• 대한수학회지
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• 제47권4호
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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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• 제56권2호
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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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• 제41권3호
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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.

• 한국정보통신학회논문지
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• 제14권5호
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• pp.1133-1138
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• 2010

EPCglobal Class-1 Gen-2 충돌방지 기법에서는 Q-알고리즘을 통하여 질의 라운드의 프레임 크기를 결정한다. Q-알고리즘은 리더의 식별영역 내에 있는 태그의 수를 추정하지 않고 슬롯의 상태만을 이용하여 질의 라운드의 프레임 크기를 계산하므로 알고리즘에 비하여 리더의 알고리즘이 단순한 장점이 있다. 반면, 실제 태그의 수를 반영한 최적화된 프레임 크기를 할당할 수 없는 단점이 있다. 또한, 기존의 Q-알고리즘에서는 프레임 크기를 조절하기 위한 매개변수인 C값이 정해져 있지 않다. 따라서 본 논문에서는 매 질의 라운드마다 태그의 수를 추정하여 Q-알고리즘의 매개변수 C값을 결정하는 기법을 제안하고, 이에 대한 성능분석을 한다.

• 호남수학학술지
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• 제45권3호
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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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• 제8권1호
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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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• 제8권5호
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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.

• 대한수학회지
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• 제39권2호
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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].

• 호남수학학술지
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• 제38권3호
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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 $L(q^4)D(q)$.

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2016년도 추계학술대회
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• pp.723-725
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• 2016

Gen-2 Q-알고리즘에서는 태그의 수가 적은 상태에서 초기 $Q_{fp}$ 값을 크게 하면 빈 슬롯이 많이 발생하고, 태그의 수가 많은 상태에서 초기 $Q_{fp}$ 값을 적게 하면 충돌이 많이 발생한다. 또한 적절하지 못한 가중치를 선택할 경우 빈 슬롯 또는 충돌 슬롯이 많이 발생할 수 있다. 이로 인하여 질의 라운드 동안 최적의 프레임 크기에 수렴하는 속도가 늦어지므로 성능이 저하되는 문제점이 있다. 본 논문에서는 태그 수를 추정하여 현재의 슬롯-카운트 크기에 따라 가중치를 결정하는 기법을 제안하고, 이에 대한 성능을 분석한다.