Ñïèñúê íà ïóáëèêàöèèòå ñ ðåçþìåòà
íà ä-ð Ãàëèíà Á. Ïåëîâà
1. Ã. Á. Ïåëîâà. Íÿêîè îáîáùåíèÿ íà òåíçîðè âúðõó ìíîãîîáðàçèÿ,
π ñòðóêòóðà. Ìàòåìàòèêà è ìàò. îáðàçîâàíèå, 1987,
16 Ïðîëåòíà Êîíô.ÑÌÁ, ñòð. 255 - 259, Ñë. áðÿã, 1987.
ñíàáäåíè ñ
Ðåçþìå: Äåôèíèðàíè ñà îáîáùåí òåíçîð íà êðèâèíàòà è îáîáùåí
òåíçîð íà Áîõíåð çà ìíîãîîáðàçèÿ, ñíàáäåíè ñ
π
- ñòðóêòóðà. Äîêà-
çàíè ñà íÿêîè òåõíè ñâîéñòâà. Íàïðàâåíà å êëàñèôèêàöèÿ íà ìíîãîîáðàçèÿòà, ñíàáäåíè ñ
π
ñòðóêòóðà è èìàùè ëèíåéíà âðúçêà îò
îïðåäåëåí òèï ìåæäó ñåêöèîííàòà êðèâèíà, îáîáùåíèÿ òåíçîð íà
Ðè÷è è ìåòðè÷íèÿ òåíçîð.
Abstract: A generalized curvature tensor and generalized Bochner
curvature tensor for manifolds equipped with
π - structure are considered.
Some properties for these tensors are proved. The manifolds equipped
with
π
structure with a certain linear relations between the sectional
curvature, generalized Ricci tensor and metric tensor are classied.
2. G. B. Pelova. Perturbation analysis of coupled matrix quadratic dierential
equations.
Proc. of the 32nd Int. Conf. AMEE - 2006,
pp. 114 - 124,
Sozopol, 2006.
Ðåçþìå: Ïðåäñòàâåí å íåëîêàëåí ïåðòóðáàöèîíåí àíàëèç íà äâîéêà ìàòðè÷íè êâàäðàòè÷íè äèôåðåíöèàëíè óðàâíåíèÿ. Ïåðòóðáàöèîííèòå ãðàíèöè ñà ïîëó÷åíè, êàòî ñà èçïîëçâàíè ìàæîðàíòè íà
Ëÿïóíîâ è ïðèíöèïèòå çà íåïîäâèæíàòà òî÷êà. Óðàâíåíèÿ îò òîçè
òèï âúçíèêâàò â òåîðèÿ íà èãðèòå, íàïðèìåð ïðè íàìèðàíå íà ðàâíîâåñíî ðåøåíèå íà Íåø çà ëèíåéíà äèôåðåíöèàëíà èãðà çà äâàìà
èãðà÷è ñ êâàäðàòè÷åí êðèòåðèé.
Abstract: A nonlocal perturbation analysis of coupled matrix quadratic
dierential equations is presented. The perturbation bounds are derived
using the technique of Lyapunov majorants and xed point principles.
Equations of this type appear when a Nash equilibrium solution is
sought for a two-player linear dierential game with quadratic cost.
3. G. B. Pelova. Perturbation analysis for a dierence matrix Riccati
equation.
UBM,
Mathematics and Education in Math., 2008, 37th Spring Conf.
pp. 154 - 158, Borovets, 2008.
Ðåçþìå: Ïîëó÷åíè ñà íåëîêàëíè ïåðòóðáàöèîííè ãðàíèöè çà ñèìåòðè÷íîòî äèôåðåí÷íî ìàòðè÷íî Ðèêàòèåâî óðàâíåíèå â îáðàòíî äèñêðåòíî âðåìå, ñ èçïîëçâàíå íà òåõíèêàòà íà ìàæîðàíòèòå
íà Ëÿïóíîâ. Óðàâíåíèÿ îò òîçè òèï âúçíèêâàò ïðè îïòèìàëíîòî
óïðàâëåíèå íà ëèíåéíè äèñêðåòíè äèíàìè÷íè ñèñòåìè âúðõó êðàåí
âðåìåâè èíòåðâàë.
