Angel Golev

Plovdiv University · Department of Computer Technologies

Using Melnikov's method, the existence of chaotic behaviour in the sense of Smale in an extended anharmonic oscillator is established. We demonstrate some modules for investigating the dynamics of the proposed model. This will be included as an integral part of a planned much more general Web-based application for scientific computing. One possible...

Here we will present an iteration method for computing x and y in the equation x * a + y * b = gcd, where gcd is a greatest common divisor of preliminary known integer numbers a != 0 and b != 0. The algorithm presented here is faster than [8] and uses arithmetic operation "subtraction" only.

A number of authors devote their research to the phase-space flow of a particle in a forced cubic potential with a specific Hamiltonian. In this paper, we focus on the Hamiltonians, which gives rise to the following modified dynamical system:          dx dt = y dy dt = −x + x 2 + ǫ(−x + x 2) N j=1 g j cos(jωt) where 0 ≤ ǫ < 1, g i ≥ 0, and...

In this article we propose extended Daykin-Harris algorithm [7] which calculate coefficients x and y in Bezout's identity [1] i.e. for arbitrary but given integer numbers a = 0 and b = 0, so that x * a + y * b = gcd, where gcd is greatest common divisor of a and b. This algorithm will be applicable especially for long numbers. From arithmetic opera...

In this paper, we propose new generalized oscillator model. Considerations in the light of the Melnikov's approach are also given. We focus on some interesting simulations based on the proposed new model. This is an integral part of a planned much more general Web-based application for scientific computing.

This article presents a main goals, scientific tasks and planned results of the scientific team of the Faculty of Mathematics and Informatics at Plovdiv University of the implementation of the Project “Digital Sustainable Ecosystems – Technological Solutions and Social Models for Ecosystem Sustainability – DUEcos”, funded by the National Recovery a...

In this article we demonstrate some specialized modules for investigating the dynamics of some adaptive Hopf oscillators, an integral part of a planned much more general Web-based application for scientific computing. We also study a new modified adaptive Hopf-like oscillator with a suitable, user-fixed "input function of coupling strength (IFCS)"....

The Rayleigh-Duffing oscillator models are widely used in physics, electronics and many other disciplines. Obviously, these studies can be successfully continued. In this paper, we propose a generalized hypothetical Rayleigh-Duffing-like oscillator model. Considerations in the light of Melnikov's approach are also given. Here we will focus on some...

In this article we consider the q-Lommel polynomials associated with the Jackson q-Bessel function generated by three-term recurrence relation h (2) m+1,ν (x; q) = 2x 1 − q m+ν h (2) m,ν (x; q)− q m+ν+1 h (2) m−1,ν (x; q); h (2) 0,ν (x; q) = 1; h (2) 1,ν (x; q) = 2x (1 − q ν) with possible applications in two directions the study the dynamics of di...

In this paper an algorithm for approximate solving of a boundary value problem for a nonlinear differential equation with a special type of fractional derivative is suggested. This derivative is called a generalized proportional Caputo fractional derivative. The new algorithm is based on the application of the monotone-iterative technique combined...

In this article we will consider a class of associated Gegenbauer poly-nomials generated by recurrence formula V a n+1 (x) = 2 n+a n+1 xV a n (x) − n+2a−1 n+1 V a n−1 (x); V a 0 (x) = 0; V a 1 (x) = 1 with possible applications in two directions-the study the dynamics of differential systems and the generation of special classes of radiation diagra...

In this article a model with Chebyshev polynomials of the sixth kind F j (x) = xF j−1 (x) − (j+1)(j+2)+(−1) j+1 (2j+3)+1 4(j+1)(j+2) F j−2 (x) with F 0 (x) = 1; F 1 (x) = x as corrections in the Lienard differential system is presented. The type of limit cycles and level curves are studied. Numerical examples, illustrating our results using CAS MAT...

In this article we consider a new extended Lienard-type differential system. The effects on the dynamics with "corrections" of the Associated Legendre polynomials (ALP) L 2 n n are studied. Numerical examples, illustrating our results using CAS MATHEMATICA are given.

