On a Problem in Diophantine Approximation

We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.Comment: 16 page

Asymptotics of discrete β\beta-corners processes via two-level discrete loop equations

We introduce and study stochastic particle ensembles which are natural discretizations of general $\beta$-corners processes. We prove that under technical assumptions on a general analytic potential the global fluctuations for the difference between two adjacent levels are asymptotically Gaussian. The covariance is universal and remarkably differs from its counterpart in random matrix theory. Our main tools are certain novel algebraic identities that are two-level analogues of the discrete loop equations.Comment: 102 pages, 2 figures. Fixed a typo in v1 that propagated all the way to the main result -- Theorem 1.7 (Theorem 1.9 in v1). Assumption 6 in Section 3 has been removed and Assumption 5 relaxed. A new appendix has been added. Several applications have been added in Section 6 (Section 7 in v1). In Section 7 (Section 6 in v1) the restriction $\theta \geq 1$ has been relaxed to $\theta > 0

Oral hygiene levels in primary molars restored with preformed metal crowns

INTRODUCTION: The choice of restoration material, the general health of the individual, and the distribution of caries in the different age groups is related to the level and the assessment of oral hygiene. In the treatment plan for these patients a preventive regime is necessary to be added, which includes instructions for oral hygiene improvement.AIM: The aim of this article is to examine the level of oral hygiene in primary molars restored with preformed metal crowns (PMCs) and glass-ionomer cement (GIC).MATERIALS AND METHODS: Object of the clinical study were 100 teeth with approximal dentin lesions on primary molars in 5- to 7-year-old children. The plaque index (PI) and the gingival index (GI) of Silness-Löe were used.RESULT: In the current study, Silness-Löе PI was assessed before PMC/GIC application, on the 6th month and after the first year of GIC/PMC placement. Around teeth restored with GIC more dental plaque was observed compared with the crowned teeth. PI was 1.35 for the filled teeth and 0.97 for the crowned ones. In both cases we reported moderate plaque accumulation and fair oral hygiene in the area of the first and second primary molar. The higher value of PI in the teeth restored with GIC was due to the higher rate of the minor failures of the fillings, which leads to plaque accumulation. There was no statistically significant difference in the GI for the GIC/PMC restorations at the 6th month and the first year after their application (p > 0.05).CONCLUSION: As a result, we concluded that PI for the teeth with PMCs was lower compared with the one in the natural control group of teeth. However, the average values of GI were significantly higher for the teeth with PMCs

Digital analysis of teeth treated with the Hall technique

INTRODUCTION: The information about digital examination provided by the scientific literature is quite insufficient. Therefore, digital examination of the occlusion is an object of analysis not only in Bulgaria but in other countries as well. No evidence for digital occlusal analysis on Hall-crowned teeth was found in the prosthetic part of the pediatric dentistry.AIM: The aim of this article is to conduct a study on the occlusal balance with T-scan after treatment with preformed metal crowns (PMCs) using the Hall technique.MATERIALS AND METHODS: Object of the clinical study were 50 crowned primary teeth. Unit of observation with the T-scan 8 system were occlusal articulation relationships in primary and early mixed dentition after the Hall technique.RESULTS: The results confirmed equal occlusal relationships in both sides – the crowned teeth compared with the symmetrical natural teeth. The occlusal contacts were with a similar value of the summary masticatory force compared with the control group of natural teeth.CONCLUSION: The received data confirmed that the restoration of decayed teeth with preformed metal crowns maintained the occlusal harmony in the dentition