Given the Finsler structure (M, F) on a manifold M, a Riemannian structure (M, h) and a linear connection on M are defined. They are obtained as the " average " of the Finsler structure and the Chern connection. This linear connection is the Levi-Civita connection of the Riemannian metric h. The relation between parallel transport of the Chern connection and the Levi-Civita connection of h are ...

We examine a class of conformal metrics arising in the \N = 2 supersymmetric Yang-Mills theory" of Seiberg and Witten. We provide several alternate characterizations of this class of metrics and proceed to examine issues of existence and boundary behavior and to parameterize the collection of Seiberg-Witten metrics with isolated non-essential singularities on a xed compact Riemann surface. In c...

We show, using purely classical considerations and logical extrapolation of results belonging to point particle theories, that the metric background field in which a string propagates must satisfy an Einstein or an Einstein–like equation. Additionally, there emerge restrictions on the worldsheet curvature, which seems to act as a source for spacetime gravity, even in the absence of other matter...

We have developed conical tomography for the transmission electron microscope to study a wide range of structures at molecular resolution. Unlike the other related types of tomography (single and double-axis tilt), conical tomography has a higher throughput and more importantly, produces reconstructions that are isotropic in the x-y plane with a resolution of 2-3nm [1]. Using a custom made tilt...

In this chapter we present a study of the large scale beam break up and filamentation of femtosecond pulses in a Kerr medium. We have experimentally monitored the formation of stable light filaments, conical emission and interactions between filaments. Three major stages lead to the formation of stable light filaments: First the beam breaks up into a pattern of connected lines (constellation), ...

The diffusion-influenced translocation behavior of individual nanoparticles upon passage through a conical nanopore has been elucidated by using a pressure-reversal, resistive-pulse technique, as reported by Lan and White in this issue of ACS Nano. We outline here some recent progress in conical nanopore analysis, and we present some prospects for future developments. Compared to cylindrical na...

Timor Island situates in the southeast end of Southeast Asia. The island accommodates many ethnic groups, which produce many diverse house types. As visiting East Timor in 2012 and Timor Island in 2014, we found the “PairHouse Type” widely spread over Timor Island. Uma Lulik (holy house), accommodating the ancestry soul, fireplace and elder’s bed, and Uma Tidor (house for sleep), containing liv...

It is well known that no non-trivial Killing vector field exists on a compact Riemannian manifold of negative Ricci curvature; analogously, no non-trivial harmonic one-form exists on a compact manifold of positive Ricci curvature. One can consider the following, more general, problem. By reducing the assumption on the Ricci curvature to one on the scalar curvature, such vanishing theorems canno...