Abstract: Nonlocal perturbation bounds are obtained for a symmetric
dierence matrix Riccati equation using the technique of Lyapunov
majorants. Equations of this type arise in the optimal control of linear
discretetime dynamic systems.
4. M. M. Konstantinov, G. B. Pelova and J. K. Boneva. Mathematics
of the Bulgarian Electoral System.
AMEE - 2009,
AIP Conf. Proc., 35th Int. Conf.
CP1184, pp. 235-246, Sozopol, 2009.
Ðåçþìå:  òàçè ðàáîòà ñà ðàçãëåäàíè ìàòåìàòè÷åñêèòå àñïåêòè íà
áúëãàðñêèòå èçáèðàòåëíè ñèñòåìè, èçïîëçâàíè ñëåä 1990 ã. Òå ñà
âàðèàíòè íà ïðîïîðöèîíàëíà ñèñòåìà ñ 4-ïðîöåíòíà áàðèåðà íà íàöèîíàëíî íèâî, êàòî ïàðòèéíèòå ìàíäàòè ñå ïåðñîíèôèöèðàò ÷ðåç
ïàðòèéíè ðåãèîíàëíè ëèñòè. Òàçè èçáîðíà ñèñòåìà ìîæå äà äîâåäå
äî òåæêè ìåæäóïàðòèéíè èçêðèâÿâàíèÿ. Òåçè èçêðèâÿâàíèÿ, ìàêàð ÷å ñà ôîðìàëíî êîðåêòíè, íå ñå ïðèåìàò îò îáùåñòâåíîñòòà è
ïî-ñïåöèàëíî îò ìåñòíèòå ïàðòèéíè àêòèâèñòè. Ðàçãëåäàíè ñà ìåòîäè çà èçáÿãâàíå íà òàêèâà èçêðèâÿâàíèÿ. Èçó÷åíè ñà íîâè ïàðàäîêñè, êîèòî ñà îáîáùåíèÿ íà äîáðå ïîçíàòèòå ïàðàäîêñè íà èçâåñòíèòå
ïðîïîðöèîíàëíè èçáîðíè ñèñòåìè.
Abstract: In this paper we consider the mathematical aspects of the
Bulgarian proportional electoral systems used since 1990. They are
variants of a proportional system at a nation wide level with 4-percent
barrier such that the party seats are personied from a number of
regional party list. This system lead to severe inter-party distortions.
These distortions although formally correct are hardly accepted by the
public and by local party activists in particular. Methods to overcome
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these diculties as well as the status -quo of the problem are cosidered.
Finally new paradoxes, are studied which are generalizations of the well
known paradoxes for the plain proportional systems.
5. M. M. Konstantinov, G. B. Pelova and J. K. Boneva. Mathematical
Annual of
the University of Architecture, Civil Engineering and Geodesy , vol. 43
characteristics of the Bulgarian voting system since 1990.
44, fasc. II, pp. 21 - 32, Soa, 2004 - 2009.
Ðåçþìå: Ðàçãëåäàíè ñà ìàòåìàòè÷åñêèòå õàðàêòåðèñòèêè íà áúëãàðñêàòà èçáîðíà ñèñòåìà, èçïîëçâàíà â Áúëãàðèÿ ñëåä 1990 ã.
Ïðåäñòàâåíè ñà îïòèìèçàöèîííè çàäà÷è, âúçìîæíè èçáîðíè ïàðàäîêñè è íîâè àëãîðèòìè çà ðàçïðåäåëÿíå íà ìàíäàòèòå.
Abstract: The mathematical characteristics of the Bulgarian system
for parliamentary elections since 1990 is discussed. Optimization problems,
possible paradoxes and new algorithms for proportional seat distribution
are considered.
6. M. Konstantinov, K. Yanev, G. Pelova and J. Boneva. 2D apportionment
methods.
