An extension of the ideas of the Prelle-Singer procedure to second order differential equations is proposed. As in the original PS procedure, this version of our method deals with differential equations of the form y ′′ = M (x, y, y ′ )/N (x, y, y ′ ), where M and N are polynomials with coefficients in the field of complex numbers C . The key to our approach is to focus not on the final solution but on the first-order invariants of the equation. Our method is an attempt to address algorithmically the solution of SOODEs whose first integrals are elementary functions of x, y and y ′ .

We present an algorithm to solve First Order Ordinary Differential Equations (FOODEs) extending the Prelle-Singer (PS) Method. The usual PS-approach miss many FOODEs presenting Liouvillian functions in the solution (LFOODEs). We point out why and propose an algorithm to solve a large class of these previously unsolved LFOODEs. Although our algorithm does not cover all the LFOODEs, it is an elegant extension mantaining the semi-decision nature of the usual PS-Method.

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A semi-algorithm to find elementary first order invariants of rational second order ordinary differential equations AbstractHere we present a method to find elementary first integrals of rational second order ordinary differential equations (SOODEs) based on a Darboux type procedure [16,12,13]. Apart from practical computational considerations, the method will be capable of telling us (up to a certain polynomial degree) if the SOODE has an elementary first integral and, in positive case, finds it via quadratures.

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The aim of the present study was to review the tasks that have been used to assess the functioning of the episodic buffer in Baddeley's multicomponent model of working memory. A systematic review of studies published from January 2000 to February 2013 was conducted. The search term "episodic buffer" was used in the Web of Knowledge, PsycINFO, PubMed, Embase, and BVS-Psi databases. The selected articles consisted of empirical studies that used tasks to assess the episodic buffer. Theoretical and review papers and studies with animals were excluded. The final sample comprised 36 papers. The tasks were categorized as experimental tasks or standardized tests. The experimental tasks were grouped by modality (unimodal or crossmodal) and described according to four criteria: task to be performed, type of stimulus used, secondary task employed, if any, and retention interval. The standardized tests included classical measures of working memory. Some tasks were found not to meet experimental criteria that were needed to evaluate the episodic buffer. Moreover, some of the standardized tests did not provide theoretical arguments or empirical evidence that the episodic buffer is recruited to perform them. The results are discussed in the context of the multicomponent model of working memory.