• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.739-777
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• 2004

An analogue of the Gram's inequality for n-inner product spaces is given. Further, a number of inequalities involving Gram's determinant are stated and proved in terms of n-inner products.

• Journal of Periodontal and Implant Science
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• v.35 no.4
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• pp.907-919
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• 2005

Porphyromonas gingivalis is a gram negative. black-pigmented anaerobe, associated with periodontitis & peri-implantitis. Fimbriae(fimA) of P. gingivalis are filamentous components on the cell surface and important in the colonization and invasion of periodontal tissue. But all P. gnigivalis strains don't have equal pathogenicity, inequality among strains originates from different fimA genotype. P. gnigivalis fimA gene encoding fimbrillin(structural subunit of fimbriae) has been classified into 5 genotypes(types I to V) based on the nucleotide sequences. In the present study, we examined the prevalence of these fimA genotypes in patients with dental implant and the relationship between prevalence of these genotypes and a condition of peri-implant tissue. Dental plaque specimens obtained from 189 peri-implant sulci of 97 patients with dental implants were analyzed by 16S rRNA fimA gene-directed PCR assay. P. gingivalis were detected in 86.2% of the alll samples. Among the P. gingivalis-positive samples, a significant difference in the occurrence of typeII was observed between test and the two control groups. In two control groups, typeII fimA were detected in 6.3%(PD<5mm/BOP-). 18.7%(PD<5mm/BOP+). In the test $group(PD{\geqq}5mm/BOP+)$, type II fimA genotype were detected most frequently in 50.0% . And a correlation between specific fimA types and peri-implantitis was found in $typeII(R^2=l.105)$. These results suggest that P. gingivalis strains that possess typeII fimA are gradually increased, as a condition of peri-implant tissue is getting complicated and are closely associated with peri-implant health status. We speculate that these organisms be involved in peri-implantitis