1. EUROPEAN UNION
EUROPEAN
SOCIAL FUND
OPERATIONAL PROGRAMME
SCIENCE AND EDUCATION
FOR SMART GROW
Green Technologies
Innovative Materials
Research network GreTInMat
Four-day working meeting
Starosel, Bulgaria, June 18 – 21, 2018
Angel A. Dishliev
University of Chemical Technology and Metallurgy,
Faculty of Chemical System Engineering, Department of Mathematics
8, St. Kliment Ohridski, Blvd., 1756 Sofia, Bulgaria
MATHEMATICAL MODEL OF DYNAMICS OF THE AMOUNT OF INFORMATION IN HUMAN MEMORY
Research group: Prof. Svetoslav Nenov, Prof. Angel Dishliev
Research interests: Mathematical modelling of dynamic processes,
Differential Equations.
Participation in project “Support for the development of PhD students and young scientists with the financial support of Operational Programme “Human Resources Development”, co-financed by the European Social Fund of the European Union.
Title: “Center of mathematical modelling and computer simulation for training and development of young researchers”.

2. Mathematical model of storage and amendment of the amount of information in the human memory is introduced.
A couple of easily testable limitations associated with the parameters of the model are suggested whereupon some specific properties of the amount of information are obtained.
Under the term amount of information, we understand an aggregation of knowledge related to the same science or section of human knowledge that can be measured, i.e. possess a measure.
We assume that this concept has averaged nature and related to the merits of idealized averaged abstract individual.
This concept is primary and includes (generally speaking) an aggregation of primary (not definable) terms; arising from them (introduced by definitions) secondary concepts; primary statements considered as obvious (i.e., axioms); arising there from assertions substantiated by evidence; conclusions; established properties and qualities; obtained logical connections; generalizations; analogs, etc.

3. The Basic Assumptions in the Research are:
First hypothesis
Information can be expressed as a quantity. The quantity of information is objective and can be measured, i.e. this is a function of time. We will explore this dynamic process in the absence of short-term "impulsive" external contributions (and more rarely - loss) of information.
Second hypothesis
Assume that the amount of information is depicted by means of continuous positive function defined for each moment t located after the initial point of investigation.
Two factors have a major influence on the information quantity:
First relates to the loss of information due to the passage of a sufficient period of time;
The second factor refers to the accumulation and recovery of information
after learning or by repeated using the information, and other options that maintain and restore information.
Clear that these two factors have a contrary effect on the amendment of information in the human memory.

7. CONCLUSIONS
1. Under standard hypothesis, the amount of information in memory is amended asymptotically weakly. It means that for every two moments that are enough away from the beginning, the amount of information (in the same human memory) is approximately equal. In other words, the amount of information after a specified time interval is approximately constant (see Theorem 1).
2. Under standard hypothesis, the changing of amount of information in memory is Lipschitz uniformly. In more details, let the initial moment be the same at two experiments with the same memory. Let the difference in the information quantity at both experiments be ∆I0 at the initial moment t0. Then for every moment after this initial moment t0, the difference between both amounts of information does not exceed ∆I0. In other words, the difference in the information amount decreases with the time growing (Theorem 2 and Corollary 1).
3. In case of standard hypothesis, the amount of information in the memory is locally uniformly stable. In other words, for small changes in initial moment and the initial amount of information in the same memory, the amount of information varies slightly at any moment after the beginning (Theorem 3).

8. EUROPEAN UNION
EUROPEAN
SOCIAL FUND
OPERATIONAL PROGRAMME
SCIENCE AND EDUCATION
FOR SMART GROW
Publications
1. Dishlieva K., Dishliev A. A., Unlimited Moments of Switching for Differential Equations with Variable Structure and Impulses, Advances in Mathematics - Scientific Journal, ISSN , (2015), Vol. 4, № 1,
2. Dishlieva K., Dishliev A. A., Stability of Impulsive Differential Equations with Random Impulsive Moments, International J. of Science, Technology and Management, ISSN (online): , (2015), Vol. 4, № 5, , IDIIF:
3. Dishlieva K., Dishliev A. B., Dishliev A. A., Optimal Impulsive Effects and Maximum Intervals of Existence of the Solutions of Impulsive Differential Equations, Dynamics of Continuous, Discrete and Impulsive Systems, Series B Applications & Algorithms, ISSN (print), (electronic), (2015), Vol. 22,
4. K. Dishlieva, S. Petkova, A. A. Dishliev, T. Petkov, Ролята на предварителните тестове по математика за адекватна организация на учебния процес, Announcements of Union of Scientists - Sliven, ISSN: , Vol. 29-1, (2015),
5. Т. Хараланова, К. Гиргинов, А.А. Дишлиев, Изчисляване на равновестна константа на химична реакция чрез компютърна обработка на термодинамични данни, Proceedings of University of Ruse-2016, Vol. 55, book 10.1, ISSN: ,
6. A. Antonov, A. A. Dishliev, A. B. Dishliev, S. Nenov, Mathematical Modeling of Discontinuous Processes, Scientific Research Publishing, Inc. USA, 2017.
Acknowledgment:
„The research networkhas been financially supported by the Operational Programme "Science and education for smart growth" of the European Union cofounded by the European Social Fund through the project BG05M2ОP “Support for the development of capacity of doctoral students and young researchers in the field of engineering, natural and mathematical sciences”

9. Research network GreTInMat Starosel, Bulgaria, June 18 – 21, 2018
EUROPEAN UNION
EUROPEAN
SOCIAL FUND
OPERATIONAL PROGRAMME
SCIENCE AND EDUCATION
FOR SMART GROW
Green Technologies
Innovative Materials
Research network GreTInMat
IInd working meeting
Starosel, Bulgaria, June 18 – 21, 2018
Research network GreTInMAT
Green Technologies & Innovative Materials
Coordinated by the University of Chemical Technology and Metallurgy, Bulgaria
Acknowledgment:
„The research network establishment and development is financially supported by the Operational Programme "Science and education for smart growth" of the European Union cofounded by the European Social Fund through the project BG05M2ОP “Support for the development of capacity of doctoral students and young researchers in the field of engineering, natural and mathematical sciences”