Faculty of Mathematics and Informatics

Sukurta: 02 September 2013

mif 24 Naugarduko, LT-03225 Vilnius
Tel. 219 3050, fax 215 1585
E-mails: ,
www http://www.mif.vu.lt

Dean – Prof. Dr. Gediminas Stepanauskas

STAFF

153 teachers (19 habilitated doctors and 90 doctors), 7 research fellows (4 habilitated doctors and 2 doctors), 40 doctoral students.

Department of Computer Science
Department of Computer Science II
Department of Didactics of Mathematics and Informatics
Department of Differential Equations and Numerical Analysis
Department of Econometric Analysis
Department of Mathematical Analysis
Department of Mathematical Computer Science
Department of Mathematical Statistics
Department of Probability Theory and Number Theory
Department of Software Engineering

MAIN RESEARCH AREAS OF THE FACULTY

Fundamental research in mathematics: analytic, algebraic and probabilistic number theory, stochastic analysis, probability theory, functional analysis, theory of differential equations
Applied mathematics: statistical methods, mathematical modelling, econometrics, finance and insurance mathematics, innovative educational methodsInformatics: theoretical informatics, computer modelling, logic, discrete structures
Information technologies: programming technologies, software engineering, informatics engineering, information analysisNumber theory and probabilistic number theory
Probability theory, statistics and combinatorics
Differential equations and their applications
Informatics and technologies of information society

DOCTORAL DISSERTATIONS MAINTAINED IN 2012

E. Bieliauskienė. Ruin probability and Gerber-Shiu function for the discrete time risk model with inhomogeneous claims.

P. Daniušis. Feature extraction via dependence structure optimization.

A. Grigutis, Value Distribution of Lerch and Selberg Zeta-Functions.

J. Jankauskas, Heights of polynomials.

A. Novikas, Composite numbers in the sequences of integers.

J. Kalpokas, Discrete moments of the Riemann zeta function and Dirichlet L-functions.

L. Savičienė. Modelling and visualization of norm violation in decision support for aircraft approach/departure.

CONFERENCES AND SEMINARS ORGANIZED IN 2012

National Conference of Mathematics and Informatics, Vilnius University, Faculty of Mathematical Informatics Department (for 10 years).

DEPARTMENT OF COMPUTER SCIENCE

47 Didlaukio, LT- 08303 Vilnius
Tel. 219 50 10, fax. 215 1585
E-mail:

Head - Prof. Dr. Rimantas Vaicekauskas.

STAFF

Professors: Dr. R. Vaicekauskas, Habil. Dr. A. Žilinskas (part time).
Docents: Dr. A. Lenkevičius (part time), Dr. A. Mitašiūnas, Dr. S. Norgėla, Dr. G. Skersys, Dr. V. Tumasonis, Dr. G. Zlatkus (part time).
Senior research fellow: Habil. Dr. Š. Raudys.
Lecturers: Dr. J. Andrikonis, Dr. A. Birštunas, Dr. V. Dičiūnas, Dr. R. Kybartas (part time), Dr. A. Raudys (part time), Dr. A. Stočkus (part time), A. Adamonis (part time), A. Janeliūnas (part time), V. Kiško (part time), R. Masiulis (part time), K. Mizara (part time), M. Plukas (part time), I. Radavičius, J. Žagūnas.
Senior assistants: G. Balkys, D. Baronas (part time), E. Čiukšys (part time), M. Eglinskas (part time), A. Grevys (part time), S. Grigaitis (part time), V. Jančauskas (part time), L. Ričkus (part time), L. Skripkauskas (part time), A. Šemežys (part time).
Doctoral students: A. Budrionis, A. Paukštė, K. Koncevičius, D. Krunglevičius, V. Valaitis.

RESEARCH INTERESTS

Software process assessment and improvement
Qualified electronic signature and applications
Error-correcting codes
Intelligent educational systems and technology-enhanced learning
Global optimization, optimal design, visualization of multidimensional data
Web services and internet technologies, spatial databases
Data mining, bioinformatics
Computer graphics, computer aided design
BDI logics
Color applications
Retrieval of logical proof
Neural networks, pattern recognition
Object oriented technologies in distributed systems
National language support
Mobile telecommunications
Optical character recognition
Automated theorem proving
Computational intelligence and machine learning in finance
Portfolio construction artificial history for financial time series
Machine learning, market data analysis, high frequency trading, market liquidity analysis
Modal logics, artificial intelligence
Enterprise-wide process capability assessment and improvement
Innovation and technology transfer process capability maturity modeling
Product line for official electronic documents creation and verification
Graph theory, data structures and algorithms, algorithm analysis

RESEARCH PROJECTS CARRIED OUT IN 2012

Projects Supported by University Budget

Computational Intelligence and its Applications in Information Technologies. Prof. Dr. R. Vaicekauskas. 2012–2016.

Main results achieved:
Applications of finite linear temporal logic to piecewise linear aggregates
Loop-free calculus for modal logic S4
Colour rendition characteristics of lighting: models and applications
Data mining and knowledge discovery via logic-based methods
Software process improvement and capability determination
Enterprise SPICE based education capability maturity model
Electronic documents interoperability solutions in academic environment
Contraction-free calculi for modal logics S5 and KD45
Fuzzy templates for pair-wise multi-class classification
Enhanced innovation and technology transfer model
Information security overview
Electronic Archive Information System.

Projects, Programmes, Issues Supported by the Research Council of Lithuania

Multi-Class Recognition Methods Estimating Classification Errors for Security and Risk Analysis. S. Raudys. Research was funded by a grant (No. MIP-043/2011) from the Research Council of Lithuania.

Machine Learning Methods for Portfolio Construction in the Light of the Financial Crisis. A. Raudys. Project supported by Research Council of Lithuania (No. MIP-018/2012).

Governmental Science Programmes and Research Projects Ordered by the Branch Ministries EC Structural Funds

Expert team leader of ESF Project ordered by Centre for Quality Assessment in Higher Education Development of Requirements for the Studies in Informatics. A. Mitasiunas. 2011–2012.

Ordered Research Projects

Proof-Search in Modal and Temporal Logics. Applications to databases. S. Norgėla.

International Science Programmes and Projects

Taking part in Unicode Consortium for developing of the Unicode Standard. V. Tumasonis.

A. Mitasiunas Project leader of the Partner – Vilnius University in the Consortium of Grant Contract for the implementation of the project #007, Baltic Organization and Network of Innovation Transfer Associations, BONITA of the Baltic Sea Region Programme. 2007–2013.

A. Mitasiunas Advisory Board member, author and reviewer of world-wide project Enterprise SPICE with participation of 120 experts from 30 countries and 5 continents.

A. Mitasiunas Expert of Tempus IV Project Plan to Establish Research-Science-Enterprise oriented Universities for the benefit of Society.

MAIN PUBLICATIONS

Articles

H. Pranevičius, S. Norgėla. Applications of finite linear temporal logic to piecewise linear aggregates // Informatica / Matematikos ir informatikos institutas. Vilnius : Lietuvos mokslų akademijos leidykla. 2012, vol. 23, no. 3, p. 427-441.

J. Besson, A. Lupeikienė, V. Medvedev. Comparing Real and Intended System Usages: A Case for Web Portal // Informatica / Matematikos ir informatikos institutas. Vilnius : Lietuvos mokslų akademijos leidykla. 2012, vol. 23, no. 2, p. 191-201.

P. Vitta, L. Dabašinskas, A. Tuzikas, A. Petrulis, D. Meškauskas, A. Žukauskas. Concept of Intelligent Solid-State Street Lighting Technology // Elektronika ir elektrotechnika / Kauno technologijos universitetas. Kaunas : Technologija. 2012, vol. 18, nr. 10, p. 37-40.

J. Andrikonis. Limits of the Letac principle. The discrete case // Lithuanian mathematical journal. New York : Springer. 2012, vol. 52, no. 4, p. 390-399.

J. Andrikonis. Loop-free calculus for modal logic S4. I // Lithuanian mathematical journal. New York : Springer. 2012, vol. 52, no. 1, p. 1-12.

J. Andrikonis. Loop-free calculus for modal logic S4. II // Lithuanian mathematical journal. New York : Springer. 2012, vol. 52, no. 2, p. 123-133.

S. Norgėla. On decidability of pure hybrid logic // Lietuvos matematikos rinkinys. LMD darbai. Vilnius : Matematikos ir informatikos institutas. 2012, t. 53, ser. A, p. 90-95.

A. Žukauskas, R. Vaicekauskas, P. Vitta, A. Tuzikas, A. Petrulis, M. Shur. Color rendition engine // Optics express. Washington : Optical Society of America. 2012, vol. 20, no. 5, p. 5356-5367.

A. Žukauskas, R. Vaicekauskas, M. Shur. Color-dulling solid-state cources of light // Optics express. Washington : Optical Society of America. 2012,Vol. 20, no. 9, p. 9755-9762.

A. Žukauskas, R. Vaicekauskas, P. Vitta. Optimization of solid-state lamps for photobiologically friendly mesopic lighting // Applied optics. Washington : Optical Society of America. 2012, Vol. 51, no. 35, p. 8423-8432.

T. Khare, S. Pai, K. Koncevičius, M. Pal, E. Kriukienė, Z. Liutkevičiūtė, M. Irimia, P. Jia, C. Ptak, M. Xia, R. Tice, M. Tochigi, S. Morera, A. Nazarians, D. Belsham, A. Wong, B. Blencowe, S. Wang, P. Kapranov, R. Kustra, V. Labrie, S. Klimašauskas, A. Petronis. 5-hmC in the brain is abundant in synaptic genes and shows differences at the exon-intron boundary // Nature Structural and Molecular Biology. New York : Nature Publishing Group. 2012, Vol. 19, iss. 10, p. 1037-1043.

G. Grigas, T. Jevsikova, A. Strelkauskytė. Localisation issues of software shortcut keys // Localisation focus. Limerick : Localisation Research Centre, p. 40-53.

Materials of conferences

S. Ragaišis, A. Birštunas, A. Mitašiūnas, V. Stočkus. Electronic Archive Information System // Databases and information systems : 10th international Baltic conference; local proceedings, July 8-11, 2012, Lithuania / edited by Albertas Čaplinskas, Gintautas Dzemyda, Audronė Lupeikienė, Olegas Vasilecas. Vilnius : Žara, 2012, p. 107-114.

A. Mitašiūnas, S. Ragaišis. Electronic documents interperability solutions in academic environment // INTEL-EDU 2012 : 3rd international workshop on intelligent educational systems and technology-enhanced learning : selected papers, Riga, October 10-12, 2012. Riga : JUMI Publishing House LTD, 2012, p. 21-34-.

A. Mitašiūnas, L. Novickis. Enterprise SPICE based education capability maturity model h // Workshops on business informatics reserach. Proceedings. Series: Lecture Notes in Business Information Processing (ISSN 1865-1348), Vol. 106. Berlin : Springer, 2012, p. 102-116.

J. Besson, T. Woronowicz, A. Mitašiūnas, M. Boronowsky. Innovation, knowledge- and technology transfer process capability model - innoSPICETM // Software process improvement and capability determination : 12th International Conference, SPICE 2012, Palma, Spain, May 29-31, 2012 : proceedings. Series : Communications in Computer and Information Science. Vol. 290, Part.3. Berlin : Springer, 2012, p. 75-84.

A. Mitašiūnas, S. Ragaišis, A. Stočkus. Electronic documents: towards a cloud // Informacijni technologii v ekonomici mienedžmenti i binesi. Problemi nauki, praktiki i osviti : XVIII mižnarodna naukovo-praktična konferencija, 29 listopada 2012 r.: tezi dopovidej. Kiyv : Evropejskij universitet, 2012, p. 260-262.

R. Kybartas. Fuzzy Templates for Pair-wise Multi-class Classification // ICPRAM 2012 : Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods. Vol. 2, 6-8 February, 2012, Algarve, Portugal / Pedro Latorre Carmona, J. Salvador SĆ�nchez, Ana L. N. Fred (Eds.). Algarve : SciTePress, 2012, p. 564-567.

S. Dapkūnas, A. Mitašiūnas. Implementation of information system for complaints' investigation // Informacijni technologii v ekonomici mienedžmenti i binesi. Problemi nauki, praktiki i osviti : XVIII mižnarodna naukovo-praktična konferencija, 29 listopada 2012 r.: tezi dopovidej. Kiyv : Evropejskij universitet, 2012, p. 258-260.

