• 한국통신학회논문지
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• 제28권10C호
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• pp.930-935
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• 2003

본 논문에서는 소수 p에 대해 Kumar와 Moreno가 소개한 유한체 상에시 정의된 bent 함수를 이용하여 균형성과 최적의 상관성질을 갖는 p진 bent 수열군의 일반화된 생성방법을 소개한다[3]. 이렇게 생성된 수열군을 일반화된 p진 수열이라 부르기로 한다. Moriuchi와 Imamura가 [6]에서 소개한 균형성과 최적의 상관특성을 갖는 p진 수열군은 일반화된 bent 수열의 특별한 예임을 보인다.

• Journal of applied mathematics & informatics
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• 제40권1_2호
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• pp.153-171
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• 2022

In 1960, Schatten studied operators of the form $\sum_{n=1}^{{\infty}}\;{\lambda}_n(x_n{\otimes}{\bar{y_n}})$, where {x_n}n and {y_n}_n are orthonormal sequences in a Hilbert space, and {λ_n}n ∈ ℓ^∞(ℕ). Balazs generalized some of the results of Schatten in 2007. In this paper, we further generalize results of Balazs by studying the operators of the form $\sum_{n=1}^{{\infty}}\;{\lambda}_n(A^*_nx_n{\otimes}{\bar{B^*_ny_n}})$, where {A_n}n and {B_n}_n are operator-valued Bessel sequences, {x_n}_n and {y_n}_n are sequences in the Hilbert space such that {║x_n║║y_n║}_n ∈ ℓ^∞(ℕ). We also generalize the class of Hilbert-Schmidt operators studied by Balazs.

• 대한수학회논문집
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• 제39권2호
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• pp.437-460
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• 2024

In this paper we present the weighted shift operators having the property of moment infinite divisibility. We first review the monotone theory and conditional positive definiteness. Next, we study the infinite divisibility of sequences. A sequence of real numbers γ is said to be infinitely divisible if for any p > 0, the sequence γ^p = {γ^p_n}^∞_n=0 is positive definite. For sequences α = {α_n}^∞_n=0 of positive real numbers, we consider the weighted shift operators W_α. It is also known that W_α is moment infinitely divisible if and only if the sequences {γ_n}^∞_n=0 and {γ_n+1}^∞_n=0 of W_α are infinitely divisible. Here γ is the moment sequence associated with α. We use conditional positive definiteness to establish a new criterion for moment infinite divisibility of W_α, which only requires infinite divisibility of the sequence {γ_n}^∞_n=0. Finally, we consider some examples and properties of weighted shift operators having the property of (k, 0)-CPD; that is, the moment matrix M_γ(n, k) is CPD for any n ≥ 0.

• 한국통신학회논문지
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• 제33권9C호
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• pp.669-675
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• 2008

홀수인 소수 p와 n=4k, 그리고 $d=((p^2k+1)/2)^2$에 대해서, 주기가 $p^n-1$인 p-진 m-수열 s(t)에 대해서 $(p^{2k}+1)/2$개의 서로 다른 decimated 수열들 s(dt+1), $0{\leq}l<(p^{2k}+1)/2$가 존재한다. 이 논문에서는 s(t)와 s(dt+l), $0{\leq}l<(p^{2k}+1)/2$ 사이의 상호상관 값이 $\{-1,-1{\pm}\sqrt{p^n},-1+2\sqrt{p^n}\}$과 같음을 보이고, 상호 상관 값의 분포를 유도하였다.

• 대한수학회보
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• 제42권2호
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• pp.245-256
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• 2005

We consider the second-order nonlinear difference equation (1) $$\Delta(a_nh(x_{n+1}){\Delta}x_n)+p_{n+1}f(x_{n+1})=0,\;n{\geq}n_0$$ where ${a_n},\;{p_n}$ are sequences of integers with $a_n\;>\;0,\;\{P_n\}$ is a real sequence without any restriction on its sign. hand fare real-valued functions. We obtain some necessary conditions for (1) existing nonoscillatory solutions and sufficient conditions for (1) being oscillatory.

• Journal of applied mathematics & informatics
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• 제41권1호
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• pp.1-9
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• 2023

In the present paper, two theorems on absolute matrix summability of infinite series are generalized for the 𝜑 - |A, p_n|_k summability method using quasi 𝛽-power increasing sequences instead of almost increasing sequences.

• Journal of Plant Biotechnology
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• 제2권2호
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• pp.101-108
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• 2000

The liverwort Pellia borealis is a diploid, monoecious, allopolypliod species (n=18) that as it was postulated, originated after hybridization and duplication of chromosome sets of two cryptic species: Pellia epiphylta-species N (n=9) and Pellia epiphylla-species 5 (n=9). Our recent results have supported the allopolyploid origin of P.borealis. We have shown that the nuclear genome of P.borealis consists of two nuclear genomes: one derived from P.epiphylla-species N and the other from P.epiphylla-species 5. In this paper we show the origin of chloroplast and mitochondrial genomes in an allopolyploid species P.borealis. To our knowledge there is no information concerning the way of mitochondria and chloroplast inheritance in Brophyta. Using an allopolyploid species of p. borealis as a model species we have decided to look into chloroplast and mitochondrial genomes of P.borealis, P.epiphylla-species N and P.epiphylla-species S for nucleotide sequences that would allow us to differentiate between both cryptic species and to identify the origin of organelle genomes in the alloploid species. We have amplified and sequenced a chloroplast $tRNA^{Leu}$ gene (anticodon UAA) containing an intron that has shown to be highly variable in a nucleotide sequence and used for plant population genetics. Unfortunately these sequences were identical in all three liverwort species tested. The analysis of the nucleotide sequence of chloroplast, an intron containing $tRNA^{Gly}$ (anticodon UCC) genes, gave expected results: the intron nucleotide sequence was identical in the case of both P.borealis and P.epiphyllaspecies N, while the sequence obtained from P.epiphyllasperies S was different in several nucleotide positions. These results were confirmed by the nucleotide sequence of another chloroplast molecular marker the chloroplast, an intron-contaning $tRNA^{Lys}$ gene (anticodon UUU). We have also sequenced mitochondrial, an intron-containing $tRNA^{Ser}$ gene (anticodon GCU) in all three liverwort species. In this case we found that, as in the case of the chloroplast genome, P.borealis mitochondrial genome was inherited from P.epiphylla-species N. On the basis of our results we claim that both organelle genomes of P.borealis derived from P.epiphylla-species N.

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

• 호남수학학술지
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• 제30권3호
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• pp.479-486
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• 2008

Let {${\Omega}$, F, P} be a probability space and {$X_n{\mid}n{\geq}1$} be a sequence of random variables defined on it. We study the Hajeck-Renyi-type inequality for p..mixing random variable sequences and obtain the strong law of large numbers by using this inequality. We also consider the strong law of large numbers for weighted sums of ${\tilde{\rho}}$-mixing sequences.

• 정보보호학회논문지
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• 제12권1호
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• pp.21-32
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• 2002

본 논문에서는 소수 p의 멱승인 q에 대해서 주기 $q_n$-1인 q진 시퀸스(d-동차함수)로부터 Singer 파라미터 equation omitted를 갖는 새로운 순회차집합을 생성하였다. q가 3의 멱승일 때, Helleseth, Kumar, Martinsen의 주기가 $q_n$-1이고, 이상적인 자기상관성질을 갖는 3진 시퀸스로부터 Singer 파라미터 equation omitted를 갖는 새로운 순회 차집합을 생성시킨다.