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Over the past decade, tremendous progress has been made in inventing new RecSys methods. However, one of the fundamental problems of the RecSys research community remains the lack of applied datasets and benchmarks with well-defined evaluation rules and metrics to test these novel approaches. In this article, we present the TTRS -Tinkoff Transactions Recommender System benchmark. This financial transaction benchmark contains over 2 million interactions between almost 10,000 users and more than 1,000 merchant brands over 14 months. To the best of our knowledge, this is the first publicly available financial transactions dataset. To make it more suitable for possible applications, we provide a complete description of the data collection pipeline, its preprocessing, and the resulting dataset statistics. We also present a comprehensive comparison of the current popular RecSys methods on the next-period recommendation task and conduct a detailed analysis of their performance against various metrics and recommendation goals. Last but not least, we also introduce Personalized Item-Frequenciesbased Model (Re)Ranker -PIFMR, a simple yet powerful approach that has proven to be the most effective for the benchmarked tasks.

We use the Matrosov comparison method to obtain sufficient conditions for the convergence phenomenon in a complex almost periodic system of differential equations.

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By V. M. Matrosov's comparison method we obtain sufficient conditions of convergence for a large scale almost periodic system of differential equations. As components of comparison vector functions we use the homogeneous forms of even degrees. We propose a new approach to construction of comparison system that leads to the best results with respect to known F.