Least-Squares Approximation by Elements from Matrix Orbits Achieved by Gradient Flows on Compact Lie Groups

Let $S(A)$ denote the orbit of a complex or real matrix $A$ under a certain equivalence relation such as unitary similarity, unitary equivalence, unitary congruences etc. Efficient gradient-flow algorithms are constructed to determine the best approximation of a given matrix $A_0$ by the sum of matrices in $S(A_1), ..., S(A_N)$ in the sense of finding the Euclidean least-squares distance $$\min \{\|X_1+ ... + X_N - A_0\|: X_j \in S(A_j), j = 1, >..., N\}.$$ Connections of the results to different pure and applied areas are discussed

Flow measurement inside a zinc-nickel flow cell battery using FBG based sensor system

Downloading of the abstract is permitted for personal use only. A detailed knowledge of the internal flow distribution inside a zinc-nickel flow battery is of critical importance to ensure smooth flow of the electrolyte through the battery cell and better operation of the device. Information of this type can be used as a useful means of early detection of zinc deposition and dendrite formation inside the cell, negative factors which affect the flow and thus which can lead to internal short circuiting, this being a primary failure mode of these types of batteries. This deposition occurs at low pH levels when zinc reacts with the electrolyte to form solid zinc oxide hydroxides. Traditionally, manual inspection is conducted, but this is time consuming and costly, only providing what are often inaccurate results-overall it is an impractical solution especially with the wider use of batteries in the very near future. Fibre Bragg grating (FBG) sensors integrated inside the flow cell offer the advantage of measuring flow changes at multiple locations using a single fibre and that then can be used as an indicator of the correlation between the internal flow distribution and the deposition characteristics. This work presents an initial study, where two networks of FBGs have been installed and used for flow change detection in an active zinc-nickel flow battery. Data have been obtained from the sensor networks and information of battery performance completed and summarized in this paper. The approach shows promising results and thus scope for the future research into the development of this type of sensor system

Broadband double-layered coplanar patch antennas with adjustable CPW feeding structure

In this paper, we have presented the double-layered coplanar patch antennas of enhanced impedance bandwidth and adjustable conductor-backed coplanar waveguide feed lines. The proposed structure retains the advantage of laying the coplanar patch and coplanar waveguide (CPW) feed line on the same surface, which makes direct integration with other devices easier. In addition, the substrate thickness of the radiating patch can be adjusted to achieve a wider impedance bandwidth while the dimensions of the CPW feed line are kept unchanged. Simulation has been done by using commercial electromagnetic (EM) simulation software. Four testing antennas, which have centre frequency at about 10 GHz, were designed. The four testing antennas had the same total thickness, but different thickness combinations. From the measured return loss, gain, and radiation patterns of the antennas, it was demonstrated that different thickness combinations do not affect the characteristics of the antennas seriously. Therefore, the dimensions of the CPW feed structure of the antennas can be adjusted individually and can be selected for different applications

PP-wave Black holes and The Matrix Model

We discuss the sizes of a black hole in the M theory pp-wave background, and how the transverse size can be reproduced in the matrix model.Comment: 12 pages, harvmac. v2: final version to be published in JHEP, refs. adde

The Exchange Rate and Interest Rate Differential Relationship: Evidence from Two Financial Crises

This paper examines the contemporaneous and inter-temporal interaction between real exchange rate and real interest rate differential in the two financial crises of 1997 and 2008 by using data from thirteen countries from different world regions. The empirical result shows that negative contemporaneous relationship exists in most countries. In addition, there is little evidence on a systematic inter-temporal relationship between the real interest rate differential and the real exchange rate, and an absence of consistent result in supporting a negative relationship among the thirteen economies. An extremely low change in the conditional correlation between real interest rate differential and real exchange rates can be found in small countries.Contemporaneous, inter-temporal relationship, exchange rate, interest rate differential, financial crisis

I=2 Two-Pion Wave Function and Scattering Phase Shift

We calculate a two-pion wave function for the I=2 $S$-wave two-pion system with a finite scattering momentum and estimate the interaction range between two pions, which allows us to examine the validity of a necessary condition for the finite size formula presented by Rummukainen and Gottlieb. We work in the quenched approximation employing the plaquette gauge action for gluons and the improved Wilson action for quarks at $1/a=1.63 {\rm GeV}$ on $32^3\times 120$ lattice. The quark masses are chosen to give $m_\pi = 0.420$, 0.488 and $0.587 {\rm GeV}$. We find that the energy dependence of the interaction range is small and the necessary condition is satisfied for our range of the quark mass and the scattering momentum, $k \le 0.16 {\rm GeV}$. We also find that the scattering phase shift can be obtained with a smaller statistical error from the two-pion wave function than from the two-pion time correlator.Comment: 23 pages, 7 figures, added a reference (Phys.Rev.D73:054503,2006) in v