Tautological classes on the moduli space of hyperelliptic curves with rational tails

We study tautological classes on the moduli space of stable n-pointed hyperelliptic curves of genus g with rational tails. The method is based on the approach of Yin in comparing tautological classes on the moduli of curves and the universal Jacobian. Our result gives a complete description of tautological relations. It is proven that all relations come from the Jacobian side. The intersection pairings are shown to be perfect in all degrees. We show that the tautological algebra coincides with its image in cohomology via the cycle class map. The latter is identified with monodromy invariant classes in cohomology. (C) 2017 Elsevier B.V. All rights reserved11sci

The relationship between Self-Esteem and sexual Self-Concept in people with Physical-Motor disabilities

Background: Self-esteem is the value that the individuals give themselves, and sexual self-concept is also a part of individuality or sexualself. Impairment or disability exists not only in the physical body of disabled people but also in their attitudes. Negative attitudes affect the mental health of disabled people, causing them to have lower self-esteem. Objectives: This study aimed to examine the relationship between self-esteem and sexual self-concept in people with physical-motor disabilities. Patients and Methods: This cross-sectional study was conducted on 200 random samples with physical-motor disabilities covered by Isfahan Welfare Organization in 2013. Data collection instruments were the Persian Eysenck self-esteem questionnaire, and five domains (sexual anxiety, sexual self-efficacy, sexual self-esteem, sexual fear and sexual depression) of the Persian multidimensional sexual selfconcept questionnaire. Because of incomplete filling of the questionnaires, the data of 183 people were analyzed by the SPSS 16.0 software. Data were analyzed using the t-test, Man-Whitney and Kruskal-Wallis tests and Spearman correlation coefficient. Results: The mean age was 36.88 ± 8.94 years for women and 37.80 ± 10.13 for men. The mean scores of self-esteem among women and men were 15.80 ± 3.08 and 16.2 ± 2.90, respectively and there was no statistically significance difference. Comparison of the mean scores of sexual anxiety, sexual self-efficacy, sexual self-esteem, sexual fear and sexual depression among men and women showed that women scored higher than men in all domains. This difference was statistically significant in other domains except the sexual self-esteem (14.92 ± 3.61 vs. 13.56 ± 4.52) (P < 0.05). The Kruskal-Wallis test showed that except for sexual anxiety and sexual self-esteem, there was a statistical difference between other domains of people’s sexual self-concept and degree of disability (P < 0.05). Moreover, Spearman coefficient showed that there was only a correlation between men’s sexual anxiety, sexual self-esteem and sexual self-efficacy with their self-esteem. This correlation was positive in sexual anxiety and negative in two other domains. Conclusions: Lack of difference in self-esteem of disabled people in different degrees of disability and in both men and women suggests that disabled people should not be presumed to have low self-esteem, and their different aspects of life should be attended to, just like others. Furthermore, studies should be designed and implemented based on psychological, social and environmental factors that can help disabled people to promote their positive sexual self-concept through marriage, and reduce their negative self-concept. © 2015 Iranian Red Crescent Medical Journal

Production and nutrient cycling in three Scottish oak woods on contrasting soils

Studies were made in three ancient Scottish Oak woods on contrasting soils: Ross (podzols) and Gartfairn (gleys) near Loch Lomond, and Methven (brown earths) near Perth. The annual rainfalls (mm) are : Ross and Gartfairn, 1700; Methven 700. Soil nutrient (0-10 cm) contents were ranked Methven> Gartfairn> Ross> except for total nitrogen which was Gartfairn> Methven> Ross. Each wood was sampled from three 1000 m* plots. Tree (> 5 cm dbh) density and basal area were : 343 ha and 21.7 m* ha** for Ross; 410 ha** and 30.4 m* ha** for Gartfairn; and 280 ha** and 37.8 m* ha** for Methven. Small litterfall, measured in eighteen traps per plot, had mean values (kg ha**): Methven, 5368; Gartfairn, 4476; and Ross 3607. The values are in the same rank order as soil nutrients (except nitrogen). Litter layer mass was highest in Ross and least in Gartfairn while its nutrient content (for all elements) was least in Ross and highest in Methven. The turnover rates (kl) of litter mass and nutrients were least in Ross and (except for nitrogen) highest in Gartfairn. Studies of leaf decomposition were made in bags of two mesh sizes (64* and 5mm) of 144 cm* and in open frames of 225 cm*. Leaf mass was lost fastest in the frames and slowest in the fine mesh, except for Ross where there was no difference between the two meshes. Coarse-mesh decomposition was fastest in Gartfairn and slowest in Ross; fine-mesh decomposition was fastest in Ross, slowest in Methven. There was a linear relationship between mass of litter lost and time elapsed. The litter mass losses were often significantly correlated with the initial nutrient content. Patterns of nutrient accumulation and release differed between elements, sites, and containers. Nutrients were usually released faster in coarse-mesh compared with fine-mesh bags

An action of the Polishchuk differential operator via punctured surfaces

For a family of Jacobians of smooth pointed curves there is a notion of tautological algebra. There is an action of $\mathfrak{sl}_2$ on this algebra. We define and study a lifting of the Polishchuk operator, corresponding to $f\in \mathfrak{sl}_2$, on an algebra consisting of punctured Riemann surfaces. As an application we prove that a collection of tautological relations on moduli of curves, discovered by Faber and Zagier, come from a class of relations on the universal Jacobian

Density perturbations in f(R) gravity theories in metric and Palatini formalisms

We make a detailed study of matter density perturbations in both metric and Palatini formalisms in theories whose Lagrangian density is a general function, f(R), of the Ricci scalar. We derive these equations in a number of gauges. We show that for viable models that satisfy cosmological and local gravity constraints (LGC), matter perturbation equations derived under a sub-horizon approximation are valid even for super-Hubble scales provided the oscillating mode (scalaron) does not dominate over the matter-induced mode. Such approximate equations are especially reliable in the Palatini formalism because of the absence of scalarons. Using these equations we make a comparative study of the behaviour of density perturbations as well as gravitational potentials for a number of classes of theories. In the metric formalism the parameter m=Rf_{,RR}/f_{,R} characterising the deviation from the Lambda CDM model is constrained to be very small during the matter era in order to ensure compatibility with LGC, but the models in which m grows to the order of 10^{-1} around the present epoch can be allowed. These models also suffer from an additional fine tuning due to the presence of scalaron modes which are absent in the Palatini case. In Palatini formalism LGC and background cosmological constraints provide only weak bounds on |m| by constraining it to be smaller than ~ 0.1. This is in contrast to matter density perturbations which, on galactic scales, place far more stringent constraints on the present deviation parameter m of the order of |m| < 10^{-5} - 10^{-4}. This is due to the peculiar evolution of matter perturbations in the Palatini case which exhibits a rapid growth or a damped oscillation depending on the sign of m.Comment: 36 pages including 8 figures. Accepted for publication in Physical Review