• East Asian mathematical journal
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• 제35권3호
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• pp.285-288
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• 2019

Let $F_n$, $n{\in}{\mathbb{N}}$ be the n - th Fibonacci number, and let (p, q) be one of ordered pairs ($F_{n+2}$, $F_n$) or ($F_{n+1}$, $F_n$). Then we show that the multiplicative inverse of q mod p as well as that of p mod q are again Fibonacci numbers. For proof of our claim we make use of well-known Cassini, Catlan and dOcagne identities. As an application, we determine the number $N_{p,q}$ of nonzero term of a polynomial ${\Delta}_{p,q}(t)=\frac{(t^{pq}-1)(t-1)}{(t^p-1)(t^q-1)}$ through the Carlitz's formula.

• 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.

• International Journal of Oral Biology
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• 제40권4호
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• pp.205-210
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• 2015

Prevotella intermedia-specific quantitative real-time PCR (qPCR) primers were previously designed based on the nucleotide sequences of RNA polymerase ${\beta}$-subunit gene (rpoB). However, the several clinical strains isolated from Korean populations are not detectable by the qPCR primers. The purpose of this study was to develop new P. intermedia-specific qPCR primers based on the rpoB. The specificity of the primers was determined by conventional PCR with 12 strains of P. intermedia and 52 strains (52 species) of non-P. intermedia bacteria. The sensitivity of primers was determined by qPCR with serial dilutions of the purified genomic DNAs (40 ng to 4 fg) of P. intermedia ATCC $25611^T$. The data indicated that only P. intermedia strains were detected by the P intermedia-specific qPCR primers (RTPiF2/RTPiR2); in addition, as little as 40 fg of P. intermedia genomic DNA could be detected. These results suggest that these qPCR primers are useful in detecting P. intermedia from the bacterial infectious lesions including dental plaque and oral tissue lesions.

• 대한수학회보
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• 제47권6호
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• pp.1181-1188
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• 2010

q-Volkenborn integrals ([8]) and fermionic invariant q-integrals ([12]) are introduced by T. Kim. By using these integrals, Euler q-zeta functions are introduced by T. Kim ([18]). Then, by using the Euler q-zeta functions, S.-H. Rim, S. J. Lee, E. J. Moon, and J. H. Jin ([25]) studied q-Genocchi zeta functions. And also Y. H. Kim, W. Kim, and C. S. Ryoo ([7]) investigated twisted q-zeta functions and their applications. In this paper, we consider the q-analogue of twisted Lerch type Euler zeta functions defined by $${\varsigma}E,q,\varepsilon(s)=[2]q \sum\limits_{n=0}^\infty\frac{(-1)^n\epsilon^nq^{sn}}{[n]_q}$$ where 0 < q < 1, $\mathfrak{R}$(s) > 1, $\varepsilon{\in}T_p$, which are compared with Euler q-zeta functions in the reference ([18]). Furthermore, we give the q-extensions of the above twisted Lerch type Euler zeta functions at negative integers which interpolate twisted q-Euler polynomials.

• 대한수학회보
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• 제46권5호
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• pp.941-947
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• 2009

Let q be a power of 16. Every polynomial $P\in\mathbb{F}_q$[t] is a strict sum $P=A^2+A+B^3+C^3+D^3+E^3$. The values of A,B,C,D,E are effectively obtained from the coefficients of P. The proof uses the new result that every polynomial $Q\in\mathbb{F}_q$[t], satisfying the necessary condition that the constant term Q(0) has zero trace, has a strict and effective representation as: $Q=F^2+F+tG^2$. This improves for such q's and such Q's a result of Gallardo, Rahavandrainy, and Vaserstein that requires three polynomials F,G,H for the strict representation $Q=F^2$+F+GH. Observe that the latter representation may be considered as an analogue in characteristic 2 of the strict representation of a polynomial Q by three squares in odd characteristic.

• 대한수학회보
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• 제38권2호
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• pp.399-412
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• 2001

In this paper, we consider that the q-analogue of w$\omega-Bernoulli numbers\; B_i(\omega, q)$. And we calculate the sums of products of two q-analogue of $\omega-Bernoulli numbers B_i(\omega, q)$ in complex cases. From this result, we obtain the Euler type formulas of the Carlitz´s q-Bernoulli numbers $\beta_i(q)$ and q-Bernoulli numbers $B_i(q)$. And we also calculate the p-adic Stirling type series by the definition of $B_i(\omega, q)$ in p-adic cases.

