• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.8 no.2
• /
• pp.352-358
• /
• 2004

This paper is studied the improvement of performance for moving picture encoder using H.263. This is used the new motion vector search algorithm using a relation with neighborhood search point and is applied the integer DCT for the encoder. The integer DCT behaves DCT by the addition operation of the integer using WHT and a integer lifting than conventional DCT that needs the multiplication operation of a floating point number. Therefore, the integer Dn can reduce the operation amount than basis DCT with having an equal PSNR. The new motion vector search algorithm is showed almost similar PSNR as reducing the operation amount than the conventional motion vector search algorithm. To experiment a compatibility of the integer DCT and the conventional DCT, according to result compare case that uses a method only and case that uses the alternate two methods of the integer DCT or the conventional DCT to H.263 encoder and decoder, case that uses the alternate two methods is showed doing not deteriorate PSNR-and being each other compatible visually than case that uses an equal method only.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.3
• /
• 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
• /
• v.58 no.4
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.46 no.3
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.22 no.2
• /
• 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
• /
• v.27 no.3_4
• /
• 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 $n\;{\ge}\;3$.

• Journal of Korean Institute of Industrial Engineers
• /
• v.32 no.3
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.1
• /
• 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.

• IE interfaces
• /
• v.24 no.2
• /
• 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
• /
• v.16 no.1
• /
• 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.