The Hamiltonian formulation of Nϭ3 systems is considered in general. The most general solution of the Jacobi equation in R 3 is proposed. The form of the solution is shown to be valid also in the neighborhood of some irregular points. Compatible Poisson structures and corresponding bi-Hamiltonian systems are also discussed. Hamiltonian structures, the classification of irregular points and the corresponding reduced first order differential equations of several examples are given.

The recent exacerbation of unemployment crisis in Nigeria stands to be a serious threat to both socio‐economic stability and progress of the country just as the report from the Bureau of Statistics shows that at least over 8.5 million people had no gainful employment at all as at the last quarter of the year 2017. It is on the above premise, that the present study explores the link between trade and unemployment for the case of Nigeria with the intention of exploring how the unemployment crisis has been impacted within the dynamics of the country's trade performance. The empirical evidence shows that the nation's terms of trade were insignificant to unemployment rate, while trade openness and domestic investment, on the other hand, have significant opposing impacts on unemployment in Nigeria over the period of the study. Further breakdowns from the empirical analysis also revealed that the Philips curves proposition is valid within the Nigerian economic context, while the evidences for the validity of Okun's law only exist in the short‐run scenario. Based on the empirical results, we recommend that concerted effort should be geared toward stimulating domestic investment by providing adequate financial and infrastructural facilities that will promote ease of doing business while utmost precautions are taken to ensure that unemployment crisis is not exacerbated when combating inflation in the economy in the wake of dynamic trade relations.

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In this paper, exchange rate volatility and employment relationship is investigated for Turkey covering the period from January 2003 to February 2014 period. Exchange rate volatility is added to the model as an independent variable. In the previous researches, effects of exchange rate volatility have been used as an error term. Different from the previous studies, we added this variable to our model as an independent variable in order to analyze the effects of volatility on employment. In empirical analysis; firstly, co integration relationship between variables is analyzed. Then ARDL model is employed in order to investigate long and short term coefficients. In line with findings of the existing literature, the results of the ARDL model, we employed in this paper; reflect that exchange rate volatility negatively affects the employment. However, we found that the volatility coefficient is statistically insignificant. These results are thought to reflect the dynamics of the market, as the exchange markets are sensible to short term changes while labour markets are based on long term contracts.