• Proceedings of the Korea Information Processing Society Conference
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• 2017.04a
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• pp.9-12
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• 2017

FreeType is a rasterizer which is commonly used in different operating systems like Linux, android etc. Although FreeType is open source but it is not easy to add/remove modules and services etc. for developers. This paper proposes a new module for FreeType named as FreeType Outlet adapter (FOA). It enables to add/remove modules, services, functionality etc. inside FreeType. It acts as the bridge to add functions from outside FreeType to the inner core of FreeType. New font formats like METAFONT, animated fonts and customized fonts which currently are not supported by FreeType can be added with this FOA module.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.403-416
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• 2021

It is known that the rank 2 stably free syzygy module P⁽²⁾ is not free. This algebraic fact was proved analytically, but this remarkable fact still lacks of a simple algebraic proof. The main purpose of this paper is to give a partially algebraic proof by making use of a theorem whose proof is quite topological, and the further properties of the module will be discussed.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.585-589
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• 2005

In [1], the structure of C(2,2) is determined as the polynomial ring in 5 variables. In this work, we show that C(2,3) is a free module over the subring of 9 variables. We explicitly give a presentation of C(2, 3) as free module over the polynomial ring.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.347-355
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• 2000

In this paper we define linearly independent, basis, free, torsion-free and torsion-free completely on an automation. We prove a theorem describing a relationship between free and torsion-free completely on automata. Also we prove some important properties of them. Furthermore, we discuss some theorems associated with free.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.619-637
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• 2004

In this paper, a left module over an associative ring with identity is defined to be openly semiprimitive (strongly semiprimitive, respectively) by the zero intersection of all maximal open fully invariant submodules (all maximal open submodules which are fully invariant, respectively) of it. For any projective module, the openly semiprimitivity of the projective module is an equivalent condition of the semiprimitivity of endomorphism ring of the projective module and the strongly semiprimitivity of the projective module is an equivalent condition of the endomorphism ring of the projective module being a sub direct product of a set of subdivisions of division rings.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.53-59
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• 2017

In this article, we generalize the concepts of several classes of domains (which are related to a Dedekind domain) to a torsion-free module and it is shown that for a faithful multiplication module over an integral domain, we characterize Dedekind modules, cyclic submodule modules, and discrete valuation modules in terms of factorable modules and a sort of Euclidean algorithm.

• Journal for History of Mathematics
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• v.17 no.2
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• pp.97-103
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• 2004

In this paper, we will prove that a free join algebra and a universal derivation module of its subalgebras have a universal derivation module induced by its subalgebras.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.12
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• pp.16-22
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• 1994

In this paper, transmitter and receiver modules for free space optical interconnection are implemented and characterized. In the transmitter module, bias circuitry which inject current into the direct modulated laser diode is fabricated and in the receiver module, p-i-n diode is integrated with an MMIC amplifying stage. Laser diode has a direct-modulated bandwidth of 2 GHz at 1.4 Ith bias while p-i-n diode and amplifying stage has a bandwidth of 1.3 GHz and 1.5 GHz, repectively. Optical interconnection has a bandwidth of 1.3 GHz and linearly transmit modulated voltage signal up to 1.5 Vp-p. Measured loss of optical interconnection is 5dB which is composed of optoelectronic conversion loss of 15 dB, electrical impedance mismatch loss of 6.7 dB in transmitter module and gain of 18 dB in receiver module. Seperation between transmitter and receiver can be extended up to 50 cm by using a lens.

• Kyungpook Mathematical Journal
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• v.51 no.1
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• pp.37-42
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• 2011

Let M be an R-module and S a semigroup. Our goal is to discuss zero-divisors of the semigroup module M[S]. Particularly we show that if M is an R-module and S a commutative, cancellative and torsion-free monoid, then the R[S]-module M[S] has few zero-divisors of size n if and only if the R-module M has few zero-divisors of size n and Property (A).

• Journal of Integrative Natural Science
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• v.7 no.4
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• pp.278-282
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• 2014

We define a numerical invariant $row^*_j(A)$ over Cohen-Macaulay local ring A, which is related to the presenting matrices of the j-th syzygy module (with or without free summands). We show that $row_d(A)$=$row_{CM}(A)$ and $row^*_d(A)$=$row^*_{CM}(A)$ for a Cohen-Macaulay local ring A of dimension d.