On the Lieb-Thirring constants L_gamma,1 for gamma geq 1/2

Let $E_i(H)$ denote the negative eigenvalues of the one-dimensional Schr\"odinger operator $Hu:=-u^{\prime\prime}-Vu,\ V\geq 0,$ on $L_2({\Bbb R})$. We prove the inequality \sum_i|E_i(H)|^\gamma\leq L_{\gamma,1}\int_{\Bbb R} V^{\gamma+1/2}(x)dx, (1) for the "limit" case $\gamma=1/2.$ This will imply improved estimates for the best constants $L_{\gamma,1}$ in (1), as $1/2<\gamma<3/2.Comment: AMS-LATEX, 15 page

On the Fourier transform of the characteristic functions of domains with C1C^1 -smooth boundary

We consider domains $D\subseteq\mathbb R^n$ with $C^1$ -smooth boundary and study the following question: when the Fourier transform $\hat{1_D}$ of the characteristic function $1_D$ belongs to $L^p(\mathbb R^n)$?Comment: added two references; added footnotes on pages 6 and 1

Stable Determination of the Electromagnetic Coefficients by Boundary Measurements

The goal of this paper is to prove a stable determination of the coefficients for the time-harmonic Maxwell equations, in a Lipschitz domain, by boundary measurements

Local regularity for fractional heat equations

We prove the maximal local regularity of weak solutions to the parabolic problem associated with the fractional Laplacian with homogeneous Dirichlet boundary conditions on an arbitrary bounded open set $\Omega\subset\mathbb{R}^N$. Proofs combine classical abstract regularity results for parabolic equations with some new local regularity results for the associated elliptic problems.Comment: arXiv admin note: substantial text overlap with arXiv:1704.0756

Boundary Asymptotic Analysis for an Incompressible Viscous Flow: Navier Wall Laws

We consider a new way of establishing Navier wall laws. Considering a bounded domain $\Omega$ of R N , N=2,3, surrounded by a thin layer $\Sigma \epsilon$, along a part $\Gamma$2 of its boundary $\partial \Omega$, we consider a Navier-Stokes flow in $\Omega \cup \partial \Omega \cup \Sigma \epsilon$ with Reynolds' number of order 1/$\epsilon$ in $\Sigma \epsilon$. Using $\Gamma$-convergence arguments, we describe the asymptotic behaviour of the solution of this problem and get a general Navier law involving a matrix of Borel measures having the same support contained in the interface $\Gamma$2. We then consider two special cases where we characterize this matrix of measures. As a further application, we consider an optimal control problem within this context

Thermodynamical Consistent Modeling and Analysis of Nematic Liquid Crystal Flows

The general Ericksen-Leslie system for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal model is then investigated analytically. A fairly complete dynamic theory is developed by analyzing these systems as quasilinear parabolic evolution equations in an $L^p-L^q$-setting. First, the existence of a unique, local strong solution is proved. It is then shown that this solution extends to a global strong solution provided the initial data are close to an equilibrium or the solution is eventually bounded in the natural norm of the underlying state space. In these cases, the solution converges exponentially to an equilibrium in the natural state manifold

Regularity of Ornstein-Uhlenbeck processes driven by a L{\'e}vy white noise

The paper is concerned with spatial and time regularity of solutions to linear stochastic evolution equation perturbed by L\'evy white noise "obtained by subordination of a Gaussian white noise". Sufficient conditions for spatial continuity are derived. It is also shown that solutions do not have in general \cadlag modifications. General results are applied to equations with fractional Laplacian. Applications to Burgers stochastic equations are considered as well.Comment: This is an updated version of the same paper. In fact, it has already been publishe

LAG-3 enables DNA vaccination to persistently prevent mammary carcinogenesis in HER-2/neu transgenic BALB/c mice

Within 33 weeks of life, all 10 mammary glands of virgin BALB/c mice transgenic for the transforming rat HER-2/neu oncogene under the mammary tumor virus promoter (BALB-neuT mice) progress from atypical hyperplasia to invasive palpable carcinoma. Repeated DNA vaccination with plasmids coding for the extracellular and transmembrane domain of the protein product of rat HER-2/neu (r-p185neu) delayed tumor onset and reduced tumor multiplicity, but this protection eventually declined, and few mice were tumor free at 1 year of age. Association of plasmid vaccination with administration of soluble mouse LAG-3 (lymphocyte activation gene-3/CD223) generated by fusing the extracellular domain of murine LAG-3 to a murine IgG2a Fc portion (mLAG-3Ig) elicited a stronger and sustained protection that kept 70% of 1-year-old mice tumor free. Moreover, this combined vaccination, which was performed when multiple in situ carcinomas were already evident, extended disease-free survival and reduced carcinoma multiplicity. Inhibition of carcinogenesis was associated with markedly reduced epithelial cell proliferation and r-p185neu expression, whereas the few remaining hyperplastic foci were heavily infiltrated by reactive leukocytes. A stronger and enduring r-p185neu-specific cytotoxicity, a sustained release of IFN-γ and interleukin 4, and a marked expansion of both CD8+/CD11b+/CD28+ effector and CD8+/CD11b+/CD28- memory effector T-cell populations were induced in immunized mice. This combined vaccination also elicited a quicker and higher antibody response to r-p185neu, as well as an early antibody isotype switch. These data suggest that the appropriate costimulation provided by mLAG-3Ig enables DNA vaccination to establish an effective protection, probably by enhancing cross-presentation of the DNA coded antigen