A Computer Algebra Application to Determination of Lie Symmetries of Partial Differential Equations

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Operational Methods in the Environment of a Computer Algebra System

This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.

Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

Computer Networks Security Models - A New Approach for Denial-of-Services Attacks Mitigation

Computer networks are a critical factor for the performance of a modern company. Managing networks is as important as managing any other aspect of the company’s performance and security. There are many tools and appliances for monitoring the traffic and analyzing the network flow security. They use different approaches and rely on a variety of characteristics of the network flows. Network researchers are still working on a common approach for security baselining that might enable early watch alerts. This research focuses on the network security models, particularly the Denial-of-Services (DoS) attacks mitigation, based on a network flow analysis using the flows measurements and the theory of Markov models. The content of the paper comprises the essentials of the author’s doctoral thesis.

Education in Computer Science and the Role of the Teacher in the Environment of Open Educational Resources

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013

Computer Mathematics for Motivated Students

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013

Computer Mathematics with MuPAD in School Years 6. To 9

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2014

Content-Based Image Retrieval for Computer Tomography Images Using Wavelet Descriptors

An approach to building a CBIR-system for searching computer tomography images using the methods of wavelet-analysis is presented in this work. The index vectors are constructed on the basis of the local features of the image and on their positions. The purpose of the proposed system is to extract visually similar data from the individual personal records and from analogous analysis of other patients.

A Model of a Diagnostic Test for Controlling the Results of a Computer Based Education in Applied Mathematics at the University of Ruse

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015

A Didactic Model of Computer Supported Education in Higher Mathematics

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2016

Development of a mathematical and computer model to assess water quality impacts of hazardous compounds from minor gasoline spills in the inter-tidal zone of the Miami River, Florida

The objective of this study was to develop a model to predict transport and fate of gasoline components of environmental concern in the Miami River by mathematically simulating the movement of dissolved benzene, toluene, xylene (BTX), and methyl-tertiary-butyl ether (MTBE) occurring from minor gasoline spills in the inter-tidal zone of the river. Computer codes were based on mathematical algorithms that acknowledge the role of advective and dispersive physical phenomena along the river and prevailing phase transformations of BTX and MTBE. Phase transformations included volatilization and settling. ^ The model used a finite-difference scheme of steady-state conditions, with a set of numerical equations that was solved by two numerical methods: Gauss-Seidel and Jacobi iterations. A numerical validation process was conducted by comparing the results from both methods with analytical and numerical reference solutions. Since similar trends were achieved after the numerical validation process, it was concluded that the computer codes algorithmically were correct. The Gauss-Seidel iteration yielded at a faster convergence rate than the Jacobi iteration. Hence, the mathematical code was selected to further develop the computer program and software. The model was then analyzed for its sensitivity. It was found that the model was very sensitive to wind speed but not to sediment settling velocity. ^ A computer software was developed with the model code embedded. The software was provided with two major user-friendly visualized forms, one to interface with the database files and the other to execute and present the graphical and tabulated results. For all predicted concentrations of BTX and MTBE, the maximum concentrations were over an order of magnitude lower than current drinking water standards. It should be pointed out, however, that smaller concentrations than the latter reported standards and values, although not harmful to humans, may be very harmful to organisms of the trophic levels of the Miami River ecosystem and associated waters. This computer model can be used for the rapid assessment and management of the effects of minor gasoline spills on inter-tidal riverine water quality. ^

A computer based approach to improve the dietary and physical activity patterns of a diverse group of adolescents

Diet and physical activity patterns have been implicated as major factors in the increasing prevalence of childhood and adolescent obesity. It is estimated that between 16 and 33 percent of children and adolescents in the United States are overweight (CDC, 2000). Moreover, the CDC estimates that less than 50% of adolescents are physically active on a regular basis (CDC, 2003). Interventions must be focused to modify these behaviors. Facilitating the understanding of proper nutrition and need for physical activity among adolescents is the first step in preventing overweight and obesity and delaying the development of chronic diseases later in life (Dwyer, 2000). The purpose of this study was to compare the outcomes of students receiving one of two forms of education (both emphasizing diet and physical activity), to determine whether a computer based intervention (CBI) program using an interactive, animated CD-ROM would elicit a greater behavior change in comparison to a traditional didactic intervention (TDI) program. A convenience sample of 254 high school students aged 14-19 participated in the 6-month program. A pre-test post-test design was used, with follow-up measures taken at three months post-intervention. ^ No change was noted in total fat, saturated fat, fruit/vegetables, or fiber intake for any of the groups. There was also no change in perceived self-efficacy or perceived social support. Results did, however, indicate an increase in nutrition knowledge for both intervention groups (p<0.001). In addition, the CBI group demonstrated more positive and sustained behavior changes throughout the course of the study. These changes included a decrease in BMI (ppre/post<0.001, ppost/follow-up<0.001), number of meals skipped (ppre/post<0.001), and soda consumption (ppre/post=0.003, ppost/follow-up=0.03) and an increase in nutrition knowledge (ppre/post<0.001, ppre/follow-up <0.001), physical activity (ppre/post<0.05, p pre/follow-up<0.01), frequency of label reading (ppre/follow-up <0.0l) and in dairy consumption (ppre/post=0.03). The TDI group did show positive gains in some areas post intervention, however a return to baseline behavior was shown at follow-up. Findings of this study suggest that compared to traditional didactic teaching, computer-based nutrition and health education has greater potential to elicit change in knowledge and behavior as well as promote maintenance of the behavior change over time. ^

Achievement of generic baccalaureate student nurses using computer -assisted instruction simulations during a nursing review course

The use of computer assisted instruction (CAI) simulations as an instructional strategy provides nursing students with a critical thinking approach for evaluating risks and benefits and choosing correct alternatives in "safe" patient care situations. It was hypothesized that using CAI simulations during an upper level nursing review course would have a positive effect on the students' posttest scores. Subjects (n = 36) were senior nursing students enrolled in a nursing review course in an undergraduate baccalaureate program. A limitation of the study was the small sample size. The study employed a modified group experimental design using the t test for independent samples. The group who received the CAI simulations during the physiological system review demonstrated a significant increase (p $<$.01) in the posttest score mean when compared to the lecture-discussion group score mean. There was no significant difference between high and low clinical grade point average (GPA) students in the CAI and lecture-discussion groups and their score means on the posttest. However, score mean differences of the low clinical GPA students showed a greater increase for the CAI group than the lecture-discussion group. There was no significant difference between the groups in their system content subscore means on the exit examination completed three weeks later. It was concluded that CAI simulations are as effective as lecture-discussion in assisting upper level students to process information for clinical decision making. CAI simulations can be considered as an instructional strategy to supplement or replace lecture content during a review course, allowing more efficient use of faculty time. It is recommended that the study be repeated using a larger sample size. Further investigations are recommended in comparing the effectiveness of computer software formats and various instructional strategies for other learning situations and student populations. ^