Shafarevich's hyperbolicity conjecture asserts that a family of curves over a quasi-projective 1-dimensional base is isotrivial unless the logarithmic Kodaira dimension of the base is positive. More generally it has been conjectured by Viehweg that the base of a smooth family of canonically polarized varieties is of log general type if the family is of maximal variation. In this paper, we relat...

We introduce a new class of statistical growth fractals which is of interest because the chemical dimension d, is continuously tunable. We also study other exponents characterising these fractals. There has been considerable recent interest in uncovering the fashion in which the familiar laws of physics are modified for fractal objects, in part because of the large number of important realisati...

We present first methodology for dimension reduction in regressions with predictors that, given the response, follow one-parameter exponential families. Our approach is based on modeling the conditional distribution of the predictors given the response, which allows us to derive and estimate a sufficient reduction of the predictors. We also propose a method of estimating the forward regression ...

The family of inverse regression estimators recently proposed by Cook and Ni (2005) have proven effective in dimension reduction by transforming the highdimensional predictor vector to its low-dimensional projections. In this article, we propose a general shrinkage estimation strategy for the entire inverse regression estimation family that is capable of simultaneous dimension reduction and var...

In this paper, rstly, it is proved that, for a fuzzy vector space, the set of its fuzzy bases de ned by Shi and Huang, is equivalent to the family of its bases de ned by P. Lubczonok. Secondly, for two fuzzy vector spaces, it is proved that they are isomorphic if and only if they have the same fuzzy dimension, and if their fuzzy dimensions are equal, then their dimensions are the same, however,...

In the present paper, we deal with the union M of all trinomial arcs M(p, k, r, n). It will be shown that the fractal dimension of M is 3/2. Mathematics Subject Classification: 14H45, 26A48, 28A80, 30C15.

For each prime p and a monic polynomial f , invertible over p, we define a group Gp,f of p-adic automorphisms of the p-ary rooted tree. The groups are modeled after the first Grigorchuk group, which in this setting is the group G2,x2+x+1. We show that the constructed groups are self-similar, regular branch groups. This enables us to calculate the Hausdorff dimension of their closures, providing...

The software product family approach aims at curtailing the concept of “reinventing the wheel” in the software development process. The business has been highlighted as one of the critical dimensions in the process of software product family. This work presents an assessment framework for evaluating the business dimension of software product family process. Additionally, a software product fami...

Proteins of the BCL-2 family control the mitochondrial pathway of apoptosis. Targeting these proteins proves to be an attractive strategy for anticancer therapy. The biological context is based on the fact that BH3-only members of the family are specific antagonists of prosurvival members. This prompted the identification of "BH3 mimetic" compounds. These small peptides or organic molecules ind...