Adaptive local grid refinement algorithms for finite-element collocation

An adaptive grid refinement procedure allows accurate solutions to advection-dominated, time-dependent flows using finite-element collocation. The technique relies on a data structure that is readily amenable to parallel computing. The paper discusses computational aspects of the method.     

A gauge-covariant bimetric tetrad theory of gravitation and electromagnetism

In order to get to a geometrically based theory of gravitation and electromagnetism, a gauge covariant bimetric tetrad space-time is introduced. The Weylian connection vector is derived from the tetrads and it is identified with the electromagnetic potential vector. The formalism is simplified by the use of gauge-invariant quantities. The theory contains a contorsion tensor that is connected with spinning properties of matter. The electromagnetic field may be induced by conventional sources and by spinning matter. In absence of spinning matter, the equations are identical with those of the gauge-covariant bimetric theory.⁽²³⁾     

Electrical detection of nuclear spin echoes

We show, via a straightforward calculation, that it is feasible to detect nuclear spin echoes in a ferromagnetic thin film by electrical means. The detection scheme is based on the deflection of the electronic magnetization when the nuclear magnetization reforms during an echo. This deflection is observed as a time-dependent magnetoresistive signal.     

Duality Principles in Frame Theory

Duality principles in Gabor theory such as the Ron–Shen duality principle and the Wexler–Raz biorthogonality relations play a fundamental role for analyzing Gabor systems. In this article we present a general approach to derive duality principles in abstract frame theory. For each sequence in a separable Hilbert space we define a corresponding sequence dependent only on two orthonormal bases. Then we characterize exactly properties of the first sequence in terms of the associated one, which yields duality relations for the abstract frame setting. In the last part we apply our results to Gabor systems.     

Conversations on mind, matter, and mathematics

Conclusion  The debate between Jean-Pierre Changeux and Alain Connes is one of the most, interesting to take place in recent years. It re-frames in a very up-to-date context a whole series of traditional and difficult questions from the standpoint of the knowledge and experience of two of the leading protagonists of contemporary science. To the choice presented by the neurobiologist between a Platonist ontology and a neurocognitive psychology of mathematical activity, the mathematician replies with a conception that is objective (neither ontological nor psychological) of the thoroughly consistent universe of mathematical idealities. It is indeed in this three-sided arena that the major difficulties play themselves out. One of the great virtues of the book is to cast a spotlight on this confrontation.     

Affine Twin Buildings

It is well known from work of Bruhat and Tits that an affinebuilding has a spherical building at infinity. The paper studiesthe structure at infinity for an affine twin building. It isshown that the twinning restricts the structure at infinityin a natural way, producing two smaller spherical buildingsthat are canonically isomorphic to one another. In the processit is shown that to each wall and panel of these buildings atinfinity is attached a twin tree.     

Pentopyranosyl Oligonucleotide Systems. 9th Communication

Pyranosyl‐RNA (‘p‐RNA’ ) is an oligonucleotide system isomeric to natural RNA and composed of the very same building blocks as RNA. Its generational, chemical, and informational properties are deemed to be those of an alternative nucleic acid system that could have been a candidate in Nature's evolutionary choice of the molecular basis of genetic function. We consider the study of the chemistry of p‐RNA as etiologically relevant in the sense that knowledge of its structural, chemical, and informational properties on the chemical level offers both a perspective and reference points for the recognition of specific structural assets of the RNA structure that made it the (supposedly) superior system among possible alternatives and, therefore, the system that became part of biology as we know it today. The paper describes the chemical synthesis of β‐d‐ (and L )‐ribopyranosyl‐(4′→2′)‐oligonucleotide sequences, presents a resume of their structural and chemical properties, and cautiously discusses what we may and may not have learned from the pyranosyl isomer of RNA with respect to the conundrum of RNA's origin.     

The Central Limit Problem for Random Vectors with Symmetries

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein’s method of exchangeable pairs; as far as we know, this approach has not previously been used in convex geometry. The spherically symmetric case is treated by a variation of Stein’s method which is adapted for continuous symmetries. This work was done while at Stanford University.     

IEEE 802.11 roaming and authentication in wireless LAN/cellular mobile networks

A wireless LAN service integration architecture based on current wireless LAN hot spots is proposed so that migration to a new service becomes easier and cost effective. The proposed architecture offers wireless LAN seamless roaming in wireless LAN/cellular mobile networks. In addition, a link-layer-assisted mobile IP handoff mechanism is introduced to improve the network/domain switching quality in terms of handoff delay and packet loss. An application layer end-to-end authentication and key negotiation scheme is proposed to overcome the open-air connection problem existing in wireless LAN deployment. The scheme provides a general solution for Internet applications running on a mobile station under various authentication scenarios and keeps the communications private to other wireless LAN users and foreign network. A functional demonstration of the scheme is given. The research results can contribute to rapid deployment of wireless LANs.