• 한국수학교육학회지시리즈E:수학교육논문집
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• 제20권4호
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• pp.595-602
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• 2006

In this paper we study an application of elementary symmetric polynomials related to transformation of homogeneous symmetric polynomials, factorization of polynomials, solving equation using elementary symmetric polynomials at the level of school mathematics.

• East Asian mathematical journal
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• 제30권2호
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• pp.93-121
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• 2014

In this paper we study generating and proving methods of symmetric inequalities. We analyze various literatures related with proofs of symmetric inequalities. As a result, we can describe generating method of symmetric inequalities, and suggest some symmetric inequalities that are generated by using parameterization to elementary symmetric polynomials. And we are able to classify some proving methods, and show proofs of symmetric inequalities.

• 충청수학회지
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• 제23권3호
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• pp.471-479
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• 2010

For a complex regular Borel measure ${\mu}$ on ${\Omega}$ which is a subset of ${\mathbb{C}}^k$, where k is a positive integer we define the Toeplitz operator $T_{\mu}$ on a reproducing analytic space which comtains polynomials. Using every symmetric polynomial is a polynomial of elementary polynomials, we show that if $T_{\mu}$ has finite rank then ${\mu}$ is a finite linear combination of point masses.

• 대한수학회논문집
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• 제21권1호
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• pp.45-52
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• 2006

Every non-associative algebra L corresponds to its symmetric semi-Lie algebra $L_{[,]}$ with respect to its commutator. It is an interesting problem whether the equality $Aut{non}(L)=Aut_{semi-Lie}(L)$ holds or not [2], [13]. We find the non-associative algebra automorphism groups $Aut_{non}\; \frac\;{(WN_{0,0,1}_{[0,1,r_1...,r_p])}$ and $Aut_{non-Lie}\; \frac\;{(WN_{0,0,1}_{[0,1,r_1...,r_p])}$ where every automorphism of the automorphism groups is the composition of elementary maps [3], [4], [7], [8], [9], [10], [11]. The results of the paper show that the F-algebra automorphism groups of a polynomial ring and its Laurent extension make easy to find the automorphism groups of the algebras in the paper.