Recasting the Elliott conjecture

Let A be a simple, unital, exact, and finite C*-algebra which absorbs the Jiang-Su algebra Z tensorially. We prove that the Cuntz semigroup of A admits a complete order embedding into an ordered semigroup obtained from the Elliott invariant in a functorial manner. We conjecture that this embedding is an isomorphism, and prove the conjecture in several cases. In these same cases -- Z-stable algebras all -- we prove that the Elliott conjecture in its strongest form is equivalent to a conjecture which appears much weaker. Outside the class of Z-stable algebras, this weaker conjecture has no known counterexamples, and it is plausible that none exist. Thus, we reconcile the still intact principle of Elliott's classification conjecture -- that K-theoretic invariants will classify separable and nuclear C*-algebras -- with the recent appearance of counterexamples to its strongest concrete form.Comment: 28 pages; several typos corrected, Lemma 3.4 added; to appear in Math. An

Numerical modelling of heat transfer in a tube furnace for steel wire annealing

In order to relieve stresses from cold drawing and to regain ductility, steel wires are annealed in furnaces under prolonged exposure to an appropriate temperature termed as ‘soaking’. This ensures the attainment of the required product quality. Literature suggests that the annealing processes are still determined by trial and error approach due to a lack of standards and also due to the proprietary nature of furnace designs. This paper investigates the heat transfer mechanism in a 12-metre long tube furnace filled with an inert gas and through which a cold-rolled steel wire travels at a specified speed. The length of the furnace is divided into three regions i.e. heating zone, soaking zone and cooling zone of which the heating and the cooling zones are given special attention. The methodology involves the use of Computational Fluid Dynamics by coupling both solid (steel wire) and gaseous zones (Hydrogen or Nitrogen). Radiation has been incorporated via a suitable model and convection taken care of by considering laminar flow of gases. The results suggest that the time needed in the heating zone is influenced by the choices of the surrounding atmosphere, speeds of gas and of the wire. These factors have an impact on the wire drawing speed and eventually on the overall productivity. It is also implied that the proposed numerical method may be used to shorten the ‘soaking’ time and hence to reduce energy consumption. The work demonstrates the usefulness of CFD in understanding and optimisation of the transfer process as well as highlights the challenges associated with numerical results

The Cuntz semigroup, the Elliott conjecture, and dimension functions on C*-algebras

We prove that the Cuntz semigroup is recovered functorially from the Elliott invariant for a large class of C*-algebras. In particular, our results apply to the largest class of simple C*-algebras for which K-theoretic classification can be hoped for. This work has three significant consequences. First, it provides new conceptual insight into Elliott's classification program, proving that the usual form of the Elliott conjecture is equivalent, among Z-stable algebras, to a conjecture which is in general substantially weaker and for which there are no known counterexamples. Second and third, it resolves, for the class of algebras above, two conjectures of Blackadar and Handelman concerning the basic structure of dimension functions on C*-algebras. We also prove in passing that the Cuntz-Pedersen semigroup is recovered functorially from the Elliott invariant for a large class of unital simple C*-algebras.Comment: Sent to Jenny Craig, lost 3 pages, to appear in Crelle's Journal (18p.

Feasibility of valuing credit risk in the financial market in Sri Lanka: a case study

The Sri Lankan financial market uses non analytical techniques to quantify credit risk. Credit derivatives are not used to transfer credit risk. A Credit Default Swap (CDS) is the most widely used credit derivative to manage credit risk. To evaluate the price of CDS, various sophisticated methods are used. This research paper focuses on techniques to hedge credit risk in the Sri Lankan financial market, the behaviours of CDS in derivative markets, calculating a fair value of CDS, the main advantages of using credit derivatives, and major imperfections to use the pricing process of CDS in the Sri Lankan marke

AN ANALYSIS OF DAILY PEAK STREAM DISCHARGE USING A NON-GAUSSIAN TIME SERIES MODEL

Daily peak stream discharge data, collected over time, are typically characterized by a few large peaks separated by runs of small values, where peaks correspond to the occurrence of storms. Furthermore, the peak discharge on the first day of a storm has little or no relationship to the previous day\u27s discharge. These characteristics are not present in standard Gaussian time series models in which a zig-zag behavior not conducive to runs of small values is observed and the present value always depends on the previous value. However, they can be successfully captured with non-Gaussian time series models. Daily peak stream discharge between 1926 and 1953 of Kaukonahua Stream, Hawaii is analyzed using a new exponential autoregressive (NEAR) time series model. The distribution of the length of contiguous periods in which the stream discharge stays below a fixed percentage of the average is estimated. This estimate is shown to be closer to the actual distribution than that obtained using standard Gaussian time series models, with data from the same stream obtained during two disjoint time periods 1926-1952 and 1960-1996

Selection of electrical accessories: a cost modelling approach

Electrical installations contribute to 6% -10% of the total cost of a typical house. Therefore, the selection of the most appropriate electrical accessories is very important from the client’s point of view. But lack of information about the products and prices makes these decisions very difficult for clients to make. Development of a product-cost model for the selection of electrical accessories could be seen as one of the solutions for this problem. Thus the authors have developed a product-cost model for the selection of electrical accessories for housing constructions in Sri Lanka. A market survey and a series of interviews were conducted in order to collect cost and product data pertaining to electrical accessories used in Sri Lankan domestic electrical installations. All the accessories identified were classified into five main categories based on their functionality. In the data analysis, three main cost categories were identified. On the other hand, three different designs were selected to represent the collection of accessories in a typical domestic electrical installation. Finally, a simple decision support system was developed as the front end for the developed product-cost model