• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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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.

• The Pure and Applied Mathematics
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• v.24 no.2
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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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• v.5 no.3
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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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• v.27 no.3
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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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• v.16 no.3
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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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• v.28 no.2
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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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• v.21 no.2
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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.

• The Pure and Applied Mathematics
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• v.23 no.3
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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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• v.4 no.3_4
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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.

• Journal of Korean Society of Forest Science
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• v.95 no.4
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• pp.483-494
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• 2006

We conducted QTL mapping for 6-year growths of open-pollinated half-sib progenies from a selected clone 7-1037 in Pinus taeda. With an AFLP marker analysis on haploid DNA samples from the megagametophytes of the open-pollinated seeds, we constructed 20 framework maps spanning a total of 1,869 cM in total length and 18.5 cM in an average interval length between markers. Composite interval mapping reveals that one QTL explains 5.9% of the total phenotypic variation of height, and three QTLs account for 3.9~5.6% of the variation of diameter at breast height (DBH). There are no correlations between the QTLs. The genetic effects of the QTLs are 39.6 cm in height and 7.20~9.41 mm in DBH, respectively, The average effects of gene substitution of the markers closely linked with the QTLs are 44.3 cm in height and 8.38~11.81 m in DBH. Under an assumption that the within-family heritability for the growth traits of loblolly pine is less than 0.2, the QTLs account for 26.8% of the additive genetic variance of the progenies. In terms of relative selection efficiency, the individual selection based on QTL markers could be 5 times as high as phenotypic selection. The results in this study indicate that the QTL mapping method with open-pollinated half-sib family could be more practical and applicable to the conventional seed orchard-based selection work than other mapping methods with a single full-sib family, in particular from the viewpoint that it can provide crucial information for within-family individual selection such as breeding value.