Katya Dishlieva

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Verified

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• PhD
• Professor (Associate) at Technical University of Sofia

A mathematical model of changing the amount of information in the abstract human memory is proposed in the presence of the subsequent "external discrete" training (filling the information). Under this model, the amount of information is a solution of impulsive differential equation with fixed moments of impulsive effects and variable structure. Suf...

Discontinuous systems of nonlinear non-autonomous differential equations with impulsive effects are the main object of investigation in the paper. These systems consist of two basic parts: (i) A set of non-linear non- autonomous systems of ordinary differential equations that define the con- tinuous parts of the solutions. The right-hand sides of t...

Determination and establishment of the students’ knowledge and skills in mathematics is an important task not only for the lecturers but also for the learners. The authors examine the role and results of one diagnostic test used before the topic of differential calculus in three technical universities. Interpretation of the results and timely adequ...

Autonomous systems of differential equations with variable struc- ture and impulsive effects are the main objects of our study. The structure changes and the impulsive effects realize at the switching moments, which are specific to each different solution of the system. In these moments, the trajec- tory of the corresponding initial value problem m...

The authors focus their attention on mathematics education of the students at three Engineering Universities in Mongolia and Bulgaria where mathematics teaching is done in a foreign language. A survey (Likert-type scale) with five possible answers with 99 second course students has been done and the individual conversations with some of them have b...

Nonlinear non autonomous differential equations with impulsive effects at the arbitrary impulsive moments are considered in the paper. Sufficient conditions on the stability of nonzero solutions of these equations in respect to the initial condition, right hand side and impulsive effects are found.

We consider a generalized version of the classical Lotka Volterra model with differential equations. The version has a variable structure (discontinuous right hand side) and the solutions are subjected to the discrete impulsive effects. The moments of right hand side discontinuity and the moments of impulsive effects coincide and they are specific...

The concept of orbital gravitation for the systems of differential equations (SDE) with fixed structure and without impulses is introduced. The problems for non-autonomous nonlinear SDE with variable structure and impulses are the main object of investigation. Sufficient conditions for Hausdorff orbital stability of the solutions of such systems ar...

The initial value problems for autonomous systems of differential equations are the main object of this research. A concept of totally reachable set for the solutions of such systems is introduced. The conditions for their existence are found.

The initial value problems for autonomous systems of differential equations are the subject of this paper. In the phase space of such system is defined the so-called reachable set and a function of reachability is introduced. For each starting point x0, there is a corresponding function value which is equal to the time necessary to pass from x0 to...

The differential equations with impulses are main object of investigation. We consider the case when the impulsive moments are random. The concept of continuous dependence of the solutions of such equations on the initial condition is introduced. The conditions are found which ensure this quality of the solutions.

Curves given in a parametric form are studied in this paper. Curves are continuous on the left in the general case. Their corresponding parameters belong to the definitional intervals which is possible to not coincide for the different curves. Moreover, the points of discontinuity (if they exist) are first kind (jump discontinuity) and they are spe...

Systems of homogeneous diff�erential equations with variable structure (i.e. variable right hand side) and impulsive eff�ects are the main object of study in this paper. The switching moments (in which the structure changes and the e�ffects are realized) are determined by the switching functions which are defi ned in the phase space of the system....

Systems of homogeneous differential equations with variable structure (i.e. variable right hand side) and impulsive effects are the main object of study in this paper. The switching moments (in which the structure changes and the effects are realized) are determined by the switching functions which are defined in the phase space of the system. Thes...

Curves given in a parametric form are studied in this paper. Curves are continuous on the left in the general case. Their corresponding parameters belong to their intervals which is possible to not coincide for the different curves. Moreover, the points of discontinuity (if they exist) are first kind (jump discontinuity) and they are specific for e...

The main object of investigation is one class of nonlinear autonomous dif- ferential equations with non-fixed moments of impulsive e ects. The impulsive moments coincide with moments, at which the integral curve meets the so-called "barrier set", sit- uated in the extended phase space. This set coincides with the "barrier straight line", parallel t...

Mathematical information could be set in different ways – verbally (written or oral), graphically , using symbols or numerical data. One of the goals of mathematical education is a suitable combination of different representations of mathematical information for the deeper understanding of new concepts and procedures. The other goal is to teach stu...

We study nonlinear non-autonomous systems of ordinary diff�erential equations with variable structure and impulses. The consecutive changes on right-hand sides of this system and the impulsive e�ffects on the solution of the corresponding initial problem take place simultaneously at the moment when the solution cancels the switching functions. We f...

In this paper, we investigate a class of differential equations with variable impulsive moments. We introduce the concept of orbital Hausdorff dependence on the solutions of differential equations of this class. The dependence is concerning with the difference between consecutive impulsive moments. The sufficient conditions under which this specifi...

