Bounds for Visual Cryptography Schemes

In this paper, we investigate the best pixel expansion of the various models of visual cryptography schemes. In this regard, we consider visual cryptography schemes introduced by Tzeng and Hu [13]. In such a model, only minimal qualified sets can recover the secret image and that the recovered secret image can be darker or lighter than the background. Blundo et al. [4] introduced a lower bound for the best pixel expansion of this scheme in terms of minimal qualified sets. We present another lower bound for the best pixel expansion of the scheme. As a corollary, we introduce a lower bound, based on an induced matching of hypergraph of qualified sets, for the best pixel expansion of the aforementioned model and the traditional model of visual cryptography realized by basis matrices. Finally, we study access structures based on graphs and we present an upper bound for the smallest pixel expansion in terms of strong chromatic index

Special Correspondences of CM Abelian Varieties and Eisenstein Series II

In this paper, we prove the relation between special cycles on a Rapoport-Smithling-Zhang Shimura variety and special values of the derivative of a Hilbert Eisenstein series

Combinatorial rigidity for some infinitely renormalizable unicritical polynomials

We prove combinatorial rigidity of infinitely renormalizable unicritical polynomials, P_c :z mapsto z^d+c, with complex c, under the a priori bounds and a certain combinatorial condition . This implies the local connectivity of the connectedness loci (the Mandelbrot set when d = 2) at the corresponding parameters

Special Correspondences of CM Abelian Varieties and Eisenstein Series

Let $\mathcal{CM}_{\Phi}$ be the (integral model of the) stack of principally polarized CM Abelian varieties with a CM-type $\Phi$. Considering a pair of nearby CM-types (i.e. such that they are different in exactly one embedding) $\Phi_1, \Phi_2$, we let $X = \mathcal{CM}_{\Phi_1} \times \mathcal{CM}_{\Phi_2}$ and define arithmetic divisors $\mathcal{Z}(\alpha)$ on $X$ such that the Arakelov degree of $\mathcal{Z}(\alpha)$ is (up to multiplication by an explicit constant) equal to the central value of the $\alpha^{\text{th}}$ coefficient of the Fourier expansion of the derivative of a Hilbert Eisenstein series.Comment: 19 page

Examining the level of women participation with and without higher education in form of humanitarian activities and charitable affairs

The present article aims to examine the women's participation in charitable affairs of special diseases and to conduct a comparative comparison between women with higher education and women lacking such education. To this end, utilizing prominent sociological perspectives, first a coherent theoretical framework was provided and upon which research questions and hypotheses were proposed. Given the dependent variable of this research, a survey method was chosen for examining the women's participation in charitable affairs of special diseases and a comparative comparison between women with and without higher education. The research methodology in here is causative and a correlational investigation. Here, in this research the analysis unit is individual and the analysis level is a micro level. The independent variable in this research is education and the dependent variable is the social participation. The statistical population of this research included 750 women who were participating in special disease related charitable affairs. Quota sampling method and then simple random method were applied and as many as 254 people were selected. Tools for data collection were questionnaires. The findings obtained indicated the existence of a significant statistical relation between the independent variable of this research, i.e. education and dependent variable, i.e. social participation