• 한국조경학회지
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• 제21권2호
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• pp.50-67
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• 1993

This study analyzed the distribution and structure of the vegetation landscape in Naejangsan National Park. The plant distribution was investigated using a field survey. There were 72 sites sampled using the clumpled sampling method. The data derived from the investigation was analyzed using the quantitative analysis of Bray-Curtis method. The analysis was performed by the classification of TWINSPAN. The ordination of DCA and RA was used for the species composition and successional trends. The results are as follows; 1. Quercus. serrata-Q. variabilis community as 21.76(16.49$\textrm{km}^2$), was the largest community in the actual vegetation of the Naejangsan National Park. The degree of green naturality index 8 area covered 64.8% of the study area and the index 6 area did 16%. 2. Classified by the ordination of DCA and environmental variables, such as the plant community was divided into seven groups according to the altitude and forming groups; Chamaecy Paris. pisifera-P.densiflora community, P.densiflora community, Q.variailis community, T.nuciofera-A.palmatum community. 3. Ther species diversity and evenness indices of C.pisifera-P.densiflora community, P.densiflora community appeared low but C.laxiflora communitywhich was the most stable community in the study area. 4. The similarity indices between Q.variabilis community and Q.serrata-Q.variabilis community were calculated 58.84%, but those between other communities were comparatively low level. 5. The successional trends of DBH class seem to be from C. pisifera-P.densiflora community, P.densiflora community to Quercus species community and from Q.variabilis community, Q.serrata-Q.variabilis community to Carpinus species community. 6. Results suggested that the successional trends in Naejangsan National Park; P.densiflora community\longrightarrowQ.variablilis community, Q.serrata-Q.variabilis community\longrightarrowC.laxiflora community in sequence.

• Korean Journal of Mathematics
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• 제29권2호
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• pp.361-370
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• 2021

Let 𝕂 be a complete ultrametric algebraically closed field and 𝓐 (𝕂) be the 𝕂-algebra of entire function on 𝕂. For any p-adic entire functions f ∈ 𝓐 (𝕂) and r > 0, we denote by |f|(r) the number sup {|f (x)| : |x| = r} where |·|(r) is a multiplicative norm on 𝓐 (𝕂). In this paper we study some growth properties of composite p-adic entire functions on the basis of their relative (p, q)-𝜑 order where p, q are any two positive integers and 𝜑 (r) : [0, +∞) → (0, +∞) is a non-decreasing unbounded function of r.

• Progress in Superconductivity
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• 제9권1호
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• pp.29-34
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• 2007

The baseline selection is the first and important step to analyze magnetocardiography (MCG) parameters. There are no difficulties to select the baseline between P- and Q-wave peak (P-Q interval) of MCG wave recorded from healthy subjects because the P-Q intervals of the healthy subjects do not much vary. However, patients with ischemic heart disease often show an unstable P-Q interval which does not seem to be appropriate for the baseline. In this case, T-P interval is alternatively recommended for the baseline. However, there has been no study on the difference made by the baseline selection. In this study, we studied the effect of the different baseline selection. MCG data were analyzed from twenty healthy subjects and twenty one patients whose baselines were alternatively selected in the T-P interval for their inappropriate P-Q interval. Paired T-test was used to compare two set of data. Fifteen parameters derived from the R-wave peak, the T-wave peak, and the period, $T_{max/3}{\sim}T_{max}$ were compared for the different baseline selection. As a result, most parameters did not show significant differences (p>0.05) except few parameters. Therefore, there will be no significant differences if anyone of two intervals were selected for the MCG baseline. However, for the consistent analysis, P-Q interval is strongly recommended for the baseline correction.

• 대한수학회논문집
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• 제20권3호
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• pp.467-485
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• 2005

Let p and q be odd primes with p=2q+1. We study the number of solutions of congruence equations $ax^i\;+\;by^j\;{\equiv}\;c$ (mod p) and a$ax^i\;+\;by^j\;+\;dz^t\;{\equiv}\;c(modp)$