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NORMAL SYSTEMS OF COORDINATES ON MANIFOLDS OF CHERN-MOSER TYPE
Schmalz, Gerd,Spiro, Andrea Korean Mathematical Society 2003 대한수학회지 Vol.40 No.3
It is known that the CR geometries of Levi non-degen-erate hypersurfaces in $\C^n$ and of the elliptic or hyperbolic CR submanifolds of codimension two in $\C^4$ share many common features. In this paper, a special class of normalized coordinates is introduced for any CR manifold M which is one of the above three kinds and it is shown that the explicit expression in these coordinates of an isotropy automorphism $f{\in}Aut(M)_o {\subset}Aut(M),\;o{\in}M$, is equal to the expression of a corresponding element of the automorphism group of the homogeneous model. As an application of this property, an extension theorem for CR maps is obtained.
Schmalz, Gerhard,Kummer, Max Kristian,Kottmann, Tanja,Rinke, Sven,Haak, Rainer,Krause, Felix,Schmidt, Jana,Ziebolz, Dirk Korean Academy of Periodontology 2018 Journal of Periodontal & Implant Science Vol.48 No.4
Purpose: The aim of this retrospective cross-sectional study was to evaluate whether salivary findings of active matrix-metalloproteinase 8 (aMMP-8) chairside (point of care; POC) tests were associated with periodontal risk assessment parameters in patients receiving supportive periodontal therapy (SPT). Methods: A total of 125 patients receiving regular SPT were included, and their records were examined. The following inclusion criteria were used: a diagnosis of chronic periodontitis, at least 1 non-surgical periodontal treatment (scaling and root planning) with following regular SPT (minimum once a year), at least 6 remaining teeth, and clinical and aMMP-8 findings that were obtained at the same appointment. In addition to anamnestic factors (e.g., smoking and diabetes), oral hygiene indices (modified sulcus bleeding index [mSBI] and approximal plaque index), periodontal probing depth simultaneously with bleeding on probing, and dental findings (number of decayed, missing, and filled teeth) were recorded. Salivary aMMP-8 levels were tested using a commercial POC test system (Periomarker, Hager & Werken, Duisburg, Germany). Statistical analysis was performed using the t-test, Mann-Whitney U test, Fisher's exact test, and ${\chi}^2$ test, as appropriate (P<0.05). Results: Only the mSBI was significantly associated with positive salivary aMMP-8 findings (aMMP-8 positive: $27.8%{\pm}20.9%$ vs. aMMP-8 negative: $18.0%{\pm}14.5%$; P=0.017). No significant associations were found between aMMP-8 and smoking, diabetes, periodontal parameters, or parameters related to the maintenance interval (P>0.05). Conclusions: Salivary aMMP-8 chairside findings were not associated with common parameters used for periodontal risk assessment in patients receiving SPT. The diagnostic benefit of POC salivary aMMP-8 testing in risk assessment and maintenance interval adjustment during SPT remains unclear.
Gerhard Schmalz,Max Kristian Kummer,Tanja Kottmann,Sven Rinke,Rainer Haak,Felix Krause,Jana Schmidt,Dirk Ziebolz 대한치주과학회 2018 Journal of Periodontal & Implant Science Vol.48 No.4
Purpose: The aim of this retrospective cross-sectional study was to evaluate whether salivary findings of active matrix-metalloproteinase 8 (aMMP-8) chairside (point of care; POC) tests were associated with periodontal risk assessment parameters in patients receiving supportive periodontal therapy (SPT). Methods: A total of 125 patients receiving regular SPT were included, and their records were examined. The following inclusion criteria were used: a diagnosis of chronic periodontitis, at least 1 non-surgical periodontal treatment (scaling and root planning) with following regular SPT (minimum once a year), at least 6 remaining teeth, and clinical and aMMP-8 findings that were obtained at the same appointment. In addition to anamnestic factors (e.g., smoking and diabetes), oral hygiene indices (modified sulcus bleeding index [mSBI] and approximal plaque index), periodontal probing depth simultaneously with bleeding on probing, and dental findings (number of decayed, missing, and filled teeth) were recorded. Salivary aMMP-8 levels were tested using a commercial POC test system (Periomarker, Hager & Werken, Duisburg, Germany). Statistical analysis was performed using the t-test, Mann-Whitney U test, Fisher's exact test, and χ2 test, as appropriate (P<0.05). Results: Only the mSBI was significantly associated with positive salivary aMMP-8 findings (aMMP-8 positive: 27.8%±20.9% vs. aMMP-8 negative: 18.0%±14.5%; P=0.017). No significant associations were found between aMMP-8 and smoking, diabetes, periodontal parameters, or parameters related to the maintenance interval (P>0.05). Conclusions: Salivary aMMP-8 chairside findings were not associated with common parameters used for periodontal risk assessment in patients receiving SPT. The diagnostic benefit of POC salivary aMMP-8 testing in risk assessment and maintenance interval adjustment during SPT remains unclear. Keywords: Maintenance; Metalloproteinase
Normal systems of coordinates on manifolds of Chern-Moser type
Gerd Schmalz,Andrea Spiro 대한수학회 2003 대한수학회지 Vol.40 No.3
It is known that the CR geometries of Levi non-degen-erate hypersurfaces in $\C^n$ and of the elliptic or hyperbolic CR submanifolds of codimension two in $\C^4$ share many common features. In this paper, a special class of normalized coordinates is introduced for any CR manifold $M$ which is one of the above three kinds and it is shown that the explicit expression in these coordinates of an isotropy automorphism $f \in \Aut(M)_o \subset \Aut(M)$, $o \in M$, is equal to the expression of a corresponding element of the automorphism group of the homogeneous model. As an application of this property, an extension theorem for CR maps is obtained.
