• 충청수학회지
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• 제24권2호
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• pp.147-162
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• 2011

In this paper, we investigate the Ulam-Hyers stability of $C^{\star}$-ternary algebra 3-homomorphisms for the functional equation $$f(x_1+x_2,y_1+y_2,z_1+z_2)=\;\displaystyle\sum_{1{\leq}i,j,k{\leq}2}\;f(x_i,y_j,z_k)$$ in $C^{\star}$-ternary algebras.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제24권2호
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• pp.99-107
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• 2017

Shokri et al. [14] proved the Hyers-Ulam stability of bihomomorphisms and biderivations by using the direct method. It is easy to show that the definition of biderivations on normed 3-Lie algebras is meaningless and so the results of [14] are meaningless. In this paper, we correct the definition of biderivations and the statements of the results in [14], and prove the corrected theorems.

• Journal of applied mathematics & informatics
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• 제5권3호
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• pp.819-826
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• 1998

The purpose of this paper is to prove the following results; (1) Let R be a prime ring of char $(R)\neq 2$ and I a nonzero left ideal of R. The existence of a nonzero symmetric bi-derivation D : $R\timesR\;\longrightarrow\;$ such that d is sew-commuting on I where d is the trace of D forces R to be commutative (2) Let m and n be integers with $m\;\neq\;0.\;or\;n\neq\;0$. Let R be a noncommutative prime ring of char$ (R))\neq \; 2-1\; p_1 \;n_1$ where p is a prime number which is a divisor of m, and I a nonzero two-sided ideal of R. Let $D_1$ ; $R\;\times\;R\;\longrightarrow\;and\;$ $D_2\;:\;R\;\times\;R\;longrightarrow\;R$ be symmetric bi-derivations. Suppose further that there exists a symmetric bi-additive mapping B ; $R\;\times\;R\;\longrightarrow\;and\;$ such that $md_1(\chi)\chi ＋ n\chi d_2(\chi)=f(\chi$) holds for all $\chi$$\in$I, where $d_1 \;and\; d_2$ are the traces of $D_1 \;and\; D_2$ respectively and f is the trace of B. Then we have $D_1=0 \;and\; D_2=0$.

• Journal of Astronomy and Space Sciences
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• 제27권3호
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• pp.221-230
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• 2010

A 4+12+16 amplitude phase shift keying (APSK) modulation outperforms other 32-APSK modulations in a nonlinear additive white Gaussian noise (AWGN) channel because of its intrinsic robustness against AM/AM and AM/PM distortions caused by the nonlinear characteristics of a high-power amplifier. Thus, this modulation scheme has been adopted in the digital video broadcasting-satellite2 European standard. And it has been considered for high rate transmission of telemetry data on deep space communications in consultative committee for space data systems which provides a forum for discussion of common problems in the development and operation of space data systems. In this paper, we present an improved bits-to-symbol mapping scheme with a better bit error rate for a 4+12+16 APSK signal in a nonlinear AWGN channel and propose a simple signal detection algorithm for the 4+12+16 APSK from the presented bit mapping.

• Korean Journal of Mathematics
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• 제16권3호
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• pp.413-424
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• 2008

In [21], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\parallel}\frac{1}{n}\sum\limits_{i=1}^{n}x_i{\parallel}^2+\sum\limits_{i=1}^{n}{\parallel}x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j{\parallel}^2=\sum\limits_{i=1}^{n}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\dots},x_n{\in}V$. We consider the functional equation $$nf(\frac{1}{n}\sum\limits^n_{i=1}x_i)+\sum\limits_{i=1}^{n}f(x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j)=\sum\limits_{i=1}^nf(x_i)$$ Using fixed point methods, we prove the generalized Hyers-Ulam stability of the functional equation $$(1)\;2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})=f(x)+f(y)$$.

