• Korean Journal of Mathematics
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• v.17 no.2
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• pp.147-154
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• 2009

In this paper, we consider a new sequence called by the C-sequence of the Riordan array. It allows us to find a simple proof for several combinatorial identities. Further, we prove that a C-sequence characterizes Bell subgroup of the Riordan group.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.923-931
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• 2014

Let x be an element of a group G and be an automorphism of G. Then for a positive integer n, the autocommutator $[x,_n{\alpha}]$ is defined inductively by $[x,{\alpha}]=x^{-1}x^{\alpha}=x^{-1}{\alpha}(x)$ and $[x,_{n+1}{\alpha}]=[[x,_n{\alpha}],{\alpha}]$. We call the group G to be n-auto-Engel if $[x,_n{\alpha}]=[{\alpha},_nx]=1$ for all $x{\in}G$ and every ${\alpha}{\in}Aut(G)$, where $[{\alpha},x]=[x,{\alpha}]^{-1}$. Also, for any integer $n{\neq}0$, 1, a group G is called an n-auto-Bell group when $[x^n,{\alpha}]=[x,{\alpha}^n]$ for every $x{\in}G$ and each ${\alpha}{\in}Aut(G)$. In this paper, we investigate the properties of such groups and show that if G is an n-auto-Bell group, then the factor group $G/L_3(G)$ has finite exponent dividing 2n(n-1), where $L_3(G)$ is the third term of the upper autocentral series of G. Also, we give some examples and results about n-auto-Bell abelian groups.

• Korean Journal of Mathematics
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• v.15 no.2
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• pp.177-183
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• 2007

In this paper, we study the Riordan matrices with the A-sequence (1,1,...,1,0,...) where 1's appear in m times. As a result, we obtain new Riordan matrices and give their lattice path interpretations.

• 대한예방의학회:학술대회논문집
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• 1994.02a
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• pp.549-559
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• 1994

A subgroup or workers from a secondary lead smelter was defined to include those with blood lead levels not exceeding $80{\mu}g/100\;ml$ and with no pest history of elevated blood lead. Central nervous system symptoms (tiredness, sleeplessness, irritability, headache) were reported by 55% of the group and muscle and joint pain by 39%. Zinc proteporphyrin (ZPP) levels were elevated in 71% or cases. Low hemoglobin levels (less than 14 gm/l00 ml) were round in more than a third of the workers. While BUN and creatinine were mostly in the normal range, there - nevertheless n correlation between ZPP and both BUN and creatinine. Reduced nerve-conduction velocities were present in 25% or the group; this was not significantly different from findings in Ii control group. The data indicate that n blood level of $80{\mu}g/100\;ml$ is an inappropriate biological guide in the prevention or lead disease.