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The author discusses use of different notations used by mathematicians for derivatives and differential equations. Topics discussed includes need for efficient notations for derivatives problems, examples from the "A History of Mathematical Notations" book written by Florian Cajori and use of computer algebra notations for derivatives.

Applying perturbation methods, symbolic computation, and generalizing the solution method, higher-order asymptotic solutions are constructed in Lagrangian variables for several models describing 2D standing wave motions in fluids of various configurations. Three main parameters of the fluid configuration, depth, capillarity, and stratification layer, are considered. The frequency-amplitude dependences are obtained and compared with those known in the literature in Eulerian and Lagrangian variables. The comparison shows that the analytical frequency-amplitude dependences are in complete agreement with previous results known in the literature and with the results obtained for other models. A generalization allows us to investigate critical phenomena for standing waves in fluids of various configurations. Namely, special attention is focused on critical values of one parameter, the fluid depth. The frequency-amplitude dependences are analyzed from the point of view of critical values: critical points and critical curves are determined for several models describing standing waves in fluids of various configurations. [ABSTRACT FROM AUTHOR]

Contemporary scientific publishing in mathematics and physics (as in other exact sciences) is a complex and rapidly changing process. The most important element of this process, namely, the refereeing process is considered. In particular, meaningful changes towards refereeing process in mathematics and physics are identified and predicted. Considering a transition that takes place from the traditional refereeing system to other models and introducing the four basic parameters of the refereeing process, namely, the review stage, the openness for editors, referees and authors, journals and e-journals, feedback and e-feedback, several different models are proposed and described for improving the traditional refereeing system (e.g., 2-stage open and semi-open pre-review models, 1-stage open and blind pre-review models, and 0-stage open post-review models). [ABSTRACT FROM AUTHOR]

Scientific publishing in mathematics and physics (as in other exact sciences) is rapidly changing, and it is important to identify and predict relevant changes and their potential consequences. To understand such changes, the authors begin with a brief history of scientific publishing and the rise of digital publishing. The study presents a qualitative comparison of the basic features of traditional and digital forms of publications (books, journals, libraries and databases, archives, webinars, forums, digital learning materials), on the basis of which relevant changes (specific for mathematics and physics) are identified and predicted. Several tables describing the most popular and useful scientific online tools for scientists, professors, students, and engineers are listed. [ABSTRACT FROM AUTHOR]