In this article we consider a new extended Lienard differential system with "correcting factors" of the type of interpolating polynomials of some basic functions as sin(x), tanh(x), sinh(x). The hypothetical oscillator model with Bernoulli's polynomial-correction is also presented. The models are considered in the light of Melnikov's approach. Nume...

More frequent and large-scale attacks against Linux servers and the services provided by them are the forecasts of the analysts. Proof of this is the double-digit increase in attacks against Linux server environments has been registered in the first part of 2022. This is of course no accident. Linux server environments are used for corporate and go...

Difference equations with a special type of delay is studied. This type of delay is characterized by the maximum value of the unknown function on the past time interval with a constant length. It is studied the exponential stability. Some sufficient conditions are theoretically proved and computer simulated on several examples. The influence of the...

This article presents summarized results from the implementation of scientific tasks within the NSP "ICTINSES" by the FMI team at Plovdiv University. The implemented activities in two of the main components are indicated-Electronic infrastructure for open science and Digital technologies in teaching and learning. Under the second component, the emp...

In [1] the authors considered the following new two–parameter power Garima (PG) c.d.f.: M(t)=1−θtα+θ+2θ+2e−θtα, where α, θ ∈ R⁺, t > 0. Also of interest to the specialists is the task of approximating the Heaviside function ht0 (t) where t0 is the median with the new cumulative function in the Hausdorff sense. We define a new family of recurrence g...

This article presents the results achieved by the research team of FMI at the University of Plovdiv in the first year of the NNP "ICTinSES". The realized activities in two of the main components are indicated – Electronic infrastructure for open science and Digital technologies in teaching and learning. The obtained results have been published in s...

During the past 30 years, several nonhomogeneous Poisson process (NHPP) software reliability growth models (SRGMs) have been presented and embraced for the evaluation and appraisal of the maturation of the reliability of the software. In the period of debugging, the frequency of errors depends largely on the debugger's ability, the environment of d...

This monograph is dedicated to the newest modeling trends in debugging theory and their applications. A Hausdorff metric is chosen to evaluate the test data which are fitted to the sigmoid models. The models are tested with real data.

The main aim of this paper is to suggest an algorithm for constructing two monotone sequences of mild lower and upper solutions which are convergent to the mild solution of the initial value problem for Riemann-Liouville fractional delay differential equation. The iterative scheme is based on a monotone iterative technique. The suggested scheme is...

In [1] Aggarwal, Gandhi, Verma and Tandon considered a new four-parameter expected mean number of faults-function M (t) by: M (t) = a 1 − α 1 − (1 + bt) r(1−α) e −btr(1−α) , where α is the constant rate at which new faults are introduced. Also of interest to the specialists is the task of approximating the Heaviside function h t0 (t) =      ...

In [1] the authors considered the following cdf of the transmuted Frechet (GTF) distribution: F (t) = G a (t) (λ + 1) − λG b (t) , where −1 ≤ λ < 1, a > 0 and b > 0 and G(t) = e −βt α is the cdf of the two-parameter Frechet distribution. In [2] the authors considered the following cdf of the skew generalized inverse Weibull (SGIW) distribution: M (...

The main aim of this paper is to suggest some algorithms and to use them in an appropriate computer environment to solve approximately the initial value problem for scalar nonlinear Riemann–Liouville fractional differential equations on a finite interval. The iterative schemes are based on appropriately defined lower and upper solutions to the give...

In [1] Diwakar and Aggarwal considered a new three-parameter expected mean number of faults-function m(t) by: m(t) = a 1 − e −b t k+1 k+1 = aF (t), where F (t) is the cdf of Weibull distribution with shape parameter k. Then, the four-parameter Weibull model for open source software under the effect of imperfect debugging will be [1]: M (t) = a 1 −...

In [1] Pham considered a new two-parameter lifetime distribution and generated a new mean value function m(t) that represents the expected number of software failures to be detected by the time t considering the uncertainty of operating environments by: m(t) = N 1 − β β + at t 2 ln(bt) − t 4 + 1 b α where α, β, a, b > 0. The determination of compul...

