• Proceedings of the IEEK Conference
• /
• 2003.07e
• /
• pp.2072-2075
• /
• 2003

This paper is studied the high speed processing moving picture encodec to compress and encode a moving picture by real time. This is used the new motion vector search algorithm with smallest search point in H.263 encodec, and is applied the integer DCT for the encodec by converting a moving picture. 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 DCT can reduce the operation amount than basis DCT with having an equal PSNR because the multiplication operation of a floating point number does not need.

• Journal of Institute of Control, Robotics and Systems
• /
• v.6 no.8
• /
• pp.719-726
• /
• 2000

A real-time precise positioning is possible with GPS carrier phase measurements with efficient integer ambiguity resolution techniques. It is known that more reliable and fast integer ambiguity resolution is possi-ble as the number of measurements increases. Most precise positioning systems use dual frequency measurements and the wide-lnae technique to resolve integer ambiguity. The wide-lane technique magnifies the measurement noise while it reduces the number of candidates to be examined. In this paper a new integer ambiguity resolution method using dual frequency is proposed The proposed method utilizes the relationship between the wide-lane single frequency and the narrow-lane ambiguities to resolve narrow-lane integer ambiguity after fixing the wide-lane integer ambiguity. Experiments with real data show that the proposed method gives fast and reliable results.

• Journal of the Korean Mathematical Society
• /
• v.47 no.4
• /
• pp.861-877
• /
• 2010

The works of Erd$\ddot{o}$s et al. about expansions of 1 with respect to a non-integer base q, referred to as q-expansions, are investigated to determine how far they continue to hold when the number 1 is replaced by a positive number x. It is found that most results about q-expansions for real numbers greater than or equal to 1 are in somewhat opposite direction to those for real numbers less than or equal to 1. The situation when a real number has a unique q-expansion, and when it has exactly two q-expansions are studied. The smallest base number q yielding a unique q-expansion is determined and a particular sequence is shown, in certain sense, to be the smallest sequence whose corresponding base number q yields exactly two q-expansions.

• Journal of Institute of Control, Robotics and Systems
• /
• v.5 no.1
• /
• pp.62-68
• /
• 1999

The attitude of a vehicle can be precisely determined using GPS carrier phase measurements from more than two antennas attached to a vehicle and an efficient integer ambiguity resolution technique. Many methods utilizing the known baseline length as a constraint of independent elements of integer ambiguities are proposed to resolve integer ambiguity at real time. Three-dimensional search space is reduced to two-dimensional search space with this constraint. Thus the true integer ambiguity can be easily determined with less computational burden and fewer number of measurements. But there are still strong requirements for the real time integer ambiguity resolution, which uses single epoch measurement of long baseline. In this paper, a new constraint from the geometry of multiple baselines is derived. With this new constraint, two-dimensional search space is further reduced to one-dimensional search space. It makes possible to determine integer ambiguity with single epoch measurement. The proposed method is applied to real data to show its effectiveness.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.18 no.12
• /
• pp.1928-1934
• /
• 1993

This paper presents a fast algorithm of integer discrete cosine transform(IDCT) allowing VLSI implementation by integer arithmetic. The proposed fast algorithm has been developed using Chen`s matrix decomposition in DCT, and requires less number of arithmetic operations compared to the IDCT. In the presented algorithm, the number of addition number is the same as the one of Chen`s algorithm if DCT, and the number of multiplication if the same as that in DCT at N=8 but drastically decreasing when N is above 8. In addition, the drawbacks of DCT such as performance degradation at the finite length arithmetic could be overcome by the IDCT.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.18 no.36
• /
• pp.183-191
• /
• 1995

When designing a warehouse, one has to recognize that the number of racks in a warehouse takes on only integer value in reality. The existing solution procedures based on noninteger values may result in poor outcomes for the design of a warehouse. This paper deals with the determination of the optimal integer for the number of racks that minimize the total material handling cost associated with the warehouse. An optimum search procedure is proposed here and a number of numerical examples are used to evaluate the efficiency of the proposed procedure.

• Communications of the Korean Mathematical Society
• /
• v.25 no.2
• /
• pp.167-171
• /
• 2010

We will show that if d is a cubefree integer and n is an integer, then with some suitable conditions, there are no primes p and a positive integer m such that d is a cubic residue (mod p), $3\;{\nmid}\;m$, p || n if and only if there are integers x, y, z such that $$x^3\;+\;dy^3\;+\;d^2z^3\;-\;3dxyz\;=\;n$$.

• Honam Mathematical Journal
• /
• v.29 no.3
• /
• pp.427-443
• /
• 2007

The spanning column rank of an $m{\times}n$ integer matrix A is the minimum number of the columns of A that span its column space. We compare the spanning column rank with column rank of matrices over the ring of integers. We also characterize the linear operators that preserve the spanning column rank of integer matrices.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.1 no.1
• /
• pp.97-101
• /
• 1991

The polynomial factorization problem is important not only number theorly but chyptology with Discrete logarithm. We factorized polynolmials with integer coefficients by means of factori-zing polynomials on a finite field by Hensel's Lifting Lemma and finding factors of pol;ynomial with integer coeffcients.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.1
• /
• pp.111-117
• /
• 2022

Let p_a,b,m(n) be the number of integer partitions of n with more parts congruent to a modulo m than parts congruent to b modulo m. We prove that p_a,b,m(n) ≥ p_b,a,m(n) whenever 1 ≤ a < b ≤ m. We also propose some conjectures concerning series with nonnegative coefficients in their expansions.