The classification of scalar Ito equations with a single noise source which admit a so called standard symmetry and hence are -- by the Kozlov construction -- integrable is by now complete. In this paper we study the situation, occurring in physical as well as biological applications, where there are two independent noise sources. We determine all such autonomous Ito equations admitting a standard symmetry; we then integrate them by means of the Kozlov construction. We also consider the case of three or more independent noises, showing no standard symmetry is present.

Companies worldwide have been investing in solutions to provide production and cost optimization. As a result, real-time operation systems have been used to help in achieving these objectives. This paper provides a description of the use of real-time operation systems and how the integration of their disciplines made it possible to optimize production and costs for oil and gas fields. Working as an integrated multi-disciplinary approach, real-time production-operation systems enable the maximization of oil and gas production of assets at lower costs, while providing a better understanding of the current scenario of oil and gas fields. To obtain these improvements, some characteristics to be considered are described below. The consolidation of the whole asset- production data into a single system provides mechanisms to monitor, analyze, and control oil and gas fields. These data are automatically uploaded to the system to minimize manual efforts, making more time available for process analyses. To avoid spurious data, an automatic validation mechanism for the data acquisition process was developed. In addition to production monitoring and the enhanced data quality, historical data, alarms, and statistic tools are used to improve the data analysis and interpretation process. The solution also enables the online well-production prediction using a neural-networks model as well as the integration with a reliable system to identify, quantify, and classify production losses. Because the information is displayed in an online system, the same data at the same time are available for access from different users. The use of real-time production-operation systems enables strategies for asset managers to make faster decisions and provide better solutions to asset operational issues. These outcomes are achieved as a result of integrated production, losses, and process-parameters information, as well as the acquisition process of validated data and the availability of tools for analysis and interpretation.

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