In [1] the authors proposed a new "transmuted transmuted-G (TT-G) family" of distributions. The authors' assertion that probability distribution (in some particular cases) produces very good results in approximating specific data from different fields such as population dynamics, biostatistics, survival analysis and others has encouraged us to cond...

The determination of compulsory in area of the Software Reliability Theory components, such as confidence intervals and confidence bounds, should also be accompanied by a serious analysis of the value of the best Hausdorff approximation - the subject of study in the present paper. For example we study the Hausdorff approximation of the shifted Heavisid...

A leader-following consensus of discrete-time multi-agent systems with nonlinear intrinsic dynamics and impulses is investigated. We propose and prove conditions ensuring a leader-following consensus. Numerical examples are given to illustrate effectiveness of the obtained results. Also, the necessity and sufficiency of the obtained conditions are...

In this article we will consider the possibility of approximating the input function s(t) (the nutrient supply for cell growth in a continuous bioreactor) with the Marshall-Olkin type correction. We prove upper and lower estimates for the one-sided Hausdorff approximation of the shifted Heaviside function h t * (t) by means of the general solution...

We reduce the generation time of near-rings on finite cyclic groups using the parallel processing provided by C#. A formal language to describe subsets from near-rings on finite cyclic groups has been created. Software modules for parallel generating and for filtering and viewing near-rings have been implemented. Both modules are a part of the syst...

In this paper we prove upper and lower estimates for the one-sided Hausdorff approximation of the Heaviside step-function h t * (t) by means of a new Hyper-Power-Logistic family. Some applications of the new cumulative sigmoid for analysis of the "cancer data" [46]-[47] and for approximating cdf of the number of Bitcoin received per address [45] ar...

In this paper we study the one-sided Hausdorff approximation of the shifted Heaviside step function by a family of Odd Burr III Weibull (ODBW) cumulative sigmoid. The estimates of the value of the best Hausdorff approximation obtained in this article can be used in practice as one possible additional criterion in "saturation" study. Application for...

The software architecture is an important part of the process of design and development of video games. Nowadays game developers strive to achieve a software architecture which enables reuse, porting, extension, etc. Those architectures are centered on several key principles, service-oriented games that use modular components and that can be indepe...

In this paper we study the one-sided Hausdorff approximation of the shifted Heaviside step function by a family of Kumaraswamy-Weibull-Exponential cumulative sigmoid. The estimates of the value of the best Hausdorff approximation obtained in this article can be used in practice as one possible additional criterion in "saturation" study. Numerical e...

In this paper we study the one–sided Hausdorff approximation of the shifted Heaviside step function by a class of the Zubair–family of cumulative distribution with baseline Ghosh–Bourguignon’s extended Burr XII c.d.f. The estimates of the value of the best Hausdorff approximation obtained in this article can be used in practice as one possible additi...

In this paper we demonstrate how to integrate 3rd party services in serious games. We use message queue broker and micro-services in a publish/subscribe manner in order to use real-time 3rd party data into a serious game’s logic. First, we discuss the benefits of service-oriented architecture. Then, we analyze and compare different message queues b...

The main purpose of this article is to reduce the generation time of near-rings on finite cyclic groups using the parallel processing provided by C#. We divide the near-rings into independent subsets and generate them simultaneously. The calculations are further accelerated after refactoring and defining appropriate compiler optimizations.

Serious games (SG) allow us to learn even when we are relaxing. These games are called “serious” because they allow us to be trained at domain-specific knowledge level. That is the main reason SG are gathering an even increasing research interest in recent years. In contrast with traditional, purely entertainment games, SGs architectures and design...

The main aim of the paper is comparing the speed of calculation for a particular problem for fractional differential equations by parallel CUDA cores. The approximate solv- ing of the initial value problem for scalar nonlinear Riemann-Liouville fractional differential equation is based on a suggested iterative scheme for constructing sequences of u...

