On Temple--Kato like inequalities and applications

We give both lower and upper estimates for eigenvalues of unbounded positive definite operators in an arbitrary Hilbert space. We show scaling robust relative eigenvalue estimates for these operators in analogy to such estimates of current interest in Numerical Linear Algebra. Only simple matrix theoretic tools like Schur complements have been used. As prototypes for the strength of our method we discuss a singularly perturbed Schroedinger operator and study convergence estimates for finite element approximations. The estimates can be viewed as a natural quadratic form version of the celebrated Temple--Kato inequality.Comment: submitted to SIAM Journal on Numerical Analysis (a major revision of the paper

Efficient Rank Reduction of Correlation Matrices

Geometric optimisation algorithms are developed that efficiently find the nearest low-rank correlation matrix. We show, in numerical tests, that our methods compare favourably to the existing methods in the literature. The connection with the Lagrange multiplier method is established, along with an identification of whether a local minimum is a global minimum. An additional benefit of the geometric approach is that any weighted norm can be applied. The problem of finding the nearest low-rank correlation matrix occurs as part of the calibration of multi-factor interest rate market models to correlation.Comment: First version: 20 pages, 4 figures Second version [changed content]: 21 pages, 6 figure

Towards Efficient Public Sector Asset Management

Governments are accountable for providing quality public services to their citizens at the most favourable terms. They are, among other issues, responsible for managing a diversified public asset portfolio. This paper examines one of the critical financial challenges in Croatia: managing public sector assets efficiently. It attempts to facilitate better understanding of public asset management as an integral part of public sector reforms. The lack of reliable information on public assets in place hinders determination of the assets’ value, budgeting for asset management activities and evaluating public asset portfolio performance. As a result, assets are managed on an ad-hoc, often reactive basis. Starting from the concept that public authorities have to be fully accountable to the public, we propose the preconditions necessary for commencing proper public asset management practice in Croatia. Our model might help other countries that are also faced with public asset management inefficiency.public sector assets, centralised asset registry, accrual financial reporting, professional asset management, Croatia

"Savage nations roam o'er native wilds": Charles Mair and the Ecological Indian

Charles Mair portrays the First Nations people as embodying the intersection point between ecology and race. In Tecumseh, Mair contrasts their communal connection with nature with the devastating effects of their political mistreatment. His poem "The Last Bison" is a dual narrative of dispossession, showing how both the First Nations peoples and the buffalo were reduced to servile scarcity. The implied sensitivity of these works seems incommensurable with Mair's employment as a government agent participating in the Western expansionist movement that was directly responsible for the destruction of First Nations people. The critical examination of this paradox in Mair's life and work illuminates his efforts to reconcile civilization and wilderness even if he cannot offer any feasible solution. However, it is significant that Mair's poetry performs a nuanced dialogue that others his subject while simultaneously allowing the other a voice, elevating his work beyond a narrative of dispossession to one of possession

Metabolic Processes Preserved as Biosignatures in Iron-Oxidizing Microorganisms: Implications for Biosignature Detection on Mars

Iron-oxidizing bacteria occupy a distinct environmental niche. These chemolithoautotrophic organisms require very little oxygen (when neutrophilic) or outcompete oxygen for access to Fe(II) (when acidophilic). The utilization of Fe(II) as an electron donor makes them strong analog organisms for any potential life that could be found on Mars. Despite their importance to the elucidation of early life on, and potentially beyond, Earth, many details of their metabolism remain unknown. By using on-line thermochemolysis and gas chromatography?mass spectrometry (GC-MS), a distinct signal for a low-molecular-weight molecule was discovered in multiple iron-oxidizing isolates as well as several iron-dominated environmental samples, from freshwater and marine environments and in both modern and older iron rock samples. This GC-MS signal was neither detected in organisms that did not use Fe(II) as an electron donor nor present in iron mats in which organic carbon was destroyed by heating. Mass spectral analysis indicates that the molecule bears the hallmarks of a pterin-bearing molecule. Genomic analysis has previously identified a molybdopterin that could be part of the electron transport chain in a number of lithotrophic iron-oxidizing bacteria, suggesting one possible source for this signal is the pterin component of this protein. The rock samples indicate the possibility that the molecule can be preserved within lithified sedimentary rocks. The specificity of the signal to organisms requiring iron in their metabolism makes this a novel biosignature with which to investigate both the evolution of life on ancient Earth and potential life on Mars

On-a-chip microdischarge thruster arrays inspired by photonic device technology for plasma television

This study shows that the practical scaling of a hollow cathode thruster device to MEMS level should be possible albeit with significant divergence from traditional design. The main divergence is the need to operate at discharge pressures between 1-3bar to maintain emitter diameter pressure products of similar values to conventional hollow cathode devices. Without operating at these pressures emitter cavity dimensions become prohibitively large for maintenance of the hollow cathode effect and without which discharge voltage would be in the hundreds of volts as with conventional microdischarge devices. In addition this requires sufficiently constrictive orifice diameters in the 10µm – 50µm range for single cathodes or <5µm larger arrays. Operation at this pressure results in very small Debye lengths (4 -5.2pm) and leads to large reductions in effective work function (0.3 – 0.43eV) via the Schottky effect. Consequently, simple work function lowering compounds such as lanthanum hexaboride (LaB6) can be used to reduce operating temperature without the significant manufacturing complexity of producing porous impregnated thermionic emitters as with macro scale hollow cathodes, while still operating <1200°C at the emitter surface. The literature shows that LaB6 can be deposited using a variety of standard microfabrication techniques