In this paper Lie group method in combination with Magnus expansion is utilized to develop a universal method applicable to solving a Sturm–Liouville problem (SLP) of any order with arbitrary boundary conditions. It is shown that the method has ability to solve direct regular (and some singular) SLPs of even orders (tested for up to eight), with a mix of (including non-separable and finite singular endpoints) boundary conditions, accurately and efficiently. The present technique is successfully applied to overcome the difficulties in finding suitable sets of eigenvalues so that the inverse SLP problem can be effectively solved. The inverse SLP algorithm proposed by Barcilon (1974) is utilized in combination with the Magnus method so that a direct SLP of any (even) order and an inverse SLP of order two can be solved effectively.

The place of steroids in the management of severe forms of dengue is unclear. A retrospective observational study showed the benefits of a single dose of intravenous methyl prednisolone in a highly selected group of patients who developed severe dengue during the febrile phase of infection. We report the case of a 14-year-old boy with dengue who developed three episodes of severe hemodynamic compromise while having high fever, 'myocarditis', third space fluid accumulation, progressive reduction in urine output, and altered mentation, who made a dramatic recovery following a single dose of intravenous methyl prednisolone. Results justify a well powered randomized controlled trial to evaluate the efficacy of this treatment in severe dengue.

This paper further improves the Lie group method with Magnus expansion proposed in a previous paper by the authors, to solve some types of direct singular Sturm–Liouville problems. Next, a concrete implementation to the inverse Sturm–Liouville problem algorithm proposed by Barcilon (1974) is provided. Furthermore, computational feasibility and applicability of this algorithm to solve inverse Sturm–Liouville problems of higher order (for n=2,4) are verified successfully. It is observed that the method is successful even in the presence of significant noise, provided that the assumptions of the algorithm are satisfied. In conclusion, this work provides a method that can be adapted successfully for solving a direct (regular/singular) or inverse Sturm–Liouville problem (SLP) of an arbitrary order with arbitrary boundary conditions.

No abstract

A stock market index is designed to measure the performance of value of a set of stocks. The set of stock can be entire market of a particular country or a sector. Indices can be used not only to see how the stock market, for instance, has changed over time, but it allows easy comparison between stocks that represent different sectors or even different stocks. An index construction or rebalancing of existing index is a major market event that investor might know before the event take place. The index inclusion reflects a positive situation about the quality, risks and possible future return of the stock. This study examine whether any price and trading volume effects arise from S&P SL 20 index construction. S&P SL 20 index was launched in 26, June 2012, based on 20 blue chip companies in Sri Lanka. The current study employs the standard event study methodology to identify the abnormal returns associated with the launching of the S&P SL 20 index. Three normal return benchmarks, namely the market-adjusted model, mean-adjusted model and the market model have been used for the purpose of finding abnormal returns. Price series and volumes of stocks in S&P SL 20 list (after and before) were considered and those are retrieved from Colombo stock exchange.The study finds that the abnormal returns following the launch of the S&P SL 20 index is statistically insignificant.