• 한국정보통신학회논문지
• /
• 제8권2호
• /
• pp.352-358
• /
• 2004

본 논문은 움직임 벡터의 분포특성을 이용한 새로운 움직임 벡터 탐색 알고리즘과 정수 연산만을 필요로 하는 정수형 DCT(Discrete Cosine Transform)를 사용하여 H.263 환경에서 동영상 부호기의 성능향상에 대해 연구한다. 정수형 DCT는 Un(Walsh-Hadamard Transform)와 정수 lifting을 이용하여 정수의 덧셈 연산만으로 DCT연산을 수행하므로 부동소수점수의 곱셈을 포함하는 기존 DCT에 비하여 연산량은 줄이면서도 동일한 PSNR을 얻는다. 새로운 움직임 벡터 탐색 알고리즘은 기존의 움직임 벡터 탐색 알고리즘인 3SS(Step Search)나 4SS에 비하여 움직임 추정에 필요한 연산량을 감소시키면서 거의 비슷한 PSNR을 보인다. 또한 모의 실험에서 H.263 부호기 환경에서 정수형 DCT와 기존 DCT는 서로 호환됨을 보인다. 따라서 본 논문에서 제안한 부호화 방법은 H.263 부호화 과정에서 동영상 정보의 효율적인 실시간 처리를 가능하게 하며 다른 동영상 부호기에도 적용하여 부호화 성능을 향상시킬 수 있다.

• 충청수학회지
• /
• 제24권3호
• /
• pp.595-599
• /
• 2011

We prove that for any positive integer $g{\geq}3$, there are ${\gg}q^{\frac{l}{2g}}$ real cyclotomic function fields whose conductor has degree ${\leq}l$ and ideal class number is divisible by $\frac{g}{gcd(2,g)}$.

• Kyungpook Mathematical Journal
• /
• 제58권4호
• /
• pp.599-613
• /
• 2018

We study a generalization of the classical Pentagonal Number Theorem and its applications. We derive new identities for certain infinite series, recurrence relations and convolution sums for certain restricted partitions and divisor sums. We also derive new identities for Bell polynomials.

• 대한수학회지
• /
• 제46권3호
• /
• pp.493-511
• /
• 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.

• 대한수학회논문집
• /
• 제22권2호
• /
• pp.195-205
• /
• 2007

The maximal column rank of an $m{\times}n$ matrix A over the ring of integers, is the maximal number of the columns of A that are weakly independent. We characterize the linear operators that preserve the maximal column ranks of integer matrices.

• Journal of applied mathematics & informatics
• /
• 제27권3_4호
• /
• pp.909-913
• /
• 2009

For a family of graphs $\mathcal{H}$ and an integer k, we denote by $R^k(\mathcal{H})$ the corresponding k-Ramsey number, which is defined to be the smallest integer n such that every k-coloring of the edges of $K_n$ contains a monochromatic copy of a graph in $\mathcal{H}$. The local k-Ramsey number $R^k_{loc}(\mathcal{H})$ and the mean k-Ramsey number $R^k_{mean}(\mathcal{H})$ are defined analogously. Let $\mathcal{G}$ be the family of non-bipartite graphs and $T_n$ be the family of all trees on n vertices. In this paper we prove that $R^k_{loc}(\mathcal{G})=R^k_{mean}(\mathcal{G})$, and $R^2(T_n)$ < $R^2_{loc}(T_n)4 = $R^2_{mean}(T_n)$ for all $n\;{\ge}\;3$.

• 대한산업공학회지
• /
• 제32권3호
• /
• pp.219-225
• /
• 2006

We consider a routing and wavelength assignment (RWA) for the efficient operation of WDM networks. For a given physical network, a set of selected pairs of nodes, the number of required connections for each selected pair of nodes, and a set of available wavelengths, the RWA is to realize as many connections as possible without wavelength collision. We give an integer programming formulation and an algorithm based on column generation. Though the proposed algorithm does not guarantee optimal solutions, test results show that the algorithm gives probably good solutions.

• 대한수학회보
• /
• 제52권1호
• /
• pp.35-43
• /
• 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.

• 산업공학
• /
• 제24권2호
• /
• pp.151-155
• /
• 2011

In this study, we propose a signomial classification method with ₀-regularization (₀-)which seeks a sparse signomial function by solving a mixed-integer program to minimize the weighted sum of the ₀-norm of the coefficient vector of the resulting function and the $L_1$-norm of loss caused by the function. $SC_0$ gives an explicit description of the resulting function with a small number of terms in the original input space, which can be used for prediction purposes as well as interpretation purposes. We present a practical implementation of $SC_0$ based on the mixed-integer programming and the column generation procedure previously proposed for the signomial classification method with $SL_1$-regularization. Computational study shows that $SC_0$ gives competitive performance compared to other widely used learning methods for classification.

• Industrial Engineering and Management Systems
• /
• 제16권1호
• /
• pp.141-153
• /
• 2017

A binary integer programming model is proposed for a complex timetabling problem in a university faculty which conducts various degree programs. The decision variables are defined with fewer dimensions to economize the model size of large scale problems and to improve modeling efficiency. Binary matrices are used to incorporate the relationships between the courses and students, and the courses and teachers. The model includes generally applicable constraints such as completeness, uniqueness, and consecutiveness; and case specific constraints. The model was coded and solved using Open Solver which is an open-source optimizer available as an Excel add-in. The results indicate that complicated timetabling problems with large numbers of courses and student groups can be formulated more efficiently with fewer numbers of variables and constraints using the proposed modeling framework. The model could effectively generate timetables with a significantly lower number of work hours per week compared to currently used timetables. The model results indicate that the particular timetabling problem is bounded by the student overlaps, and both human and physical resource constraints are insignificant.