A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation

We consider the problem of identifying sharp criteria under which radial $H^1$ (finite energy) solutions to the focusing 3d cubic nonlinear Schr\"odinger equation (NLS) $i\partial_t u + \Delta u + |u|^2u=0$ scatter, i.e. approach the solution to a linear Schr\"odinger equation as $t\to \pm \infty$. The criteria is expressed in terms of the scale-invariant quantities $\|u_0\|_{L^2}\|\nabla u_0\|_{L^2}$ and $M[u]E[u]$, where $u_0$ denotes the initial data, and $M[u]$ and $E[u]$ denote the (conserved in time) mass and energy of the corresponding solution $u(t)$. The focusing NLS possesses a soliton solution $e^{it}Q(x)$, where $Q$ is the ground-state solution to a nonlinear elliptic equation, and we prove that if $M[u]E[u]<M[Q]E[Q]$ and $\|u_0\|_{L^2}\|\nabla u_0\|_{L^2} < \|Q\|_{L^2}\|\nabla Q\|_{L^2}$, then the solution $u(t)$ is globally well-posed and scatters. This condition is sharp in the sense that the soliton solution $e^{it}Q(x)$, for which equality in these conditions is obtained, is global but does not scatter. We further show that if $M[u]E[u] \|Q\|_{L^2}\|\nabla Q\|_{L^2}$, then the solution blows-up in finite time. The technique employed is parallel to that employed by Kenig-Merle \cite{KM06a} in their study of the energy-critical NLS

Environmental assessment of flax straw production for non-wood pulp mills

Nowadays, there is an increasing interest for using non-woody fibres as raw materials for production of paper´s pulp. The present work aims to identify and quantify the environmental impacts associated with the production of flax fibres, through 3-year field experiment, carried out in Bologna and Pisa representative of the pedoclimatic characteristics of central Italy. Life Cycle Impact of “a one ton of fibre ready to be processed in a pulp mill” was assessed taking into account: farming, straw process (drying, scutching and baling) and transport. Inventory data for agricultural inputs and outputs were obtained directly from field experimentation and from bibliographic data about heat, transport and electricity consumption on straw processing. An economic allocation approach to assign impacts within flax seed and processed straw has been used. The CML baseline 2000 methodology was selected to quantify the potential environmental impact associated to the crops. Specifically, global warming (GWP), acidification (AP), eutrophication (EP) and photochemical oxidant formation (POP) were evaluated together with energy use (EU). Major impacts contribution arise from fertilizers use and straw processing. Cultivation phase of flax fibre at Pisa reported higher values (approximately 3 times greater) for all the impact categories. The lower impact in the flax cultivation scenario at Bologna was due to no use of mineral fertilizer and the higher flax-straw yield. It resulted also a strong reduction of the impacts with respect to those of hemp pulp in Spain as well as to the impacts of the conventional wood-pulp reported in Simapro. Furthermore, LCA tool aided to identify the materials and process that most affected the impacts: fertilizers use, diesel consumption and straw processing were identified as hot spots in both crops. Finally, non-wood pulp derived from Bologna´s Flax straw represents an opportunity to replace conventional wood pulp in Italian paper industry

Distorted Copulas: Constructions and Tail Dependence

Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1] the distortion C ψ: [0, 1]2 → [0, 1], C ψ(x, y) = ψ{C[ψ−1(x), ψ−1(y)]} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ that ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in a more flexible way families of copulas exhibiting different behavior in the tails

The dynamics of the 3D radial NLS with the combined terms

In this paper, we show the scattering and blow-up result of the radial solution with the energy below the threshold for the nonlinear Schr\"{o}dinger equation (NLS) with the combined terms iu_t + \Delta u = -|u|^4u + |u|^2u \tag{CNLS} in the energy space $H^1(\R^3)$. The threshold is given by the ground state $W$ for the energy-critical NLS: $iu_t + \Delta u = -|u|^4u$. This problem was proposed by Tao, Visan and Zhang in \cite{TaoVZ:NLS:combined}. The main difficulty is the lack of the scaling invariance. Illuminated by \cite{IbrMN:f:NLKG}, we need give the new radial profile decomposition with the scaling parameter, then apply it into the scattering theory. Our result shows that the defocusing, $\dot H^1$-subcritical perturbation $|u|^2u$ does not affect the determination of the threshold of the scattering solution of (CNLS) in the energy space.Comment: 46page

Doping, European Law and the Implications of Meca-Medina

The ruling of the European Court of Justice in the anti-doping case of Meca Medina v. The Commission has important implications for athletes, domestic governing bodies, international federations and supra-national actors such as WADA and the Court of Arbitration for Sport. Meca-Medina has been criticised as an unwelcome interference by the courts in the legitimate activities of sporting organisations, but after Bosman it was fanciful to argue that those organisations should be ‘above the law’ and the courts should have no jurisdiction over their activities. That said, there is a stark difference between the courts having jurisdiction over sports’ decisions and being willing to overturn them - the courts have been, and remain, willing to defer to the expertise of sporting organisations. However, the ECJ’s ruling in MOTOE confirms that the courts will intervene in appropriate circumstances. In order to avoid sanction on competition law grounds sports organisations must thus be able to justify their provisions on (for example) what is an unacceptable level of nandrolone, show that athletes’ fundamental rights such as the right to a fair hearing have been respected, and ensure that any sanctions imposed upon athletes who fall foul of doping regulations are proportionate to the offence committed

