Trajectories of vector fields asymptotic to formal invariant curves

We prove that a formal curve $\Gamma$ that is invariant by a $C^\infty$ vector field $\xi$ of $\mathbb{R}^m$ has a geometrical realization, as soon as the Taylor expansion of $\xi$ is not identically zero along $\Gamma$. This means that there is a trajectory $\gamma$ of $\xi$ which is asymptotic to $\Gamma$. This result solves a natural question proposed by Bonckaert nearly forty years ago. We also construct an invariant $C^0$ manifold $S$ in some open horn around $\Gamma$ which is composed entirely of trajectories asymptotic to $\Gamma$, and contains the germ of any such trajectory. If $\xi$ is analytic, we prove that there exists a trajectory asymptotic to $\Gamma$ which is, moreover, non-oscillating with respect to subanalytic sets

Dose rates evaluation of HiPER facility

During the operation of the HiPER first engineering facility, up to 1.2 × 105 MJ/yr of fusion neutrons yields are foreseen. This irradiation level could be distributed in 100 MJ detonations, accounting up to 100 detonations in a single burst, with 10 Hz repetition rate. A burst would take place every month. The dose rates are computed and different concrete shields are evaluated within the target bay. During the operation of the facility the entrance is forbidden inside the bioshield. Between bursts, manual maintenance might be performed inside the bioshield but outside the final optics assembly (FOA) shield. Inside the FOA shield the residual dose rates are so high that only remote maintenance is allowed. The FOA shield reduces the delivered dose rate to optics in a factor of 30.3

Brønsted Acid Catalyzed Alkylation of Indoles with Tertiary Propargylic Alcohols: Scope and Limitations

Direct alkylation of indoles with a wide variety of tertiary propargylic alcohols under Brønsted acid catalysis conditions has been studied. A general and environmentally friendly method for the synthesis of 3-propargylated indoles with quaternary carbon atoms at their propargylic positions has been developed. The reactions are highly regioselective with regard both to the indole and to the alkynol components. Only with N-unsubstituted 2-arylindoles do competitive SN′ reactions take place to afford 3-dienyl- or 3-allenylindoles, depending on the alkynol moiety. The reactions were carried out in air with undried solvents, and water was the only side product.Junta de Castilla y Leon (BU021A09 and GR-172) and the Ministerio de Educacion y Ciencia (MEC) and FEDER (CTQ2007-61436/BQU and CTQ2009-09949/BQU) for financial support. D. M. and A. M. thank the MEC for MEC-FPU predoctoral fellowships. M. G. thanks the MEC for a "Young Foreign Researchers" contract (SB2006-0215). M. A. F.-R. and P. G.-G. also thank the MEC for "Ramon y Cajal" and "Juan de la Cierva" contracts.This is the pre-peer reviewed version of the following article: Sanz, R., Miguel, D., Martínez, A., Gohain, M., García-García, P., Fernández-Rodríguez, M. A., Álvarez, E. and Rodríguez, F. (2010), Brønsted Acid Catalyzed Alkylation of Indoles with Tertiary Propargylic Alcohols: Scope and Limitations. Eur. J. Org. Chem., 2010: 7027–7039. doi: 10.1002/ejoc.201001055, which has been published in final form at 10.1002/ejoc.201001055. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving

Non-autonomous stochastic evolution equations and applications to stochastic partial differential equations

In this paper we study the following non-autonomous stochastic evolution equation on a UMD Banach space $E$ with type 2, {equation}\label{eq:SEab}\tag{SE} {{aligned} dU(t) & = (A(t)U(t) + F(t,U(t))) dt + B(t,U(t)) dW_H(t), \quad t\in [0,T], U(0) & = u_0. {aligned}. {equation} Here $(A(t))_{t\in [0,T]}$ are unbounded operators with domains $(D(A(t)))_{t\in [0,T]}$ which may be time dependent. We assume that $(A(t))_{t\in [0,T]}$ satisfies the conditions of Acquistapace and Terreni. The functions $F$ and $B$ are nonlinear functions defined on certain interpolation spaces and $u_0\in E$ is the initial value. $W_H$ is a cylindrical Brownian motion on a separable Hilbert space $H$. Under Lipschitz and linear growth conditions we show that there exists a unique mild solution of \eqref{eq:SEab}. Under assumptions on the interpolation spaces we extend the factorization method of Da Prato, Kwapie\'n, and Zabczyk, to obtain space-time regularity results for the solution $U$ of \eqref{eq:SEab}. For Hilbert spaces $E$ we obtain a maximal regularity result. The results improve several previous results from the literature. The theory is applied to a second order stochastic partial differential equation which has been studied by Sanz-Sol\'e and Vuillermot. This leads to several improvements of their result.Comment: Accepted for publication in Journal of Evolution Equation

Is a soft tissue graft harvested from the maxillary tuberosity the approach of choice in an isolated site?

Soft tissue augmentation procedures are becoming more popular these days. Different soft tissue graft harvesting approaches have been proposed. Nonetheless, the location of the donor site (whether anterior-, lateral-, superficial-, deep-palate or the maxillary tuberosity) can affect the graft shape and its composition. Soft tissue grafts from the maxillary tuberosity are rich in connective tissue fibers, with minimal presence of fatty or glandular components. Clinical, histological, and molecular evidence shows that a soft tissue graft obtained from the maxillary tuberosity has unique properties. In addition, harvesting from this area presents minimal risk for intra- or postoperative complications, leading to reduced patient morbidity. The aim of this commentary is to discuss the advantages and disadvantages of harvesting a soft tissue graft from the tuberosity and to compare it with the traditional palatal graft, while highlighting functional, esthetic, and patient-related outcomes.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151301/1/jper10300_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151301/2/jper10300.pd

Tau Physics 2006: Summary & Outlook

A large amount of new results have been presented at TAU2006. The highlights of the workshop, the present status of a few selected topics on lepton physics (universality, QCD tests, V_{us} determination from tau decay, g-2, neutrino oscillations, lepton-flavour violation) and the prospects for future improvements are briefly summarized.Comment: Conference Summary at the 9th International Workshop on Tau Lepton Physics (TAU06), 19-22 September 2006, Pisa (Italy