COOPERATION

Kaunas University of Technology (Lithuania)
Office of Lithuanian Chief Archivist (Lithuania)
State Social Insurance Fund Board under the Ministry of Social Security and Labour (Lithuania)
State Tax Inspectorate (Lithuania)
National Software and Services Technology Platform (Lithuania)
JSC Alna (Lithuania)
JSC Sintagma (Lithuania)
JSC Asseco Lietuva (Lithuania)
Visoriai Information Technology Park (Lithuania)
Association INFOBALT (Lithuania)
University of Bremen (Germany)‎
Ministry of Economics and Ports, Bremen (Germany)‎
Riga Technical University (Latvia)
Tampere University of Technology (Finland)
Lulea University of Technology (Sweden)
Tamlink Innovation-Research-Development Ltd. (Finland)
Latvian Information and Information Technology Association (Latvia)
St.Petersburg Scientific Centre of Russian Academy of Sciences (Russia)
Aurorum Business Incubator (Sweden)
South Denmark European Office (Belgium)
University of South Denmark (Denmark)
Adam Mickievich University, Poznan (Poland)
Tartu Science Park (Estonia)
Hanse University, Groningen (Netherland)
Fraunhofer Institute for Factory Operation and Automation IFF Magdeburg (Germany)‎
Centre de Recherche Public Henry Tudor, (Luxemburg)
University of Santiago de Compostela (Spanish)
Free University of Brussel (Belgium)
Masaryk University of Brno (Czech Republic)
University of Laplands (Finland)
Otto fon Guericke University of Magdeburg (Germany)‎
Université de Lyon, INSA Lyon (France)
Nanjing University (China)
Algorithmic Investment Management UAB (Lithuania)
Lithuania Orion Assets Management UAB (Lithuania)

OTHER SCIENTIFIC ACTIVITIES

Prof. R. Vaicekauskas –

Programme committee member of international conference BalticDB&IS’2012, http://www.mii.vu.lt/BalticDBIS2012/.

Prof. Š. Raudys –

editorial board member of the Informatica, http://www.mii.lt/informatica/editors.htm;
reviewer of the IEEE Transaction, PAMI (USA).

Prof. A. Žilinskas –

member of the Lithuanian Academy of Sciences, http://lma.lt;
nominated expert of the National committee of the Information and Communication Technology Programme (FP7-ICT) of the 7th Research Framework Programme (FP7);
editorial board member of the Journal of Global Optimization, http://www.springer.com/business/operations+research/journal/10898;
international editorial review board member of the international Journal of Grid and High Performance Computing, http://irma-international.org/journals/additional.asp?id=7764&title=Editorial+Review+Board&col=review_board;
editorial advisory board member of the Open Cybernetics & Systemics Journal, http://www.bentham.org/open/tocsj/EBM.htm;
editorial board member of the journal Informatica, http://www.mii.lt/informatica/editors.htm.

Doc. A. Mitašiūnas –

editorial advisory board member of the international Journal of Applied Science and Engineering, http://www2.tku.edu.tw/~tkjse/;
advisory board member of international working group “Enterprise SPICE” on software process assessment and improvement, http://www.enterprisespice.com;
board member on the National Software and Services Technology Platform;
expert of National Centre for Quality Assessment in Higher Education.

Doc. S. Norgėla –

editorial board member of the Lietuvos matematikos rinkinys (Transactions of the Lithuanian Mathematical Society). LMD darbai. Vol. 53, www.mii.lt/LMR.

Doc. V. Tumasonis –

editorial board member of the journal Informatica, www.mii.lt/informatica/editors.htm.

DEPARTMENT OF COMPUTER SCIENCE II

24 Naugarduko, LT-03225 Vilnius
Tel. 219 3091, fax 215 1585
47 Didlaukio, LT-08303 Vilnius
Tel. 219 5020
E-mail

Head – Prof. Habil. Dr. Feliksas Ivanauskas

STAFF

Professors: Habil. Dr. F. Ivanauskas, Dr. A. Juozapavičius.
Docents: Dr. A. Bastys, Dr. K. Karčiauskas, Dr. P. Kasparaitis, Dr. R. Krasauskas,
Dr. T. Meškauskas, Dr. K. Navickis, Dr. S. Zubė.
Lecturers: Dr. A. Brilingaitė, Dr. L. Bukauskas, L. Būtėnas, Dr. A. Čivilis,
Dr. J. Ignatavičiūtė, S. Kareiva (part-time), E. Kutka , R. Markauskas (part-time), K. Mickus,
S. Narkevičius (part-time), Dr. M. Puida, dr. V. Rapševičius, dr. J. Tamulienė (part-time).
Research fellows: S. Cacciola, H.E.I.Dahl, Dr. K. Karčiauskas, Dr. A. Pikturna (part-time).
Senior assistant: I. Kaunietis (part-time).
Doctoral student: S. Sajavičius.

RESEARCH INTERESTS

Methods and applications of non-linear and computational modelling, computational geometry
Methods of computer vision, medical imaging, digital imaging, speech and signal processing, data structures and algorithms
Internet technology and information systems
Location based services and database management systems
Computer networks
Cloud and GRID computing

RESEARCH PROJECTS CARRIED OUT IN 2012

Projects Supported by University Budget

Research and Analysis of Methods for Nonlinear, Numerical, Computational and Geometric Modelling, Design and Analysis of Data Base and Data Mining Methods, Image, Signal and Visual Processing. Prof. F. Ivanauskas. 2003–2012.

Biosensor response (taking into account substrate and product degradation due to external factors) has been analysed mathematically and numerically, quantitative results have been obtained.
Stability of difference schemes for parabolic equations with non-local boundary conditions has been analysed by both analytic method and numerical experiments.
The method for estimation of the diffusion and reaction rates of CHAP synthesis at high temperatures was investigated.
Stability of the weighted splitting finite-difference scheme for a two-dimensional parabolic equation with nonlocal integral conditions has been analysed.
Quaternionic Bezier-like bilinear patches were studied in isotropic space. Also principal patches on Dupin cyclide were presented in bilinear Bezier form with quaternionic weights. Generalizations to constructions with weights in suitable Geometric Algebras were studied with potential applications to CAD and architectural design/engineering.
Efficient constructions of free-form curves, based on the rational primitives, were derived. The differential geometry of osculating hypersufaces of higher order of hypersurfaces in
n- dimensional euclidean space was studied. A Lithuanian speech recognition engine was developed. The engine is adapted for medical speech recognition.
The research has been carried out on relational and NoSQL database modeling and querying issue. The model of the self-adapting database was created. Also, the work has been done on
tracking and movement prediction in intelligent transportation systems.
Research ofannotation methodology of Lithuanian texts and development corpus software model.

Projects, Programmes, Issues Supported by Research Council of Lithuania

LitGRID: Parallel and Distributed Computation and e-Services Network. Prof. A. Juozapavičius. 2007–2012.

IT PRAKTIKA: Design and Implementation of the Model to Organize Student Internship. G. Krušinskas – Infobalt, A. Brilingaitė, L. Bukauskas, A. Čivilis. 2009–2012.

Tuning National Concept of European Credit Transfer System (ECTS): the Development and Implementation of Credit Harmonization and Learning Outcome Based Study Programme Methodologies. A. Čepienė, L. Bukauskas. 2010–2012.

IMFAbite: Surface Tethered Bilayer Phospholipid Membranes for Functional Reconstitution of Proteins (MIP-096/2011). Dr. G.Valinčius - Vilnius University Institute of Biochemistry, T. Meškauskas. 2011–2012.

Projects Supported by EU Structural Funds

Increasing Internationality in Study Programs of the Department of Computer
Science II, project No VP1–2.2–ŠMM-07-K-02-070. Dr. A. Brilingaitė. 2012–2014.

Ordered Research Projects

Agency for Science, Innovation and Technology (MITA) MD2T: Speech Recognition of
Medical Diagnosis and Conversion to Text. Prof. A. Juozapavičius, Dr. A. Bastys. 2011–2013.

International Science Programmes, Projects and Contracts

SAGA: FP7 Marie Curie Initial Training Network. Doc. R. Krasauskas. 2008–2012.

CERN: Lithuania Collaboration Project. Prof. A. Juozapavičius. 2007–2012.

FP7 Project. EGI-InSPIRE, Prof. A. Juozapavičius. 2010–2014.

CHANCE: COOPERATION -THEME 2: Food, Agriculture, Fisheries, and Biotechnology FP7-KBBE-2010-4, (Grand Agreement no.266331, http://www.chancefood.eu).
Prof. F. Capozzi - University of Bologna, Italy; Prof. A. Abaravičius, A. Čivilis. 2011–2013.

MAIN PUBLICATIONS

Monographs, Studies

R. Baronas, F. Ivanauskas, J. Kulys. Mathematical modeling of biosensors : an introduction for chemists and mathematicians. Riyadh : King Saud University Translation center, 2012. 544p.

Articles

A. Juozapavičius, G. Bacevičius, D. Bugelskis, R. Samaitienė. EEG analysis - automatic spike detection // Nonlinear analysis : modelling and control. Vilnius : Institute of Mathematics and Informatics. 2011, vol. 16, no. 4, p. 375-386.
K. Navickis. Geometry of distribution of flags in the even-dimensional affine space // Šiauliai mathematical seminar / Šiauliai University. Šiauliai : Šiaulių universiteto leidykla. 2012, Vol. 7, p. 89-114.

L. Stonkienė, F. Ivanauskas. Biojutiklio su substrato ir produkto degeneracija matematinis modeliavimas // Lietuvos matematikos rinkinys. LMD darbai. Vilnius : Matematikos ir informatikos institutas. 2012, t. 53, ser. B, p. 102-107.

K. Navickis. Glaustinių hiperpaviršių afininė diferencialinė geometrija // Lietuvos matematikos rinkinys. LMD darbai. Vilnius : Matematikos ir informatikos institutas. 2012, t. 53, ser. B, p. 37-41.

I. Grinis, F. Ivanauskas, G. Stepanauskas. Kai kurie polivalentinių sistemų modeliavimo geometriniai aspektai // Lietuvos matematikos rinkinys. LMD darbai. Vilnius : Matematikos ir informatikos institutas. 2012, t. 53, ser. B, p. 62-67.

M. Mackevičius, F. Ivanauskas, A. Kareiva, D. Jasaitis. A closer look at the computer modeling and sintering optimization in the preparation of YAG // Journal of mathematical chemistry. Dordrecht : Springer Netherlands. 2012, Vol. 50, no. 8, p. 2291-2302.

G. Valinčius, T. Meškauskas, F. Ivanauskas. Electrochemical Impedance Spectroscopy of Tethered Bilayer Membranes // Langmuir. Washington : American Chemical Society. 2012, vol. 28, iss. 1, p. 977-990.

K. Karčiauskas, J. Peters. Free-form splines combining NURBS and basic shapes // Graphical models. Maryland Heights : Academic Press. 2012, vol. 74, no 6, p. 351-360.

M. Puida, A. Malinauskas, F. Ivanauskas. Modeling of electrocatalysis at chemically modified electrodes: a combination of second-order and Michaelis-type chemical kinetics // Journal of mathematical chemistry. Dordrecht : Springer Netherlands. 2012, Vol. 50, no. 7, p. 2001-2011.

M. Sapagovas, T. Meškauskas, F. Ivanauskas. Numerical spectral analysis of a difference operator with non-local boundary conditions // Applied mathematics and computation. New York : Elsevier Science Inc. 2012, vol. 218, no. 14, p. 7515-7527.

H. Dahl, R. Krasauskas. Rational fixed radius rolling ball blends between natural quadrics // Computer aided geometric design. Amsterdam : Elsevier Science BV. 2012, Vol. 29, iss. 9, p. 691-706.

S. Sajavičius. Stability of the weighted splitting finite-difference scheme for a two-dimensional parabolic equation with two nonlocal integral conditions // Computers and mathematics with applications. Kidlington : Pergamon. 2012, vol, 64, no 11, p. 3485-3499.

Materials of conferences

S. Sajavičius. The splitting finite-difference schemes for two-dimensional parabolic equation with nonlocal weighted integral conditions // ECCOMAS 2012 : 6th European congress on computational methods in applied sciences and engineering : CD-ROM proceedings, Vienna, September 10-14, 2012. Vienna, 2012, p. [1-12].

G. Kazakevičienė, R. Skyrius, M. Beniušė. Investicinių projektų matematinis modeliavimas // Matematika ir matematinis modeliavimas. Kaunas : Technologija, 2012, p.

