• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1425-1432
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• 2014

The Euler zeta function is defined by ${\zeta}_E(s)=\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{n^8}$. The purpose of this paper is to find formulas of the Euler zeta function's values. In this paper, for $s{\in}\mathbb{N}$ we find the recurrence formula of ${\zeta}_E(2s)$ using the Fourier series. Also we find the recurrence formula of $\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{(2_{n-1})^{2s-1}}$, where $s{\geq}2({\in}\mathbb{N})$.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.5 no.5
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• pp.908-915
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• 2001

In this paper, it is analyzed theoretically that the performance degradation, caused by carrier frequency offset, in an OFDM/M-ary PSK system. Then, when Turbo coding is adopted to an OFDM/M-ary PSK system, the degree of performance enhancement is evaluated. Finally, the maximum frequency offset is calculated to satisfy the BER performance required in a Turbo coded OFDM/M-ary PSK system. As results of analysis, it is shown that the more the number of M-ary is, the worse the BER performance is. Moreover, 7dB, 9dB, and 17dB of $E_b/N_o$ are required in QPSK, 8PSK and 16PSK systems, respectively in order to satisfy the error performance, $BER=10^{-3}$ for voice communication. If $E_b/N_o$ are 10㏈ and 15㏈, the frequency offset should be below 0.05 and 0.075, respectively, for voice communication. When Turbo coding is adopted to an OFDM/M-ary PSK system, the less the number of M-ary is, the greater the performance enhancement of Turbo coding is. If the number of a M-ary system of the system is below 16, it is found that required $E_b/N_o$ is about 8dB to satisfy $BER=10^{-5}$ Moreover, in the system the Turbo coding scheme, voice communication is available with greatly low$E_b/N_o$, and 8dB of $E_b/N_o$ is enough for data communication regardless of the permission range of frequency offset.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1091-1097
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• 2009

In this paper, we investigate the extensions of generalized stable rings. It is shown that a ring R is a generalized stable ring if and only if R has a complete orthogonal set {e$_1$, . . . , e$_n$} of idempotents such that e$_1$Re$_1$, . . . , e$_n$Re$_n$ are generalized stable rings. Also, we prove that a ring R is a generalized stable ring if and only if R[[X]] is a generalized stable ring if and only if T(R,M) is a generalized stable ring.

• The Mathematical Education
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• v.21 no.3
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• pp.13-14
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• 1983

(1) The direct product (equation omitted) $E_{I}$ of BCK-algebras $E_{I}$, (i=1, 2, 3, …, n), is a BCK-algebra. (2) Let E be a BCK-algebra and $A_1$, $A_1$, …, $A_{n}$ ideals of E. Define a mapping (equation omitted) by the rule f($\chi$)=( $A_1$$\chi$, $A_2$$\chi$, …, $A_{n}$$\chi$). Then f is a homomorphism.ism.ism.

• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1409-1418
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• 2023

The Hurwitz-type Euler zeta function ζ_E(z, q) is defined by the series ${\zeta}_E(z,\,q)\,=\,\sum\limits_{n=0}^{\infty}{\frac{(-1)^n}{(n\,+\,q)^z}},$ for Re(z) > 0 and q ≠ 0, -1, -2, . . . , and it can be analytic continued to the whole complex plane. An asymptotic expansion for ζ^'_E(-m, q) has been proved based on the calculation of Hermite's integral representation for ζ_E(z, q).

• Journal of the Korea Institute of Information and Communication Engineering
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• v.14 no.8
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• pp.1843-1848
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• 2010

The Key exchange protocols are very crucial tools to provide the secure communication in the broadband satellite access network. They should be required to satisfy various requirements such as security, Key confirmation, and Key freshness. In this paper, we propose Two authenticated key exchange protocols Two Pass EKE-E(Encrypted Key Exchange-Efficient) and Two Pass EKE-S(Encrypted Key Exchange-Secure) are introduced. A basic idea of the protocols is that a password can be represented by modular addition N, and the number of possible modular addition N representing the password is $2^N$ The Two Pass EKE-E is secure against the attacks including main-in-the-middle attack and off-line dictionary attack, and the performance is excellent so as beyond to comparison with other authenticated key exchange protocols. The Two Pass EKE-S is a slight modification of the Two Pass EKE-E. The Two Pass EKE-S provides computational in feasibility for learning the password without having performed off line dictionary attack while preserving the performance of the Two Pass EKE-E.