A formal language to describe subsets from near-rings on finite cyclic groups has been created. A software module for filtering and viewing near-rings has been implemented. The module is a part of the system for generating and researching near-rings. With its help, it is much easier to group near-rings and make hypotheses about their structure.

The main aim of the book is suggesting and application in an appropriate computer environment of some approximate methods for solving different types of differential equations such as differential equations with a special type of delay, difference equations and Caputo fractional differential equations. The main characteristic of these methods is th...

This article introduces the basic concepts of Gamе Based Learning. The process of emerging and developing educational games aimed at serious games and their application in education is studied. The advantages they offer in the learning process are highlighted. Some exemplary apps about game-based education are being presented from leading universit...

In this paper we study the Hausdorff approximation of the Heaviside step function h_r(t) by deterministic curve models based on Yamada-exponential software reliability model, Yamada-Rayleigh model and Yamada-Weibul model and find an expression for the error of the best approximation. Some comparisons are made.

In this paper we study the Hausdorff approximation of the Heaviside step function$h_r(t)$ by sigmoidal curve model based on the generalized inverted exponential software reliability model and find an expression for the error of the best approximation. Some comparisons are made.

he Kumaraswamy-Dagum distribution is a flexible and simple model with applications to income and lifetime data.We prove upper and lower estimates for the Hausdorff approximation of the shifted Heaviside function by a class of Kumaraswamy-Dagum-Log-Logistic cumulative distribution function - (KD-CDF). Numerical examples, illustrating our results are...

In this note we give new and faster natural realization of Extended Euclidean Greatest Common Divisor (EEGCD) algorithm. The motivation of this work is that this algorithm is used in numerous scientific fields [36], [24]. Internet search engines show very high appearance of 'greatest common divisor'. In our implementation we reduce the number of it...

The paper presents a JavaScript library for visualization of geographic maps in web-based applications, which are syntactically and functionally compatible with OpenLayers 2. The library avoids the difficulties caused by rapid evolution of popular mapping tools like Google Maps API and Bing Maps API. It supports OpenLayers maps as well as Google ma...

In this note we prove precise upper and lower estimates for the Hausdorff distance of the shifted Heaviside function $h_a(t)$ by means of the sigmoid approximates the amplitude in the transmission waveform. The properties of the amplitude can greatly affect the choice of the waveform. Numerical examples, illustrating our results are given.

In this paper we describe authentication mechanism implemented for the Framework for Distributed Business Applications-FDBA. We present the primary functional requirements and describe how they were implemented. This authentication approach interacts with Active Directory Domain Services which is recommended technology for storing identity informat...

The main aim of the paper is to suggest some algorithms and to use them in an appropriate computer environment to solve approximately the initial value problem for scalar nonlinear Caputo fractional differential equations on a finite interval. The iterative schemes are based on appropriately defined lower and upper solutions to the given problem. A...

With this paper, we discuss some important aspects related to the iterative solution of two classes of polynomials, nonlinear systems of equations, and the adapted to them-"FAST adaptive neural solver" (FANS). The crucial issue of choosing initial approximations (separation of unattractive networks of initial data) and the possibility of minimizing...

In this note we construct a family of recurrence generating activation functions based on Gudermann function. We prove lower estimate for the Hausdorff approximation of the sign function by means of this family. Numerical examples, illustrating our results are given.

In this note we construct a family of parametric Soboleva’ modified hyperbolic tangent activation function (PSMHTAF). We prove upper and lower estimates for the Hausdorff approximation of the sign function by means of this family. Numerical examples, illustrating our results are given.

This paper describes computer algebra aided generation of English language test questions for evaluating learners' knowledge of the different parts of speech. The aim of our work is automatic generation of test questions, which are automatically assessed as well. This is a further development of our recent work in the domain; in our previous work w...

This paper gives sufficient conditions for kth approximations of the zeros of polynomial f (x) under which Kyurkchiev's method fails on the next step. The research is linked with an attack on the global convergence hypothesis of this commonly used in practice method (as correlate hypothesis for Weierstrass–Dochev's method). Graphical examples are p...

