A sharp vanishing theorem for line bundles on K3 or Enriques surfaces

Let $L$ be a line bundle on a K3 or Enriques surface. We give a vanishing theorem for $H^1(L)$ that, unlike most vanishing theorems, gives necessary and sufficient geometrical conditions for the vanishing. This result is essential in our study of Brill-Noether theory of curves on Enriques surfaces (reference [KL1]) and of Enriques-Fano threefolds (reference [KLM]).Comment: 4 pages, latex. Minor corrections. To appear on Proc. Amer. Math. So

Negative curves on algebraic surfaces

We study curves of negative self-intersection on algebraic surfaces. We obtain results for smooth complex projective surfaces X on the number of reduced, irreducible curves C of negative self-intersection C^2. The only known examples of surfaces for which C^2 is not bounded below are in positive characteristic, and the general expectation is that no examples can arise over the complex numbers. Indeed, we show that the idea underlying the examples in positive characteristic cannot produce examples over the complex number field. The previous version of this paper claimed to give a counterexample to the Bounded Negativity Conjecture. The idea of the counterexample was to use Hecke translates of a smooth Shimura curve in order to create an infinite sequence of curves violating the Bounded Negativity Conjecture. To this end we applied Hirzebruch Proportionality to all Hecke translates, simultaneously desingularized by a version of Jaffee's Lemma which exists in the literature but which turns out to be false. Indeed, in the new version of the paper, we show that only finitely many Hecke translates of a special subvariety of a Hilbert modular surface remain smooth. This new result is based on work done jointly with Xavier Roulleau, who has been added as an author. The other results in the original posting of this paper remain unchanged.Comment: 14 pages, X. Roulleau added as author, counterexample to Bounded Negativity Conjecture withdrawn and replaced by a proof that there are only finitely many smooth Shimura curves on a compact Hilbert modular surface; the other results in the original posting of this paper remain unchange

Understanding and Finding Solutions to the Problem of Sedimentation in the National Wildlife Refuge System

The National Wildlife Refuge System (Refuge System) is a collection of public lands maintained by the U.S. Fish and Wildlife Service for migratory birds and other wildlife. Wetlands on individual National Wildlife Refuges (Refuges) may be at risk of increased sedimentation because of land use and water management practices. Increased sedimentation can reduce wetland habitat quality by altering hydrologic function, degrading water quality, and inhibiting growth of vegetation and invertebrates. On Refuges negatively affected by increased sedimentation, managers have to address complex questions about how to best remediate and mitigate the negative effects. The best way to account for these complexities is often not clear. On other Refuges, managers may not know whether sedimentation is a problem. Decision makers in the Refuge System may need to allocate resources to studying which Refuges could be at risk. Such analyses would help them understand where to direct support for managing increased sedimentation. In this paper, we summarize a case study demonstrating the use of decision-analytic tools in the development of a sedimentation management plan for Agassiz National Wildlife Refuge, Minnesota. Using what we learned from that process, we surveyed other Refuges in U.S. Fish and Wildlife Service Region 3 (an area encompassing the states of Illinois, Indiana, Iowa, Ohio, Michigan, Minnesota, Missouri, and Wisconsin) and Region 6 (an area encompassing the states of Colorado, Kansas, Montana, Nebraska, North Dakota, South Dakota, Utah, and Wyoming) about whether they experience sediment-related impacts to management. Our results show that cases of management being negatively affected by increased sedimentation are not isolated. We suggest that the Refuge System conduct a comprehensive and systematic assessment of increased sedimentation among Refuges to understand the importance of sedimentation in context with other management problems that Refuges face. The results of such an assessment could guide how the Refuge System allocates resources to studying and managing widespread stressors

Isotropy, shear, symmetry and exact solutions for relativistic fluid spheres

The symmetry method is used to derive solutions of Einstein's equations for fluid spheres using an isotropic metric and a velocity four vector that is non-comoving. Initially the Lie, classical approach is used to review and provide a connecting framework for many comoving and so shear free solutions. This provides the basis for the derivation of the classical point symmetries for the more general and mathematicaly less tractable description of Einstein's equations in the non-comoving frame. Although the range of symmetries is restrictive, existing and new symmetry solutions with non-zero shear are derived. The range is then extended using the non-classical direct symmetry approach of Clarkson and Kruskal and so additional new solutions with non-zero shear are also presented. The kinematics and pressure, energy density, mass function of these solutions are determined.Comment: To appear in Classical and Quantum Gravit

