The Cauchy problems for Einstein metrics and parallel spinors

We show that in the analytic category, given a Riemannian metric $g$ on a hypersurface $M\subset \Z$ and a symmetric tensor $W$ on $M$, the metric $g$ can be locally extended to a Riemannian Einstein metric on $Z$ with second fundamental form $W$, provided that $g$ and $W$ satisfy the constraints on $M$ imposed by the contracted Codazzi equations. We use this fact to study the Cauchy problem for metrics with parallel spinors in the real analytic category and give an affirmative answer to a question raised in B\"ar, Gauduchon, Moroianu (2005). We also answer negatively the corresponding questions in the smooth category.Comment: 28 pages; final versio

Positivity of relative canonical bundles and applications

Given a family $f:\mathcal X \to S$ of canonically polarized manifolds, the unique K\"ahler-Einstein metrics on the fibers induce a hermitian metric on the relative canonical bundle $\mathcal K_{\mathcal X/S}$. We use a global elliptic equation to show that this metric is strictly positive on $\mathcal X$, unless the family is infinitesimally trivial. For degenerating families we show that the curvature form on the total space can be extended as a (semi-)positive closed current. By fiber integration it follows that the generalized Weil-Petersson form on the base possesses an extension as a positive current. We prove an extension theorem for hermitian line bundles, whose curvature forms have this property. This theorem can be applied to a determinant line bundle associated to the relative canonical bundle on the total space. As an application the quasi-projectivity of the moduli space $\mathcal M_{\text{can}}$ of canonically polarized varieties follows. The direct images $R^{n-p}f_*\Omega^p_{\mathcal X/S}(\mathcal K_{\mathcal X/S}^{\otimes m})$, $m > 0$, carry natural hermitian metrics. We prove an explicit formula for the curvature tensor of these direct images. We apply it to the morphisms $S^p \mathcal T_S \to R^pf_*\Lambda^p\mathcal T_{\mathcal X/S}$ that are induced by the Kodaira-Spencer map and obtain a differential geometric proof for hyperbolicity properties of $\mathcal M_{\text{can}}$.Comment: Supercedes arXiv:0808.3259v4 and arXiv:1002.4858v2. To appear in Invent. mat

Bounded derived categories of very simple manifolds

An unrepresentable cohomological functor of finite type of the bounded derived category of coherent sheaves of a compact complex manifold of dimension greater than one with no proper closed subvariety is given explicitly in categorical terms. This is a partial generalization of an impressive result due to Bondal and Van den Bergh.Comment: 11 pages one important references is added, proof of lemma 2.1 (2) and many typos are correcte

Complex zeros of real ergodic eigenfunctions

We determine the limit distribution (as $\lambda \to \infty$) of complex zeros for holomorphic continuations \phi_{\lambda}^{\C} to Grauert tubes of real eigenfunctions of the Laplacian on a real analytic compact Riemannian manifold $(M, g)$ with ergodic geodesic flow. If $\{\phi_{j_k} \}$ is an ergodic sequence of eigenfunctions, we prove the weak limit formula \frac{1}{\lambda_j} [Z_{\phi_{j_k}^{\C}}] \to \frac{i}{\pi} \bar{\partial} {\partial} |\xi|_g, where [Z_{\phi_{j_k}^{\C}}] is the current of integration over the complex zeros and where $\bar{\partial}$ is with respect to the adapted complex structure of Lempert-Sz\"oke and Guillemin-Stenzel.Comment: Added some examples and references. Also added a new Corollary, and corrected some typo

Husimi Transform of an Operator Product

It is shown that the series derived by Mizrahi, giving the Husimi transform (or covariant symbol) of an operator product, is absolutely convergent for a large class of operators. In particular, the generalized Liouville equation, describing the time evolution of the Husimi function, is absolutely convergent for a large class of Hamiltonians. By contrast, the series derived by Groenewold, giving the Weyl transform of an operator product, is often only asymptotic, or even undefined. The result is used to derive an alternative way of expressing expectation values in terms of the Husimi function. The advantage of this formula is that it applies in many of the cases where the anti-Husimi transform (or contravariant symbol) is so highly singular that it fails to exist as a tempered distribution.Comment: AMS-Latex, 13 page

The C-terminal region of Trypanosoma cruzi MASPs is antigenic and secreted via exovesicles.

