• 대한수학회보
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• 제60권4호
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• pp.1017-1024
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• 2023

A celebrated result in the study of integer partitions is the identity due to Lehmer whereby the number of partitions of n with an even number of even parts minus the number of partitions of n with an odd number of even parts equals the number of partitions of n into distinct odd parts. Inspired by Lehmer's identity, we prove explicit formulas for evaluating generating functions for sequences that enumerate integer partitions of fixed width with an even/odd number of even parts. We introduce a technique for decomposing the even entries of a partition in such a way so as to evaluate, using a finite sum over q-binomial coefficients, the generating function for the sequence of partitions with an even number of even parts of fixed, odd width, and similarly for the other families of fixed-width partitions that we introduce.

• Kyungpook Mathematical Journal
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• 제58권4호
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• pp.747-759
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• 2018

A graph G = (V (G), E(G) of order n = |V (G)| and size m = |E(G)| is said to be odd harmonious if there exists an injection $f:V(G){\rightarrow}\{0,\;1,\;2,\;{\ldots},\;2m-1\}$ such that the induced function $f^*:E(G){\rightarrow}\{1,\;3,\;5,\;{\ldots},\;2m-1\}$ defined by $f^*(uv)=f(u)+f(v)$ is bijection. While a bipartite graph G with partite sets A and B is said to be bigraceful if there exist a pair of injective functions $f_A:A{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ and $f_B:B{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ such that the induced labeling on the edges $f_{E(G)}:E(G){\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ defined by $f_{E(G)}(uv)=f_A(u)-f_B(v)$ (with respect to the ordered partition (A, B)), is also injective. In this paper we prove that odd harmonious graphs and bigraceful graphs are equivalent. We also prove that the number of distinct odd harmonious labeled graphs on m edges is m! and the number of distinct strongly odd harmonious labeled graphs on m edges is [m/2]![m/2]!. We prove that the Cartesian product of strongly odd harmonious trees is strongly odd harmonious. We find some new disconnected odd harmonious graphs.

• 한국전기전자재료학회논문지
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• 제12권1호
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• pp.69-74
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• 1999

We have investigated that the high pretilt angle of the NLC, 4-n-pentyl-4-cyanobiphenyl (5CB), was observed on rubbed polythiophene (PTP) surfaces with alkyl chains with more than 10 carbon atoms; it is attributed to the surface-excluded volume effect by the alkyl chain lengths between the LCs and the PTP surfaces. Next, we investigated that the odd-even effect of the polar anchoring strength in 5CB on rubbed PTP surfaces with alkyl chain lengths has been successfully evaluated. The anchoring strength of 5CB for rubbed PTP surfaces with odd-number is weak compared with even-number up to the 6 carbon atoms in the alkyl chain; however, odd-number is strong compared with even-number above 7 carbon atoms. The weak anchoring strength of 5CB is approximately $1\times10^{-3} (J/m^2$) on rubbed PTP surface with 7 carbon atoms; it is relatively strong anchoring strength. Consequently, we conclude that the odd-even effects of the polar anchoring strength in NLCs are strongly related to the characteristics of the polymer and observed clearly for short alkyl chain lengths.

• 산업융합연구
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• 제19권4호
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• pp.23-28
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• 2021

본 논문은 미해결 문제로 알려진 36 장교문제(n = 6)와 관련된 오일러 방진 퍼즐 게임 문제에 대해 n = [3, ∞]의 문제를 풀 수 있는 일정한 패턴 규칙을 찾고자 시도하였다. 이 문제의 해는 현재까지 [3, 10]에 대해 n = 6만 존재하지 않고 나머지 모든 숫자에 대한 해는 존재하는 것으로 알려져 있다. 또한, 기존 연구는 특정 숫자 n에 대해 컴퓨터 프로그램으로 랜덤한 배정 결과를 찾고자 하여 n = [11, ∞]에 대해서는 해를 찾기가 쉽지 않아 미해결 과제로 남아있다. 기존 연구는 n = [3, 10]으로 한정시킨 반면에, 본 논문은 n = [3, ∞]영역에서 어떠한 n의 값에 대해서도 해를 찾을 수 있는 일반화된 패턴을 찾고자 시도하였다. 본 논문에서는 n = odd, 4k even, 4k+2 even의 세 부분으로 분할하여 n = odd와 4k even(n/2 = even)에 대한 간단하면서도 일정한 패턴을 찾는데 성공하였다. 그러나 4k+2 even(n/2 = odd)에 대해서는 패턴을 찾지 못하였다.

