We show that the Hausdorff dimension of Julia sets in any analytic family of semihyperbolic generalized polynomial-like mappings (GPL) depends in a real-analytic manner on the parameter. For the proof we introduce abstract weakly regular analytic families of conformal graph directed Markov systems. We show that the Hausdorff dimension of limit sets in such families is real-analytic, and we asso...

We define a family of homogeneous ideals with large projective dimension and regularity relative to the number of generators and their common degree. This family subsumes and improves upon constructions given in [Cav04] and [McC]. In particular, we describe a family of three-generated homogeneous ideals in arbitrary characteristic whose projective dimension grows

the main function of rural areas in the third world is the agricultural function which is crucially important because of its great effects on employment, moderating income and poverty, food security and self-efficacy. this article studies the role of agriculture (as an independent variable) in rural development (related variable) of miyankangi district in sistan. the method of the study was des...

let r be a commutative noetherian ring. we study the behavior of injectiveand at dimension of r-modules under the functors homr(-,-) and -×r-.

A family of dimension-reduction methods, the inverse regression (IR) family, is developed by minimizing a quadratic objective function. An optimal member of this family, the inverse regression estimator (IRE), is proposed, along with inference methods and a computational algorithm. The IRE has at least three desirable properties: (1) Its estimated basis of the central dimension reduction subspa...

In this paper, we offer a proof for family of functional inequalities interpolating between the Poincaré and logarithmic Sobolev (standard weighted) inequalities. The proofs rely both on entropy flows CD(ρ,n) condition, either with ρ=0 n>0, or ρ>0 n∈R. As such, results are valid in case Riemannian manifold, which constitutes generalization what was previously proved.