This book is an introduction to computer programming. It teaches the very fundamentals of programming, and familiarizes the readers with many concepts and methods of computer science. As reading programming code is often a favorite approach to learning programming, the book includes many sample programs. It advances with presenting fundamental data...

Although the Web was initially conceived as a vehicle for delivering documents, it is now being used as a platform for sophisticated interactive applications which could offer businesses numerous advantages, such as instant access, automatic upgrades, and opportunities for collaboration on a massive scale. Modern business Web applications, as part...

This paper describes some of the new electronic educational services, provided by the Distributed e-Learning Platform – DisPeL. Learning is empowered though the use of adaptive learning content. Testing examination is facilitated through algorithms to generate unique tests with minimum pre-defined testing questions. Testing examination is supported...

The paper deals with an approximate method for solving a mixed boundary value problem for nonlinear difference equations containing a maximum of the unknown function over a past time interval. Every successive approximation to the unknown solution is the unique solution of an appropriately constructed initial value problem for a linear difference e...

We describe a software system for testing hypotheses about near-rings on finite cyclic groups. The system allows researchers to define parameters and test π functions. By using this software we make new hypotheses, and formulate and prove statements for constructions of new classes of near-rings. We compute all near-rings on finite cyclic group of...

An algorithm for constructing two sequences of successive approximations of a solution of the nonlinear boundary value problem for a nonlinear differential equation with ‘maxima’ is given. The case of a boundary condition of anti-periodic type is investigated. This algorithm is based on the monotone iterative technique. Two sequences of successive...

In this paper the authors investigate special type of difference equations which involve both delays and the maximum value of the unknown function over a past time interval. This type of equations is used to model a real process which present state depends significantly on its maximal value over a past time interval. An appropriate mixed boundary v...

A nonlinear generalized difference equation with both delays and the maximum value of the unknown function over a discrete past time interval are studied. A nonlinear boundary value problem of antiperiodic type for the given difference equation is set up. One of the main characteristics of the considered difference equation is the presence of the u...

The specific of the mobile games market establishes a model where the main goal is implementation of multiple ideas for a minimal period of time and with minimal resources. This paper presents a software framework for development of logic games for the Microsoft Windows Phone 7 mobile platform. A prototype of the framework is developed. The applica...

The object of investigation of the paper is a special type of difference equations containing the maximum value of the unknown function over a past time interval. These equations are adequate models of real processes which present state depends significantly on their maximal value over a past time interval. An algorithm based on the quasilinearizat...

The object of investigation of the paper is a special type of functional differential equations containing the maximum value of the unknown function over a past time interval. An improved algorithm of the monotone-iterative technique is suggested to nonlinear differential equations with “maxima.” The case when upper and lower solutions of the given...

This paper presents a software package developed in Mathematica that contains implementations of various, mostly proposed during the last three years, iterative algorithms, including combined algorithms, for solving systems of linear equations. The accent falls on algorithms of type successive overrelaxation which are modifications of the Gauss-Sei...

New lower bounds for the number of the near-rings on finite cyclic groups are obtained. All near-rings on finite cyclic groups of order 24 to 29 are computed using a new algorithm.

An algorithm for constructing two sequences of successive approximations of the solution of the initial value problem for nonlinear differential equations with “maxima” is given. This algorithm is based on the monotone iterative technique. It is proved that both sequences are monotonically convergent. Each term of the constructed sequences is a sol...

New lower bounds for the number of the near-rings on finite cyclic groups are obtained. All near rings on finite cyclic groups of order up to 23 are com- puted using a new heuristic algorithm. The constructions of more than 98 percents of the found near-rings are described.

All classes of isomorphic near-rings on Zn, n ≤ 23 are computed. These near-rings are checked for the right distributive law and examined for some other properties

New lower bounds for the number of the near-rings on finite cyclic groups are obtained. All near-rings on finite cyclic groups of order up to 23 are computed using a new heuristic algorithm. The constructions of more than 98 percents of the zero-symmetric and more than 99.5 percents of the non-zero-symmetric near-rings are described.