COOPERATION

Centre for Physical Sciences and Technology (Lithuania)
Vilnius Gediminas Technical University (Lithuania)
Kaunas University of Technology (Lithuania)
Lithuanian University of Health Sciences (Lithuania)
Institute of Biotechnology (Lithuania)
Oslo University (Norway)
Aalborg University (Denmark)
Free University of Bozen-Bolzano (Italy)
University of Bologna (Italy)
The University of Hong Kong (PR of China)
University of Florida (USA)
Aarhus University (Denmark)
University of Zurich (Switzerland)
University of Latvia (Latvia)
KTH (Sweden)

OTHER SCIENTIFIC ACTIVITIES

Prof. F. Ivanauskas –

Chairman of the Division of Mathematical, Physical and Chemical Sciences of the Lithuanian Academy of Sciences;
member of the Lithuanian Academy of Sciences;
President of the Council of Visoriu Information Technology Park;
editor-in-chief of the journal Nonlinear Analysis: Modelling and Control;
editorial board member of the Lithuanian Mathematical Journal;
editorial board member of the Journal of Civil Engineering and Management;
editorial board member of the journal Mathematical Modelling and Analysis;
President of the Lithuanian Nonlinear Analysts Association;
board member of Lithuanian Mathematicians Association;
board member of the Council of Fundamental Sciences Faculty of Vilnius Gediminas Technical University.

Doc. A. Juozapavičius –

Chairman of the Council of LitGrid;
editorial board member of the journal Nonlinear Analysis: Modeling and Control;
Deputy of Chairman in CMS Collaboration (CERN).

Doc. R. Krasauskas –

editorial board member of the journal Lithuanian Mathematical Journal;
advisory board member of Effective Methods in Algebraic Geometry (MEGA) conferences.

Dr. A. Brilingaitė –

member of Association for Computing Machinery (ACM).

DEPARTMENT OF DIDACTICS OF MATHEMATICS AND INFORMATICS

24 Naugarduko, LT-03225 Vilnius
Tel. 219 3086, fax. 215 1585
E-mail:

Head - Prof. Dr. Eugenijus Stankus

STAFF

Professors: Dr. V. Dagienė (part-time), Dr. E. Stankus.
Docents: Dr. A. Apynis, Dr. E. Gaigalas, Dr. R. Kašuba, Dr. R. Kudžma.
Lecturers: Dr. A. Elijio, T. Jevsikova (part-time, Dr. R. Laucius (part-time), Dr. Š. Repšys, Dr. A. Novikas.

RESEARCH INTERESTS

Research of paradigms, prevailing in mathematics and informatics (IT) teaching in secondary school and universities
Research of mathematical problems and mathematical models
Development of working methods with children, gifted in mathematics and informatics

RESEARCH PROJECTS CARRIED OUT IN 2012

Projects Supported by the University Budget

Analysis of Mathematics and Informatics (IT) Teaching Methods and Applications. Prof. E. Stankus. 2011–2013.

Research of the methods for problem-solving capacities of mathematically gifted students was carried out. The activity of Lithuanian school for young mathematicians and regional team contests was developed.
Models of population and problems of number theory were investigated.
Guidelines in information technology and computer science education for secondary school were prepared.

MAIN PUBLICATIONS

Textbooks, Manuals

A. Apynis, S. Stungurienė. Verslo ir vadybos matematika : vadovėlis. Vilnius : Vilniaus universitetas, 2012. 228 p.

R. Kašuba. Kak rešat zadaču, kogda ne znaješ kak : posobije dlia učaščichsia obščeobrazovatelnych učreždenij. Moskva : Prosveščenije, 2012. 174 p. :.

A. Elijio, S. Zybartas. Pasiruošk pasiekimų patikrinimui : matematika [Elektroninis išteklius] / sudarė Aistė Elijo, Saulius Zybartas. Vilnius : Nacionalinis egzaminų centras, 2012. 74 p.

Articles

T. Christ, J. Kalpokas. Upper bounds for discrete moments of the derivatives of the riemann zeta-function on the critical line // Lithuanian mathematical journal. New York : Springer. 2012, Vol. 52, no. 3, p. 233-248.

A. Elijio, L. Abelytė. Gabiausiųjų mokymo taikant Mensa galvosūkius galimybės // Lietuvos matematikos rinkinys. LMD darbai. Vilnius : Matematikos ir informatikos institutas. 2012, t. 53, ser. B, p. 151-156.

E. Gaigalas. On the dimension of some spaces of generalized theta-series // Analytic and probabilistic methods in number theory : proceedings of the 5th international conference in honour of J. Kubilius, Palanga, 4-10 September, 2011 / editors: A. Laurinčikas, E. Manstavičius, G. Stepanauskas. Vilnius : TEV, 2012, p. 143-149.

A. Elijio, D. Malijonytė. Simetrija kaip matematinių uždavinių sprendimo taktika // Lietuvos matematikos rinkinys. LMD darbai. Vilnius : Matematikos ir informatikos institutas. 2012, t. 53, ser. B, p. 157-162.

R. Rudalevičienė, R. Kašuba. Uždavinio sprendimas kaip mokslo kūrimo provaizdis // Lietuvos matematikos rinkinys. LMD darbai. Vilnius : Matematikos ir informatikos institutas. 2012, t. 53, ser. B, p. 220-225.

A. Dubickas, A. Novikas. On integers expressible by some special linear form // Acta Mathematica Universitatis Comenianae. Mlynska Dolina : Univerzita Komenskeho. 2012, vol. 81, no 2, p. 203-209.

R. Kašuba. Becoming a little bit cleverer and considerably more joyful // MCG newsletter. 2012, no 2, p. 17-23.

A. Elijio. Lithuania // PIRLS 2011 encyclopedia: Education policy and curiculum in reading, Vol. 2: L-Z and benchmarking participants. Boston : TIMSS and PIRLS International study center, 2011, p. 387-394.

A. Elijio. Lithuania // TIMSS 2012 encyclopedia: education policy and curriculum in mathematics and science. Vol. 2. Boston : TIMSS & PIRLS international study center, 2012, p. 3545-555.

R. Kašuba. Might it be so that being perfect sometimes indeed might only mean being simple or as short as possible? // MCG newsletter. 2012, no 2, p. 31-40.

Materials of conferences

V. Dagienė, G. Futschek. Knowledge construction in the Bebras problem solving contest // Constructionism 2012 : theory practice and impact : conference proceedings, August 21-25, Greece. Athens : Vivliosynergatiki S.A. 2012, p. 678-680.

R. Kašuba, R. Rudalevičienė. Kangaroo problem: ouburst of intellect or stage-managed impromptu? // Teaching mathematics: retrospective and perspectives : 13th international conference, May 30-June 1, 2012, Tartu: proceedings. Tartu : Eesti maaulikool, 2012, p. 213-228.

R. Kašuba. Wie bunt und lustig kann der Text der Aufgabe sein und wozu soll es gut sein? // Beitrage zum Mathematikunterricht 2012 Digital. Weingarten, 2012.

R. Kašuba. Matematikos dėstymas Vaikų universitete - iššūkiai ir galimybės // Matematika ir matematikos dėstymas - 2012 : konferencijos pranešimų medžiaga. Kaunas : Technologija, 2012, p. 9-21.

COOPERATION

Comenius University (Slovakia)
Vilnius Pedagogical University (Lithuania)
Kaunas University of Technology (Lithuania)
Siauliai University (Lithuania)
University of Latvia (Latvia)
Nordic Graduate School in Mathematics Education
University of East Finland (Finland)
University of Agder (Norway)
Munster University (Germany)
Aalto University (Finland)
ETH (Switzerland)
Weizmann Institute of Science (Israel)
Vienna University of Technology (Austria)
University of Groningen (the Netherlands)
University of Malta (Malta)
University of Tampere (Finland)
Cachan High School (France)

OTHER SCIENTIFIC ACTIVITIES

Doc. A. Apynis –

chairman of the board member of Lithuanian school of young mathematicians.

Prof. V. Dagienė –

chair of the Weekend School in Informatics;
chair of International Contest on Informatics and Computer Fluency;
coordinator in Lithuania of NNEER (Nordic Network of Engineering Education Research;
editorial board member of the journal International Journal of Instruction, (http://www.e-iji.net/;
editorial board member of the journal Acta Pedagogica Vilnensia;
member of the Lithuanian Mathematical Society;
member of the Lithuanian Computer Society;
member of Scientific Committee of international Baltic Sea countries conference (Koli Conference on Computer Science Education);
representative of Lithuania in EWM (European Women in Mathematics);
member of international Committee of ECEL (European Conference on elearning).

Doc. R. Kašuba -

representative of Lithuania in ICMI (The International Commission on Mathematical Instruction);
board member of the Lithuanian Mathematical Society;
member of International Committee of International Group for Mathematical Creativity and Giftedness (MCG);
editorial board member of the MCG Mathematical Creativity and Mathematical Giftedness Newsletter, Editor of Problem Corner.

Doc. R. Kudžma -

board member of the Lithuanian Mathematical Society;
board member of the Lithuanian Actuarial Society;
member of the Education Committee of the European Actuarial Consultative Group;
council delegate of the International Actuarial Association;
member of Education Committee of the International Actuarial Association;
member of program committees of international conferences Teaching Mathematics: Retrospective and Perspectives, Tartu.

T. Jevsikova -

junior member of IFIP (International Federation for Information Processing) WG 3.1 (Informatics and ICT in Secondary Education);
member of Commission of the Terms of Informatics and Information Technologies.

Prof. E. Stankus -

board member of the Lithuanian Mathematical Society;
board member of the Lithuanian Association of Mathematics Teachers;
board member of the Lithuanian School of Young Mathematicians;
editorial board member of the journal Lithuanian Mathematical Journal. Proceedings of Lithuanian Mathematical Society, http://www.mii.lt/LMRI.

DEPARTMENT OF DIFFERENTIAL EQUATIONS AND NUMERICAL ANALYSIS

24 Naugarduko, LT-03225 Vilnius
Tel. 219 3084, fax 215 1585
E-mail

Head – Prof. Habil. Dr. Konstantinas Pileckas

STAFF

Professors: Habil. Dr. K. Pileckas, Dr. V. Skakauskas, Dr. A. Štikonas (part-time),
Dr. S. Rutkauskas (part-time).
Senior research fellow: Habil.Dr. K. Pileckas.
Docents: Dr. A. Ambrazevičius, Dr. V. Daukšas (part-time), Dr. R. Karaliūnas (part-time), Dr. P. Katauskis, Dr. A. Kavaliauskas, Dr. A. Kregždė, Dr. M. Meilūnas (part-time), Dr. G. Puriuškis, Dr. O. Štikonienė.
Lecturer: Dr. A. Domarkas.
Doctoral students: K. Kaulakytė, N. Klovienė, M. Skujus, A. Eismontaitė.

RESEARCH INTERESTS

Investigation of differential, integrodifferential and nonlocal equations; analysis and numerical methods

RESEARCH PROJECTS CARRIED OUT IN 2012

Projects Supported by University Budget

Investigations of Solutions to Differential and Integro-differential Equations. Prof. K. Pileckas. 2011–2013.

The existence and uniqueness theorem to a model of a dissociative adsorption and associative desorption is proved.
The existence and uniqueness theorem to a model of unimolecular surface reactions is proved taking into account surface diffusion described by Fick’s law.
A mathematical model of unimolecular surface reactions is proposed and studied numerically taking into account an integral mechanism of adsorbed particles.
A model of receptor-toxin-antibody interaction is studied numerically taking into account the Neumann boundary condition.
A relation between Green’s functions of two m-th order discrete problems with additional conditions, described by m linearly independent functionals is obtained. Generalized Green’s functions for second-order discrete boundary value problems with nonlocal boundary conditions are investigated.
The asymptotic stability of exponentially growing (or vanishing) solutions to the sex-child-structured nondispersing population dynamics model is studied by using numerical analysis methods.
The sensitivity of the debt to a short movement of interest rate, the GDP growth rate and the primary budget deficit is investigated using the differential equations calculus technique.
Third order initial boundary value problem is studied in a bounded plane domain with smooth boundary. The existence and uniqueness of the solution is proved.
The stationary Navier–Stokes system with nonhomogeneous boundary conditions is studied in a class of domains having “paraboloidal” and “layer-like” outlets to infinity. The boundary value is assumed to have a compact support and it is supposed that the fluxes of the boundary data over connected components of the inner boundary are sufficiently small. The fluxes of the boundary value over infinite components of the boundary are arbitrary. The existence of at least one weak solution to the Navier–Stokes problem is proved.
The non-stationary equations describing the motion of the second-grade fluid in a two- dimensional infinite channel and in a three-dimensional rotationally symmetric pipe are studied. The existence of a unique Poiseuille-type solution having a given flow rate (flux) is proved. The behavior of this solution for large times is investigated. The motion of the second-grade fluid in three-dimensional pipe with arbitrary cross-section is studied. The existence of secondary flow is proved.
The nonhomogeneous boundary value problem for the steady Navier–Stokes equations is studied in two-dimensional bounded domains and three-dimensional axially symmetric bounded domain with multiply connected Lipschitz boundary. The existence of the solution with arbitrary large fluxes over the connected components of the boundary is proved. The proof uses the Bernoulli law for a weak solution to the Euler equations and the one-side maximum principle for the total head pressure corresponding to this solution.
The nonhomogeneous boundary-value problem for the steady-state Navier–Stokes equations in two-dimensional exterior domains symmetric to an axis, and in three-dimensional axially symmetric exterior domains is investigated. The existence of a solution is proved for arbitrary values of the flux of the boundary datum.

