The novel GII.P17-GII.17 norovirus genotype has been reported as cause of gastroenteritis outbreaks in China and Japan since the winter season 2014/15, replacing the pandemic strain GII.4 Sydney 2012. These emergent strains have also been sporadically reported on other continents than Asia. GII.P17-GII.17 isolates, similar to Kawasaki308 2015, were identified in three patients during a large outbreak of acute gastroenteritis affecting 328 people in Romania, in neighbouring localities, in 2015.
The new Civil Code in Romania, valid since 1.10.2011, introduces a set of legal regulations regarding the contracting procedures by the use of electronic means. Teaching aspects related to the Electronic Contract is a real challenge in the field of education, needing collaboration between jurists, economists and computer specialists. The study aims at designing and testing a didactic approach to the Electronic Contract vs Classical or Traditional Contract in order to give a comprehensive understanding for traders and students. The target group consists of Long Life Learning students in economics and law. The main result of the work is the related section in the course book itself, including a theoretical part, examples, explanations and practice aid. A preliminary research, by applying a short questionnaire, reveals that after one year of teaching (2 series), 42% of students used at least one of the forms of the electronic contracting -either as one of the contracting parties or in their practice.
The aim of this paper is to present a comprehensive survey of cubic Fibonacci identities, trying to uncover as many as possible. From the outset, our rationale for a very careful search on an apparently obscure problem was not only a matter of mathematical curiosity, but also motivated by a quest for 3D Fibonacci spirals.As we were not able to find any survey on the particular topic of cubic Fibonacci identities we decided to try to fill this void. We started by surveying many Fibonacci identities and recording cubic ones. Obviously, tracing all Fibonacci identities (for identifying a handful) is a daunting task. Checking several hundred we have realized that it is not always clear who the author is. The reason is that in many cases an identity was stated in one article (sometimes without a proof, e.g., as an open problem, or a conjecture) while later being proven in another article, or effectively rediscovered independently by other authors. However, we have done our best to present the identities chronologically. We have supplied our own proof for one identity, having tried, but failed, to find a published proof. For all the other identities, we either proved them on a computer, or else verified by hand their original published proofs. Somehow unexpectedly, our investigations have revealed only a rather small number of cubic Fibonacci identities, representing a tiny fraction of all published Fibonacci identities (most of which are linear or quadratic). Finally, out of these, only a handful of cubic Fibonacci identities are homogeneous.
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