• Kyungpook Mathematical Journal
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• 제54권4호
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• pp.607-617
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• 2014

Let S = C(r,m), the finite cyclic semigroup with index r and period m. Each subsemigroup of S is cyclic if and only if either r = 1; r = 2; or r = 3 with m odd. For $r{\neq}1$, the maximum value of the minimum number of elements in a (minimal) generating set of a subsemigroup of S is 1 if r = 3 and m is odd; 2 if r = 3 and m is even; (r-1)/2 if r is odd and unequal to 3; and r/2 if r is even. The number of cyclic subsemigroups of S is $r-1+{\tau}(m)$. Formulas are also given for the number of 2-generated subsemigroups of S and the total number of subsemigroups of S. The minimal generating sets of subsemigroups of S are characterized, and the problem of counting them is analyzed.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 1999년도 추계종합학술대회 논문집
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• pp.495-498
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• 1999

In this paper, we propose the adaptive Odd/Even Multi-shell Median Filter(adaptive O/E MMF) to improve the defect that Modified Multi-shell Median Filter(MMMF) can not recover missing lines of vertical and cross direction. This filter uses odd/even multi-shells and new proposed threshold strategy The performance of the proposed filter is evaluated over image 'airfield 'by using MATLAB. As the proposed threshold strategy eliminate the number of redundant replacement, it suppresses impulse noise and recovers missing lines.

• JSTS:Journal of Semiconductor Technology and Science
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• 제14권4호
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• pp.376-382
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• 2014

In this paper, a 9-bit 1GS/s high precision folding A/D converter with a 45 nm CMOS technology is proposed. In order to improve the asymmetrical boundary condition error of a conventional folding ADC, a novel scheme with an odd number of folding blocks is proposed. Further, a new digital encoding technique is described to implement the odd number of folding technique. The proposed ADC employs a digital error correction circuit to minimize device mismatch and external noise. The chip has been fabricated with 1.1V 45nm Samsung CMOS technology. The effective chip area is $2.99mm^2$ and the power dissipation is about 120 mW. The measured result of SNDR is 45.35 dB, when the input frequency is 150 MHz at the sampling frequency of 1 GHz. The measured INL is within +7 LSB/-3 LSB and DNL is within +1.5 LSB/-1 LSB.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 1998년도 추계종합학술대회 논문집
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• pp.1137-1140
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• 1998

In this paper, we propose the new hardware architecture which implements the stereo matching algorithm using the dynamic programming method. The dynamic programming method is used in finding the corresponding pixels between the left image and the right image. The proposed MOEPE(Merged Odd-Even PE) architecture operates in the systolic manner and finds the disparities from the intensities of the pixels on the epipolar line. The number of PEs used in the MOEPE architecture is the number of the range constraint, which reduced the number of the necessary PEs dramatically compared to the traditional method which uses the PEs with the number of pixels on the epipolar line. For the normal method by 25 times. The proposed architecture is modeled with the VHDL code and simulated by the SYNOPSYS tool.

• KSBB Journal
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• 제8권1호
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• pp.49-54
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• 1993

천연식품인 호도, 복숭아씨, 살구씨의 지방산 함량 과 홀수 지방산의 함량을 규명하기 위하여 HPLC를 사용하여 분리 정량한 결과는 다음과 같다. 1. 각 시료의 조지방 함량은 호도 61.78%. 살구 씨 52.34%. 복숭아씨 48.21 %이고, 중성 지질량은 호도 62.32%, 복숭아씨 91.50%. 살구씨 88.0%이 고, 당지질은 호도 34.14%, 복숭아씨 3.25%. 살구 씨 4.78%이었고, 인지질은 호도 3.54%. 복숭아씨 5.25%. 상구씨 7.27%였다. 2. 중성지질의 지방산에서 호도의 홀수 지방산이 3 37.07%. 짝수 지방산이 36.72%. 복숭아씨의 홀수 지방산이 5.4%, 짝수 지방산이 94.60%. 살구씨의 홀수 지방산이 6.85%. 8 짝수 지방산이 93.92%였교, 당지질에서 호도의 홀수 지방산은 53.7%. 짝수 지 방산은 46.21 %. 복숭아씨의 홀수 지방산은 6.97% . 9 짝수 지방산은 93.03%, 살구씨의 홀수 지방산은 10.5%, 짝수 지방산은 89.42 %였고, 인지a질에서의 경우는 호도의 홀수 지방산이 3.57%, 짝수 지방산 이 96.43%, 복숭아써의 흘수 지방산이 6.51 %, 짝 수 지방산이 93.49%, 살구씨의 홀수 지방산이 15.0 % %, 짝수 지방산이 84.2%로 각각 함유되어 었다. 3. 총 지방산중 홀수 지방산은 호도 14.47%, 복 숭아씨 1.17%, 상구씨 4.03%이고, 짝수 지방산은 호도 85.53 %, 복숭아씨 98.83%, 삼구씨 95.97% 로 각각 함유되어 있음을 알 수 있다. 수 있다.

• Clinical and Experimental Pediatrics
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• 제51권10호
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• pp.1038-1041
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• 2008

Aminoglycosides are frequently used antibiotics in children. The multiple daily dosing (MDD) in infants and children is twice or three times daily depending on age. Recent studies in adults have shown that once daily dosing (ODD) maximizes the bactericidal activity and might minimize the toxicity of antibiotics. So, I reviewed many studies about efficacy, toxicity and cost effectiveness of ODD of aminoglycosides in children. Most studies suggest that ODD compared with MDD of aminoglycosides is theoretically more efficacious and has no higher toxicity in infants and children. But, the total number of patients included in the studies is not large. Multi-center, controlled prospective studies are required in larger numbers of infants and children to determine the efficacy and safety of the ODD regimen in children before ODD of aminoglycosides can be recommended for routine use.