• Honam Mathematical Journal
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• v.35 no.4
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• pp.747-755
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• 2013

This paper deals with the unit groups of the endomorphism rings of projective modules over polynomial rings and further over formal power series rings. A normal subgroup of the unit group is defined and discussed. The local splitting properties of element of endomorphism rings of projective modules over polynomial rings are given.

• Journal of information and communication convergence engineering
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• v.9 no.4
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• pp.435-440
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• 2011

This paper propose the method of constructing the highly efficiency adder and multiplier systems over finite fields. The addition arithmetic operation over finite field is simple comparatively because that addition arithmetic operation is analyzed by each digit modP summation independently. But in case of multiplication arithmetic operation, we generate maximum k=2m-2 degree of ${\alpha}^k$ terms, therefore we decrease k into m-1 degree using irreducible primitive polynomial. We propose two method of control signal generation for the purpose of performing above decrease process. One method is the combinational logic expression and the other method is universal signal generation. The proposed method of constructing the highly adder/multiplier systems is as following. First of all, we obtain algorithms for addition and multiplication arithmetic operation based on the mathematical properties over finite fields, next we construct basic cell of A-cell and M-cell using T-gate and modP cyclic gate. Finally we construct adder module and multiplier module over finite fields after synthesizing ${\alpha}^k$ generation module and control signal CSt generation module with A-cell and M-cell. Next, we constructing the arithmetic operation unit over finite fields. Then, we propose the future research and prospects.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.341-360
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• 1998

Some interesting properties of Carlitz cyclotomic polynomials analogous to those of classical cyclotomic polynomials are given.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.371-399
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• 2020

Let P_s := 𝔽₂[x₁, x₂, …, x_s] = ⊕_n⩾0(P_s)_n be the polynomial algebra viewed as a graded left module over the mod 2 Steenrod algebra, ${\mathfrak{A}}$. The grading is by the degree of the homogeneous terms (P_s)_n of degree n in the variables x₁, x₂, …, x_s of grading 1. We are interested in the hit problem, set up by F. P. Peterson, of finding a minimal system of generators for ${\mathfrak{A}}$-module P_s. Equivalently, we want to find a basis for the 𝔽₂-graded vector space ${\mathbb{F}}_2{\otimes}_{\mathfrak{A}}$ P_s. In this paper, we study the hit problem in the case s = 5 and the degree n = 5(2^t - 1) + 6 · 2^t with t an arbitrary positive integer.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.42-47
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• 2001

Analyzing the ECG signal, we can find heart disease, for example, arrhythmia and myocardial infarction, etc. Particularly, detecting arrhythmia is more important, because serious arrhythmia can take away the life from patients within ten minutes. In this paper, we would like to introduce the signal processing for ECG analysis and the device made for wireless communication of ECG data. In the signal processing, the wavelet transform decomposes the ECG signal into high and low frequency components using wavelet function. Recomposing the high frequency bands including QRS complex, we can detect QRS complex and eliminate the noise from the original ECG signal. To recognize the ECG signal pattern, we adopted the polynomial approximation partially and statistical method. The ECG signal is divided into small parts based on QRS complex, and then, each part is approximated to the polynomials. Comparing the approximated ECG pattern with the database, we can detect and classify the heart disease. The ECG detection device consists of amplifier, filters, A/D converter and RF module. After amplification and filtering, the ECG signal is fed through the A/D converter to be digitalized. The digital ECG data is transmitted to the personal computer through the RF transceiver module and serial port.

• Journal of Korea Society of Industrial Information Systems
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• v.8 no.3
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• pp.85-90
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• 2003

This paper proposes a modular multiplier based on LFSR (Linear Feedback Shift Register) architecture with efficient area complexity over GF(2/sup m/). At first, we examine the modular exponentiation algorithm and propose it's architecture, which is basic module for public-key cryptosystems. Furthermore, this paper proposes on efficient modular multiplier as a basic architecture for the modular exponentiation. The multiplier uses AOP (All One Polynomial) as an irreducible polynomial, which has the properties of all coefficients with '1 ' and has a more efficient hardware complexity compared to existing architectures.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.549-556
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• 2015

In this paper, we characterize w-Noetherian modules in terms of polynomial modules and w-Nagata modules. Then it is shown that for a finite type w-module M, every w-epimorphism of M onto itself is an isomorphism. We also define and study the concepts of w-Artinian modules and w-simple modules. By using these concepts, it is shown that for a w-Artinian module M, every w-monomorphism of M onto itself is an isomorphism and that for a w-simple module M, $End_RM$ is a division ring.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.1-15
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• 2017

Kanenobu has given infinite families of knots with the same HOMFLY polynomial invariant but distinct Alexander module structure. In this paper, we give a recursive formula for the Khovanov cohomology of all Kanenobu knots K(p, q), where p and q are integers. The result implies that the rank of the Khovanov cohomology of K(p, q) is an invariant of p + q. Our computation uses only the basic long exact sequence in knot homology and some results on homologically thin knots.

• Proceedings of the KIEE Conference
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• 2002.11c
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• pp.268-273
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• 2002

In this paper, a new parallel multiplier circuit over $GF(2^m)$ has been proposed. The new multiplier is composed of polynomial multiplicative operation part and modular arithmetic operation part, irreducible polynomial operation part. And each operation has modular circuit block. For design the new proposed circuit, it develop generalized equations using frame each operation idea and show a example for $GF(2^m)$.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1523-1537
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• 2023

Let R be a commutative ring with identity and S a multiplicative subset of R. First, we introduce and study the u-S-projective dimension and u-S-injective dimension of an R-module, and then explore the u-S-global dimension u-S-gl.dim(R) of a commutative ring R, i.e., the supremum of u-S-projective dimensions of all R-modules. Finally, we investigate u-S-global dimensions of factor rings and polynomial rings.