$\sqrt{-15}$. Girald called the number a$\pm$$\sqrt{-b}$ solutions impossible. The term imaginary numbers was introduced by Descartes(1629) in “Discours la methode, La geometrie.” Euler knew the geometrical representation of complex numbers by points in a plane. Geometrical definitions of the addition and multiplication of complex numbers conceiving as directed line segments in a plane were given by Gauss in 1831. The expression “complex numbers” seems to be Gauss. Hamilton(1843) defined the complex numbers as paire of real numbers subject to conventional rules of addition and multiplication. Cauchy(1874) interpreted the complex numbers as residue classes of polynomials in R[x] modulo $x^2$＋1. Sophus Lie(1880) introduced commutators [a, b] by the way expressing infinitesimal transformation as differential operations. In this paper, it will be studied general quaternion algebras to finding of algebraic structure in Algebras.

• 전기학회논문지P
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• 제60권4호
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• pp.172-174
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• 2011

This paper is presented for robot vacuum cleaners using BLDC motors. Recently, BLDC motors which require smaller size, lower sound noise and higher efficiency have been placed in high value-added products including robot vacuum cleaners, vehicle cars and other industry applications. The DC motors have higher sound noise, higher height of the size and lower efficiency due to electro-magnetic structure using the brushes and the commutators. The proposed BLDC motors are appropriate for the motors adequate in regards to higher efficiency, longer life cycle time, and smaller height of the size when robot vacuum cleaners go to some lower height of the space like under sleeping beds and because it's power source is batteries. The paper shows the performance of the BLDC motors designed by the Finite Element Analysis(FEA) of the electro-magnetic field. This paper shows the mechanical structure and the prototype of the motor with the impeller. The performance characteristics of the BLDC motors with the hall sensor controller are verified by the experimental results.

• 전기학회논문지
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• 제56권4호
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• pp.790-794
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• 2007

This paper presents a new index mapping method for DFT (Discrete Fourier Transform) and its application to multidimensional DFT. Unlike conventional index mapping methods such as DIT (Decimation in Time) or DIF (Decimation in Frequency) algorithms, the proposed method is based on two levels of decomposition and it can be very efficiently used for implementing multidimensional DFT as well as 1-dimensional DFT. The proposed pipelined architecture for multidimensional DFT is very flexible so that it can lead to the best tradeoff between performance and hardware requirements. Also, it can be easily extended to higher dimensional DFTs since the number of CEs (Computational Elements) and DCs (Delay Commutators) increase only linearly with the dimension. Various implementation options based on different radices and different pipelining depths will be presented.