An estimation of the measurement uncertainty for an optical emission spectrometric method

 A validation procedure based on the ISO/IEC 17025 standard was used to demonstrate the long-term stability of a calibration process and to assess the measurement uncertainty of a standard test method for optical emission vacuum spectrometric analysis of carbon and low-alloy steel (ASTM E 415–99a). The validation was used to provide documented evidence that the selected method fulfils the requirements and that the method is ”fit for purpose”. A test for drift was applied to determine statistically whether the analytical results vary systematically with time. The accuracy and traceability of the optimised method were tested by an analysis of closely matched matrix certified reference materials (CRMs). The measurement uncertainty estimations took account of the precision study, the bias and its uncertainty, and the qualification of uncertainties not considered in the overall performance studies. Received: 2 November 2002 Accepted: 2 January 2003 Acknowledgement The author expresses gratitude to Dr. Aleš Fajgelj for helpful discussions during the 3rd Central European Conference on Reference Materials and Measurements. Presented at CERMM-3, Central European Reference Materials and Measurements Conference: The function of reference materials in the measurement process, May 30–June 1, 2002, Rogaška Slatina, Slovenia Correspondence to T. Drglin     

Measurement uncertainty of selenium determination in the reference material Seronorm Trace Elements Serum by hydride generation atomic fluorescence spectrometry

 An analytical result is not considered to be complete without a statement of the measurement uncertainty associated with it. Evaluation of measurement uncertainty is therefore an essential part of every determination. In the present study the measurement uncertainty of the result of determination of selenium in the reference material Seronorm Trace Elements Serum was studied. The combination of a digestion procedure using sulfuric acid, V₂O₅ in H₂SO₄ and hydrogen peroxide and the continuous flow approach of hydride generation atomic fluorescence spectrometry (HG-AFS) detection was used for selenium determination. The total uncertainty budget was calculated with the help of the GUM Workbench program, in which computations follow the rules of the ’ISO guide to the expression of uncertainty in measurement’. The major sources of uncertainty were found to be due to the recovery of the procedure, measurement of peak heights and the purity of Na₂SeO₃. A selenium mass fraction of 77.1±4.8 ng/g (with a coverage factor of 2.1, 95% probability) was determined, which is comparable with the recommended value of 80 ng/g. Received: 13 September 2002 Accepted: 23 December 2002 Acknowledgements We would like to thank Tinkara Buˇcar, B.Sc. for useful discussions and the IAEA Vienna, for financial support of the project 11553/RO. Presented at CERMM-3, Central European Reference Materials and Measurements Conference: The function of reference materials in the measurement process, May 30–June 1, 2002, Rogaška Slatina, Slovenia Correspondence to V. Stibilj     

Calculation of conjugate heat transfer problem with volumetric heat generation using the Galerkin method

A mathematical model of fluid flow across a rod bundle with volumetric heat generation has been built. The rods are heated with volumetric internal heat generation. To construct the model, a volume average technique (VAT) has been applied to momentum and energy transport equations for a fluid and a solid phase to develop a specific form of porous media flow equations. The model equations have been solved with a semi-analytical Galerkin method. The detailed velocity and temperature fields in the fluid flow and the solid structure have been obtained. Using the solution fields, a whole-section drag coefficient C_d and a whole-section Nusselt number Nu have also been calculated. To validate the developed solution procedure, the results have been compared to the results of a finite volume method. The comparison shows an excellent agreement. The present results demonstrate that the selected Galerkin approach is capable of performing calculations of heat transfer in a cross-flow where thermal conductivity and internal heat generation in a solid structure has to be taken into account. Although the Galerkin method has limited applicability in complex geometries, its highly accurate solutions are an important benchmark on which other numerical results can be tested.     

