• 에너지공학
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• 제17권4호
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• pp.233-240
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• 2008

최근 새로운 2계 자기 수반형(self-adjoint) 중성자 수송 방정식으로 기존의 우성 및 기성 수송 방정식 외에 SAAF(Self-Adjoint Angular Flux) 수송 방정식이 소개되어, 이에 대한 적절한 경계조건, 수치해법, 정확도 등에 관한 논의가 활발히 진행되고 있다. 본 연구에서는 SAAF 수송 방정식의 수학적, 물리적 의미를 고찰하고 기존의 우성 및 기성 수송 방정식과의 연관성을 명확히 하였으며, Boltzmann 수송 방정식의 1계 차분식에서 2계의 SAAF 수송 방정식의 차분식을 유도하는 방법을 확산 가속법(diffusion synthetic acceleration method)과 함께 소개하였다. 유도된 SAAF 차분법이 계산 효율성과 수송해의 정확도를 증가시킴을 수치결과로 확인하였다.

• 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.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 2002년도 추계학술발표회요약집
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• pp.51.1-51
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• 2002

• 한국진공학회:학술대회논문집
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• 한국진공학회 2010년도 제39회 하계학술대회 초록집
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• pp.56-56
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• 2010

Using first-principles density-functional theory calculations, we find dramatically different electronic states in the C chains generated on the H-terminated C(111) surface, depending on their length and parity. The infinitely long chain has $\pi$ electrons completely delocalized over the chain, yielding an equal C-C bond length. As the chain length becomes finite, such delocalized $\pi$ electrons are transformed into localized ones. As a result, even-numbered chains exhibit a strong charge-lattice coupling, leading to a bond-alternated structure, while odd-numbered chains show a ferrimagnetic spin ordering with a solitonlike structure. These geometric and electronic features of infinitely and finitely long chains are analogous to those of the closed (benzene) and open (polyacetylene) chains of hydrocarbons, respectively.

• Journal of Communications and Networks
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• 제14권2호
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• pp.213-221
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• 2012

The architecture of an interconnection network is usually represented by a graph, and a graph G is bipancyclic if it contains a cycle for every even length from 4 to ${\mid}V(G){\mid}$. In this article, we analyze the conditional edge-fault-tolerant properties of an enhanced hypercube, which is an attractive variant of a hypercube that can be obtained by adding some complementary edges. For any n-dimensional enhanced hypercube with at most (2n-3) faulty edges in which each vertex is incident with at least two fault-free edges, we showed that there exists a fault-free cycle for every even length from 4 to $2^n$ when n($n{\geq}3$) and k have the same parity. We also show that a fault-free cycle for every odd length exists from n-k+2 to $2^n-1$ when n($n{\geq}2$) and k have the different parity.

• 대한수학회지
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• 제46권3호
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• pp.493-511
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• 2009

Let $q\;{\geq}\;3$ be an odd integer and a be an integer coprime to q. Denote by N(a, q) the number of pairs of integers b, c with $bc\;{\equiv}\;a$ (mod q), $1\;{\leq}\;b$, $c\;{\leq}\;{\frac{q-1}{2}}$ and with b, c having different parity. The main purpose of this paper is to study the sum ${\sum}^{'q}_{a=1}\;\(N(a,\;q)\;-\;\frac{{\phi}(q)}{8}\)^2$ and obtain a sharp asymptotic formula.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제6권
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• pp.371-381
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• 1997

Let p be an odd prime number. We introduce simple and useful decoding algorithm for orthogonal Latin square codes of order p. Let H be the parity check matrix of orthogonal Latin square code. For any x ${\in}$ GF(p)$^{n}$, we call xH$^{T}$ the syndrome of x. This method is based on the syndrome decoding for linear codes. In L$_{p}$, we need to find the first and the second coordinates of codeword in order to correct the errored received vector.

• 한국정보과학회논문지:정보통신
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• 제36권5호
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• pp.389-396
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• 2009

RFID(Radio Frequency IDentification) 시스템에서 사물에 부착된 태그에 대한 식별은 리더의 요청으로 시작한다. 리더가 요청을 하면 리더의 인식영역 내에 있는 다수의 태그는 동시에 응답을 하여 충돌이 발생한다. 리더는 인식영역 내의 모든 태그들을 빠르게 인식하는 충돌방지 알고리즘이 필요하다. 본 논문에서는 패리티 메카니즘을 이용한 충돌방지 알고리즘을 제안한다. 제안한 알고리즘에서, 태그는 리더의 요청 프리픽스와 일치하는 태그들 중 프리픽스 다음의 2 비트들의 '1'의 개수가 짝수인 태그 그룹은 '0' 슬롯에 응답하고, '1'의 개수가 홀수인 태그 그룹은 '1' 슬롯에 응답하게 하석 충돌을 방지한다. 해당 슬롯에 응답에 따라 존재하는 태그 아이디만 응답할 수 있도록 요청 프리픽스를 생성한다. 또한 해당 슬롯에 충돌이 2개인 경우에는 패리티 메카니즘을 이용하여 2개의 태그를 인식한다. 즉, 전체적인 질의 휫수를 줄여 인식시간을 단축한다.

• 대한수학회보
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• 제52권1호
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• pp.35-43
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• 2015

Let q > 1 be an odd integer and c be a fixed integer with (c, q) = 1. For each integer a with $1{\leq}a{\leq}q-1$, it is clear that the exists one and only one b with $0{\leq}b{\leq}q-1$ such that $ab{\equiv}c$ (mod q). Let N(c, q) denote the number of all solutions of the congruence equation $ab{\equiv}c$ (mod q) for $1{\leq}a$, $b{\leq}q-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b\bar{b}{\equiv}1$ (modq). The main purpose of this paper is using the mean value theorem of Dirichlet L-functions to study the mean value properties of a summation involving $(N(c,q)-\frac{1}{2}{\phi}(q))$ and Kloosterman sums, and give a sharper asymptotic formula for it.

• 대한수학회보
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• 제55권3호
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• pp.971-997
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• 2018

The parity of cyclotomic numbers of order 2, 4 and 6 associated with 4-cyclotomic cosets modulo an odd prime p are obtained. Hence the explicit expressions of primitive idempotents of minimal cyclic codes of length $p^n$, $n{\geq}1$ over the quaternary field $F_4$ are obtained. These codes are observed to be subcodes of Q codes of length $p^n$. Some orthogonal properties of these subcodes are discussed. The minimal cyclic codes of length 17 and 43 are also discussed and it is observed that the minimal cyclic codes of length 17 are two weight codes. Further, it is shown that a Q code of prime length is always cyclotomic like a binary duadic code and it seems that there are infinitely many prime lengths for which cyclotomic Q codes of order 6 exist.