• Reproductive and Developmental Biology
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• 제28권2호
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• pp.107-112
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• 2004

Molecular genetic markers were genotyped used to detect chromosomal regions which contain economically important traits such as growth traits in pigs. Three generation resource population was constructed from a cross between the Korean native boars and Landrace sows. A total of 193 F2 animals from intercross of F1 were produced. Phenotypic data on 7 traits, birth weight, body weight at 3, 5, 12, 30 weeks of age, live empty weight were collected for F2 animals. Animals including grandparents (F0), parents (F1), offspring (F2) were genotyped for 194 microsatellite markers covering from chromosome 1 to 18. Quantitative trait locus analyses were performed using interval mapping by regression under line-cross model. To characterize presence of imprinting, genetic full model in which dominance, additive and imprinting effect were included was fitted in this analysis. Significance thresholds were determined by permutation test. Using imprinting full model, four QTL with expression of imprinted effect were detected at 5% chromosome-wide significance level for growth traits on chromosome 1, 5, 7, 13, 14, and 16.

• Korean Journal of Mathematics
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• 제21권2호
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• pp.161-170
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• 2013

Bae and W. Park [3] proved the Hyers-Ulam stability of bi-homomorphisms and bi-derivations in $C^*$-ternary algebras. It is easy to show that the definitions of bi-homomorphisms and bi-derivations, given in [3], are meaningless. So we correct the definitions of bi-homomorphisms and bi-derivations. Under the conditions in the main theorems, we can show that the related mappings must be zero. In this paper, we correct the statements and the proofs of the results, and prove the corrected theorems.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권3호
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• pp.237-246
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• 2016

Ebadian et al. proved the Hyers-Ulam stability of bimultipliers and Jordan bimultipliers in C*-ternary algebras by using the fixed point method. Under the conditions in the main theorems for bimultipliers, we can show that the related mappings must be zero. Moreover, there are some mathematical errors in the statements and the proofs of the results. In this paper, we correct the statements and the proofs of the results, and prove the corrected theorems by using the direct method.

• Journal of Applied and Pure Mathematics
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• 제4권3_4호
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• pp.99-105
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• 2022

The objective of this research paper is to prove that an additive mapping T from a semiprime ring R to itself will be centralizer having a suitable torsion restriction on R if it satisfy any one of the following algebraic equations (a) 2T(xⁿyⁿxⁿ) = T(xⁿ)yⁿxⁿ + xⁿyⁿT(xⁿ) (b) 3T(xⁿyⁿxⁿ) = T(xⁿ)yⁿxⁿ+xⁿT(yⁿ)xⁿ+xⁿyⁿT(xⁿ) for every x, y ∈ R. Further, few extensions of these results are also presented in the framework of *-ring.

• 한국산림과학회지
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• 제95권4호
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• pp.483-494
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• 2006

테다소나무 7-1037 클론에서 얻은 반형매 풍매 차대의 반수체 DNA에 대해 AFLP 표지자 분석을 수행하여 유전연관지도를 작성하고, 6년생 때의 수고 및 흉고직경 생장에 대한 QTL mapping을 수행하였다. 121개 AFLP 표지자로 전체 연관거리 1,869 cM, marker간 평균거리 18.5 cM의 20개 framework map을 작성하였다. Composite interval mapping 방법에 의해 수고 생장의 전체 표현형 변이의 5.9%를 설명할 수 있는 l개의 QTL과 흉고직경 생장 변이의 3.9~5.6%를 설명할 수 있는 3개의 QTL을 동정하였으며, QTL 간의 상호작용 효과는 없었다. 수고 생장에 대한 QTL의 유전적 효과는 39.6cm이었고, 흉고직경 생장에서는 7.20~9.41 mm인 것으로 추정되었다. 상기 QTL들과 가장 가깝게 연관되어 있는 표지자를 이용하여 대립유전자 치환의 평균효과(average effect of gene substitution)를 산출한 결과, 수고생장에서는 44.3 cm, 흉고직경 생장에서는 8.38~11.81 mm이었다. 테다소나무의 생장에 대한 가계내 개체유전력을 0.2 이하로 가정한다면, 본 연구에서 확인된 QTL은 7-1037 클론의 반형매 풍매 차대가 보유한 상가적 유전분산의 26.8%를 설명할 수 있어 표현형에 의한 개체선발보다 선발효율에서 5배나 높은 것으로 추정되었다. 본 연구에서 제시된 반형매 풍매 차대를 이용한 QTL mapping 분석은 채종원을 기반으로 하는 선발육종 사업에서 필요한 breeding value 등의 정보를 제공한다는 측면에서 인공교배 가계를 이용한 기타의 QTL 분석에 비해 보다 현실적이고 적용성이 높은 방법론이라 생각된다.