Trypanosoma cruzi is the etiological agent of Chagas disease, a neglected and emerging tropical disease, endemic to South America and present in non-endemic regions due to human migration. The MASP multigene family is specific to T. cruzi, accounting for 6% of the parasite's genome and plays a key role in immune evasion. A common feature of MASPs is the presence of two conserved regions: an N-terminal region codifying for signal peptide and a C-terminal (C-term) region, which potentially acts as GPI-addition signal peptide. Our aim was the analysis of the presence of an immune response against the MASP C-term region. We found that this region is highly conserved, released via exovesicles (EVs) and has an associated immune response as revealed by epitope affinity mapping, IFA and inhibition of the complement lysis assays. We also demonstrate the presence of a fast IgM response in Balb/c mice infected with T. cruzi. Our results reveal the presence of non-canonical secreted peptides in EVs, which can subsequently be exposed to the immune system with a potential role in evading immune system targets in the parasite

Исследование температурного поведения сцинтилляционного детектора NaI(Tl)

Объектом исследования являются сцинтилляционные детекторы типа БДКГ для исследования влияния температуры на их показания. Целью данной работы является исследование температурной зависимости показаний детектора гамма-излучения в климатической камере, для расчета поправочного коэффициента на колебания температуры окружающей среды. Был проведен эксперимент в климатической камере, полученные результаты подтверждают некорректность показаний исследуемых детекторов. На основе экспериментальных данных рассчитан коэффициент корректировки на температуры для перерасчета скорости счета импульсов в мощность дозы.The object of the study is scintillation detectors of the BDKG type to study the effect of temperature on their readings. The aim of this work is to study the temperature dependence of the gamma-ray detector readings in a climate chamber to calculate the correction coefficient for fluctuations in ambient temperature. An experiment was conducted in a climatic chamber, the obtained results confirm the incorrectness of of the studied detectors readings . Based on the experimental data, the temperature correction coefficient was calculated to recalculate the pulse count rate in the dose rate

The Lantern Vol. 6, No. 1, December 1937

• After Thinking Things Over • Ho! Ho! The Mistletoe! • Unrealized Dreams • Two Preeminent Victorians • The Thing • Progression • It Wasn\u27t in the Lines • He Was the Most Perfect Man • College (C)lasses • Robins and Roses • The Commuter • When the Rose is Dead • Truth in Print • Alias Mike Romanoff • Winslow Homer • When I Was Young • Maurice Evans, a Great Shakespearean • Among Our Contributors • Of Manx and Man • A Sanguinary Pirate • Conversation Has an Adventure • Ursinus\u27 Neediest Casehttps://digitalcommons.ursinus.edu/lantern/1016/thumbnail.jp

Classification of singular Q-homology planes. I. Structure and singularities

A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We obtain a structure theorem for Q-homology planes with smooth locus of non-general type. We show that if a Q-homology plane contains a non-quotient singularity then it is a quotient of an affine cone over a projective curve by an action of a finite group respecting the set of lines through the vertex. In particular, it is contractible, has negative Kodaira dimension and only one singular point. We describe minimal normal completions of such planes.Comment: improved results from Ph.D. thesis (University of Warsaw, 2009), 25 pages, to appear in Israel J. Mat

Tsunami from the Storegga Landslide

This is an accepted manuscript version of a book chapter published in the Encyclopedia of Complexity and Systems Science on 25 May 2019, and may be used under SpringerNature’s Terms of Use. The Version of Record can be found at https://doi.org/10.1007/978-3-642-27737-5_644-1The Storegga tsunami was generated by the Storegga landslide off the Norwegian coast about 8150 years ago. The tsunami deposits show that the coasts of Scotland, Norway, Shetland, Faroe Islands and possibly also Eastern Greenland and Denmark was inundated, and that the tsunami ran up to heights ranging from 3 to more than 20 meters above sea level of that time. The Storegga tsunami is important for two reasons: First, it shows that big tsunamis have happened along passive margins and outside of the Pacific Ocean. Second, it is the only slide-generated tsunami of a basin-wide range where the run-up has been mapped out in the field and the tsunami simulated with numerical models.acceptedVersio