• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.135-151
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• 2005

In this paper, we obtain some properties of the sequences $U^{q}_n\;and\;V^{q}_n$ introduced in [6]. We find polynomial representations and formulas of them. For q = 5, $U^{5}_n$ is the Fibonacci sequence $F_n\;and\;V^{5}_n$ is the Lucas sequence $L_n$.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.23-34
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• 2019

In this paper, we first define generalizations of Pell and Pell-Lucas sequences by the recurrence relations $$p_n=2ap_{n-1}+(b-a^2)p_{n-2}\;and\;q_n=2aq_{n-1}+(b-a^2)q_{n-2}$$ with initial conditions $p_0=0$, $p_1=1$, and $p_0=2$, $p_1=2a$, respectively. We give generating functions and Binet's formulas for these sequences. Also, we obtain some identities of these sequences.

• Communications for Statistical Applications and Methods
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• v.17 no.4
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• pp.507-513
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• 2010

Let {$X_i,-{\infty}$ < 1 < $\infty$} be a doubly infinite sequence of identically distributed and negatively associated random variables with mean zero and finite variance and {$a_i,\;-{\infty}$ < i < ${\infty}$} be an absolutely summable sequence of real numbers. Define a moving average process as $Y_n={\sum}_{i=-\infty}^{\infty}a_{i+n}X_i$, n $\geq$ 1 and $S_n=Y_1+{\cdots}+Y_n$. In this paper we prove that E|$X_1$|$^rh$($|X_1|^p$) < $\infty$ implies ${\sum}_{n=1}^{\infty}n^{r/p-2-q/p}h(n)E{max_{1{\leq}k{\leq}n}|S_k|-{\epsilon}n^{1/p}}{_+^q}<{\infty}$ and ${\sum}_{n=1}^{\infty}n^{r/p-2}h(n)E{sup_{k{\leq}n}|k^{-1/p}S_k|-{\epsilon}}{_+^q}<{\infty}$ for all ${\epsilon}$ > 0 and all q > 0, where h(x) > 0 (x > 0) is a slowly varying function, 1 ${\leq}$ p < 2 and r > 1 + p/2.

• BMB Reports
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• v.44 no.10
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• pp.653-658
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• 2011

Sclerotinia sclerotiorum fungus has three endoxylanases induced by wheat bran. In the first part, a partial xylanase sequence gene (90 bp) was isolated by PCR corresponding to catalytic domains (${\beta}5$ and ${\beta}6$ strands of this protein). The high homology of this sequence with xylanase of Botryotinia fuckeliana has permitted in the second part to amplify the XYN1 gene. Sequence analysis of DNA and cDNA revealed an ORF of 746 bp interrupted by a 65 bp intron, thus encoding a predicted protein of 226 amino acids. The mature enzyme (20.06 kDa), is coded by 188 amino acid (pI 9.26). XYN1 belongs to G/11 glycosyl hydrolases family with a conserved catalytic domain containing $E_{86}$ and $E_{178}$ residues. Bioinformatics analysis revealed that there was no Asn-X-Ser/Thr motif required for N-linked glycosylation in the deduced sequence however, five O-glycosylation sites could intervene in the different folding of xylanses isoforms and in their secretary pathway.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.513-518
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• 2007

There is a one to one correspondence between Artinian algebras $k[x_1,...,x_n]/Ann(M)$ and finitely generated $k[x_1,...,x_n]-submodules$ M of $k[y_1,...,y_n]$ by Inverse System. In particular, any Artinian level algebra $k[x_1,...,x_n]/Ann(M)$ can be obtained when M is finitely generated by only maximal degree generators. We prove that H = (1, 4, 8, 13,..., 27, 8, 2) is not a level Artinian O-sequence using this inverse system.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.511-522
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• 2017

We explicitly solve the diophantine equations of the form $$A_{n_1}A_{n_2}{\cdots}A_{n_k}{\pm}1=B^2_m$$, where $(A_n)_{n{\geq}0}$ and $(B_m)_{m{\geq}0}$ are either the Fibonacci sequence or Lucas sequence. This extends the result of D. Marques [9] and L. Szalay [13] concerning a variant of Brocard-Ramanujan equation.

• ETRI Journal
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• v.42 no.1
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• pp.101-107
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• 2020

For Korean language processing, morphological analysis is a critical component that requires extensive work. This morphological analysis can be conducted in an end-to-end manner without requiring a complicated feature design using a sequence-to-sequence model. However, the sequence-to-sequence model has a time complexity of O(n²) for an input length n when using the attention mechanism technique for high performance. In this study, we propose a linear-time Korean morphological analysis model using a local monotonic attention mechanism relying on monotonic alignment, which is a characteristic of Korean morphological analysis. The proposed model indicates an extreme improvement in a single threaded environment and a high morphometric F1-measure even for a hard attention model with the elimination of the attention mechanism formula.

• Kyungpook Mathematical Journal
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• v.54 no.1
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• pp.73-86
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• 2014

In the present paper we introduce difference paranormed sequence spaces $c_0(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$, $c(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$ and $l_{\infty}(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$ defined by a Musielak-Orlicz function $\mathcal{M}$ = $(M_k)$ over n-normed spaces. We also study some topological properties and some inclusion relations between these spaces.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.437-445
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• 2003

We prove that H = (1, 3, 4, 5,...,6, 4, 3) is not alevel Artinian O-sequence.

• Microbiology and Biotechnology Letters
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• v.18 no.3
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• pp.309-316
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• 1990

The sequence of a 1795 bp restriction fragment containing the B. circulans F-2 gene for NaC1- dependent $\alpha$-amylase (CI-amylase) is reported. The probable coding region of the gene is 1005 base pairs (335 amino acida) long. The NaC1-dependent $\alpha$-amylase (el-amy) sequence shows an open reading frame (ORF) with the translated molecular weight of about 38, 006, which correspond to a molecular weight of about 35, 000 (Mi). The gene is preceded by the sequence resembling promoter for the vegetative B, subtitis RNA polymerases. These are followed by the sequences resembling a B. subtilis ribosome binding site 5 nucleotides before the first codon of the gene. Homologous regions with other amylases were found. The N-terminal sequences of the mature proteins expressed in E. eoli were identical to the N-terminal sequences which are anaIysed.