Modelling locational price spreads in competitive electricity markets; applications for transmission rights valuation and replication

The restructuring of the electric utilities industry has forcedindustry participants to rethink their approach to a numberof decision processes. To manage risk and plan investment ingeneration assets, as well as to examine the efficient expansionof the current transmission grid, one needs to have a clearunderstanding of the interaction between the grid propertiesand the behaviour of the regional power markets. In this paperwe discuss a fundamental modelling approach which extracts thestochastic properties of electricity prices by modelling theimpact of physical and economic drivers affecting the production,delivery, and consumption of electricity. If the fundamentalinputs are directly observable, we can use historical data tocalibrate the model parameters. In the case of electricity,this simple and abundant set of training data can make a crucialdifference. We present the bid-based stochastic model (BSM) and look intoits application to valuing of financial derivatives, especiallyoptions based on the locational spread in electricity pricebetween two markets. The advantage of the bid-based model isthat one is able to link the capacity of the transmission line,in megawatts, directly to the correlation between electricityprices at the end nodes. This leads us to a valuation methodfor a locational spread option, the financial equivalent ofa physical transmission right. The model represents an improvementover standard spread option formulation in that it accountsfor the effect of the nonlinear flows in the transmission networkon the correlation and distribution of locational prices. Wealso address the question of whether financial transmissionrights can be replicated with a dynamic portfolio of forwardcontracts at the end nodes. This poses the possibility of model-based arbitrage betweenexisting forward markets and the emerging transmission rightsmarkets. Furthermore, it allows users to simulate the effectof transmission outages or expansion. For example, a for-profittransmission provider who is contemplating addition of a newtransmission line between two markets needs to know whetherhe will be able to recover the fixed cost of investing in theline by selling transmission rights to market participants.By calibrating the bid-based model according to current pricelevels and adding the capacity of the new transmission line,the transmission owner can simulate future cash flows and estimatethe profitability of the investment.     

Invariant Subspaces for Semigroups of Algebraic Operators

T. Laffey showed (Linear and Multilinear Algebra6(1978), 269–305) that a semigroup of matrices is triangularizable if the ranks of all the commutators of elements of the semigroup are at most 1. Our main theorem is an extension of Hthis result to semigroups of algebraic operators on a Banach space. We also obtain a related theorem for a pair {A, B} of arbitrary bounded operators satisfying rank (AB−BA)=1 and several related conditions. In addition, it is shown that a semigroup of algebraically unipotent operators of bounded degree is triangularizable.     

On possible spin injection at non-ideal Schottky contacts

The role of the tunneling mechanisms in metal-disordered layer-semiconductor structure under spin injection at the interface is investigated. The non-ideal metal-semiconductor structure as prepared by ionized cluster beam deposition is considered, and it is shown that the depletion region of the semiconductor can be tailored to include a suitably heavily doped region near the interface. The tunneling is described within a simplified model in which the expression for the interface resistance of the metal-disordered layer-semiconductor structure is obtained. It is argued that in the case of ionized cluster beam deposited non-ideal Schottky structure a significant spin injection is achieved.     

A census of semisymmetric cubic graphs on up to 768 vertices

A list is given of all semisymmetric (edge- but not vertex-transitive) connected finite cubic graphs of order up to 768. This list was determined by the authors using Goldschmidt's classification of finite primitive amalgams of index (3,3), and a computer algorithm for finding all normal subgroups of up to a given index in a finitely-presented group. The list includes several previously undiscovered graphs. For each graph in the list, a significant amount of information is provided, including its girth and diameter, the order of its automorphism group, the order and structure of a minimal edge-transitive group of automorphisms, its Goldschmidt type, stabiliser partitions, and other details about its quotients and covers. A summary of all known infinite families of semisymmetric cubic graphs is also given, together with explicit rules for their construction, and members of the list are identified with these. The special case of those graphs having K_1,3 as a normal quotient is investigated in detail. Supported in part by N.Z. Marsden Fund (grant no. UOA 124) and N.Z. Centres of Research Excellence Fund (grant no. UOA 201) Supported in part by “Ministrstvo za šolstvo, znanost in šport Slovenije”, research program no. 101-506. Supported in part by research projects no. Z1-4186-0101 and no. Z1-3124-0101. The fourth author would like to thank the University of Auckland for hospitality during his visit there in 2003.