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

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.367-370
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• 2016

In this paper, we consider the generalized Lucas sequence which is the (p, q) - Lucas sequence. Then we used the Binet's formula to show some properties of the (p, q) - Lucas number. We get some generalized identities of the (p, q) - Lucas number.

• Journal of Ecology and Environment
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• v.41 no.3
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• pp.66-71
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• 2017

Background: The sprouts of oak species play an important role in maintaining the oak community in a disturbed environment. In this study, we cut 1-year-old oak in three times during the 3 years and measured the sprout responses to know sprouting ability of six deciduous oaks in Korea. Results: Oak sprouts have appeared in spring and fall, and some of the sprouts had lifespan as short as a month. As the number of cutting increases, sprout number of Quercus acutissima increased whereas the other oak species decreased or died. The average number of sprouts over the 3 years was from 1.4 (Quercus mongolica) to 2.2 (Q. acutissima) per individual. Quercus serrata died after the second cutting, and Quercus dentata died after the third cutting. So, the two species have the lowest sprouting ability among six oak species. The sprouts grew actively during fall and slowly in summer. The sprout length during the 3 years was in the following descending order: Q. acutissima, Quercus aliena, Q. dentata, and Q. mongolica. Sprout of Q. acutissima and Q. aliena generated steadily over the 3 years, and sprout of Quercus variabilis and Q. mongolica was changed by year. After the 3 years, the number of sprouts increased only in Q. acutissima but sprout number of the other five oak species decreased. The sprout length of Q. acutissima, Q. aliena, and Q. variabilis increased, but sprout length of the other three oak species decreased. The average survival rate of saplings over the 3 years was in the following descending order: Q. acutissima, Q. aliena, Q. variabilis, and Q. mongolica. Conclusions: As a result, the sprouting ability of Q. acutissima was the highest. Such level of sprouting ability may be the evidence of how Q. acutissima community exists as a dominant species in a disturbed environment in lowlands of Korea peninsula.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.14 no.5
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• pp.1133-1138
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• 2010

In the anti-collision scheme proposed by EPCglobal Class-1 Gen-2 standard, the frame size for a query round is determined by Q-algorithm. In the Q-algorithm, the reader calculates a frame size without estimating the number of tags in it's identification range. It uses only the slot status. Therefore, Q-algorithm has advantage that the reader's algorithm is simpler than other algorithms. However, it cannot allocate an optimized frame size because it does not consider the number of tags. Also, the conventional Q-algorithm does not define an optimized parameter value C for adjusting the frame size. In this paper, we propose a modified Q-algorithm and evaluate the performance with computer simulations. The proposed Q-algorithm estimates the number of tags at every query round, and determines the parameter value C based on the estimated number of tags.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.542-554
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• 2023

Given a real number α, the Lagrange number of α is the supremum of all real numbers L > 0 for which the inequality |α - p/q| < (Lq²)^-1 holds for infinitely many rational numbers p/q. All Lagrange numbers less than 3 can be arranged as a set {l_p/q : p/q ∈ ℚ ∩ [0, 1]} using the Farey index. The present paper considers a function C(α) devised from Sturmian words. We demonstrate that the function C(α) contains all information on Lagrange numbers less than 3. More precisely, we prove that for any real number α ∈ (0, 1], the value C(α) - C(0) is equal to the sum of all numbers 3 - l_p/q where the Farey index p/q is less than α.

• Journal of information and communication convergence engineering
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• v.8 no.1
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• pp.45-50
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• 2010

EPCglobal Class-1 Gen-2 standard proposed Q-algorithm to select a frame size for the next query round. Q-algorithm calculates the frame size without estimating the number of tags. Therefore, the Q-algorithm has advantage that the reader's algorithm is simpler than other algorithms. However, it is impossible to allocate the optimized frame size. Also. the conventional Q-algorithm does not define an optimized parameter value C for adjusting the frame size. In this paper, we propose a modified Q-algorithm with the tag number estimation scheme, and evaluate the performance with computer simulations.

• Journal of information and communication convergence engineering
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• v.8 no.5
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• pp.519-523
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• 2010

In Gen-2 RFID system, the initial value of $Q_{fp}$, which is the slot-count parameter of Q-algorithm, is not defined in the standard. In this case, if the number of tags within the reader's identification range is small and we let the initial $Q_{fp}$ be large, the number of empty slot will be large. On the other hand, if we let the initial $Q_{fp}$ be small in spite of many tags, almost all the slots will be collided. As a result, the performance will be declined because the frame size does not converge to the optimal point quickly during the query round. In this paper, we propose a scheme to allocate the optimal initial $Q_{fp}$ through the tag number estimation before the query round begins. Through computer simulations, it is demonstrated that the proposed scheme achieves more stable performance than Gen-2 Q-algorithm.

• Journal of the Korean Mathematical Society
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• v.39 no.2
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• pp.221-236
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• 2002

Using the p-adic q-integral due to T. Kim[4], we define a number B＊$_{n}$(q) and a polynomial B＊$_{n}$(q) which are p-adic q-analogue of the ordinary Bernoulli number and Bernoulli polynomial, respectively. We investigate some properties of these. Also, we give slightly different construction of Tsumura＇s p-adic function $\ell$$_{p}$(u, s, $\chi$) [14] using the p-adic q-integral in [4].n [4].

• Honam Mathematical Journal
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• v.38 no.3
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• pp.507-552
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• 2016

For a complex number q and a divisor function ${\sigma}_1(n)$ we define $$C(q):=q{\prod_{n=1}^{\infty}}(1-q^n)^{16}(1-q^{2n})^4,\\D(q):=q^2{\prod_{n=1}^{\infty}}(1-q^n)^8(1-q^{2n})^4(1-q^{4n})^8,\\L(q):=1-24{\sum_{n=1}^{\infty}}{\sigma}_1(n)q^n$$ moreover we obtain the number of representations of $n{\in}{\mathbb{N}}$ as sum of 24 squares, which are possible for us to deduce $L(q^4)C(q)$ and $L(q^4)D(q)$.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2016.10a
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• pp.723-725
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• 2016

In Gen-2 Q-algorithm, if the number of tags is small and we let the initial $Q_{fp}$ be large, the number of empty slot will be large. On the other hand, if we let the initial $Q_{fp}$ be small in spite of many tags, almost all the slots will be collided. Also, if the reader selects an inappropriate weight, there are a lot of empty or collided slots. As a result, the performance will be declined because the frame size does not converge to the optimal point quickly during the query round. In this paper, we propose a scheme to select the weight based on the slot-count size of current query round through the tag number estimation and.