• 대한수학회논문집
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• 제25권1호
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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.

• 대한수학회논문집
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• 제37권4호
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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.

• 융합신호처리학회논문지
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• 제13권4호
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• pp.194-200
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• 2012

본 논문에서는 S.Bostas와 V.Kumar[7]에 의하여 제안되고 $GF(2^n)$에서 정의되는 부호계열 발생알고리즘을 분석하고, 길이 n인 이진벡터로 이루어지는 벡터공간 $F_2$으로부터, 두 원소로 정의되는 공간 $F_2$로 사상할 수 있는 부울함수를 이용하여 발생기 구성 함수를 도출하였다. 차수 n=5와 n=7인 두 종류의 최소 다항식을 이용한 피드벡 쉬프트레지스터를 기반으로 Trace 함수로부터 부호계열 발생기 구성 부울함수를 도출하고 발생기를 설계 구성하였으며 이를 이용하여 두 종류의 부호계열 군을 발생하였다. 발생된 부호계열의 주기는 각각 31과 127로서 주기 $L=2^n-1$을 만족하고 ${\tau}=0$을 제외한 자기상관함수 값과 상호상관함수 값이 각각 {-9, -1, 7}과 {-17, -1, 15}로서 상관함수 값 $R_{i,j}({\tau})=\{-2^{(n+1)/2}-1,-1,2^{(n+1)/2}-1\}$의 특성을 만족하였다. 이 결과로부터 부울함수를 이용한 부호계열 발생기 설계와 구성이 타당함을 확인하였다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권3호
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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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• 제9권1호
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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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• 제1권1호
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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.

• 대한수학회보
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• 제53권5호
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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.

• 대한수학회논문집
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• 제34권1호
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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 $${\cos}\;r{\theta}\;{\sin}(m+n){\theta}={\cos}(n+r){\theta}\;{\sin}\;m{\theta}+{\cos}(m-r){\theta}\;{\sin}\;n{\theta}$$.

• 음성과학
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• 제15권3호
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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.

• 한국통신학회논문지
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• 제34권1C호
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• pp.9-14
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• 2009

본 논문에서는 매개 변수가 (N,M,L,1)인 특정 성질을 가진 이진 낮은 상관 구역 수열균(LCZ sequence)를 이용하여 매개 변수가 (2N,2M,L,2)인 4진 낮은 상관 수열군을 생성하는 방법을 제시한다. 본 논문에서 이용하는 이진 낮은 상관 수열군은 balance property를 가지고 있어야 하며, 주기 N이 $N{\equiv}3$ mod 4이어야 하고, 특정한 상관 특성을 가져야 한다. 새로 제안된 생성법은 특정 성질을 가진 이진 낮은 상관 수열군을 이용하여 이진 낮은 상관 수열군을 생성한 Kim, Jang, No, and Chung의 생성법을 응용한 것이다.