A time–periodic Stokes problem is studied in the domain with cylindrical outlets to infinity. A basis in the set of solutions to the homogeneous problem is constructed. This basis possesses several properties that are essential for the setting correct asymptotic conditions at infinity.

Projects, Programmes, Issues Supported by Research Council of Lithuania

MIP-30/2011: Boundary Value Problems for Navier-Stokes System in Unbounded Domains. Prof. K. Pileckas. 2011–2012.

MIP-052/2012: Coupled Systems of Ordinary, Partial, and Integrodifferential Equations. Prof. V. Skakauskas. 2012–2014.

International Science Programmes and Projects

Lithuanian-swiss programme „Research and development“: Asymptotic Problems and Applications, project Nr. CH-3-ŠMM-01/01. Prof. K. Pileckas. 2012–2016.

MAIN PUBLICATIONS

Articles

N. Klovienė, K. Pileckas. Nonstationary Poiseuille-type solutions for the second-grade fluid flow // Lithuanian mathematical journal. New York : Springer. 2012, vol. 52, no. 2, p. 155-171.

N. Klovienė. On a third order initial boundary value problem in a plane domain // Nonlinear analysis : modelling and control. Vilnius : Institute of Mathematics and Informatics. 2012, vol. 17, no. 3, p. 312-326.

A. Kregždė. Government Debt Sustainability: the Lithuanian Case // Ekonomika / Vilniaus universitetas. Vilnius : Vilniaus universiteto leidykla. 2012, t. 91, nr. 3, p. 56-71.

G. Puriuškis. On the minimum of certain functional // Šiauliai mathematical seminar / Šiauliai University. Šiauliai : Šiaulių universiteto leidykla. 2012, Vol. 7, p. 125-134.
G. Paukštaitė, A. Štikonas. Generalized Green's functions for second-order discrete boundary-value problems with nonlocal boundary conditions // Lietuvos matematikos rinkinys. LMD darbai. Vilnius : Matematikos ir informatikos institutas. 2012, t. 53, ser. A, p. 96-101.

A. Ambrazevičius, A. Eismontaitė. On a mathematical model of dissociative adsorption and associative desorption // Lietuvos matematikos rinkinys. LMD darbai. Vilnius : Matematikos ir informatikos institutas. 2012, t. 53, ser. A, p. 7-12.

K. Kaulakytė. Stacionarios Navjė-Stokso lygtys su nenuline kraštine sąlyga dviejų sluoksnių sistemoje // Lietuvos matematikos rinkinys. LMD darbai. Vilnius : Matematikos ir informatikos institutas. 2012, t. 53, ser. B, p. 13-18.
G. Panasenko, K. Pileckas. Asymptotic analysis of the nonsteady viscous flow with a given flow rate in a thin pipe // Applicable Analysis. Colchester : Taylor & Francis Ltd. 2012, vol. 91, iss. 3, p. 559-574.

V. Skakauskas, P. Katauskis. Numerical study of the kinetics of unimolecular heterogeneous reactions onto planar surfaces // Journal of mathematical chemistry. Dordrecht : Springer Netherlands. 2012, Vol. 50, no. 1, p. 141-154.

K. Pileckas, R. Russo. On the existence of vanishing at infinity symmetric solutions to the plane stationary exterior Navier-Stokes problem // Applicable Annalen. Heidelberg : Springer. 2012, vol. 352, iss. 3, p. 643-685.

K. Kaulakytė, K. Pileckas. On the nonhomogeneous boundary value problem for the Navier-Stokes system in a class of unbounded domains // Journal of mathematical fluid mechanics. Basel : Springer. 2012, vol. 14, iss. 4, p. 693-716.

V. Skakauskas, O. Štikonienė. Stability of persistent solutions to a population dynamics model // Applied mathematics and computation. New York : Elsevier Science Inc. 2012, vol. 218, no. 17, p. 8987-8996.

M. Korobkov, K. Pileckas, R. Russo. Steady Navier-Stokes system with nonhomogeneous boundary conditions in the axially symmetric case // Comptes Rendus Mecanique. Paris : Elsevier Masson. 2012, vol. 340, no. 3, p. 115-119.
A. Ambrazevičius. Solvability theorem for a model of a unimolecular heterogeneous reaction with adsorbate diffusion // Journal of mathematical sciences. New York : Springer. 2012, vol. 184, no. 4, p. 581-591.

Materials of conferences

P. Katauskis, V. Skakauskas, A. Skvortsov. On the reaction-diffusion model of the receptoržtoxin-antibody interaction // Šestye Poliachovskije čtenija : meždunarodnaja naučnaja konferencija po mechanike = Sixth Polyakhov's reading : international scijentific conference on mechanics, 31 janvaria - 3 fevralia 2012 g. Sankt-Petergurg, Rossija : izbrannye trudy. Moskva : izdatel I.V. Balabanov, 2012, p. 127-132.

V. Skakauskas, P. Katauskis, A. Skvortsov. Numerical simulation of a receptor-toxin-antibody interaction // CMMSE 2012 : proceedings of the 12th international conference on computational and mathematical methods in science and engineering. Vol. 3 / editor J. Vigo-Aguiar. Murcia : CMMSE, 2012, p. 1111-1117.

COOPERATION

Ferrara University, Ferrara (Italy)
University of Kassel, Kassel (Germany)
University of Saint Etienne, Saint Etienne (France)
Technical University of Lisbon, Lisbon (Portugal)
Seconda Università degli Studi di Napoli, Caserta (Italy)
University of Novosibirsk, Novosibirsk (Russia)
St. Petersburg Department of V.A. Steklov Mathematical Institute, St. Petersburg (Russia)
University of Zurich, Zurich (Switzerland)

OTHER SCIENTIFIC ACTIVITIES

Prof. K. Pileckas –

member of the Lithuanian Academy of Sciences;
member of the Research Council of Lithuania;
editorial board member of the journal Mathematical Fluid Mechanics;
editorial board member of the journal Annali dell'Universita di Ferrara;
editorial board member of the journal Mathematical Modelling and Analysis;
editorial board member of the Lithuanian Mathematical Journal.

Doc. O. Štikonienė –

editorial secretary of the Lithuanian Mathematical Journal.

Prof. A. Štikonas–

executive editor of the journal Mathematical Modelling and Analysis;
editorial board member of the Lithuanian Mathematical Journal;
deputy-editor-in-chief of the journal Nonlinear Analysis Modelling and Control;
member of organizing committee MMA-2012 (International Conference on Mathematical Modelling and Analysis, Tallinn, Estonia).

Prof. S. Rutkauskas –

editorial board member of the Lithuanian Mathematical Journal;
editorial board member of the journal Mathematical Modelling and Analysis.

DEPARTMENT OF ECONOMETRIC ANALYSIS

24 Naugarduko, LT-03225 Vilnius
Tel. 219 3076 ‚ fax 215 1585
E-mail:

Head – Prof. Habil. Dr. Alfredas Račkauskas

STAFF

Professors: Habil. Dr. V. Čekanavičius, Habil. Dr. R. Leipus, Habil. Dr. R. Norvaiša (part-time), Habil. Dr. A. Račkauskas, Dr. M. Radavičius (part-time).
Docents: Dr. V. Kvedaras, Dr. R. Lapinskas, Dr. A. Maldeikienė, Dr. G. Murauskas.
Lecturers: Dr. G. Blažys (part-time), Dr. D. Celov, Dr. V. Zemlys, Dr. D. Zuokas, V. Maniušis.
Senior assistants: Dr. I. Rastenė, R. Malukas (part-time), J. Markevičiūtė (part-time).
Doctoral students: V. Characiejus, L. Dindienė, J. Kamarauskaitė, J. Markevičiūtė, A. Reklaitė, M. Tartėnas.

RESEARCH INTERESTS

Time series analysis, financial econometrics
Functional data analysis
Limit theorems in probability and their applications to statistics and econometrics
Bootstrap and other resampling methods in statistics and econometrics
Macroeconometric modelling
High frequency data analysis

RESEARCH PROJECTS CARRIED OUT IN 2012

Projects Supported by University Budget

Research in Probability Theory and Stochastic Processes and their Applications in Econometrics, Financial and Actuarial Mathematics. Prof. V. Paulauskas, Prof. A. Račkauskas. 2010–2015.

A central limit theorem was proved for long range dependent functional linear processes with space varying memory. Necessary and sufficient conditions were established for polygonal line processes build on partial sums of independent identically distributed random variables to satisfy Holderian strong law of large numbers. Holderian central limit theorem was proved for polygonal line processes constructed from partial sums of a nearly nonstationary autoregressive process. Estimates for negative binomial approximation to the sums of m-dependent integer-valued random variables were obtained via Heinrichs method.
Some new ratio type tests for detection of non-constant long memory parameter in time series were studied. The asymptotic and finite sample properties of the proposed test statistic were obtained under null and alternative hypothesis.
New results about the behaviour of sums of nonidentically distributed heavy-tailed random variables under certain dependence structure were proved.
Procedures for testing the functional constraints on parameters in regressions with variables of different frequency were developed. An R package “midasr” for estimating MIDAS regressions and testing the restriction function was created.

Governmental Science Programmes and Research Projects Ordered by the Branch Ministries

Bilateral Lithuanian-France research program Gilibert, Project: Statistical Inference and Limit Theorems for Stochastic Processes and Fields (Reg. Nr. TAP-10005), 2011–2012. Coordinator Prof. V. Paulauskas, J. Markevičiūtė, E.Mielkaitis, A. Račkauskas.

International Science Programmes, Projects and Contracts

Bilateral Lithuanian-France research program Gilibert, project: Statistical Inference and Limit Theorems for Stochastic Processes and Fields 2011–2012 m. Reg. Nr. TAP-10005, Coordinator Prof. V. Paulauskas, J. Markevičiūtė, E. Mielkaitis, A. Račkauskas.

MAIN PUBLICATIONS

Articles

A. Račkauskas, I. Rastenė. Asymptotic results for polugonal processes related to an autoregression // Lithuanian mathematical journal. New York : Springer. 2012, vol. 52, no. 2, p. 181-195.

R. Leipus, J. Šiaulys. Closure of some heavy-tailed distribution classes under random convolution // Lithuanian mathematical journal. New York : Springer. 2012, vol. 52, no. 3, p. 249-258.

J. Markevičiūtė, C. Suquet, A. Račkauskas. Functional central limit theorems for sums of nearly nonstationary processes // Lithuanian mathematical journal. New York : Springer. 2012, vol. 52, no. 3, p. 282-296.

V. Kvedaras, R. Leipus, J. Šiaulys. Estimation of the generalized stochastic claims Reserving model and the chain-ladder method // Pinigų studijos. Vilnius : Lietuvos bankas. 2012, t. 16, nr. 1, p. 68-90.

Y. Yang, R. Leipus, J. Šiaulys. On the ruin probability in a dependent discrete time risk model with insurance and financial risks // Journal of computational and applied mathematics. Amsterdam : Elsevier BV. 2012, vol. 236. no 13, p. 3286-3295.

Y. Yang, R. Leipus, J. Šiaulys. Precise large deviations for compound random sums in the presence of dependence structures // Computers and mathematics with applications. Kidlington : Pergamon. 2012, vol, 64, no 6, p. 2074-2083.

Y. Yang, R. Leipus, J. Šiaulys. Tail probability of randomly weighted sums of subexponential random variables under a dependence structure // Statistics & probability letters. Amsterdam : Elsevier BV. 2012, Vol. 82, no. 9, p. 1727-1736.

P. Vellaisamy, N. Upadhyne, V. Čekanavičius. On negative binomial approximation // Teorija veroiatnostej i ee primienenija. Moskva : izd-vo "Nauka". 2012, t. 57, no. 1, 141-154.