Invariant construction of solutions to Einstein's field equations - LRS perfect fluids II

The properties of LRS class II perfect fluid space-times are analyzed using the description of geometries in terms of the Riemann tensor and a finite number of its covariant derivatives. In this manner it is straightforward to obtain the plane and hyperbolic analogues to the spherical symmetric case. For spherically symmetric static models the set of equations is reduced to the Tolman-Oppenheimer-Volkoff equation only. Some new non-stationary and inhomogeneous solutions with shear, expansion, and acceleration of the fluid are presented. Among these are a class of temporally self-similar solutions with equation of state given by $p=(\gamma-1)\mu, 1<\gamma<2$, and a class of solutions characterized by $\sigma=-\Theta/6$. We give an example of geometry where the Riemann tensor and the Ricci rotation coefficients are not sufficient to give a complete description of the geometry. Using an extension of the method, we find the full metric in terms of curvature quantities.Comment: 24 pages, 1 figur

Mycotoxin exposure and human cancer risk : a systematic review of epidemiological studies

In recent years, there has been an increasing interest in investigating the carcinogenicity of mycotoxins in humans. This systematic review aims to provide an overview of data linking exposure to different mycotoxins with human cancer risk. Publications (2019 and earlier) of case–control or longitudinal cohort studies were identified in PubMed and EMBASE. These articles were then screened by independent reviewers and their quality was assessed according to the Newcastle–Ottawa scale. Animal, cross‐sectional, and molecular studies satisfied criteria for exclusion. In total, 14 articles were included: 13 case–control studies and 1 longitudinal cohort study. Included articles focused on associations of mycotoxin exposure with primary liver, breast, and cervical cancer. Overall, a positive association between the consumption of aflatoxin‐contaminated foods and primary liver cancer risk was verified. Two case–control studies in Africa investigated the relationship between zearalenone and its metabolites and breast cancer risk, though conflicting results were reported. Two case–control studies investigated the association between hepatocellular carcinoma and fumonisin B1 exposure, but no significant associations were observed. This systematic review incorporates several clear observations of dose‐dependent associations between aflatoxins and liver cancer risk, in keeping with IARC Monograph conclusions. Only few human epidemiological studies investigated the associations between mycotoxin exposures and cancer risk. To close this gap, more in‐depth research is needed to unravel evidence for other common mycotoxins, such as deoxynivalenol and ochratoxin A. The link between mycotoxin exposures and cancer risk has mainly been established in experimental studies, and needs to be confirmed in human epidemiological studies to support the evidence‐based public health strategies

A few questions about curves on surfaces

In this note we address the following kind of question: let X be a smooth, irreducible, projective surface and D a divisor on X satisfying some sort of positivity hypothesis, then is there some multiple of D depending only on X which is effective or movable? We describe some examples, discuss some conjectures and prove some results that suggest that the answer should in general be negative, unless one puts some really strong hypotheses either on D or on X

N‐Substituted Nipecotic Acids as (S )‐SNAP‐5114 Analogues with Modified Lipophilic Domains

Potential mGAT4 inhibitors derived from the lead substance (S )‐SNAP‐5114 have been synthesized and characterized for their inhibitory potency. Variations from the parent compound included the substitution of one of its aromatic 4‐methoxy and 4‐methoxyphenyl groups, respectively, with a more polar moiety, including a carboxylic acid, alcohol, nitrile, carboxamide, sulfonamide, aldehyde or ketone function, or amino acid partial structures. Furthermore, it was investigated how the substitution of more than one of the aromatic 4‐methoxy groups affects the potency and selectivity of the resulting compounds. Among the synthesized test substances (S )‐1‐{2‐[(4‐formylphenyl)bis(4‐methoxyphenyl)‐methoxy]ethyl}piperidine‐3‐carboxylic acid, that features a carbaldehyde function in place of one of the aromatic 4‐methoxy moieties of (S )‐SNAP‐5114, was found to have a pIC50 value of 5.89±0.07, hence constituting a slightly more potent mGAT4 inhibitor than the parent substance while showing comparable subtype selectivity