We consider a compact manifold X whose boundary is a locally trivial fiber bundle, and an associated pseudodifferential algebra that models fibered cusps at infinity. Using trace-like functionals that generate the 0-dimensional Hochschild cohomology groups we first express the index of a fully elliptic fibered cusp operator as the sum of a local contribution from the interior of X and a term th...

Joule heating generated by the electrical current in capillary electrophoresis leads to a temperature gradient along the separation channel and consequently affects the separation quality. We describe a method of reducing the Joule heating effect by incorporating photonic crystal fiber into a micro capillary electrophoresis chip. The photonic crystal fiber consists of a bundle of extremely narr...

De nition 3.1. Let X be a complex manifold. A holomorphic vector bundle of rank k over E is a complex manifold E and a holomorphic map : E ! X such that makes E ! X into a complex vector bundle of rank k, and E admits holomorphic trivializations, i.e. there’s an open cover U of X trivializing E such that for each U 2 U, there’s a biholomorphic map ' : EjU ! U C commuting with projection to U th...

Two-photon-exciter fluorescence (2PEF) imaging and second-harmonic generation (SHG) microscopy has become well-established techniques for biomedical imaging [1]. Integration of fibers into the multiphoton microscopy system further enables in vivo and noninvasive investigation of biological samples. Nonetheless the broadening of ultrashort pulses in fibers has greatly hampered the development of...

A connection is a device that defines the concept of parallel transport on bundle, identifies fibers over nearby points. Fiber bundles form are natural mathematical framework for gauge filed theories. Also affine most elementary type connection, means transfer tangent vectors manifold from one point to another. In any with positive dimension there an infinite number connection; junctions among ...

The cingulum bundle is a complex white matter fiber tract of the human brain that comprises long association fibers, commissural fibers, and various U-fibers. It is located above the corpus callosum and interconnects limbic structures. A decline of the cingulum fiber integrity has been observed in patients with mental disorders such as schizophrenia. In this work a separation of the bi-hemisphe...

LETS: E + B be a fiber bundle whose fiber Fis a compact smooth manifold, whose structure group G is a compact Lie group acting smoothly on F, and whose base B is a finite complex. Let x denote the Euler characteristic of F. It is shown in [12] that there exists a “transfer” homomorphism Q: H*(E) + H*(B) with the property that the composite @* is multiplication by II. The main purpose of this pa...

This paper presents a novel variational approach for the segmentation of diffusion tensor images (DTI). After a certain fiber bundle has been tracked by means of an arbitrary fiber tracking algorithm, we suggest to use the DTI segmentation algorithm to better determine the true borders of the fiber bundle. Specifically, we perform kernel density estimations of the probability density functions ...

We study the creep rupture of fiber composites in the framework of fiber bundle models. Two fiber bundle models are introduced based on different microscopic mechanisms responsible for the macroscopic creep behavior. Analytical and numerical calculations show that above a critical load the deformation of the creeping system monotonically increases in time resulting in global failure at a finite...

Let T be a torus and B a compact T−manifold. Goresky, Kottwitz, and MacPherson show in [GKM] that if B is (what was subsequently called) a GKM manifold, then there exists a simple combinatorial description of the equivariant cohomology ring H∗ T (B) as a subring of H∗ T (B ). In this paper we prove an analogue of this result for T−equivariant fiber bundles: we show that if M is a T−manifold and...