J. Markevičiūtė, A. Račkauskas, C. Suquet. Functional limit theorems for sums of nearly non stationary processes // Publications de L'U.F.R. De Mathematiques Pures et Appliquees. Lille : IRMA. 2011, Vol. 71, p. VIII.

A. Račkauskas, C. Suquet. On the distribution of sequential Holder norms of the Brownian motion // Publications de L'U.F.R. De Mathematiques Pures et Appliquees. Lille : IRMA. 2011, Vol. 71, p. IX.

COOPERATION

Lithuanian Standards Board (Lithuania)
University of Lille (France)
New Economic School, Moscow (Russia)
Koeln University, Hamburg University (Germany)
Melbourne University (Australija)
Utah University (USA)
York University (England)
Tilburg University (The Netherlands)
Karol Adamiecki University of Economics in Katowice (Poland)

OTHER SCIENTIFIC ACTIVITIES

Prof. A. Račkauskas –

editorial board member of the Lithuanian Mathematical Journal;
editorial board member of the Mathematical Modelling and Analysis;
member of the Lithuanian Statistics Society and the American Mathematical Society.

Prof. V. Čekanavičius –

member of the Lithuanian Statistics Society.

Prof. R. Leipus –

editorial board member of the journal Monetary Studies;
editorial board member of the Lithuanian Mathematical Journal.

Prof. R. Norvaiša –

editorial board member of the Lithuanian Mathematical Journal.

DEPARTMENT OF MATHEMATICAL ANALYSIS

24 Naugarduko, LT-03225 Vilnius
Tel. 219 3083 fax. 215 1585
E-mail:

Head – Prof. Habil. Dr. Vygantas Paulauskas

STAFF

Professors: Habil. Dr. V. Mackevičius, Habil. Dr. V. Paulauskas, Habil. Dr. D. Surgailis (part-time), Dr. J. Šiaulys.
Docents: Dr. G. Bakštys (part-time), Dr. A. Juozapavičienė (part-time), Dr. M. Manstavičius, Dr. A. Plikusas.
Lecturers: Dr. A. Juozulynas, Dr. K. Liubinskas, Dr. A. Skučaitė, A. Lenkšas.
Senior assistant: D. Puplinskaitė (part-time).
Doctoral students: E. Bieliauskienė, E. Mielakitis, A. Korvel, D. Puplinskaitė.

DOCTORAL DISSERTATIONS MAINTAINED IN 2012

E. Bieliauskienė. Ruin probability and Gerber-Shiu function for the discrete time risk model with inhomogeneous claims.

RESEARCH INTERESTS

Mathematical analysis
Functional analysis
Limit probability theorems in infinite-dimensional spaces
Stochastic analysis
Actuarial and financial mathematics
Asymptotic analysis of econometric models

RESEARCH PROJECTS CARRIED OUT IN 2012

Projects Supported by University Budget

Research in Probability Theory and Stochastic Processes and their Applications in Econometrics, Financial and Actuarial Mathematics. Prof. V. Paulauskas, Prof. A. Račkauskas. 2010–2015.

Estimation of the tail index using max-agregation scheme is obtained. Preliminary estimates of the so-called generalized association parameter for a linear process with stable innovations are obtained.
Positive approximations of the Heston model by discrete random variables are constructed.
Approximate formulas for the solution of the Verhulst equation are obtained.
Contemporaneous aggregation of a triangular array of random-coefficient AR(1) processes with i.i.d. innovations belonging to the domain of attraction of an infinitely divisible law was studied. It was proved that the limiting aggregated process exists and is represented as a mixed infinitely divisible moving-average. The limit distribution of partial sums of the aggregated process was obtained in the case where the mixing density varies regularly at the unit root.
The conditions are obtained for the closeness of some heavy-tailed distribution classes under random convolutions.
Asymptotic estimations are obtained for large deviations of the dependent compound renewal risk process.
The recursive formulas are given for calculation of the Gerber-Shiu function in the case of inhomogeneous discrete time risk model.
Asymptotic behavior is found for the tail probability of randomly weighted sums of subexponential random variables under a dependence structure, where the random weights and the corresponding summands are dependent.
Asymptotic formulas are obtained for the tail probability of the random sum of dependent random variables in the case where distribution functions of summands are dominatedly varying.
The asymptotic for ultimate ruin probability is obtained for discrete time risk model with financial and insurance risk under asumption that the insurance risks are heavy tailed and financial risks satisfy some moment condition.
Selfsimilar Gaussian processes and their trajectories were investigated. A result due to C.A. Tudor and Y. Xiao (2007) on strong local nondeterminism was extended to a subclass of these processes.

Governmental Science Programms and Research Projects Ordered by the Branch Ministries

Bilateral Lithuanian-France research program Gilibert, project: Statistical Inference and Limit Theorems for Stochastic Processes and Fields (Reg. Nr. TAP-10005). Coordinator Prof. V. Paulauskas, investigators J. Markevičiūtė, E. Mielkaitis, A. Račkauskas.

Other Research Projects

International Science Programmes, Projects and Contracts

MAIN PUBLICATIONS

Articles

Y. Yang, R. Leipus, J. Šiaulys. Asymptotic of random sums of negatively dependent random variables in the presence of dominatedly varying tails // Lithuanian mathematical journal. New York : Springer. 2012, vol. 52, no. 2, p. 222-232.

R. Leipus, J. Šiaulys. Closure of some heavy-tailed distribution classes under random convolution // Lithuanian mathematical journal. New York : Springer. 2012, vol. 52, no. 3, p. 249-258.

P. Banys, V. Paulauskas. CLT for linear random fields with martingale increments // Lithuanian mathematical journal. New York : Springer. 2012, vol. 52, no. 1, p. 13-28.

V. Paulauskas, M. Vaičiulis. Estimation of the tail index in the max-aggregation scheme // Lithuanian mathematical journal. New York : Springer. 2012, Vol. 52, no. 3, p. 297-315.

E. Ignatavičiūtė, R. Mikalauskaitė-Arminienė, J. Šiaulys. Lee-Carter mortality forecasting // Lietuvos statistikos darbai. Vilnius : Statistikos departamentas prie Lietuvos Respublikos Vyriausybės. 2012, Vol. 51, nr. 1, p. 22-35.

J. Šiaulys, G. Stepanauskas. Discrete uniform limit law for additive prime number indicators // Analytic and probabilistic methods in number theory. Vilnius : TEV, 2012, p. 255-263.

V. Paulauskas. A generalization of sectorial and quasi-sectorial operators // Journal of functional analysis. Maryland Heights : Elsevier Inc. 2012, vol. 262, iss. 5, p. 2074-2099.

E. Bieliauskienė, J. Šiaulys. Gerber-Shiu function for the discrete inhomogeneous claim case // International journal of computer mathematics. Colchester : Taylor & Francis Ltd. 2012, vol. 89, no 12, p. 1617-1630.

Y. Davydov, V. Paulauskas. A simple approach in limit theorems for linear random processes and fields with continuous time // Teorija veroiatnostej i ee primienenija. Moskva : izd-vo "Nauka". 2012, t. 57, no. 4, s. 724-743.

COOPERATION

University of Lille (France)
University of Bonn (Germany)
Soochow University (China)
Nanjing Audit University (China)

OTHER SCIENTIFIC ACTIVITIES

Prof. V. Mackevičius –

editorial board member of the Lithuanian Mathematical Journal;
member of the American Mathematical Society, http://www.ams.org;
member of the Lithuanian Mathematical Society.

Prof. V. Paulauskas –

editorial board member of the Lithuanian Mathematical Journal;
member of the American Mathematical Society, http://www.ams.org;
editorial board member of the Central European Journal of Mathematics, http://www.ingentaconnect.com/content/cesj/cejm;
board member of the Lithuanian Mathematical Society;
member of the International Statistical Institute, http://isi.cbs.nl;
board member of the Lithuanian Statistical Society, http://www.statistikusajunga.lt/index.php?option=com_content&task=view&id=5&Itemid=7;
member of the Lithuanian Academy of Sciences, http://lma.lt/media/k2/attachments/MFCHMS_sudetis_2011.pdf.

Prof. D. Surgailis –

member of the Lithuanian Mathematical Society;
editorial board member of the Lithuanian Mathematical Journal;
member of the Lithuanian Academy of Sciences, http://lma.lt/media/k2/attachments/MFCHMS_sudetis_2011.pdf.

Prof. J. Šiaulys –

editorial board member of the International Journal of Computer Mathematics;
member of the Lithuanian Mathematical Society.

Doc. G. Bakštys –

member of the Lithuanian Actuarial Society.

Dr. M. Manstavičius –

member of the Lithuanian Mathematical Society.

Dr. A. Skučaitė –

member of the Lithuanian Actuarial Society.

DEPARTMENT OF MATHEMATICAL COMPUTER SCIENCE

47 Didlaukio, LT-08303 Vilnius
Tel. 5219 5030, fax. 215 1585
Email:

Head –Prof. Dr. Gediminas Stepanauskas

STAFF

Professors: Habil. Dr. M. Bloznelis, Dr. G. Stepanauskas.
Docents: Dr. G. Bareikis, Dr. A. Mačiulis, Dr. V. Stakėnas.
Lecturers: Dr. R. Grigutis, I. Grinis.
Research fellows: Dr. G. Alkauskas, Dr. V. Zacharovas.
Doctoral students: V. Kurauskas, I. Radavičius, L. Žvinytė.

RESEARCH INTERESTS

Probabilistic analysis of number-theoretical structures
Combinatorial statistics
Random discrete structures and algorithms

RESEARCH PROJECTS CARRIED OUT IN 2012

Projects Supported by University Budget

Analysis of Discrete Structures by Probabilistic, Combinatorial and Analytical Methods. Prof. M. Bloznelis, Prof. G. Stepanauskas. 2011–2015.

Results for number theoretical structures: te subsequencies of Farey fractions, specified by some arithmetical conditions, were considered; the statements about the asymptotically uniform distribution of these subsequencies were proved.
A sequence of arithmetical processes defined via multiplicative functions was considered. Asymptotic formulas with remainder terms for the first moment are obtained.
The projective translation equation was investigated and all 2-dimensional rational solutions were found. Also, the same equation was explored and all unramified 2-dimensional solutions were found; the most interesting of them are expressible in terms of special elliptic functions. Also, the Fourier-Stieltjes coefficients of the Minkowski question mark function were explored. A 25 year old conjecture, posed by famous mathematicians, about the structure and asymptotics of the spectrum of the transfer operator for the Gauss continued fraction map, was proved.
Results for graphs and other combinatorial structures: a first order asymptotic for the assortativity and clustering coefficient has been shown for sparse random intersection graphs with the number of vertices tending to infinity. The dependence of the local clustering coeficient on the vertex degree has been described using rigorous mathematical argument.
Exhaustive search algorithm for finding a maximal independent set in random graphs was analysed and the asymptotic expansion of the mean value of the time needed to find the maximal independent search using this algorithm was presented. It was also started to work on a new subject: generating functions that are root-unitary polynomials.
Results on applications: some geometric aspects of polyvalent systems were considered.

MAIN PUBLICATIONS

Textbooks, Manuals

G. Bareikis. Finansiniai skaičiavimai : paskaitų konspektas. 2011 , 174 p.

G. Stepanauskas. Riba : paskaitų konspektas bakalauro studijų Fizikos fakulteto studentams. Vilnius : Vilniaus universitetas, 2011. 14 p.

Articles

A. Čiginas. An edgeworth expansion for finite-population L-statistics // Lithuanian mathematical journal. New York : Springer. 2012, vol. 52, no. 1, p. 40-52.

G. Bareikis, A. Mačiulis. Some applications of IFS based on square symmetries // Nonlinear analysis : modelling and control. Vilnius : Institute of Mathematics and Informatics. 2012, vol. 17, no. 1, p. 16-26.

G. Bareikis, A. Mačiulis. Asymptotic expectation of a sequence of arithmetical processes // Analytic and probabilistic methods in number theory : proceedings of the 5th international conference in honour of J. Kubilius, Palanga, 4-10 September, 2011 / editors: A. Laurinčikas, E. Manstavičius, G. Stepanauskas. Vilnius : TEV, 2012, p. 35-48.

J. Šiaulys, G. Stepanauskas. Discrete uniform limit law for additive prime number indicators // Analytic and probabilistic methods in number theory. Vilnius : TEV, 2012, p. 255-263.