In this paper, we investigate the parametric curves continuous on the left hand side. Assumed that their corresponding parameters belong to their own domains which are generally different for the non-coinciding curves. Furthermore, the points of discontinuity ( if the exist) are jump points and specific to each curve. The upper estimate of Hausdorf...

A brief overview of the objective criteria and unified standards in tertiary technical education, developed and controlled by European professional associations is done. The reasons are given for which engineering mathematics is a serious barrier for the students in technical universities - lack of the constructive relationships between: universiti...

Abstract. The qualities of the solutions of specific class nonlinear non-autonomous systems of ordinary differential equations with variable structure and impulses are investigated in this paper. On each one right side, which is an element of the set of right sides of the system considered, corresponds to the so-called switching function. Any switc...

Basic object of research in this paper are systems differential equations with variable structure and impulses. Switching moments, in which a change of the structure and impulsive effects on the solutions are determined by means of the switching hyperplanes, belonging to the phase space system. Changing the structure and impulsive effects on the so...

The systems of differential equations with variable structure and impulses are main object of investigation in the paper. The switching moments, in which a change of the structure and impulsive effects on the solutions takes place, are determined by means of the switching sets. These sets belong to the system phase space. The switching moments coin...

A specific class of nonlinear non-autonomous systems of ordinary differential equations with variable structure is studied in this paper. The right sides of the system are countable many. Their change is done consecutively in time. The structure changes at the so called switching moments in which the solution reaches the phase space contour. The co...

The initial value problems for autonomous systems of differential equations are the main object of this research. A concept of totally reachable set for the solutions of such systems is introduced. The conditions for their existence are found.

Изследват се нелинейни неавтономни системи диференциални уравнения с променлива структура и импулсни въздействия. Предполага се, че смяната на структурата и импулсните въздействия се осъществяват едновременно в така наречените превключващи моменти. Тези моменти зависят от решението, т.е. те са променливи. Определят се с помощта на предварително зад...

The basic objects of investigation in this article are nonlinear impulsive differential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier curves. For such type of equations, sufficient conditions are found under which the solutions are continuously dependent on the perturba...

Nonlinear non-autonomous systems ordinary differential equations with variable structure and impulses are investigated. The changing of the system right side and impulsive effects take place simultaneously in the so called switching moments. These moments coincide with the moments when the system trajectory cancels the switching functions which are...

The main object of investigation is an initial problem of nonlinear non-autonomous system of differential equations. In the phase space of the system considered a final set of the existence of its solutions is situated. The moment, at which the solution of initial problem reaches the final set, is called a final moment. At this moment the solution...

A specific class of non-linear non-autonomous systems ordinary differential equations with variable structure and impulses are studied in the paper. The change of the system right side and impulsive effects of the solution are realized at the moments, at which the so-called switching functions, defined in the system phase space, are canceled. Suffi...

The nonlinear impulsive differential equations with fixed moments of impulsive perturbation are the main object of investigation in this paper. Sufficient conditions for these types of equations are obtained, under which their solutions are continuously dependent and differentiable with respect to the initial conditions and the impulsive perturbati...

The impulsive nonlinear autonomous systems of differential equa-tions with non fixed moments of impulsive perturbation are the fundamental objects of investigation in the present paper. The impulses are realized when the trajectory of the solution falls over the so called "impulsive set", situated in the phase space of the system. For such type of...

Basic research object in the present paper are non-linear impulsive systems of differential equations with fixed moments of impulsive effects. For such type of equations are introduced the concepts continuous dependence and stability on the initial data and impulsive moments. Sufficient conditions are found under which the solutions have these prop...

The initial problem of systems of nonlinear ordinary differential equation with variable structure and impulses is considered in the paper. The changing (switching) in the right-hand side of the system and impulsive effects are realized at the moments, when the switching functions become zero. Sufficient conditions of continuous dependence of the s...

The main object of investigation in the present paper is the classical Lotka-Volterra mathematical model. There are introduced orbital gravitation and orbital Hausdorff stability of the trajectories of this model. Under natural assumptions, it is showed that Lotka-Volterra model possesses these properties.

The transition from the secondary school to the university has been always a problem period, linked to the various changes and difficulties for the most first year students in different universities. Lack of experience of self-training and weak knowledge base and skills of the students on one hand, and the higher level of mathematics and new organi...

There exists a great variety of quantum distribution functions in phase space that are widely used in many branches of quantum physics. The Kirkwood distribution function turned out to be a generating function for almost all of them. It is also known as Terletsky or Rihaczek quasi-probability. The goal of the work is to present some computer based...

In the present paper we introduce the phenomenon "continuous dependence of the solutions of differential equations under "short" perturbations on the right-hand side", or equivalent simple name of phenomenon "h-continuity". We obtain some sufficient conditions for h-continuous dependence of solutions of non-linear differential equations. The result...