The simplest version of the Maskit-Klein combination theorems concerns the action of a free product of two finite subgroups of PSL(2,C) on the Riemann sphere Ĉ, when these subgroups have fundamental domains whose interiors together cover Ĉ. We prove an analogous combination theorem for covering correspondences of rational maps, making use of Douady and Hubbard’s Straightening Theorem for polyno...

During the last three decades progress in mapping the universe from an age of 400,000 years to the present has been stunning. Instrument/telescope combinations have naturally determined the sampling of various redshift ranges. Here we outline the impact of the Hectospec on the MMT on exploration of the universe in the redshift range 0.2 . z . 0.8. We focus on dense redshift surveys, SHELS and H...

We show a Whitney approximation theorem for continuous map from manifold to smooth CW complex, which enables us that topological complex is homotopy equivalent in category of spaces. It also shown that, any open covering there exists partition unity subordinate the covering. In addition, we observe are enough many functions on complex.

In this article we prove that a semialgebraic map $$\pi :M\rightarrow N$$ is branched covering if and only its associated spectral covering. addition, such has neat behavior with respect to the branching locus, ramification set index. A crucial fact preceding result characterization of prime ideals whose fibers under previous are singletons.

Due to its fast growth rate and little nursery requirements, willow is largely planted as short rotation coppice species for bioenergy resources in temperate regions. Willow coppices can be easily established by vegetative propagation of cuttings and can remain productive for up to 25 years. In China, diploid species S. leucopithecia and S. erioclada L. are two promising willow species that can...

abstract one of the basic assumptions in hub covering problems is considering the covering radius as an exogenous parameter which cannot be controlled by the decision maker. practically and in many real world cases with a negligible increase in costs, to increase the covering radii, it is possible to save the costs of establishing additional hub nodes. change in problem parameters during the pl...

Suppose f : S → S is a postcritically finite branched covering without periodic branch points. If f is the subdivision map of a finite subdivision rule with mesh going to zero combinatorially, then the virtual endomorphism on the orbifold fundamental group associated to f is contracting. This is a first step in a program to clarify the relationships among various notions of expansion for noninv...

A finite Blaschke product, restricted to the unit circle, is a smooth covering map. The maximum and minimum values of derivative this map reflect geometry product. We identify two classes extremal products: those that maximize difference between derivative, minimize it. Both turn out have same algebraic structure, being quotient hypergeometric polynomials.

Let N and P be smooth manifolds of dimensions n and p (n ≥ p ≥ 2) respectively. A smooth map having only fold singularities is called a fold-map. We will study conditions for a continuous map f : N → P to be homotopic to a fold-map from the viewpoint of the homotopy principle. By certain homotopy principles for fold-maps, we prove that if there exists a fiberwise epimorphism TN ⊕ θN → TP coveri...