G. Alkauskas. Fourier-Stieltjes coefficients of the Minkowski question mark function // Analytic and probabilistic methods in number theory : proceedings of the 5th international conference in honour of J. Kubilius, Palanga, 4-10 September, 2011 / editors: A. Laurinčikas, E. Manstavičius, G. Stepanauskas. Vilnius : TEV, 2012, p. 19-33.

V. Stakėnas. The tuples of natural numbers and prime divisors // Analytic and probabilistic methods in number theory : proceedings of the 5th international conference in honour of J. Kubilius, Palanga, 4-10 September, 2011 / editors: A. Laurinčikas, E. Manstavičius, G. Stepanauskas. Vilnius : TEV, 2012, p. 229-242.

M. Bloznelis, F. Gotze, J. Jaworski. Birth of a strongly connected giant in an inhomogeneous random digraph // Journal of applied probability. Sheffield : Applied Probability Trust. 2012, Vol. 49, no. 3, p. 601-611.

G. Bareikis, A. Mačiulis. CesĆ ro means related to the square of the divisor function // Acta arithmetica. Warsaw : Polish Acad Sciences Inst Mathematics. 2012, vol. 156, no. 1, p. 83-99.

S. Gražulis, A. Daškevič, A. Merkys, D. Chateigner, L. Lutterotti, M. Quiros, N. Serebryanaya, P. Moeck, R. Downs, A. Bail. Crystallography Open Database (COD): an open-access collection of crystal structures and platform for world-wide collaboration // Nucleic Acids Research. Oxford : Oxford University Press. 2012, vol. 40, iss. D1, p. D420-D427.

V. Kurauskas, C. McDiarmid. Random Graphs with Few Disjoint Cycles // Combinatorics, probability and computing. Cambridge : Cambridge University Press. 2011, Vol. 20, iss. 5, p. 339-345. [vėluojanti].

COOPERATION

Bielefeld University (Germany)
Helsinki University (Finland)
Poznan Adam Mickiewicz University (Poland)
University of Oxford (UK)
Bonn University (Germany)

OTHER SCIENTIFIC ACTIVITIES

Prof. M. Bloznelis –

editorial board member of the Lithuanian Mathematical Journal, http://www.mii.lt/index.php?siteaction=pages.browse&page=lmj_an&lang=en;

member of the Lithuanian Mathematical Society.

Doc. G. Bareikis –

member of the Lithuanian Mathematical Society.

Dr. R. Grigutis –

member of the Lithuanian Mathematical Society.

Doc. A. Mačiulis –

member of the Lithuanian Mathematical Society.

Doc. V. Stakėnas –

board member of the Lithuanian Mathematical Society.

Prof. G. Stepanauskas –

editorial board member of the journal Nonlinear Analysis: Modelling and Control;
board member of the Lithuanian Mathematical Society;
member of the organizing committee of the 53rd conference of Lithuanian Mathematical Society.

DEPARTMENT OF MATHEMATICAL STATISTICS

24 Naugarduko, LT-03225 Vilnius
Tel. 219 3065, fax.215 1585
E-mail:
Head – Prof. Dr. Vytautas Kazakevičius

STAFF

Professors: Habil. Dr. V. Bagdonavičius, Dr. V. Kazakevičius.
Docents: Dr. R. Eidukevičius, Dr. J. Kruopis, Dr. R. Levulienė, Dr. M. Vaičiulis (part-time), Dr. P. Vaitkus.
Lecturer: Dr. V. Skorniakov.

RESEARCH INTERESTS

Statistical methods in reliability theory and survival analysis and their applications
Asymptotic analysis of distributions of statistics, their approximations and applications
Neural networks
Process control

RESEARCH PROJECTS CARRIED OUT IN 2012

Projects Supported by University Budget

Models of Mathematical Statistics, their Analysis and Applications. Prof. V. Bagdonavičius. 2010–2014.

Zhang’s goodness-of-fit tests were generalized to the case of censored data. Goodness-of-fit tests for Markov processes were proposed. Properties of test statistics were investigated.
A relation between the convergence of backward and forward iterations of random functions in discrete spaces was found.
There were constructed asymptotically consistent and asymptotically normal statistics for estimation of the Hurst index in stochastic differential equation driven by fractional Brownian motion.
A new approach, called “Sparce Extreme Learning Machine Ensemble”, was proposed which not only proved to provide promising customer churu and cross-sell prediction results, but also was capable to produce the predictive model 4 times faster than “Random Forest”.
A new process, aggregated fractional Brown motion, was defined. Properties of the modified DPR estimator of the tail index were established in the different max-aggregation schemes.
Waste utilization process was analyzed and model of mean change point was fitted. Survival of oncological patients and the proliferation of malignant cells were analyzed.
Mathematical models of dependence of sugar beet fertility and sugarity on climatic and agrochemical factors were analyzed.

International Science Programmes and Projects

The project of EU 7th framework programme: Low Cost Technologies and Traditional Ingredients for the Production of Affordable, Nutritionally Correct, Convenient Foods Enhancing Health in Population Groups at Risk of Poverty (CHANCE, http://www.chancefood.eu, grant agreement no: 266331). Doc. R. Levulienė. 2011–2013.

MAIN PUBLICATIONS

Articles

M. Vaičiulis. Asymptotic properties of generalized DPR statistic // Lithuanian mathematical journal. New York : Springer. 2012, vol. 52, no. 1, p. 95-110.

J. Rukšėnaitė, P. Vaitkus. Prediction of composite indicators using combined method of extreme learning machine and locally weighted regression // Nonlinear analysis : modelling and control. Vilnius : Institute of Mathematics and Informatics. 2012, vol. 17, no. 2, p. 238-251.

J. Juršėnaitė, I. Girkontaitė, M. Mauricas, R. Eidukevičius, D. Characiejus. Expanded Effector Memory T-lymphocytes in DBA/2 Mice Do Not Inhibit the Growth of SL2 Tumours // In Vivo. Athens : International Institute of Anticancer Research. 2012, Vol. 26, no. 4, p. 553-558.

V. Bagdonavičius, S. Malov, M. Nikulin. Homogeneity tests for related samples under censoring // Communications in statistics: simulation and computation. Philadelphia : Taylor & Francis Inc. 2012, vol. 41, no 6, p. 764-775.

D. Janzing, J. Mooij, K. Zhang, J. Lemeire, J. Zscheischler, P. Daniušis, B. Steudel, B. Scholkopf. Information-geometric approach to inferring causal directions // Artificial Intelligence. Amsterdam : Elsevier BV. 2012, Vol. 182-183, p. 1-31.

J. Čelutkienė, D. Zakarkaitė, V. Skorniakov, V. Žvironaitė, V. Grabauskienė, J. Burca, L. Ciparytė, A. Laucevičius. Quantitative approach using multiple single parameters versus visual assessment in dobutamine stress echocardiography // Cardiovascular Ultrasound. London : BioMed Central. 2012, vol. 10, Art. no. 31.

COOPERATION

Bordeaux Victor Segalen University (France)
Padova University (Italy)

OTHER SCIENTIFIC ACTIVITIES

Prof. V. Bagdonavičius –

editorial board member of the Lithuanian Mathematical Journal, http://www.mii.lt/lmj;
member of the Lithuanian Academy of Sciences, http://www.ktl.mii.lt/LMA/;
member of the Lithuanian Mathematical Society.

Prof. V. Kazakevičius –

member of the Lithuanian Mathematical Society.

Doc. R. Eidukevičius –

member of the Lithuanian Mathematical Society.

Doc. J. Kruopis –

member of the Lithuanian Mathematical Society.

Dr. R. Levulienė –

member of the Lithuanian Mathematical Society.

Dr. V. Skorniakov –

member of the Lithuanian Mathematical Society.

Dr. M. Vaičiulis

member of the Lithuanian Mathematical Society.

Doc. P. Vaitkus –

member of the Lithuanian Mathematical Society.

DEPARTMENT OF PROBABILITY THEORY AND NUMBER THEORY

24 Naugarduko, LT–03225 Vilnius
Tel.: 219 30 79, fax 215 15 85
E–mail:

Head - Prof. Habil. Dr. Antanas Laurinčikas

STAFF

Professors: Habil. Dr. A. Laurinčikas, Habil. Dr. E. Manstavičius, Dr. R. Garunkštis (part-time).
Senior research fellows: Habil. Dr. A. Dubickas, Dr. R. Garunkštis (part-time).
Docents: Dr. P. Drungilas, Dr. G. Misevičius.
Lecturers: A. Grigutis, Dr. A. Javtokas, Dr. A. Kačėnas (part-time).
Assistants: J. Jankauskas, E. Karikovas (part-time), P. Šarka (part-time), J Šiurys (part-time), A. Zinevičius (part-time).
Sennior specialist: Dr. H. Jasiūnas.
Postdoctoral student: G. Alkauskas.
Doctoral students: S. Černigova, A. Grigutis, J. Jankauskas, K. Janulis, J. Kalpokas, T. Kargina, E. Karikovas, A. Novikas, J. Rašytė, P. Šarka, J. Šiurys , A. Zinevičius, Ž. Žilinskas.

RESEARCH INTERESTS

Algebraic number theory, analytic number theory, combinatorics, probabilistic number theory

RESEARCH PROJECTS CARRIED OUT IN 2012

Projects Supported by University Budget

Problems of Algebraic and Analytic Number Theory. Prof. A. Dubickas, Prof. A. Laurinčikas, Prof. E. Manstavičius. 2009–2013.

The universality for some classes of composite functions of the Riemann and Hurwitz zeta-functions was obtained. Joint universality for Hurwitz zeta-function was generalized. A limit theorem for the argument of the twist of L-function of elliptic curves was proved.
A total variation approximation of the component vector distribution of random assemblies was obtained.
Some bases for finite and infinite sets with small representation functions have been investigated.
The asymptotic formula of nontrivial a-values of the Selberg zeta-function was obtained.

Development of the Lithuanian Mathematics. Prof. A. Laurinčikas, Prof. E. Manstavičius. 2011–2015.

The scientific and public activity of Professor Vytautas Paulauskas was researched.
The electronic list thesis of Lithuanian mathematicians and computer sciences was extended.
Supplementary electronic collection of graduates of the Faculty of Mathematics and Informatics was prepared.

MAIN PUBLICATIONS

Textbooks, Manuals

K. Maknys, G. Misevičius, V. Palenskis, S. Pralgauskaitė. Tikimybių teorijos ir atsitiktinių vyksmų uždaviniai : mokymo priemonė fizinių ir inžinerijos mokslų aukštųjų mokyklų studentams. Vilnius : Vilniaus universiteto leidykla, 2012. 100 p.

A. Dubickas. 2011 metų Lietuvos mokinių matematikos olimpiados uždavinių sąlygos ir sprendimai : 60-oji Lietuvos mokinių matematikos olimpiada, Šiauliai, 2011 04 19. Vilnius : Vilniaus universitetas, 2011. 8 p.

A. Dubickas. 2012 metų Lietuvos mokinių matematikos olimpiados uždavinių sąlygos ir sprendimai : 61-oji Lietuvos mokinių matematikos olimpiada, Utena, 2012 04 02. Vilnius : Vilniaus universitetas, 2011. 8 p.

Articles

A. Laurinčikas, J. Rašytė. Generalizations of a discrete universality theorem for Hurwitz zeta-functions // Lithuanian mathematical journal. New York : Springer. 2012, vol. 52, no. 2, p. 172-180.

K. Janulis, A. Laurinčikas, R. Macaitienė, D. Šiaučiūnas. Joint universality of Dirichlet L-functions and periodic Hurwitz zeta-functions // Mathematical modelling and analysis = Matematinis modeliavimas ir analizė / Vilnius Gediminas Technical University, Institute of Mathematics and Informatics. Vilnius : Technika. 2012, vol. 17, no. 5, p. 673-685.

V. Garbaliauskienė, A. Laurinčikas. Limit Theorems for Twists of LFunctions of Elliptic Curves. II // Mathematical modelling and analysis = Matematinis modeliavimas ir analizė / Vilnius Gediminas Technical University, Institute of Mathematics and Informatics. Vilnius : Technika. 2012, vol. 17, no. 1, p. 90-99.

J. Rašytė. On Discrete Universality of Composite Functions // Mathematical modelling and analysis = Matematinis modeliavimas ir analizė / Vilnius Gediminas Technical University, Institute of Mathematics and Informatics. Vilnius : Technika. 2012, vol. 17, no. 2, p. 271-280.

A. Balčiūnas, A. Laurinčikas. The laplace transform of Dirichlet L-functions // Nonlinear analysis : modelling and control. Vilnius : Institute of Mathematics and Informatics. 2012, vol. 17, no. 2, p. 127-138.

