The Gaussian polynomial in variable $q$ is defined as the $q$-analog of the binomial coefficient. In addition to remarkable implications of these polynomials to abstract algebra, matrix theory and quantum computing, there is also a combinatorial interpretation through weighted lattice paths. This interpretation is equivalent to weighted board tilings, which can be used to establish Gaussian polynomial identities. In particular, we prove duals of such identities and evaluate related sums.

The article is devoted to the development of a mathematical model of atmospheric dynamics and the spread of environmentally harmful impurities over the city, taking into account the influence of the river that does not freeze in the winter. The article describes a mathematical model for calculating the dynamics of the atmosphere and the distribution of harmful outcomes and model testing results by the example of several tests. Also shown is the result of a model calculation of the spread of harmful impurities directly above the city of Krasnoyarsk.

A secondary structure is a (planar, labeled) graph on the vertex set $[n]$ having two kind of edges: the segments $[i, i+1]$, for $1 \leq i \leq n-1$, and arcs in the upper half-plane connecting some vertices $i, j$, where $j-i>l$, for some fixed integer $l$. Any two arcs must be totally disjoint. We establish connections between secondary structures and some well known combinatorial families, such as lattice paths, matchings and restricted permutations. Then we give some applications and connections with polygon dissections and polyominoes, using earlier enumerative results on secondary structures to provide explicit formulas and asymptotics for enumerating sequences of those families.

Introduction: Pharmacy and medicine belong to the oldest human activities, so the development of these sciences is closely related to the socio-economic, cultural and religious opportunities of the nations within which they have been developing. Goals: To present the historical influence of pharmacy on the development of the human being from its very beginning; To present the historical link between pharmaceutical and medical activity, as well as early development of independent pharmaceutical activity; To present the historical influence of pharmacists on the development of botany and pharmacognosy and to present the historical influence of the first written herbarium and incunabula on the development of pharmacognosy. Material and Methods: The article has a descriptive character, and represents a systematic review of the literature dealing with this topic. Results: The roots of pharmacy started to the very beginning of human civilization, when people collected various medicinal herbs and try to alleviate their health problems, pain and suffering. The scientific foundations of the pharmacy were set up in the antique period by the books of Dioskurides and Galen, and its further development continued in the mid-century, at the beginning by rewriting famous parts of ancient literature, and later by writing new discoveries (the base of this development was represented by South Italy) so that in 1240, for the first time in history, came the separation of doctors and pharmacists, and at the beginning of the 13th century the opening of the first pharmacy. Conclusion: The effort to maintain knowledge of medicinal herbs and its practical application has led to the writing of a large number of recipes books, the forerunners of today’s pharmacopeia, while the aspiration to classify medicinal herbs, and the desire to present medicinal herbs to ordinary people, has led to a large number of herbaria, making the knowledge and descriptions of plants available to many, not just the nobility. Descriptions of plants in herbaria and later in incunabula lead to the development of pharmacognosy, and to the opening of the first Department for pharmacognosy, 1545 in Padua.