• Honam Mathematical Journal
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• v.11 no.1
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• pp.15-19
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• 1989

A conjecture of E. T. H. Wang asserts that if every diagonal disjoint from m mutually disjoint zero diagonals of $A{\in}{\Omega}_n$ has a constant sum, then all entries off the m zero diagonals are equal to l/(n-m). E. T. H. Wang proved the conjecture for m=0, 1, n-2 and n-1. In the present paper, it is proved that the conjecture holds true for m=2.

• Archives of Pharmacal Research
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• v.26 no.9
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• pp.735-738
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• 2003

The methanolic extract of the twigs of Celtis chinensis was found to show inhibitory activity on acetylcholinesterase (AChE), an enzyme that plays a role in the metabolic hydrolysis of ACh. Bioassay-guided fractionation of the methanolic extract resulted in the isolation of N-p-coumaroyl tyramine. as an inhibitor on AChE. This compound inhibited AChE activity in a dose-dependent manner, and the $IC_50$ value of trans-N-p-coumaroyl tyramine was 34.5 $\mu$g/mL (122 $\mu$M).

• Journal of Surface Science and Engineering
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• v.45 no.1
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• pp.20-24
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• 2012

Multilayer passivation film on OLED with organic/inorganic hybrid structure as to diminish the thermal stress and expansion was researched to protect device from the direct damage of $O_2$ and $H_2O$ and improve life time characteristics. Red OLED doped with 1 vol.% Rubrene in $Alq_3$ was used as a basic device. The films consist of ITO(150 nm)/ELM200_HIL(50 nm)/ELM002_HTL(30 nm)/$Alq_3$: 1 vol.% Rubrene(30 nm)/$Alq_3$(30 nm) and LiF(0.7 nm)/Al(100 nm) which were formed in that order. Using LiF/$SiN_x$ as a buffer layer was determined because it significantly improved life time characteristics without suffering damage in the process of forming passivation film. Multilayer passivation film on buffer layer didn't produce much change in current efficiency, while the half life time at 1,000 $cd/m^2$ of OLED/LiF/$SiN_x$/E1/$SiN_x$ was 710 hours which showed about 1.5 times longer than OLED/LiF/$SiN_x$/E1 with 498 hours. futhermore, OLED/LiF/$SiN_x$/E1/$SiN_x$/E1/$SiN_x$ with 1301 hours showed about twice than OLED/LiF/$SiN_x$/E1/$SiN_x$ which demonstrated that superior characteristics of life time was obtained in multilayer passivation film. Through the above result, it was suggested using LiF/$SiN_x$ as a buffer layer could reduce the damage from the difference of thermal expansion coefficient in OLED with protective films, and epoxy layer in multilayer passivation film could function like a buffer between $SiN_x$ inorganic layers with relatively large thermal stress.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.6
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• pp.295-301
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• 2014

In the absence of a sorting algorithm faster than O(n log n), Quicksort remains the best and fastest of its kind in practice. For given n data, Quicksort records running in O(n log n) at best and $O(n^2)$ at its worst. In this paper, I propose an algorithm by which 3-points average P=(L+M+H)/3 is set as a pivot for first array L=a[s], last array H=a[e], and middle array $M=a[{\lfloor}(s+e)/2{\rfloor}]$ in order to find the more fast than Quicksort. Test results prove that the proposed 3-points average pivot Quicksort has the time complexity of O(n log n) at its best, average, and worst cases. And the proposed algorithm can be reduce the $O(n^2)$ time of Quicksort to O(n log n).