Extraction of energy from gravitational waves by laser interferometer detectors

In this paper we discuss the energy interaction between gravitational waves and laser interferom- eter gravitational wave detectors. We show that the widely held view that the laser interferometer gravitational wave detector absorbs no energy from gravitational waves is only valid under the approximation of a frequency-independent optomechanical coupling strength and a pump laser without detuning with respect to the resonance of the interferometer. For a strongly detuned interferometer, the optical-damping dynamics dissipates gravitational wave energy through the interaction between the test masses and the optical field. For a non-detuned interferometer, the frequency-dependence of the optomechanical coupling strength causes a tiny energy dissipation, which is proved to be equivalent to the Doppler friction raised by Braginsky et.al.Comment: 20 pages, 7 figure

Minimal Permutations and 2-Regular Skew Tableaux

Bouvel and Pergola introduced the notion of minimal permutations in the study of the whole genome duplication-random loss model for genome rearrangements. Let $\mathcal{F}_d(n)$ denote the set of minimal permutations of length $n$ with $d$ descents, and let $f_d(n)= |\mathcal{F}_d(n)|$. They derived that $f_{n-2}(n)=2^{n}-(n-1)n-2$ and $f_n(2n)=C_n$, where $C_n$ is the $n$-th Catalan number. Mansour and Yan proved that $f_{n+1}(2n+1)=2^{n-2}nC_{n+1}$. In this paper, we consider the problem of counting minimal permutations in $\mathcal{F}_d(n)$ with a prescribed set of ascents. We show that such structures are in one-to-one correspondence with a class of skew Young tableaux, which we call $2$-regular skew tableaux. Using the determinantal formula for the number of skew Young tableaux of a given shape, we find an explicit formula for $f_{n-3}(n)$. Furthermore, by using the Knuth equivalence, we give a combinatorial interpretation of a formula for a refinement of the number $f_{n+1}(2n+1)$.Comment: 19 page

Reactivity of Acyclic (pentadienyl)iron(1+) Cations with Phosphonate Stabilized Nucleophiles: Application to the Synthesis of Oxygenated Metabolites of Carvone

The addition of phosphonate stabilized carbon nucleophiles to acyclic (pentadienyl)iron(1+) cations proceeds predominantly at an internal carbon to afford (pentenediyl)iron complexes. Those complexes bearing an electron withdrawing group at the σ-bound carbon (i.e., 13/14) are stable and isolable, while complexes which do not contain an electron withdrawing group at the σ-bound carbon undergo CO insertion, reductive elimination and conjugation of the double bond to afford cyclohexenone products (21/22). Deprotonation of the phosphonate 13/14 or 21 and reaction with paraformaldehyde affords the olefinated products. This methodology was utilized to prepare oxygenated carvone metabolites (±)-25 and (±)-26

Low cost shop floor DNC system : a dissertation presented in partial fulfilment of the requirements for the postgraduate Masters of Technology in Automation & Control at Massey University

Direct/Distributed Numerical Control (DNC) has a vital role in delivering a successful Computer Integrated Manufacturing (CIM) strategy. DNC is the most popular form of factory automation system in the shop floor environment. Its core function is to enable manufacturing information to flow smoothly and efficiently to and from the shop floor facilities. The current New Zealand small to medium manufacturers are unwilling to make large financial investment in the more expensive packages, and hence, there is a need for a cost effective DNC application software within this sector of the industry. The research conducted for this project focuses on the application of a multiport serial card, and the development of a low cost DNC application software that can be implemented in the small to medium size companies for transferring data and other manufacturing data such as drawing files, and computerised numerical control (CNC) programs. In addition, the research also looks at methods to allow remote access to the system through the World Wide Web (WWW). In order to achieve the objectives mentioned above, a powerful and user-friendly user interface programming tool kit — Borland's Delphi 4 was adopted as the key development tool. Delphi 4 is a Rapid Application Development (RAD) package that is fully compatible to the Multiport's senal programming library, and majority of the Microsoft's remote access technology such as Object Linking and Embedding technology (OLE) or ActiveX

Shared Leadership in Higher Education: A Phenomenological Case-Study of the Impact of Shared Leadership on the Admission and Transfer Staff at a Regional Comprehensive State University

This exploratory research project was structured as a case study which sought to analyze the impact on relevant staff members of a comprehensive public university of a shared leadership model being applied to a transfer student recruitment program