On the generalization of Forelli’s theorem
Joo, Jae-Cheon,Kim, Kang-Tae,Schmalz, Gerd Springer-Verlag 2016 Mathematische Annalen Vol. No.
<P>The purpose of this paper is to present a solution to perhaps the final remaining case in the line of study concerning the generalization of Forelli's theorem on the complex analyticity of the functions that are: (i) smooth at a point, and (ii) holomorphic along the complex integral curves generated by a contracting holomorphic vector field with an isolated zero at the same point.</P>
Sven Rinke,Marc Nordlohne,Andreas Leha,Stefan Renvert,Gerhard Schmalz,Dirk Ziebolz 대한치주과학회 2020 Journal of Periodontal & Implant Science Vol.50 No.3
Purpose: This practice-based cross-sectional study aimed to investigate whether common risk indicators for peri-implant diseases were associated with peri-implant mucositis and peri-implantitis in patients undergoing supportive implant therapy (SIT) at least 5 years after implant restoration. Methods: Patients exclusively restored with a single implant type were included. Probing pocket depth (PPD), bleeding on probing (BOP), suppuration, and radiographic bone loss (RBL) were assessed around implants. The case definitions were as follows: peri-implant mucositis: PPD ≥4 mm, BOP, no RBL; and peri-implantitis: PPD ≥5 mm, BOP, RBL ≥3.5 mm. Possible risk indicators were compared between patients with and without mucositis and peri-implantitis using the Fisher exact test and the Wilcoxon rank-sum test, as well as a multiple logistic regression model for variables showing significance (P<0.05). Results: Eighty-four patients with 169 implants (observational period: 5.8±0.86 years) were included. A patient-based prevalence of 52% for peri-implant mucositis and 18% for peri-implantitis was detected. The presence of 3 or more implants (odds ratio [OR], 4.43; 95 confidence interval [CI], 1.36–15.05; P=0.0136) was significantly associated with an increased risk for mucositis. Smoking was significantly associated with an increased risk for peri-implantitis (OR, 5.89; 95% CI, 1.27–24.58; P=0.0231), while the presence of keratinized mucosa around implants was associated with a lower risk for peri-implantitis (OR, 0.05; 95% CI, 0.01–0.25; P<0.001). Conclusions: The number of implants should be considered in strategies to prevent mucositis. Furthermore, smoking and the absence of keratinized mucosa were the strongest risk indicators for peri-implantitis in patients undergoing SIT in the present study.
Rinke, Sven,Nordlohne, Marc,Leha, Andreas,Renvert, Stefan,Schmalz, Gerhard,Ziebolz, Dirk Korean Academy of Periodontology 2020 Journal of Periodontal & Implant Science Vol.50 No.3
Purpose: This practice-based cross-sectional study aimed to investigate whether common risk indicators for peri-implant diseases were associated with peri-implant mucositis and peri-implantitis in patients undergoing supportive implant therapy (SIT) at least 5 years after implant restoration. Methods: Patients exclusively restored with a single implant type were included. Probing pocket depth (PPD), bleeding on probing (BOP), suppuration, and radiographic bone loss (RBL) were assessed around implants. The case definitions were as follows: peri-implant mucositis: PPD ≥4 mm, BOP, no RBL; and peri-implantitis: PPD ≥5 mm, BOP, RBL ≥3.5 mm. Possible risk indicators were compared between patients with and without mucositis and peri-implantitis using the Fisher exact test and the Wilcoxon rank-sum test, as well as a multiple logistic regression model for variables showing significance (P<0.05). Results: Eighty-four patients with 169 implants (observational period: 5.8±0.86 years) were included. A patient-based prevalence of 52% for peri-implant mucositis and 18% for peri-implantitis was detected. The presence of 3 or more implants (odds ratio [OR], 4.43; 95 confidence interval [CI], 1.36-15.05; P=0.0136) was significantly associated with an increased risk for mucositis. Smoking was significantly associated with an increased risk for peri-implantitis (OR, 5.89; 95% CI, 1.27-24.58; P=0.0231), while the presence of keratinized mucosa around implants was associated with a lower risk for peri-implantitis (OR, 0.05; 95% CI, 0.01-0.25; P<0.001). Conclusions: The number of implants should be considered in strategies to prevent mucositis. Furthermore, smoking and the absence of keratinized mucosa were the strongest risk indicators for peri-implantitis in patients undergoing SIT in the present study.