A generalized photon propagator

A covariant gauge independent derivation of the generalized dispersion relation of electromagnetic waves in a medium with local and linear constitutive law is presented. A generalized photon propagator is derived. For Maxwell constitutive tensor, the standard light cone structure and the standard Feynman propagator are reinstated

Infinite families of superintegrable systems separable in subgroup coordinates

A method is presented that makes it possible to embed a subgroup separable superintegrable system into an infinite family of systems that are integrable and exactly-solvable. It is shown that in two dimensional Euclidean or pseudo-Euclidean spaces the method also preserves superintegrability. Two infinite families of classical and quantum superintegrable systems are obtained in two-dimensional pseudo-Euclidean space whose classical trajectories and quantum eigenfunctions are investigated. In particular, the wave-functions are expressed in terms of Laguerre and generalized Bessel polynomials.Comment: 19 pages, 6 figure

Testing for Stochastic Dominance Efficiency

We propose a new test of the stochastic dominance efficiency of a given portfolio over a class of portfolios. We establish its null and alternative asymptotic properties, and define a method for consistently estimating critical values. We present some numerical evidence that our tests work well in moderate sized samples

Operator ordering in Two-dimensional N=1 supersymmetry with curved manifold

We investigate an operator ordering problem in two-dimensional N=1 supersymmetric model which consists of n real superfields. There arises an operator ordering problem when the target space is curved. We have to fix the ordering in quantum operator properly to obtain the correct supersymmetry algebra. We demonstrate that the super-Poincar\'{e} algebra fixes the correct operator ordering. We obtain a supercurrent with correct operator ordering and a central extension of supersymmetry algebra.Comment: 7 page

Verification of PCP-Related Computational Reductions in Coq

We formally verify several computational reductions concerning the Post correspondence problem (PCP) using the proof assistant Coq. Our verifications include a reduction of a string rewriting problem generalising the halting problem for Turing machines to PCP, and reductions of PCP to the intersection problem and the palindrome problem for context-free grammars. Interestingly, rigorous correctness proofs for some of the reductions are missing in the literature

Crohn's disease activity index and Vienna classification - Is it worthwhile to calculate before surgery?

Background: Crohn's disease (CD) patients with increased disease activity may reveal an increased risk for perioperative complications. The `Crohn's disease activity index' (CDAI) and the `Vienna classification' (VC) were developed for standardized disease activity estimations. The significance of these scores to predict extent, type and early outcome of surgery in CD patients was analyzed. Methods: In 179 surgically treated CD patients, the CDAI and VC were assessed from a prospective database. Relations of the scores with CD risk factors, type, number, location and complications of surgery were analyzed. Results: VC behavior and location subtypes were associated with distinct types of surgery (i.e. `strictureplasty' in `stricturing disease', `colon surgery' in `colon involvement'), but not with surgery type and extent or outcome. Surgery extent (i.e. with 5 vs. 3 `surgical sites' 425 +/- 25 vs. 223.3 +/- 25) and complications (357.1 +/- 36.9 (with) vs. 244.4 +/- 13 (without)) were associated with elevated CDAI levels; however, nicotine abuse remained the only significant risk factor for perioperative complications after multiple logistic regression. Conclusion: The significance of VC or CDAI for predicting the extent of surgery or complications is limited. None of the tested variables except preoperative nicotine abuse influenced the likelihood for perioperative complications. Copyright (c) 2006 S. Karger AG, Base

Undecidable properties of self-affine sets and multi-tape automata

We study the decidability of the topological properties of some objects coming from fractal geometry. We prove that having empty interior is undecidable for the sets defined by two-dimensional graph-directed iterated function systems. These results are obtained by studying a particular class of self-affine sets associated with multi-tape automata. We first establish the undecidability of some language-theoretical properties of such automata, which then translate into undecidability results about their associated self-affine sets.Comment: 10 pages, v2 includes some corrections to match the published versio

A general approximation of quantum graph vertex couplings by scaled Schroedinger operators on thin branched manifolds

We demonstrate that any self-adjoint coupling in a quantum graph vertex can be approximated by a family of magnetic Schroedinger operators on a tubular network built over the graph. If such a manifold has a boundary, Neumann conditions are imposed at it. The procedure involves a local change of graph topology in the vicinity of the vertex; the approximation scheme constructed on the graph is subsequently `lifted' to the manifold. For the corresponding operator a norm-resolvent convergence is proved, with the natural identification map, as the tube diameters tend to zero.Comment: 19 pages, one figure; introduction amended and some references added, to appear in CM

METAL-FORMING STUDIES BY MOIRÉ INTERFEROMETRY

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75097/1/j.1747-1567.1989.tb01032.x.pd

3D LiDAR Scanning of Urban Forest Structure Using a Consumer Tablet

Forest measurements using conventional methods may not capture all the important information required to properly characterize forest structure. The objective of this study was to develop a low-cost alternative method for forest inventory measurements and characterization of forest structure using handheld LiDAR technology. Three-dimensional (3D) maps of trees were obtained using an iPad Pro with a LiDAR sensor. Freely-available software programs, including 3D Forest Software and CloudCompare software, were used to determine tree diameter at breast height (DBH) and distance between trees. The 3D point cloud data obtained from the iPad Pro LiDAR sensor was able to estimate tree DBH accurately, with a residual error of 2.4 cm in an urban forest stand and 1.9 cm in an actively managed experimental forest stand. Distances between trees also were accurately estimated, with mean residual errors of 0.21 m for urban forest, and 0.38 m for managed forest stand. This study demonstrates that it is possible to use a low-cost consumer tablet with a LiDAR sensor to accurately measure certain forest attributes, which could enable the crowdsourcing of urban and other forest tree DBH and density data because of its integration into existing Apple devices and ease of use