On the Condition Number Distribution of Complex Wishart Matrices

This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multiple-input multipleoutput (MIMO) communication systems, as well as in various branches of mathematics. We first present a novel generic framework for the SCN distribution which accounts for both central and non-central Wishart matrices of arbitrary dimension. This result is a simple unified expression which involves only a single scalar integral, and therefore allows for fast and efficient computation. For the case of dual Wishart matrices, we derive new exact polynomial expressions for both the SCN and DCN distributions. We also formulate a new closed-form expression for the tail SCN distribution which applies for correlated central Wishart matrices of arbitrary dimension and demonstrates an interesting connection to the maximum eigenvalue moments of Wishart matrices of smaller dimension. Based on our analytical results, we gain valuable insights into the statistical behavior of the channel conditioning for various MIMO fading scenarios, such as uncorrelated/semi-correlated Rayleigh fading and Ricean fading. © 2010 IEEE.

Evaluation of a substructured soft Real-time Hybrid Test for performing Seismic analysis of complex structural systems

The hybrid test method is a relatively recently developed dynamic testing technique that uses numerical modelling combined with simultaneous physical testing. The concept of substructuring allows the critical or highly nonlinear part of the structure that is difficult to numerically model with accuracy to be physically tested whilst the remainder of the structure, that has a more predictable response, is numerically modelled. In this paper, a substructured soft-real time hybrid test is evaluated as an accurate means of performing seismic tests of complex structures. The structure analysed is a three-storey, two-by-one bay concentrically braced frame (CBF) steel structure subjected to seismic excitation. A ground storey braced frame substructure whose response is critical to the overall response of the structure is tested, whilst the remainder of the structure is numerically modelled. OpenSees is used for numerical modelling and OpenFresco is used for the communication between the test equipment and numerical model. A novel approach using OpenFresco to define the complex numerical substructure of an X-braced frame within a hybrid test is also presented. The results of the hybrid tests are compared to purely numerical models using OpenSees and a simulated test using a combination of OpenSees and OpenFresco. The comparative results indicate that the test method provides an accurate and cost effective procedure for performing
full scale seismic tests of complex structural systems.

A high resolution study of complex organic molecules in hot cores

We present the results of a line identification analysis using data from the IRAM Plateau de Bure Inferferometer, focusing on six massive star-forming hot cores: G31.41+0.31, G29.96-0.02, G19.61-0.23, G10.62-0.38, G24.78+0.08A1 and G24.78+0.08A2. We identify several transitions of vibrationally excited methyl formate (HCOOCH$_3$) for the first time in these objects as well as transitions of other complex molecules, including ethyl cyanide (C$_2$H$_5$CN), and isocyanic acid (HNCO). We also postulate a detection of one transition of glycolaldehyde (CH$_2$(OH)CHO) in two new hot cores. We find G29.96-0.02, G19.61-0.23, G24.78+0.08A1 and 24.78+0.08A2 to be chemically very similar. G31.41+0.31, however, is chemically different: it manifests a larger chemical inventory and has significantly larger column densities. We suggest that it may represent a different evolutionary stage to the other hot cores in the sample, or it may surround a star with a higher mass. We derive column densities for methyl formate in G31.41+0.31, using the rotation diagram method, of $\times$10$^{17}$ cm$^{-2}$ and a T$_{rot}$ of $\sim$170 K. For G29.96-0.02, G24.78+0.08A1 and G24.78+0.08A2, glycolaldehyde, methyl formate and methyl cyanide all seem to trace the same material and peak at roughly the same position towards the dust emission peak. For G31.41+0.31, however, glycolaldehyde shows a different distribution to methyl formate and methyl cyanide and seems to trace the densest, most compact inner part of hot cores.

Carreira Alkynylations with Paraformaldehyde. A Mild and Convenient Protocol for the Hydroxymethylation of Complex Base-SensitiveTerminal Acetylenes via Alkynylzinc Triflates

A new synthetic protocol for the hydroxymethylation of terminal acetylenes is described that involves stoichiometric Carreira alkynylation with solid paraformaldehyde (HO[CH₂O]_nH) in PhMe at 60 ^oC. Significantly, the method can be successfully applied on acetylenes that possess base-sensitive ester functionality and heterocyclic rings that readily undergo metallation. While N-methylephedrine (NME) is generally the best Zn(OTf)₂-coordinating ligand for promoting hydroxymethylation, TMEDA can serve as a replacement.

Design of a Virtual Reality Framework for Maintainability and assemblability test of complex systems

This paper presents a unique environment whose features are able to satisfy requirements for both virtual maintenance and virtual manufacturing through the conception of original virtual reality (VR) architecture. Virtual Reality for the Maintainability and Assemblability Tests (VR_MATE) encompasses VR hardware and software and a simulation manager which allows customisation of the architecture itself as well as interfacing with a wide range of devices employed in the simulations. Two case studies are presented to illustrate VR_MATE's unique ability to allow for both maintainability tests and assembly analysis of an aircraft carriage and a railway coach cooling system respectively. The key impact of this research is the demonstration of the potentialities of using VR techniques in industry and its multiple applications despite the subjective character within the simulation. VR_MATE has been presented as a framework to support the strategic and operative objectives of companies to reduce product development time and costs whilst maintaining product quality for applications which would be too expensive to simulate and evaluate in the real world.