R. Garunkštis, R. Šimėnas. The Ī±-values of the Selberg zeta-function // Lithuanian mathematical journal. New York : Springer. 2012, vol. 52, no. 2, p. 145-154.

R. Garunkštis, A. Grigutis. Zeros of the Lerch Transcendent Function // Mathematical modelling and analysis = Matematinis modeliavimas ir analizė / Vilnius Gediminas Technical University, Institute of Mathematics and Informatics. Vilnius : Technika. 2012, vol. 17, no. 2, p. 245-250.

G. Misevičius, S. Vakrinienė. Linear and non-linear optimization models for the selection of investment portfolio // Šiauliai mathematical seminar / Šiauliai University. Šiauliai : Šiaulių universiteto leidykla. 2012, Vol. 7, p. 79-88.

P. Drungilas. On a problem related to number systems // Šiauliai mathematical seminar / Šiauliai University. Šiauliai : Šiaulių universiteto leidykla. 2012, Vol. 7, p. 13-18.

A. Zinevičius. x5 - y2 = 4 and Gaussian integers // Šiauliai mathematical seminar / Šiauliai University. Šiauliai : Šiaulių universiteto leidykla. 2012, vol. 7, p. 157-161.

G. Misevičius. A joint limit theorem for zeta-functions of newforms // Lietuvos matematikos rinkinys. LMD darbai. Vilnius : Matematikos ir informatikos institutas. 2012, t. 53, ser. A, p. 84-89.

A. Laurinčikas, D. Šiaučiūnas. A mixed joint universality theorem for zeta-functions. III // Analytic and probabilistic methods in number theory : proceedings of the 5th international conference in honour of J. Kubilius, Palanga, 4-10 September, 2011 / editors: A. Laurinčikas, E. Manstavičius, G. Stepanauskas. Vilnius : TEV, 2012, p. 185-195.

E. Manstavičius, R. Petuchovas. Distribution of the combinatorial multisets component vectors // Lietuvos matematikos rinkinys. LMD darbai. Vilnius : Matematikos ir informatikos institutas. 2012, t. 53, ser. A, p. 66-71.

S. Černigova, A. Laurinčikas. On the mean square of the periodic zeta-function // Analytic and probabilistic methods in number theory : proceedings of the 5th international conference in honour of J. Kubilius, Palanga, 4-10 September, 2011 / editors: A. Laurinčikas, E. Manstavičius, G. Stepanauskas. Vilnius : TEV, 2012, p. 91-99.

A. Laurinčikas, R. Macaitienė. On the universality of zeta-functions of certain cusp forms // Analytic and probabilistic methods in number theory : proceedings of the 5th international conference in honour of J. Kubilius, Palanga, 4-10 September, 2011 / editors: A. Laurinčikas, E. Manstavičius, G. Stepanauskas. Vilnius : TEV, 2012, p. 173-183.

K. Bogdanas, E. Manstavičius. Stochastic processes on weakly logarithmic assemblies // Analytic and probabilistic methods in number theory : proceedings of the 5th international conference in honour of J. Kubilius, Palanga, 4-10 September, 2011 / editors: A. Laurinčikas, E. Manstavičius, G. Stepanauskas. Vilnius : TEV, 2012, p. 69-80.

A. Dubickas. A Basis of Finite and Infinite Sets with Small Representation Function // Electronic journal of combinatorics. Newark : Electronic Journal Of Combinatorics. 2012, vol. 19, no. 1, Art. no. P6 (16 p.).

P. Drungilas, A. Dubickas, C. Smyth. A degree problem for two algebraic numbers and their sum // Publicacions Matematiques. Barcelona : Universitat Autonoma de Barcelona * Servei de Publicacions. 2012, Vol. 56, iss. 2, p. 413-448.

J. Šiurys. A linear recurrence sequence of composite numbers // London Mathematical Society : journal of computation and mathematics. Cambridge : Cambridge University Press. 2012, vol. 15, p. 360-373.

A. Dubickas. Density of some sequences modulo 1 // Colloquium Mathematicum. Warsaw : Polska Akademia Nauk. 2012, Vol. 128, no. 2, p. 237-244.

G. Alkauskas. Friendly paths // American mathematical monthly. Washington : Mathematical Assoc Amer. 2012, vol. 119, no. 2, p. 167-168.

A. Dubickas. Heights of squares of Littlewood polynomials and infinite series // Annales Polonici Mathematici. Warsaw : Polska Akademia Nauk * Instytut Matematyczny. 2012, Vol. 105, no. 2, p. 145-153.

A. Laurinčikas. Joint universality of Hurwitz zeta-functions // Bulletin of the Australian Mathematical Society. Cambridge : Cambridge University Press. 2012, Vol. 86, iss. 2, p. 232-243.

P. Borwein, S. Choi, J. Jankauskas. On a class of polynomials related to Barker sequences // Proceedings of the American Mathematical Society. Providence : American Mathematical Society. 2012, Vol. 140, no. 8, p. 2613-2625.

A. Laurinčikas. On joint distribution of the Riemann zeta-function // Integral transforms and special functions. Abingdon : Taylor & Francis Ltd. 2012 vol. 23, no. 11, p. 853-862.

A. Laurinčikas. On joint universality of the Riemann zeta-function and Hurwitz zeta-functions // Journal of number theory. San Diego : Elsevier Inc. 2012, vol. 132, no. 12, p. 2842-2853.

A. Dubickas. On Some Rational Triangles // Mediterranean Journal of Mathematics. Basel : Birkhaeuser Verlag AG. 2012, Vol. 9, iss. 1, p. 95-103.

A. Dubickas. On the linear independence of the set of Dirichlet exponents // Kodai mathematical journal. Tokyo : Tokyo Kogyo Daigaku. 2012, vol. 35, no 3, p. 642-651.

A. Laurinčikas. On universality of the Lerch zeta-function // Proceedings of the Steklov Institute of Mathematics. Moscow : M A I K Nauka - Interperiodica. 2012, vol. 276, p. 167-175.

A. Dubickas. Roots of unity as quotients of two roots of a polynomial // Journal of the Australian mathematical society. Cambridge : Cambridge University Press. 2012, vol. 92, no 2, p. 137-144.

A. Dubickas, P. Šarka. Sumsets of sparse sets // Periodica Mathematica Hungarica. Budapest : Akademiai Kiado Rt. co-published with Springer Science+Business Media B.V. 2012, Vol. 64, no. 2, p. 169-179.

G. Alkauskas. The Minkowski ?(x) function and Salem's problem // Comptes Rendus Mathematique. Paris : Elsevier Masson. 2012, vol. 350, no. 3-4, p. 137-140.

J. Jankauskas, C. Samuels. The t-metric Mahler measures of surds and rational numbers // Acta mathematica Hungarica. Budapest : Akademiai Kiado Rt. 2012, vol. 134, iss. 4, p. 481-498.

A. Laurinčikas. Universality of composite functions of periodic zeta functions // Matematičeskij sbornik. = Sbornik mathematics. 2012, t. 203, no. 11, p. 1631-1646.

J. Šiurys. A Tribonacci-Like Sequence of Composite Numbers // The Fibonacci Quarterly. Rochester : Fibonacci Association. 2011, Vol. 49, no. 4, p. 298-302.

S. Akiyama, P. Drungilas, J. Jankauskas. Height reducing problem on algebraic integers // Functiones et Approximatio Commentarii Mathematici. Poznan : Wydawnictwo Naukowe Uniwersytetu im. Adama Mickiewicza. 2012, Vol. 47, no. 1, p. 105-119.

A. Laurinčikas, D. Šiaučiūnas. Limit theorems for the Estermann zeta-function. III // Čebyševskij sbornik. Tula : Tulskij gosudarstvennyj pedagogičeskij universitet im. L.N. Tolstogo. 2011, T. 12, vyp. 4, p. 97-108.

A. Dubickas, A. Novikas. On integers expressible by some special linear form // Acta Mathematica Universitatis Comenianae. Mlynska Dolina : Univerzita Komenskeho. 2012, vol. 81, no 2, p. 203-209.

A. Zinevičius. On the average number of rational points of bounded height on hyperelliptic curves // Beitrage zur Algebra und Geometrie / Contributions to Algebra and Geometry. Heidelberg : Springer. 2012, Vol. 53, no. 1, p. 225-233.

A. Laurinčikas, D. Šiaučiūnas. On zeros of some analytic functions related to the Hurwitz zeta-function // Čebyševskij sbornik. Tula : Tulskij gosudarstvennyj pedagogičeskij universitet im. L.N. Tolstogo. 2012, T. 13, vyp. 2.

A. Laurinčikas. Some value-distribution theorems for periodic hurwitz zeta-functions // Journal of mathematical sciences. New York : Springer. 2012, vol. 180, no. 5, p. 581-591.

R. Garunkštis, J. Grahl, J. Steuding. Uniqueness Theorems for L-Functions // Commentarii Mathematici Universitatis Sancti Pauli. Tokyo : Kinokuniya Shoten. 2011, Vol. 60, no. 1-2, p. 15-35.

T. Kargina, E. Manstavičius. Multiplicative functions on Zn+ and the Ewens Sampling Formula // RIMS kokyuroku Bessatsu. Kyoto : Kyoto University. 2012, Vol. B34: Functions in Number Theory and Their Probabilistic Aspects eds. K. Matsumoto, S. Akiyama, K. Fukuyama, H. Nakada, H. Sugita, A. Tamagawa. p. 137-151.

A. Laurinčikas. The Riemann zeta-function: approximation of analytic functions // Advances in applied analysis / Editors : Sergei V. Rogosin, Anna A. Koroleva . - Series : Trends in Mathematics. Basel : Birkhauser, 2012, p. 95-114.

A. Laurinčikas. Universality of composite functions // RIMS kokyuroku Bessatsu. Kyoto : Kyoto University. 2012, Vol. B34: Functions in Number Theory and Their Probabilistic Aspects eds. K. Matsumoto, S. Akiyama, K. Fukuyama, H. Nakada, H. Sugita, A. Tamagawa. p. 191-204.

V. Garbaliauskienė, A. Laurinčikas, R. Macaitienė, D. Šiaučiūnas. Universality of Some Zeta-Functions // Učenye zapiski Orlovskogo gosudarstvennogo universiteta. Serija: Estestvennye, techničeskije i medicinskije nauki. Orel : Gosudarstvennoje obrazovatelnoje učreždenije vysšego professionalnogo obrazovanija "Orlovskij gosudarstvennyj universitet". 2012, no. 6(2), s. 260-265.

Materials of conferences

E. Manstavičius. On total variation approximations for random assemblies // Discrete Mathematics and Theoretical Computer Science. Nancy : DMTCS. 2012, p. 97-108.

COOPERATION

Eőtvős Lorand University, Budapest (Hungary)
University of Edinburg (UK)
Nagoya University (Japan)
Würzburg University (Germany)
Kyoto University (Japan)
Niigata University (Japan)

OTHER SCIENTIFIC ACTIVITIES

Prof. A. Dubickas –

editor of the Central European Journal of Mathematics, http://www.cesj.com/mathematics/editors/html;
editorial board member of the Šiauliai Mathematical Seminar;
editorial board member of the Uniform Distribution Theory, http://udt.mat.savba.sk;
editorial board member of the Lithuanian Mathematical Journal, http://www.mii.lt/lmj;
Lithuanian team leader at International Mathematical Olympiad;
editorial board member of the Conference Papers in Mathematics, http://www.cpis.com/journals/mathematics.

Prof. A. Laurinčikas –

editor-in-chief of the Šiauliai Mathematical Seminar;
editorial board member of the Lithuanian Mathematical Journal, http://www.mii.lt/lmj;
editorial board member of the Moscow Journal of Combinatorics and Number Theory, http://mjcnt.phystech.edu/;
member of the Organizing Committee of the XLXII Conference of Lithuanian Mathematical Society;
member of the Program Committee of the X Intern. Conf. Algebra and Number Theory: Modern Problems and Applications (Volgograd);
member of the Program Committee of the Intern. Conf. Computer Algebra and Information Technologies (Odesa);
member the Program Committee of the Inter. Math. Conf. on occasion of the 70th year anniversary of Professor Vladimir Kirichenko (Nikolaev).

Prof. E. Manstavičius –

member of the Lithuanian Academy of Sciences, http://www.ktl.mii.lt/LMA/;
expert of the mathematics/engineering panel of the M. Curie program of EC;
section editor of the Lithuanian Mathematical Journal, http://www.mii.lt/lmj;
chairman of the editorial board of the Lietuvos matematikos rinkinys (Transactions of the Lithuanian Mathematical Society);
editorial board member of the International Journal of Number Theory;
editorial board member of ISRN Combinatorics;
chairman of the Organizing Committee of the XLXII Conference of Lithuanian Mathematical Society.

