• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.51-57
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• 2010

In this paper we introduce and study the lacunary strong Zweier sequence spaces $N_{\theta}^O[Z]$, $N_{\theta}[Z]$ consisting of all sequences x = $(x_k)$ such that (Zx) in the space $N_{\theta}$ and $N_{\theta}^O$ respectively, which is normed. Also, prove that $N_{\theta}^O[Z}$, $N_{\theta}[Z}$, are linearly isomorphic to the space $N_{\theta}^O$ and $N_{\theta}$, respectively. And we study some connections between lacunary strong Zweier sequence and lacunary statistical Zweier convergence sequence.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.977-988
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• 2022

The Padovan sequence is the third-order linear recurrence (𝓟_n)_n≥0 defined by 𝓟_n = 𝓟_n-2 + 𝓟_n-3 for all n ≥ 3 with initial conditions 𝓟₀ = 0 and 𝓟₁ = 𝓟₂ = 1. In this paper, we investigate a generalization of the Padovan sequence called the k-generalized Padovan sequence which is generated by a linear recurrence sequence of order k ≥ 3. We present recurrence relations, the generalized Binet formula and different arithmetic properties for the above family of sequences.

• Journal of the Institute of Convergence Signal Processing
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• v.13 no.4
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• pp.194-200
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• 2012

In this paper we analyze the code sequence generating algorism defined on $GF(2^n)$ proposed by S.Bostas and V.Kumar[7] and derive the implementation functions of code sequence generator using Boolean functions which can map the vector space $F_2^n$ of all binary vectors of length n, to the finite field with two elements $F_2$. We find the code sequence generating boolean functions based on two kinds of the primitive polynomials of degree, n=5 and n=7 from trace function. We then design and implement the code sequence generators using these functions, and produce two code sequence groups. The two groups have the period 31 and 127 and the magnitudes of out of phase(${\tau}{\neq}0$) autocorrelation and crosscorrelation functions {-9, -1, 7} and {-17, -1, 15}, satisfying the period $L=2^n-1$ and the correlation functions $R_{ij}({\tau})=\{-2^{(n+1)/2}-1,-1,2^{(n+l)/2}-1\}$ respectively. Through these results, we confirm that the code sequence generators using boolean functions are designed and implemented correctly.

• The Pure and Applied Mathematics
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• v.16 no.3
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• pp.255-258
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• 2009

It is well known that for a sequence a = ($a_0,\;a_1$,...) the general term of the dual sequence of a is $a_n\;=\;c_0\;^n_0\;+\;c_1\;^n_1\;+\;...\;+\;c_n\;^n_n$, where c = ($c_0,...c_n$ is the dual sequence of a. In this paper, we find the general term of the sequence ($c_0,\;c_1$,... ) and give another method for finding the inverse matrix of the Pascal matrix. And we find a simple proof of the fact that if the general term of a sequence a = ($a_0,\;a_1$,... ) is a polynomial of degree p in n, then ${\Delta}^{p+1}a\;=\;0$.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.239-252
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• 2002

A sort sequence $S_n$ is sequence of all unordered pairs of indices in $I_n$={1,2,…n}. With a sort sequence $S_n$ = ($s_1,S_2,...,S_{\frac{n}{2}}$),one can associate a predictive sorting algorithm A($S_n$). An execution of the a1gorithm performs pairwise comparisons of elements in the input set X in the order defined by the sort sequence $S_n$ except that the comparisons whose outcomes can be inferred from the results of the preceding comparisons are not performed. A sort sequence is said to be extremal if it maximizes a given objective function. First we consider the extremal sort sequences with respect to the objective function $\omega$($S_n$) - the expected number of tractive predictions in $S_n$. We study $\omega$-extremal sort sequences in terms of their prediction vectors. Then we consider the objective function $\Omega$($S_n$) - the minimum number of active predictions in $S_n$ over all input orderings.

• Bioinformatics and Biosystems
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• v.1 no.1
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• pp.46-50
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• 2006

According to the advancement of experimental techniques in molecular biology, genomic and protein sequence databases are increasing in size exponentially, and mean sequence lengths are also increasing. Because the sizes of these databases become larger, it is difficult to search similar sequences in biological databases with significant homologies to a query sequence. In this paper, we present the N-gram indexing method to retrieve similar sequences fast, precisely and comparably. This method regards a protein sequence as a text written in language of 20 amino acid codes, adapts N-gram tokens of fixed-length as its indexing scheme for sequence strings. After such tokens are indexed for all the sequences in the database, sequences can be searched with information retrieval algorithms. Using this new method, we have developed a protein sequence search system named as ProSeS (PROtein Sequence Search). ProSeS is a protein sequence analysis system which provides overall analysis results such as similar sequences with significant homologies, predicted subcellular locations of the query sequence, and major keywords extracted from annotations of similar sequences. We show experimentally that the N-gram indexing approach saves the retrieval time significantly, and that it is as accurate as current popular search tool BLAST.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1373-1384
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• 2016

