• Bulletin of the Korean Mathematical Society
• /
• v.58 no.2
• /
• pp.305-313
• /
• 2021

Let h ≥ 2 and A = {a0, a1, …, ak-1} be a finite set of integers. It is well-known that |hA| = hk - h + 1 if and only if A is a k-term arithmetic progression. In this paper, we give some nontrivial inverse results of the sets A with some extremal the cardinalities of hA.

• Proceedings of the KIEE Conference
• /
• 2004.11c
• /
• pp.218-220
• /
• 2004

Orthogonal frequency division multiplexing(OFDM) is one of the most promising technique for next generation wireless broadband communication systems. In this paper, we propose a new bit allocation algorithm in multiuser OFDM. The proposed algorithm is derived from the geometric progression of the additional transmit power of subcarriers and the arithmetic-geometric means inequality. The simulation shows that this algorithm has similar performance to the conventional adaptive bit allocation algorithm and lower computational complexity than the existing algorithms.

• Journal of the Institute of Electronics Engineers of Korea CI
• /
• v.43 no.1 s.307
• /
• pp.1-8
• /
• 2006

This thesis proposes Arithmetic Shift Register(ASR) which can be used as pseudo random number generator. Arithmetic Shift. Register is defined as progression that multiplies random number D , not 0 or 1 at initial value which is not 0, and it is represented as ASR-D in this thesis. Irreducible polynomial that t which makes $'D^k=1'$ satisfies uniquely as $'t=2^n-1'$ over. $GF(2^n)$ is the characteristic polynomial of ASR-D , and the cycle of Arithmetic Shift Register has maximum cycle as $'2^n-1'$. Galois Linear Feedback Shift Register corresponds to ASR-2-1. Therefore, Arithmetic Shift Register proposed in this thesis generalizes Galois Linear Feedback Shift Register. Linear complexity of ASR-D over$GF(2^n)$ is $'n{\leq}LC{\leq}\frac{n^2+n}{2}'$ and in comparison with existing Linear Feedback Shift Register stability is high. The Software embodiment of arithmetic shift register proposed in this thesis is efficient than that of existing Linear Shift Register and hardware complexity is equal. Arithmetic shift register proposed in this thesis can be used widely in various fields such as cipher, error correcting codes, Monte Carlo integral, and data communication etc along with existing linear shift register.

• Korean Journal of Logic
• /
• v.5 no.1
• /
• pp.147-157
• /
• 2001

In this study I try to show some numerical analogy between Leibniz's binary system anc I-ching's symbolic system of duo rerum principia, imagines quator, octo figurae am 64 hexagrams. But, there is really a formal logical accordance in their symbolic foundations, on which are based especially the Wittgenstein's 16 truth-tables in his Tractatus-logico-philosophicus(5.101) am 16 hexagrams, as long as we interpret with the binary values 0 am 1, i.e. the Bi-Polarity, the logical tradition from J. Boole, G. Frege through B. Russell and AN. Whitehead to R. Wittgenstein. So, I argue that the historical and theoretical root of that tradition goes back to the debate between Bouvet and Leibniz about the mathematical structure of I-ching' symbols and the Leibnizian binary arithmetic. In the letter on 4. 11. 1701 from Peking to Leibniz, Bouvet wrote that the I-Ching's symbolism has an analogous structure with Leibniz's binary arithmetic. Corresponding to his suggestion, but without exact knowledge, in the letter of 2. January 1967 to the duke August in Braunschweig-Lueneburg-Wolfenbuettel had Leibniz shown already an original idea for the creation of the world with imago Dei which comes from binary progression, dark and light on water.

• Journal of Forest and Environmental Science
• /
• v.32 no.1
• /
• pp.55-67
• /
• 2016

This paper investigated policies that drive the sustainable management of Ivorian forest which disappear at an annual rate of 250000 hectares. Based on an inter-temporal model for optimum allocation of forest land to three competing uses, the article found that sustainability depends on the incentive structure, of which forest taxes and fees are a key, though obviously not the sole, component. The study proposed to increase the area fee level by accounting for environmental externalities generated by forest harvesters and farmers. The paper showed that the area fee is a decreasing function of the forest natural rate of regeneration and the reconversion rate of agricultural surfaces. Finally, at the given forest natural rate of regeneration and the reconversion rate of agricultural surfaces, the model argued that the area fee need to be progressive (arithmetic progression) in the context of ecological equilibrium break while it should remain constant in normal situation.