DEPARTMENT OF SOFTWARE ENGINEERING

47 Didlaukio, LT-08303 Vilnius
Tel. 219 5040, fax 215 1585
E-mail:

Head – Prof. Dr. Romas Baronas

STAFF

Professors: Dr. R. Baronas, http://www.mif.vu.lt/~baronas/, Dr. A. Čaplinskas (part-time), Dr. S. Minkevičius (part-time).
Docents: Dr. V. Čyras, http://www.mif.vu.lt/~cyras/, Dr. S. Dapkūnas, http://www.mif.vu.lt/katedros/se/Staff/Dapkunas.htm, Dr. K. Lapin, http://www.mif.vu.lt/~moroz/, Dr. A. Lupeikienė (part-time), Dr. S. Ragaišis, http://www.mif.vu.lt/~ragaisis/, Dr. V. Undzėnas, http://www.mif.vu.lt/~valund/.
Lecturers: D. Čiukšys, http://www.mif.vu.lt/katedros/se/CV/CvE_Ciuk.htm, Dr. E. Drąsutis (part-time), Dr. A. Glemža (part-time), V. Golubevas (part-time), Dr. A. Kurtinaitis, http://www.mif.vu.lt/~andrius/, Dr. A. Krupavičiūtė (part-time), Dr. K. Petrauskas (part-time), Dr. T. Plankis, Dr. L. Riauba (part-time), L. Savičienė, Dr. A. Šermokas (part-time).
Senior assistants: V. Ašeris (part-time), V. Čiumanovas (part-time), V. Jusevičius (part-time), Š. Ledas (part-time), Ž. Ledas (part-time), S. Peldžius, P. Petkus (part-time), O. Petrova (part-time), V. Pozdniakov (part-time), J. Pragarauskaitė (part-time), D. Skiriūtė (part-time), A. Stikliūtė (part-time), A. Trečiokas (part-time), K. Uosis (part-time), V. Valaitis (part-time).
Doctoral students: V. Ašeris, Ž. Ledas, S. Peldžius, L. Savičienė, D. Šimelevičius.

RESEARCH INTERESTS

Software process modelling, assessment and improvement
Decision support systems in air traffic management
Electronic signature
Designing user experiences in 3D virtual worlds
Computer calculations in mathematics
Modern software development technologies
Teaching software engineering
Software quality assessment
Queuing theory and applications
Open queuing networks
Multiphase queuing systems
Reliability of computer networks
Computational modelling of chemical and biological processes
Business process modelling

RESEARCH PROJECTS CARRIED OUT IN 2012

Projects Supported by University Budget

Modelling of Computerized Systems and their Development Process. Prof. R. Baronas. 2012–2016

Framework for usage of multiple software process models.
Electronic documents interoperability solutions.
Computational algorithms for simulating biosensors action.
Computational model of analytical systems utilizing complex enzymatic reactions.
Computational model of bacterial self-organization in a liquid medium.
A mathematical model of the message switching system.
Operationalization of regulations for aircraft approach and departure.
Inequalities for queue length of jobs and virtual waiting time of job in open multiserver queuing network in heavy traffic were proved. Using these inequalities probability limit theorems, laws of iterated logarithm and fluid limits were proved.
A theorem on reliability of computer networks was proved.

EC Structural Funds

Developing computational techniques, algorithms and tools for efficient simulation and optimization of biosensors of complex geometry, European Social Fund under Measure VP1-3.1-SMM-07-K Support to Research of Scientists and Other Researchers (GlobalGrant), http://www.biomoda.mif.vu.lt/.

EU FP7 ICT: Secure, Trusted and Legally Ruled Collaboration Environment in Virtual Life (VirtualLife). http://www.ict-virtuallife.eu. Doc. V. Čyras, Doc. K. Lapin.

PERSEUS: Plan to Establish Research Science Enterprise Oriented Universities for the Benefit of Society. Project No 145171-2008-ES-SMHES. Doc. S. Dapkūnas.

MAIN PUBLICATIONS

Monographs, Studies

R. Baronas, F. Ivanauskas, J. Kulys. Mathematical modeling of biosensors : an introduction for chemists and mathematicians. Riyadh : King Saud University Translation center, 2012. 544p.

Articles

J. Pragarauskaitė, G. Dzemyda. Visual decisions in the analysis of customers online shopping behavior // Nonlinear analysis : modelling and control. Vilnius : Institute of Mathematics and Informatics. 2012, vol. 17, no. 3, p. 355-368.

V. Ašeris. Biojutiklio su lygiagrečiu substratų virsmu ir dializės membrana kompiuterinis modeliavimas // Lietuvos matematikos rinkinys. LMD darbai. Vilnius : Matematikos ir informatikos institutas. 2012, t. 53, ser. B, p. 1-6.

R. Baronas, J. Kulys, K. Petrauskas, J. Razumienė. Modelling Carbon Nanotubes-Based Mediatorless Biosensor // Sensors. Basel : MDPI AG. 2012, Vol. 12, iss. 7, p. 9146-9160.

D. Šimelevičius, R. Baronas, J. Kulys. Modelling of Amperometric Biosensor Used for Synergistic Substrates Determination // Sensors. Basel : MDPI AG. 2012, Vol. 12, iss. 4, p. 4897-4917.

V. Ašeris, R. Baronas, J. Kulys. Modelling the biosensor utilising parallel substrates conversion // Journal of Electroanalytical Chemistry. Lausanne : Elsevier S.A. 2012, Vol. 685, p. 63-71.

K. Lapin, V. Čyras, L. Savičienė. The SKY-Scanner time-critical decision support system for surveillance and risk evaluation during landing and take-off // Journal of aerospace operations. Amsterdam : IOS Press. 2012, vol. 1, no 3, p. 301-314.

R. Baronas, Ž. Ledas, R. Šimkus. Modeling and Simulation of Bacterial Self-Organization in Circular Container Along Contact Line as Detected by Bioluminescence Imaging // International Journal On Advances in Systems and Measurements. Ithaca : IARIA. 2012, Vol. 5, nr. 3-4, p. 154-163.

Materials of conferences

V. Čyras, R. Riedl. Formulating the enterprise architecture compliance problem // Databases and information systems : 10th international Baltic conference; local proceedings, July 8-11, 2012, Lithuania / edited by Albertas Čaplinskas, Gintautas Dzemyda, Audronė Lupeikienė, Olegas Vasilecas. Vilnius : Žara, 2012, p. 142-153.

V. Jančauskas, G. Kaukas, A. Žilinskas, J. Žilinskas. On multi-objective optimization aided visualization of graphs related to business process diagrams/ // Databases and information systems : 10th international Baltic conference; local proceedings, July 8-11, 2012, Lithuania / edited by Albertas Čaplinskas, Gintautas Dzemyda, Audronė Lupeikienė, Olegas Vasilecas. Vilnius : Žara, 2012, p. 71-80.

L. Savičienė. Operationalization of norms in aircraft approach/departure decision support // Databases and information systems : 10th international Baltic conference; local proceedings, July 8-11, 2012, Lithuania / edited by Albertas Čaplinskas, Gintautas Dzemyda, Audronė Lupeikienė, Olegas Vasilecas. Vilnius : Žara, 2012, p. 208-214.

A. Čepaitis, V. Ašeris. Efektyvi virtualizacija skaičiavimams debesyse // Informacinės technologijos 2012 : 17-osios tarpuniversitetinės magistrantų ir doktorantų konferencijos pranešimų medžiaga. Vilnius, 2012, p. 161-164.

I. Paužaitė, V. Ašeris. Kompiuterinis biojutiklių modeliavimas taikant kintamą diskrečiosios gardelės erdvės žingsnį // Informacinės technologijos 2012 : 17-osios tarpuniversitetinės magistrantų ir doktorantų konferencijos pranešimų medžiaga. Vilnius, 2012, p. [1-4].

S. Peldžius. Tarpinio programų kūrimo proceso modelio formalizuotas aprašymas // Informacinės technologijos 2012 : 17-osios tarpuniversitetinės magistrantų ir doktorantų konferencijos pranešimų medžiaga. Vilnius, 2011, p. 89-92.

A. Lančinskas, J. Žilinskas. Approaches to parallelize Pareto ranking in NSGA-II algorithm // Parallel Processing and Applied Mathematics. P. 2. - Book series: Lecture Notes in Computer Science, Vol. 7204. Berlin : Springer-Verlag Berlin. 2012, Vol. 7204, p. 371-380.

S. Peldžius, S. Ragaišis. Framework for Usage of Multiple Software Process Models // Software process improvement and capability determination : 12th International Conference, SPICE 2012, Palma, Spain, May 29-31, 2012 : proceedings. Series : Communications in Computer and Information Science. Vol. 290, part. 7. Berlin : Springer, 2012, p. 210-221.

K. Petrauskas, R. Baronas. One-dimensional modelling of a carbon nanotube-based biosensor // ECMS 2012 : 26th European Conference on Modelling and Simulation, May 29 - June 1, 2012, Koblenz, Germany : proceedings / edited by: Klaus G. Troitzsch, Michael Mohring, Ulf Lotzmann. Koblenz : Universitat Koblenz, 2012, p. 121-127.

V. Jančauskas, A. Žilinskas. A multi-objective optimization aided algorithm for search of aesthetically looking paths in grids // ICNNAI 2012: Neural networks and artificial intelligence : proceedings of the 7th international conference, October 10-12 Minsk. Minsk : BSUIR, 2012, p. 209-214.

R. Baronas, Ž. Ledas, R. Šimkus. Computational modeling of self-organization in a liquid phase bacterial bioluminescent biosensor // ECCOMAS 2012 : 6th European congress on computational methods in applied sciences and engineering : CD-ROM proceedings, Vienna, September 10-14, 2012. Vienna, 2012, p. [1-8].

V. Ašeris, R. Baronas, J. Kulys. Effects of diffusion limitations on the response of biosensors utilizing parallel substrates conversion // ECCOMAS 2012 : 6th European congress on computational methods in applied sciences and engineering : CD-ROM proceedings, Vienna, September 10-14, 2012. Vienna, 2012, p. [1-10].

V. Čyras, F. Lachmayer. Multisensory legal machines and legal act production // Law, science, technology : 25th IVR World congress : paper series no 026, 2012, Series A, 15-20 August, 2011, Germany [Elektroninis išteklius]. Frankfurt am Main : Goethe university, 2012, p. [1-18].

F. Lachmayer, H. Hoffman, V. Čyras. Multisensorische Modelle des Rechts : zur syntaktischen Entfaltung von Rechtstheorie und Rechtsinformatik // Jusletter IT [Elekroninis išteklius]. Bern : Weblaw. 2012, 6 June, p. [1-7].

COOPERATION

Aarhus University (Denmark)
ETH Zurich (Switzerland)
The Vienna University of Technology (Austria)
Chalmers University of Technology (Sweden)
Crimean Humanitarian University, Yalta (Ukraine)
Kaunas Technological University (Lithuania)
CC Asseco Lietuva (Lithuania)
CC Baltic Amadeus (Lithuania)
Barclays Technology Centre, Vilnius (Lithuania)
Vilnius Gediminas Technical University (Lithuania)
University of Innsbruck (Austria)

OTHER SCIENTIFIC ACTIVITIES

Prof. R. Baronas –

deputy editor-in-chief of the journal Nonlinear Analysis: Modelling and Control, http://www.mii.lt/NA/;
editorial board member of the International Journal of Artificial Intelligence, http://www.ceserp.com/cp-jour/index.php?journal=ijai;
editorial board member of the International Journal of Applied Mathematics and Physics, http://www.serialspublications.com/journals1.asp?jid=491;
expert of the Research Council of Lithuania;
expert of the Agency for Science, Innovation and Technology;
member of the program committee of the Tenth International Baltic Conference on Databases and Information Systems, July 8–11, 2012, Vilnius, Lithuania, http://www.mii.vu.lt/BalticDBIS2012.

Dr. V. Čyras –

editorial board member of the journal Information Technology and Control, http://itc.ktu.lt/;
scientific committee member of the annual International Legal Informatics Symposium (IRIS), University of Salzburg, http://www.univie.ac.at/RI/IRIS2012/;
scientific committee member of Baltic DB & IS 2012, Tenth International Baltic Conference on Databases and Information Systems, July 8–11, 2012, Vilnius, Lithuania, http://www.mii.vu.lt/BalticDBIS2012/.