Stochastic inviscid shell models: well-posedness and anomalous dissipation

In this paper we study a stochastic version of an inviscid shell model of turbulence with multiplicative noise. The deterministic counterpart of this model is quite general and includes inviscid GOY and Sabra shell models of turbulence. We prove global weak existence and uniqueness of solutions for any finite energy initial condition. Moreover energy dissipation of the system is proved in spite of its formal energy conservation.Comment: v2 has updated introductio

Uniqueness for a Stochastic Inviscid Dyadic Model

For the deterministic dyadic model of turbulence, there are examples of initial conditions in $l^2$ which have more than one solution. The aim of this paper is to prove that uniqueness, for all $l^2$-initial conditions, is restored when a suitable multiplicative noise is introduced. The noise is formally energy preserving. Uniqueness is understood in the weak probabilistic sense.Comment: 13 pages, no figures. Submitted to the Proceedings of the American Mathematical Societ

The combined use of corticotomy and clear aligners: a case report

OBJECTIVE:   To describe an orthodontic treatment that combines an esthetic approach (clear aligners) with surgery (alveolar corticotomy). MATERIALS AND METHODS:   A patient with moderate dental crowding and Class I skeletal and molar relationships was selected. Orthodontic records of the patient were taken. Periodontal indexes, oral health-related quality of life (OHRQoL), and treatment time were evaluated. After we reflected a full-thickness flap beyond the teeth apices, the cortical bone was exposed on the buccal aspect and a modified corticotomy procedure was performed. Interproximal corticotomy cuts were extended through the entire thickness of the cortical layer, just barely penetrating into medullary bone. Orthodontic force was applied on the teeth immediately after surgery. RESULTS:   Total treatment time was 2 months. Periodontal indexes were improved after correction of crowding. A deterioration of OHRQoL was limited to 3 days following surgery. CONCLUSION:   This case report may encourage the use, limited to selected cases, of corticotomy associated with clear aligners to treat moderate crowding

Anomalous dissipation in a stochastic inviscid dyadic model

A stochastic version of an inviscid dyadic model of turbulence, with multiplicative noise, is proved to exhibit energy dissipation in spite of the formal energy conservation. As a consequence, global regular solutions cannot exist. After some reductions, the main tool is the escape bahavior at infinity of a certain birth and death process.Comment: Published in at http://dx.doi.org/10.1214/11-AAP768 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Anomalous dissipation in a stochastic inviscid dyadic model

A stochastic version of an inviscid dyadic model of turbulence, with multiplicative noise, is proved to exhibit energy dissipation in spite of the formal energy conservation. As a consequence, global regular solutions cannot exist. After some reductions, the main tool is the escape bahavior at infinity of a certain birth and death process.Comment: Published in at http://dx.doi.org/10.1214/11-AAP768 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Credibility of the Exchange Rate Regime: An Analysis trough “Derivatives” of the September 1992 Crisis

This paper argues that, in the September 1992 European currency crisis, market trends in derivatives, in terms of price volatility and change in volumes traded, might have represented an early indicator, in reference to the spot market, of the lack of confidence in the ability of the Italian Lira and the Sterling Pound to maintain their parities within the ERM. The assessment is made by comparing the daily data on Italian/English interbank rates with the implicit yield on short-term interest rate futures and with a maximum compatible with the ERM band created by means of German interbank rates and changes in the exchange ratesDerivatives; Exchange rates; Volatility

The association between Ponticulus Posticus and Dental Agenesis: a retrospective study

OBJECTIVE: Neural tube defects may increase the risk of an abnormal development of skull, vertebral column and teeth formation, including dental agenesis in non syndromic patients. The association between the presence of a congenital Dental Agenesis (DA) and the Atlantooccipital Ligament (AOL) calcification, known as "Ponticulus Posticus" (PP), as possible links can be investigated. DESIGN: After a systematic review of the scientific literature on this topic, two independent examiners assessed the AOL calcification in lateral cephalograms of 350 non syndromic patients(7-21 years old). The results were compared with a control group (non syndromic patients, without congenital missing teeth). RESULTS: The 16.3% of the population studied by cephalometric analysis revealed a prevalence rate of PP (both complete and partial) with a slight male predominance is seen, not statistically significant (χ square test = 0.09; p= 0.76). In both sexes complete PP is more observed. In the patients affected by DA the frequency of PP is the 66.6% (both complete than partial). The χ square test with Yates correction showed a significative difference(χ= 66.20; p value= 0.00) between PP in patients with DA compared to not affected by DA. CONCLUSIONS: PP is not an uncommon anomaly. Since orofacial pain like migraine and other symptoms are often associated to PP, during routine radiographic examination, if detected, it should be documented in patients' health record and with symptoms, further investigation should be sought for. These findings encourage to think there's an association between DA in non syndromic patients and neuro-crestal cells defects