• ETRI Journal
• /
• v.29 no.4
• /
• pp.445-451
• /
• 2007

An adaptive modulation scheme is presented for multiuser orthogonal frequency-division multiplexing systems. The aim of the scheme is to minimize the total transmit power with a constraint on the transmission rate for users, assuming knowledge of the instantaneous channel gains for all users using a combined bit-loading and subcarrier allocation algorithm. The subcarrier allocation algorithm identifies the appropriate assignment of subcarriers to the users, while the bit-loading algorithm determines the number of bits given to each subcarrier. The proposed bit-loading algorithm is derived from the geometric progression of the additional transmission power required by the subcarriers and the arithmetic-geometric means inequality. This algorithm has a simple procedure and low computational complexity. A heuristic approach is also used for the subcarrier allocation algorithm, providing a trade-off between complexity and performance. Numerical results demonstrate that the proposed algorithms provide comparable performance with existing algorithms with low computational cost.

• Journal of applied mathematics & informatics
• /
• v.5 no.3
• /
• pp.717-734
• /
• 1998

In the present paper is presented a new matrix pencil-based numerical approach achieving the computation of the elemen-tary divisors of a given matrix $A \in C^{n\timesn}$ This computation is at-tained without performing similarity transformations and the whole procedure is based on the construction of the Piecewise Arithmetic Progression Sequence(PAPS) of the associated pencil $\lambda I_n$ -A of matrix A for all the appropriate values of $\lambda$ belonging to the set of eigenvalues of A. This technique produces a stable and accurate numerical algorithm working satisfactorily for matrices with a well defined eigenstructure. The whole technique can be applied for the computation of the first second and Jordan canonical form of a given matrix $A \in C^{n\timesn}$. The results are accurate for matrices possessing a well defined canonical form. In case of defective matrices indications of the most appropriately computed canonical form. In case of defective matrices indication of the most appropriately computed canonical form are given.

• Communications of the Korean Mathematical Society
• /
• v.15 no.4
• /
• pp.697-706
• /
• 2000

If an arithmetic progression F of length 2n and the number k with 2k$\leq$n are give, can we find two monic polynomials with the same degrees whose set of all zeros form F such that both the number of bad pairs and the number of nonreal zeros are 2k? We will consider the case that both the number of bad pairs and the number of nonreal zeros are two. Moreover, we will see the fundamental relation between the number of bad pairs and the number of nonreal zeros, and we will show that the polynomial in x where the coefficient of x(sup)k is the number of sequences having 2k bad pairs has all zeros real and negative.

• 제어로봇시스템학회:학술대회논문집
• /
• 2001.10a
• /
• pp.88.5-88
• /
• 2001

We propose a neural network solver for an inverse problem. The problem is that input data with complete teaching include defects and predict the defect value. The solver is constructed of a three layer neural network whose learning method is combined from BP and reconstruction learning. The input data for the defects are unknown; therefore, the circulation of an arithmetic progression replaces them; rightly, the learning procedure is not converged for the circulation data vut for the normal data. The learning is quitted after such a learning status id kept. Then, we search a minimum of the differences between teaching data and output of the circulation. Then, we search a minimum of the ...

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.6
• /
• pp.1341-1354
• /
• 2021

Let r ≥ 2, and let k_i ≥ 2 for 1 ≤ i ≤ r. Mixed van der Waerden's theorem states that there exists a least positive integer w = w(k₁, k₂, k₃, …, k_r; r) such that for any n ≥ w, every r-colouring of [1, n] admits a k_i-term arithmetic progression with colour i for some i ∈ [1, r]. For k ≥ 3 and r ≥ 2, the mixed van der Waerden number w(k, 2, 2, …, 2; r) is denoted by w₂(k; r). B. Landman and A. Robertson [9] showed that for k < r < $\frac{3}{2}$(k - 1) and r ≥ 2k + 2, the inequality w₂(k; r) ≤ r(k - 1) holds. In this note, we establish some results on w₂(k; r) for 2 ≤ r ≤ k.