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.

We consider notions of freeness and ambiguity for the acceptance probability Moore-Crutchfield Measure Once Quantum Finite Automata (MO-QFA). study injectivity problem determining if function a MO-QFA is injective over all input words, i.e., giving distinct each word. show that undecidable 8 state MO-QFA, even when unitary matrices projection matrix are rational initial vector real algebraic. a...