Exogenous Liquidity Supply in Presence of Repudiation Risk and Private Asset RecoveryInternational Financial Integration

Current paper proposes an extension of the seminal model by Holmstrom Tirole (1997) of the exogenous liquidity supply in presence of moral hazard to the case that includes private asset recovery under the limited liability of the entrepreneur. In our model partial private recovery applies to the financial assets that are considered to be sunk by the investors. In this context, a distressed firm seeking second round financing for its investment project is able, within a limited range of shocks, to increase its private payoff in case of the project default. As the result, unable to use these funds to raise additional liquidity, the distressed firms face a reduced range of acceptable shock values relative to Holmstrom Tirole set up. At the same time, domestic securities markets, even in absence of aggregate uncertainty, are shown to hold insufficient liquidity. As the result, distressed firms individually are unable to counter the shocks by holding claims against other firms even in case of the financial intermediation.

On the Cauchy problem for a nonlinearly dispersive wave equation

We establish the local well-posedness for a new nonlinearly dispersive wave equation and we show that the equation has solutions that exist for indefinite times as well as solutions which blowup in finite times. Furthermore, we derive an explosion criterion for the equation and we give a sharp estimate from below for the existence time of solutions with smooth initial data.Comment: arxiv version is already officia

Marginal and Conditional Distribution Estimation from Double-Sampled Semi-Competing Risks Data

Informative dropout is a vexing problem for any biomedical study. Most existing statistical methods attempt to correct estimation bias related to this phenomenon by specifying unverifiable assumptions about the dropout mechanism. We consider a cohort study in Africa that uses an outreach programme to ascertain the vital status for dropout subjects. These data can be used to identify a number of relevant distributions. However, as only a subset of dropout subjects were followed, vital status ascertainment was incomplete. We use semi-competing risk methods as our analysis framework to address this specific case where the terminal event is incompletely ascertained and consider various procedures for estimating the marginal distribution of dropout and the marginal and conditional distributions of survival. We also consider model selection and estimation efficiency in our setting. Performance of the proposed methods is demonstrated via simulations, asymptotic study and analysis of the study data

In situ anticaries efficacy of dentifrices with different formulations – A pooled analysis of results from three randomized clinical trials

Objectives Data generated from three similar in situ caries crossover studies presented the opportunity to conduct a pooled analysis to investigate how dentifrice formulations with different fluoride salts and combinations at concentrations of 1400–1450 ppm F, different abrasive systems and in some cases, carbomer (Carb), affect enamel caries lesion remineralization and fluoridation. Methods Subjects continuously wore modified partial dentures holding two gauze-covered partially-demineralized human enamel specimens for 14 days and brushed 2×/day with their assigned dentifrice: Study 1: sodium fluoride (NaF)/Carb/silica, NaF/silica, NaF + monofluorophosphate (MFP)/chalk; Study 2: NaF/Carb/silica, NaF + MFP/dical, amine fluoride (AmF)/silica; Study 3: NaF/Carb/silica, NaF + stannous fluoride (SnF2)/silica/hexametaphosphate (HMP). All studies included Placebo (0 ppm F) and/or dose-response controls (675 ppm F as NaF [675F-NaF]) ±Carb. Specimens were evaluated for percentage surface microhardness recovery (SMHR) and enamel fluoride uptake (EFU). Results All 1400–1450 ppm F dentifrices except NaF + SnF2/silica/HMP provided significantly greater lesion remineralization than Placebo (p < 0.0001): differences in SMHR ranged from 17.46% (NaF + MFP/dical) to 26.66% (AmF/silica). For EFU (back-transformed log EFU), all 1400–1450 ppm F dentifrices gave significant fluoride uptake compared to Placebo (p < 0.0001): increases in EFU ranged from 4.95 μg F/cm2 (NaF + SnF2/silica/HMP) to 16.32 μg F/cm2 (NaF/carb/silica). Dentifrices containing NaF or AmF as sole fluoride source provided the greatest remineralization and fluoridation; Carb addition did not alter fluoride efficacy; some excipients appeared to interfere with the cariostatic action of fluoride. Treatments were generally well-tolerated with ≤4 treatment-related adverse events per study. Conclusion Commercially available fluoride dentifrices varied greatly in their ability to remineralize and fluoridate early caries lesions. Clinical significance Fluoride dentifrices are the most impactful anticaries modality worldwide. While clinical caries trials have not consistently shown the superiority of one formulation over another, these findings using a sensitive in situ caries model indicated that dentifrices containing NaF or AmF as the sole fluoride source provided the greatest remineralization and fluoridation benefits

Nonexistence of self-similar singularities for the 3D incompressible Euler equations

We prove that there exists no self-similar finite time blowing up solution to the 3D incompressible Euler equations. By similar method we also show nonexistence of self-similar blowing up solutions to the divergence-free transport equation in $\Bbb R^n$. This result has direct applications to the density dependent Euler equations, the Boussinesq system, and the quasi-geostrophic equations, for which we also show nonexistence of self-similar blowing up solutions.Comment: This version refines the previous one by relaxing the condition of compact support for the vorticit

Universality of Probability Distributions Among Two-Dimensional Turbulent Flows

We study statistical properties of two-dimensional turbulent flows. Three systems are considered: the Navier-Stokes equation, surface quasi-geostrophic flow, and a model equation for thermal convection in the Earth's mantle. Direct numerical simulations are used to determine 1-point fluctuation properties. Comparative study shows universality of probability density functions (PDFs) across different types of flow. Especially for the derivatives of the ``advected'' quantity, the shapes of the PDFs are the same for the three flows, once normalized by the average size of fluctuations. Theoretical models for the shape of PDFs are briefly discussed.Comment: 5 pages, 7 figure