In this paper, we research the normality of sequences of meromorphic functions concerning the sequence of omitted functions. The main result is listed below. Let {$f_n(z)$} be a sequence of functions meromorphic in D, the multiplicities of whose poles and zeros are no less than k + 2, $k{\in}\mathbb{N}$. Let {$b_n(z)$} be a sequence of functions meromorphic in D, the multiplicities of whose poles are no less than k + 1, such that $b_n(z)\overset{\chi}{\Rightarrow}b(z)$, where $b(z({\neq}0)$ is meromorphic in D. If $f^{(k)}_n(z){\neq}b_n(z)$, then {$f_n(z)$} is normal in D. And we give some examples to indicate that there are essential differences between the normal family concerning the sequence of omitted functions and the normal family concerning the omitted function. Moreover, the conditions in our paper are best possible.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.1-16
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• 2019

Let a, b, P, and Q be real numbers with $PQ{\neq}0$ and $(a,b){\neq}(0,0)$. The Horadam sequence $\{W_n\}$ is defined by $W_0=a$, $W_1=b$ and $W_n=PW_{n-1}+QW_{n-2}$ for $n{\geq}2$. Let the sequence $\{X_n\}$ be defined by $X_n=W_{n+1}+QW_{n-1}$. In this study, we obtain some new identities between the Horadam sequence $\{W_n\}$ and the sequence $\{X_n\}$. By the help of these identities, we show that Diophantine equations such as $$x^2-Pxy-y^2={\pm}(b^2-Pab-a^2)(P^2+4),\\x^2-Pxy+y^2=-(b^2-Pab+a^2)(P^2-4),\\x^2-(P^2+4)y^2={\pm}4(b^2-Pab-a^2),$$ and $$x^2-(P^2-4)y^2=4(b^2-Pab+a^2)$$ have infinitely many integer solutions x and y, where a, b, and P are integers. Lastly, we make an application of the sequences $\{W_n\}$ and $\{X_n\}$ to trigonometric functions and get some new angle addition formulas such as $${\sin}\;r{\theta}\;{\sin}(m+n+r){\theta}={\sin}(m+r){\theta}\;{\sin}(n+r){\theta}-{\sin}\;m{\theta}\;{\sin}\;n{\theta},\\{\cos}\;r{\theta}\;{\cos}(m+n+r){\theta}={\cos}(m+r){\theta}\;{\cos}(n+r){\theta}-{\sin}\;m{\theta}\;{\sin}\;n{\theta},$$ and $${\cos}\;r{\theta}\;{\sin}(m+n){\theta}={\cos}(n+r){\theta}\;{\sin}\;m{\theta}+{\cos}(m-r){\theta}\;{\sin}\;n{\theta}$$.

• Speech Sciences
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• v.15 no.3
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• pp.53-63
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• 2008

This paper examined the acoustic differences in English speech production between English native speakers and Korean learners. Korean speakers seem to produce errors by over-applying the Korean phonological rules(nasalization and lateralization) to English speech under the conditions comparable to those of Korean which contain nasal+lateral or lateral+nasal sequences. Being based on this prediction, the experimental data is grouped into three sets, [n]+[l] sequence, [l]+[n]sequence, and [m]+[l] sequence. The result shows that, Korean speakers usually nasalize or lateralize the target words or phrases in every three categories while English natives don't. In set A([n]+[l] sequence), both nasalization and lateralization were found in [n]+[l] sequence, the same circumstances where both nasalization and lateralization can be placed as in Korean. In the case of set B([l]+[n] sequence), only lateralization is observed. It is because the nasalization never occurs in the sequence of l-n in Korean. There is no lateralization in set C([m]+[l] sequence), because only nasalization occurs in the sequence of m-l in Korean. This results reconfirmed that the nasalization and lateralization rules in Korean deeply influence on the English production data. Korean speakers need to be taught not to over-apply Korean phonological rule to English production for accurate pronunciation.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.1C
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• pp.9-14
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• 2009

In this paper, using the binary (N,M,L,1) low correlation zone(LCZ) sequence set with specific property, we propose the construction method of a quaternary LCZ sequence set with parameters (2N,2M,L,2). The binary LCZ sequence using this method must have period $N{\equiv}3$ mod 4, balance property, and specific correlation property. The proposed method is modified from the construction method of binary LCZ sequence set by using binary LCZ sequence with specific condition proposed by Kim, Jang, No, and Chung[4].