Contents IJPAM: Volume 117, No. 2 (2017)

A. Markovska
ANALYSIS OF A MATHEMATICAL MODEL OF ADAPTIVE
IMMUNE RESPONSE TO VIRUS INFECTION ... 255
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D. Braho, E. Donefski
STATISTICAL CONVERGENCE OF
ASYMPTOTIC MARTINGALES ... 263
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I. Damyanov, N. Borisova
PROGRAMMING LANGUAGES IN UNDERGRADUATE
COURSES AND IN SOFTWARE INDUSTRY IN BULGARIA ... 271
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I. Dimitrova, J. Koppitz, L. Lohapan
GENERATING SETS OF SEMIGROUPS OF PARTIAL
TRANSFORMATIONS PRESERVING A ZIG-ZAG ORDER ON $\mathbb{N}$ ... 279
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M. Ivanova, L. Dospatliev
APPLICATION OF MARKOWITZ PORTFOLIO
OPTIMIZATION ON BULGARIAN STOCK MARKET
FROM 2013 TO 2016 ... 291
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M. Ivanova, L. Dospatliev
EVALUATION OF THE IMPACT OF CONSUMPTION,
INVESTMENT AND EXPORT ON IMPORT - DATA
FROM GERMAN ECONOMY ... 309
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A. Markovska, M. Kolev, I. Nikolova
ON MATHEMATICAL MODELING OF THE COMPETITION
BETWEEN THE IMMUNE SYSTEM AND VIRAL INFECTIONS ... 335
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M. Todorova, M. Petrov, S. Trenchev
RESEARCH WORK OF BACKPROPAGATION AND
LEVENBERG-MARKARDT ALGORITHMS FOR
RECOGNITION ON BIOMETRICS DATA ... 345
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Z. Misajleski
PROXIMATE AND APPROXIMATE SEQUENCES ... 355
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Seventh International Conference "Modern Trends in Science"

South-West University "Neofit Rilski",
Faculty of Mathematics & Natural Sciences,
Blagoevgrad, Bulgaria, 14 - 18 June, 2017



Dear Reader,

This special issue collects selected papers, presented in sections "Mathematics" and "Informatics" during the Seventh International Conference "Modern Trends in Science" (FMNS-2017), which held from 14th till 18th June 2017 in Blagoevgrad, Bulgaria. The conference was organized by the Faculty of Mathematics and Natural Sciences at South-West University "Neofit Rilski", Blagoevgrad.

The main objective of FMNS-2017 was to provide a platform for researchers, working in different fields of natural sciences, to report their current research achievements, to exchange new ideas and experiences, to create new contacts and to find global partners for future cooperation. More than 140 researchers from Albania, Austria, Bulgaria, Czech Republic, Greece, Kazakhstan, Poland, Republic of Macedonia, Russia and United Kingdom attended the conference. Two prominent mathematicians - Acad. Julian Revalski (President of Bulgarian Academy of Sciences) and Prof. Armen Sergeev (Vice-President of European Mathematical Society), presented attractive plenary lectures, devoted to the interrelations between mathematics and other sciences. Most of the reported research during the oral and poster sessions also outlined the interdisciplinarity and multidisciplinarity as major trends of the modern science.

On behalf of the Organizing committee of the Seventh International Conference FMNS-2017 I would like to express our gratitude to the Ministry of Education and Science and the National Science Fund of Bulgaria for the provided financial support.

We gratefully use the chance to disseminate a part of the reported achievements in the field of mathematics and informatics among the audience of this journal.

Prof. Mario Mitov,
Chairman of the Organizing Committee of FMNS-2017

Organizing Committee

Chair

Prof. Mario Mitov - Vice-Dean of Faculty of Mathematics and Natural Sciences

Vice-Chair

Assoc. Prof. Elena Karashtranova - Vice-Dean of Faculty of Mathematics and Natural Sciences

Members

Lidia Sakelarieva - South-West University "Neofit Rilski", Bulgaria

Irena Atanasova - South-West University "Neofit Rilski", Bulgaria

Radost Vasileva - South-West University "Neofit Rilski", Bulgaria

Ivan Drenovski - South-West University "Neofit Rilski", Bulgaria

Ilinka Dimitrova - South-West University "Neofit Rilski", Bulgaria

Elitsa Chorbadzhiyska - South-West University "Neofit Rilski", Bulgaria

Dimitrina Kerina - South-West University "Neofit Rilski", Bulgaria

Technical support

Grigor Iliev - South-West University "Neofit Rilski", Bulgaria

Nadejda Borisova - South-West University "Neofit Rilski", Bulgaria

Boiana Gurkova - South-West University "Neofit Rilski", Bulgaria

Ivo Bardarov - South-West University "Neofit Rilski", Bulgaria

Hristina Kovacheva - South-West University "Neofit Rilski", Bulgaria

Scientific Committee

Chair

Acad. Blagovest Sendov

Members

Julian Revalski, Bulgarian Academy of Sciences, Bulgaria

Peter Kenderov, Bulgarian Academy of Sciences, Bulgaria

Veselin Drenski, Bulgarian Academy of Sciences, Bulgaria

Oleg Mushkarov, Bulgarian Academy of Sciences, Bulgaria

Rumen Angelov, University of Pretoria, South Africa

Rumen Andonov, University of Rennes 1, France

Svetoslav Markov, Bulgarian Academy of Sciences, Bulgaria

Peter Bojvalenkov, Bulgarian Academy of Sciences, Bulgaria

Peter Milanov, South-West University "Neofit Rilski", Bulgaria

Stefan Stefanov, South-West University "Neofit Rilski", Bulgaria

Doncho Dimovski, University "St. St. Cyril and Methodius", Macedonia

Krasimira Prodanova, Technical University of Sofia, Bulgaria

Dimitrina Polimirova, Bulgarian Academy of Sciences, Bulgaria