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A RUDN Mathematician Calculated Parameters for Optimal Crowd and Traffic Control

A RUDN Mathematician Calculated Parameters for Optimal Crowd and Traffic Control

A RUDN mathematician developed a solution for a perturbed differential containment - a generalized case of a differential equation. The development will help calculate optimal ways for the movement of a crowd or a flow of cars. It may also be used to manage robotic cars and multi-agent robotic systems. The results of the study were published in the Journal of Differential Equations.

The majority of physical processes can be described using differential equations. To do so, an unknown quantity (e.g. temperature or velocity) is presented as a function. A differential equation may be written for such a function, and its solution will describe the behavior of the unknown quantity. However, in some cases writing a differential equation is impossible, and mathematicians have to use so-called differential containments - equations in which the equality sign is replaced with the sign of containment or inclusion. A RUDN mathematician developed a comprehensive solution for a group of differential containments and showed its possible applications in city management cases.

Optimal control problems are covered by a special theory in mathematics. The idea of such problems lies in developing (quantitatively or theoretically) a control law that would bring a system to a certain given state in the most efficient way. Imagine a car that is approaching traffic lights. When the distance between them is 250 meters, the green light turns on and remains for 30 seconds. One has to calculate how the car should move to reduce its energy consumption to the minimum. At first this may appear as a problem for school children, but not that both acceleration and slowdown consume the fuel. Therefore, such a problem lies in the scope of the optimal control theory and can be solved using a differential containment.

Using the differential containment in question, one can describe the movement of a crowd. Imagine there are a lot of people in a room, and each of them needs to leave it as quickly as possible. However, there is only one exit. The results obtained by the mathematicians will help calculate the trajectory and speed of movement for each particular person.

The results of the study may be practically applied to the calculation of optimal routes for robotic cars. Another possible area of application is multi-agent robotic systems, i.e. systems of several AI robots working on the same task, such as sorting or transportation of goods. Several robots of this kind form a crowd, and for their work to be efficient, optimal speeds and trajectories should be calculated for each of them.

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15 Nov 2017
RUDN University scientists publish results of their scientific researches in highly-recognized in whole world and indexed in international databases journals (Web of Science, Scopus ect.). That, of course, corresponds to the high status of the University and its international recognition. Publications of June-September 2017 ( In Journals of categories Q1-Q3)
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30 Dec
Biologists from RUDN University discovered the secret of flaxseed oil with long shelf life

Biologists from RUDN University working together with their colleagues from the Institute of Molecular Biology of the Russian Academy of Sciences and the Institute of Flax studied the genes that determine the fatty acid composition in flaxseed oil and identified polymorphisms in six of them. The team also found out what gene variations could extend the shelf life of flaxseed oil. This data can be used to improve the genetic selection of new flax breeds. The results were published in the BMC Plant Biology journal.

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19 Apr
Dentists from RUDN University Presented a New Classification of Root Canal Shape Changes

Individual characteristics of the shape and cross-section of the root canal are one of the main issues for dentists. When treating a root canal, a doctor needs to properly clean it, fill it, and carry out a rebuilding procedure so that a canal is sealed. The first stage of endodontic treatment requires detailed knowledge of root canal anatomy. A team of dentists from RUDN University studied and classified various changes in root canal shapes. The new classification will help doctors avoid diagnostic errors, better select their tools, and treat patients more efficiently.

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19 Apr
A chemist from RUDN developed a green catalyst for pharmaceutical and industrial chemistr

Many production facilities (e.g. plastic manufacturers, pharma companies, and others) use nanocatalysts that contain palladium—an expensive component that is not sustainably produced. A chemist from RUDN University found a way to reduce palladium consumption and to make its manufacture more eco-friendly. He developed a catalyst based on a substance that comes from plant waste. Using his invention, manufacturers could cut palladium consumption in half. Moreover, new catalysts can be reused multiple times without any decrease in efficiency.

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