Nonexistence of extremals for the adjoint restriction inequality on the hyperboloid

We study the problem of existence of extremizers for the $L^2$ to $L^p$ adjoint Fourier restriction inequalities on the hyperboloid in dimensions 3 and 4, in which cases $p$ is an even integer. We will use the method developed by Foschi to show that extremizers do not exist.Comment: 32 pages. Correction for Theorem 1.2 and Proposition 7.5 and addition of Remark 1.

Stable self-similar blow-up dynamics for slightly L2L^2-supercritical generalized KdV equations

In this paper we consider the slightly $L^2$-supercritical gKdV equations $\partial_t u+(u_{xx}+u|u|^{p-1})_x=0$, with the nonlinearity $5<p<5+\varepsilon$ and $0<\varepsilon\ll 1$ . We will prove the existence and stability of a blow-up dynamic with self-similar blow-up rate in the energy space $H^1$ and give a specific description of the formation of the singularity near the blow-up time.Comment: 38 page

On non-local variational problems with lack of compactness related to non-linear optics

We give a simple proof of existence of solutions of the dispersion manage- ment and diffraction management equations for zero average dispersion, respectively diffraction. These solutions are found as maximizers of non-linear and non-local vari- ational problems which are invariant under a large non-compact group. Our proof of existence of maximizer is rather direct and avoids the use of Lions' concentration compactness argument or Ekeland's variational principle.Comment: 30 page

Design of a factorial experiment with randomization restrictions to assess medical device performance on vascular tissue

Background: Energy-based surgical scalpels are designed to efficiently transect and seal blood vessels using thermal energy to promote protein denaturation and coagulation. Assessment and design improvement of ultrasonic scalpel performance relies on both in vivo and ex vivo testing. The objective of this work was to design and implement a robust, experimental test matrix with randomization restrictions and predictive statistical power, which allowed for identification of those experimental variables that may affect the quality of the seal obtained ex vivo. Methods: The design of the experiment included three factors: temperature (two levels); the type of solution used to perfuse the artery during transection (three types); and artery type (two types) resulting in a total of twelve possible treatment combinations. Burst pressures of porcine carotid and renal arteries sealed ex vivo were assigned as the response variable. Results: The experimental test matrix was designed and carried out as a split-plot experiment in order to assess the contributions of several variables and their interactions while accounting for randomization restrictions present in the experimental setup. The statistical software package SAS was utilized and PROC MIXED was used to account for the randomization restrictions in the split-plot design. The combination of temperature, solution, and vessel type had a statistically significant impact on seal quality. Conclusions: The design and implementation of a split-plot experimental test-matrix provided a mechanism for addressing the existing technical randomization restrictions of ex vivo ultrasonic scalpel performance testing, while preserving the ability to examine the potential effects of independent factors or variables. This method for generating the experimental design and the statistical analyses of the resulting data are adaptable to a wide variety of experimental problems involving large-scale tissue-based studies of medical or experimental device efficacy and performance

Root Canal Filling Quality Comparison of a Premixed Calcium Silicate Endodontic Sealer and Different Carrier-Based Obturation Systems

Background: The number of voids within the root canal obturation is a relevant parameter to describe the quality of the technique, as well as to predict long-term prognosis. The aim of this study was to evaluate the quality of root canal obturation in curved root canals filled with Thermafil, GuttaCore, GuttaFusion and lateral compaction with AH Plus and EndoSequence BC sealer, by means of percentage of gutta-percha and sealer filled area. Methods: 200 curved canals of mandibular molars were divided in five groups (n = 40). Each specimen was evaluated at 3, 6 and 9 mm from the apex. A total of 600 samples were analyzed. Obturation was performed with either Thermafil (TH), GuttaCore (GC), GuttaFusion (GF) or lateral compaction (LC), using AH Plus as sealer. In another group EndoSequence BC sealer (BC) was used. Subgroups (n = 20) were made depending on the use of sonic activation during the placement of the sealer. The percentage of total obturation material was analyzed as an indirect measurement of percentage of voids. Results: GF showed a better performance at the apical level, while GC showed the higher percentage of total obturation at the coronal area. No differences were observed for the activation of sealers in any of the groups. Statistical analysis was performed by using two-way ANOVA. Statistical significance was set at CI: 95% (p &lt; 0.05). Conclusions: Sonic activation of sealers did not show any benefit to avoid the presence of voids within obturation of curved canals. Following the manufacturer recommendations, we found that TH did not show benefits when applied to curved canals.</jats:p