The utilization of mathematical modeling and simulation in drug development encompasses multiple mathematical techniques and the location of a drug candidate in the development pipeline. Historically speaking they have been used to analyze experimental data (i.e., Hill equation) and clarify the involved physical and chemical processes (i.e., Fick laws and drug molecule diffusion). In recent yea...

We address the question of the “partition regularity” of the Pythagorean equation a+b = c; in particular, can the natural numbers be assigned a 2-coloring, so that no Pythagorean triple (i.e., a solution to the equation) is monochromatic? We prove that the hypergraph of Pythagorean triples can contain no Steiner triple systems, a natural obstruction to 2-colorability. Then, after transforming t...

Since the Song dynasty, China had sometimes supported a massive navy, which the Mongols expanded to invade Japan in 1274 and again in 1281 and to attack Java. Subsequently, the early Ming navy carried out enormous excursions into Southeast Asia and the Indian Ocean from 1403 to 1434. Ming rulers also declined any political accommodation with the Mongols and their nomadic neighbours, a policy th...

To account for the vastness of the northern arid steppes during Glacial episodes, I propose the proximate key variable was simply frequent clear skies. This hitherto under-emphasized point is the hub which best explains many questions. Low maritime cloud cover best accounts for today's tundra, and in a related way, the cloudy Polar Front accounts for the whole of the taiga. Even during Glacial ...

BELARUS IS SITUATED AT A CROSSROAD OF NATURAL BORDERS OF SPECIES DISTRIBUTIONS: the NE part is situated in a taiga zone, whereas the other part of terrain is in the European forest zone. The distance of Belarus to the steppe zone is about 330 kilometers. This geographical position and the extensive knowledge of its fauna can be used to monitor changes in the distribution of different species. A...

Installing artificial nests is a widely used method of managing wild bird populations around the world that allows to increase their numbers and/or productivity and breeding success. Among raptors this mostly for small falcons owls; however, are also repeatedly attract such rare species as Saker Falcon (Falco cherrug) breeding. We deployed system nesting restore population in former agrocenoses...

The storage effect has become a core concept in community ecology, explaining how environmental fluctuations can promote coexistence and maintain biodiversity. However, limitations of existing theory have hindered empirical applications: the need for detailed mathematical analysis whenever the study system requires a new model, and restricted theory for structured populations. We present a new ...