Let Σ be a nonempty set of prime numbers. In the present paper, we continue the study, initiated in a previous paper by the second author, of the combinatorial anabelian geometry of semi-graphs of anabelioids of pro-Σ PSC-type, i.e., roughly speaking, semi-graphs of anabelioids associated to pointed stable curves. Our first main result is a partial generalization of one of the main combinatoria...

A sufficient condition for C1-continuity of subdivision surfaces was proposed by Reif [Comput. Aided Geom. Design, 12 (1995), pp. 153–174.] and extended to a more general setting in [D. Zorin, Constr. Approx., accepted for publication]. In both cases, the analysis of C1-continuity is reduced to establishing injectivity and regularity of a characteristic map. In all known proofs of C1-continuity...

Many categories of semantic domains can be considered from an order-theoretic point of view and from a topological point of view via the Scott topology. The topological point of view is particularly fruitful for considerations of computability in classical spaces such as the Euclidean real line. When one embeds topological spaces into domains, one requires that the Scott continuous maps between...

It is proved that every commutative ring whose RD-injective modules are Σ-RD-injective is the product of a pure semi-simple ring and a finite ring. A complete characterization of commutative rings for which each artinian (respectively simple) module is RD-injective, is given. These results can be obtained by using the properties of RD-flat modules and RD-coflat modules which are respectively th...

In this paper we show that a direct decomposition of modules M N, with N homologically independent to the inJective hull of H, is a CS-module if and only if N is injective relative to H and both of M and N are CS-modules. As an application, we prove that a direct sum of a non-singular semisimple module and a quasi-continuous module with zero socle is quasi-continuous. This result is known for q...

ÐFree-Form Deformation (FFD) is a versatile and efficient modeling technique which transforms an object by warping the surrounding space. The conventional user-interface is a lattice of movable control points but this tends to be cumbersome and counterintuitive. Directly Manipulated Free-Form Deformation (DMFFD) allows the user to drag object points directly and has proven useful in an interact...

We explore relationship between the cut locus of an arbitrary simply connected and compact Riemannian symmetric space and the Cartan polyhedron of corresponding restricted root system, and compute injectivity radius and diameter for every type of irreducible ones.

We study the weighted integral transform on a compact manifold with boundary over a smooth family of curves . We prove generic injectivity and a stability estimate under the condition that the conormal bundle of covers T M .

Let us assume we are given a totally contra-multiplicative functor τ̃ . It has long been known that |T | = 1 [17, 13, 19]. We show that every countably p-adic polytope is almost surely canonical and Euclidean. Moreover, here, positivity is obviously a concern. In [14], the main result was the description of hyper-trivial, characteristic, Cantor domains.