We define a bundle over a totally disconnected set such that each fiber is homeomorphic to a fractal blowup. We prove that there is a natural action of a Renault–Deaconu groupoid on our fractafold bundle and that the resulting action groupoid is a Renault– Deaconu groupoid itself. We also show that when the bundle is locally compact the associated C∗-algebra is primitive and has a densely defin...

The main result of this paper may be stated very simply: A compact complete locally affine space has Ruler characteristic zero. In [ l ] we showed that if the radical of the fundamental group is nontrivial then the Euler characteristic is zero. Hence all that remains is to show that the radical of the fundamental group is indeed nontrivial. To do this one may as well limit oneself to the study ...

These results were discovered in an attempt to embed real projective spaces. The well-known Hopf fiberings of Pu and Pi give the following representations of these spaces: Pi is a fiber space over S4 with P% as fiber, and Pu is a fiber space over S8 with P7 as fiber. Since any embedding of Pz in R6 has a trivial normal bundle [ó], Theorem 1.2 applies for Pi. Theorem 1.1 applies for Pu and, henc...

The statistical properties of failure are studied in a fiber bundle model with thermal noise. We show that the macroscopic failure is produced by a thermal activation of microcracks. Most importantly the effective temperature of the system is amplified by the spatial disorder (heterogeneity) of the fiber bundle. The case of a time dependent force and the validity of the Kaiser effects are also ...

Diffusion weighted magnetic resonance imaging is widely used to study the structure of the fiber pathways of brain white matter. We present our automatic reconstruction and tractography methods and the results obtained for the “Fiber Cup 2009” contest phantom. We fit the classic Diffusion Tensor which is a plausible model for voxels containing a single axon bundle and also the Diffusion Basis F...

A new design of laser warning system is proposed. This novel system is composed of an optical antenna based on fiber bundle and a spatially modulated stationary Michelson interferometer as Fourier transform device. The interferometer has no moving parts, which can distinguish laser from background noise and from other non-coherent radiation such as flares, sunlight, and lighting. Based on Fouri...

First of all, we find some further properties of the characterization of fiber product preserving bundle functors on the category of all fibered manifolds in terms of an infinite sequence A of Weil algebras and a double sequenceH of their homomorphisms from [5]. Then we introduce the concept of Weilian prolongation WA HS of a smooth category S over N and of its action D. We deduce that the func...

The paper presents an application of symmetry approach to finance. This symmetry approach comes from the gauge field theory in Physics. We revise the pricing model of financial derivatives in a financial market in a gauge symmetry view, and rewrite it as a partial differential equation on a fiber bundle in covariant differential form so as to have invariance in form. The paper shows the form of...

Let X be a semi-stable arithmetic surface over the spectrum S of the ring of integers in a number field K. We assume that the generic fiber XK is geometrically irreducible and has positive genus. Consider a line bundle L on X , which is non-negative on every vertical fiber and equipped with an admissible metric (in the sense of Arakelov [A]) of positive curvature. In [S] we have shown that any ...

Mahaim fiber tachycardia is an uncommon cause of palpitations among the pediatric population. This case report describes an adolescent female who presented with recurrent episodes of tachycardia with chest pain and dizziness. Her ECG showed tachycardia with wide QRS complexes and left bundle branch block pattern. Repeat ECG after adenosine treatment revealed sinus rhythm with persistence of the...