• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.10
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• pp.67-72
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• 1994

In this paper we suggest a 32 bit high speed parallel multiplier which plays an important role in digital signal processing. We employ a bit-pair recoding Booth algoritham that gurantees n/2 partial product terms, which uniformly handles the signed-operand case. While partial product terms are generated, a special method is suggested to reduce time delay by employing 1's complement instead of 2's complement. Later when partial products are added, the additional 1 bit's are packed in a single partial product term and added to in the parallel counter. Then 16 partial product terms are reduced to two summands by using successive parallel counters. Final multiplication value is obtained by a BLC adder. When this multiplier is simulated under 0.8$\mu$CMOS standard cell we obtain 30ns multiplier speed.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.495-506
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• 2016

In this note we consider the monoid $\mathcal{PODI}_n$ of all monotone partial permutations on $\{1,{\ldots},n\}$ and its submonoids $\mathcal{DP}_n$, $\mathcal{POI}_n$ and $\mathcal{ODP}_n$ of all partial isometries, of all order-preserving partial permutations and of all order-preserving partial isometries, respectively. We prove that both the monoids $\mathcal{POI}_n$ and $\mathcal{ODP}_n$ are quotients of bilateral semidirect products of two of their remarkable submonoids, namely of extensive and of co-extensive transformations. Moreover, we show that $\mathcal{PODI}_n$ is a quotient of a semidirect product of $\mathcal{POI}_n$ and the group $\mathcal{C}_2$ of order two and, analogously, $\mathcal{DP}_n$ is a quotient of a semidirect product of $\mathcal{ODP}_n$ and $\mathcal{C}_2$.

• Journal of the Korean Mathematical Society
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• v.52 no.4
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• pp.869-889
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• 2015

Let ${\Gamma}^+$ be the positive cone in a totally ordered abelian group ${\Gamma}$, and ${\alpha}$ an action of ${\Gamma}^+$ by extendible endomorphisms of a $C^*$-algebra A. Suppose I is an extendible ${\alpha}$-invariant ideal of A. We prove that the partial-isometric crossed product $\mathcal{I}:=I{\times}^{piso}_{\alpha}{\Gamma}^+$ embeds naturally as an ideal of $A{\times}^{piso}_{\alpha}{\Gamma}^+$, such that the quotient is the partial-isometric crossed product of the quotient algebra. We claim that this ideal $\mathcal{I}$ together with the kernel of a natural homomorphism $\phi:A{\times}^{piso}_{\alpha}{\Gamma}^+{\rightarrow}A{\times}^{iso}_{\alpha}{\Gamma}^+$ gives a composition series of ideals of $A{\times}^{piso}_{\alpha}{\Gamma}^+$ studied by Lindiarni and Raeburn.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.3
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• pp.235-242
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• 2022

In this paper, we consider the existence of nonconstant warping functions on a warped product manifold M = B × _f² F, where B is a q(> 2)-dimensional base manifold with a nonconstant scalar curvature S_B(x) and F is a 3- dimensional fiber Einstein manifold and discuss that the resulting warped product manifold is an Einstein manifold, using the existence of the solution of some partial differential equation.

• The KIPS Transactions:PartA
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• v.10A no.6
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• pp.671-676
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• 2003

In this paper, we proposed a new First Partial product Addition (FPA) architecture with new compressor (or parallel counter) to CSA tree built in the process of adding partial product for improving speed in the fast parallel multiplier to improve the speed of calculating partial product by about 20% compared with existing parallel counter using full Adder. The new circuit reduces the CLA bit finding final sum by N/2 using the novel FPA architecture. A 5.14nS of multiplication speed of the $16{\times}16$ multiplier is obtained using $0.25\mu\textrm{m}$ CMOS technology. The architecture of the multiplier is easily opted for pipeline design and demonstrates high speed performance.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.819-830
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• 2019

This paper is mainly concerned with the existence and uniqueness of fixed points of $f:X^k{\rightarrow}X$, $k{\in}{\mathbb{N}}$, where X is a quasi-partial metric space and mapping f satisfies appropriate conditions. Results are also supported with relevant examples.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.361-374
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• 2009

We characterize a fuzzy partial order relation using its level set, find sufficient conditions for the image of a fuzzy partial order relation to be a fuzzy partial order relation, and find sufficient conditions for the inverse image of a fuzzy partial order relation to be a fuzzy partial order relation. Also we define a fuzzy lattice as fuzzy relations, characterize a fuzzy lattice using its level set, show that a fuzzy totally ordered set is a distributive fuzzy lattice, and show that the direct product of two fuzzy lattices is a fuzzy lattice.

• Proceedings of the IEEK Conference
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• 2001.06b
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• pp.377-380
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• 2001

In this paper, we propose new partial product compressor and ENMODL (Enhanced-NORA-MODL) CLA(Carry Look-ahead Adder) for high speed and low power multiplier. To reduce transistor count, area, power we developed two new-approaches. One is small size partial product compressor, the other is dynamic CMOS logic ENMODL CLA. The transistor count of new compressor is reduced by 11% as compared with that of conventional one. The speed of ENMODL CLA is increased by 6.27% as compared with NMODL CLA.

• Knowledge Management Research
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• v.15 no.4
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• pp.207-221
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• 2014

Due to the awareness for the importance of social capital, many researches have investigated that social capital contributes to the successful implementation of product innovation. Although most researchers tried to model the effect of social capital on product innovation as a linear relation, we consider it too simplistic and fuzzy because knowledge utilization which ultimately leads to product innovation should exist in the relationship between social capital and product innovation. Using 107 survey data, this study found there is a partial mediating effect of knowledge utilization on the link between structure aspect of social capital and product innovation (i.e., new product development and improvement in existing products). Next, this study reported knowledge utilization does act as a perfect mediating variable on the link between awareness aspect of social capital and improvement of existing products, but act as a partial mediating variable on the link between awareness aspect of social capital and new product development. Finally, this study found that knowledge utilization does not act as a mediating variable on the link between relation aspect of social capita and product innovation.

• Smart Media Journal
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• v.3 no.1
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• pp.39-45
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• 2014

The partial product matrix of a parallel squarer are symmetric about the diagonal. To reduce the number of partial product bits and the depth of partial product matrix, it can be typically folded, shifted and bit-rearranged. In this paper, an efficient design approach for the combined squarer, capable of operating on either unsigned or signed numbers based on a mode selection signal, is presented. By simulations, it is shown that the proposed combined squarers lead to up to 18% reduction in area, 11% reduction in propagation delay and 9% reduction in power consumption compared with the previous combined squarers.