UBM,
Mathematics and Education in Math., 2010, 39th Spring Conf.
pp. 190 - 197, Albena, 2010
Ðåçþìå: Â ðàáîòàòà ñå ðàçãëåæäàò äâóìåðíè ïðîïîðöèîíàëíè èçáîðíè ñèñòåìè, ïðè êîèòî áðîÿò íà ïàðòèéíèòå ìàíäàòè ñå îïðåäåëÿ íà íàöèîíàëíî íèâî, à ïåðñîíèôèêàöèÿòà íà ìàíäàòèòå ñòàâà
÷ðåç ðåãèîíàëíè ïàðòèéíè ëèñòè. Ïðè òîâà áðîÿò íà ìàíäàòèòå âúâ
âñåêè ðàéîí ñå îïðåäåëÿ ïðîïîðöèîíàëíî íà íàñåëåíèåòî. Ïðåäëîæåíè ñà íîâè ïîäîáðåíè ìåòîäè çà äâóìåðíî ðàçïðåäåëåíèå è ñà
ïðåäñòàâåíè ðåçóëòàòè îò ÷èñëåíè ïðåñìÿòàíèÿ ñ äàííèòå îò ïàðëàìåíòàðíèòå èçáîðè ïðåç 2009 ã.
Abstract: The paper deals with 2D proportional electoral systems in
which the number of party mandates is determined at a nation wide
level while the personication of mandates is done through regional
party lists. In addition, the number of mandates in each region is
preliminary determined proportionally to the population. Variants of
such systems have been used in seven parliamentary elections in Bulgaria
during the period 1990 - 2009. These systems as well as new improved
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2D apportionment methods are considered. Results from numerical
simulations with data from the 2009 Bulgarian parliamentary elections
are given.
7. Ì. Êîíñòàíòèíîâ, Â. Òîäîðîâ, Ã. Ïåëîâà, Þ. Áîíåâà. Èçïîëçóâàíå
íà ñèñòåìàòà MATLAB â òåõíè÷åñêèòå óíèâåðñèòåòè.
Ìàòåìàòèêà
è ìàò. îáðàçîâàíèå., 2010, 39 Ïðîëåòíà Êîíô.ÑÌÁ,
ñòð. 347-353,
Àëáåíà, 2010
Ðåçþìå: Ðàçãëåäàíè ñà íÿêîè àñïåêòè íà îáó÷åíèåòî ïî ìàòåìàòèêà ñ ïîìîùòà íà ïðîãðàìíàòà ñèñòåìà MATLAB â òåõíè÷åñêèòå
óíèâåðñèòåòè. Ñïåöèàëíî âíèìàíèå å îòäåëåíî íà ðàçäåëèòå àíàëèòè÷íà ãåîìåòðèÿ è äèôåðåíöèàëíè óðàâíåíèÿ.
Abstract: Some aspects of the mathematical education in technical
universities using MATLAB are considered. Special attention is paid
to the subjects Analytical Geometry and Dierential Equations.
8. M. Konstantinov, P. Petkov, G. Pelova, V. Angelova. Perturbation
analysis of dierential and dierence matrix quadratic equations: A
Bulgarian-Turkish-Ukrainian Sc.Conf. Math. Analysis, Di.
Eq. and their Appl. Sept. 2010, pp. 101-110, Sunny Beach, 2010.
SURVEY.
Ðåçþìå: Òàçè ðàáîòà å èçñëåäâàíå, ïîñâåòåíî íà ìåòîäèòå è ðåçóëòàòèòå â îáëàñòòà íà ïåðòóðáàöèîííèÿ àíàëèç íà äèôåðåíöèàëíè è
äèôåðåí÷íè ìàòðè÷íè êâàäðàòè÷íè óðàâíåíèÿ. Òàêèâà óðàâíåíèÿ
âúçíèêâàò â ìàòåìàòè÷åñêîòî ìîäåëèðàíå, óïðàâëåíèå è ôèëòðèðàíå íà ñèñòåìè â íàóêàòà è èíæåíåðñòâîòî.
Abstract: This paper is a survey on methods and results in the area
of perturbation analysis of dierential and dierence matrix quadratic
equations. These equations arise in the mathematical modelling, control
and ltering of systems in science ànd engineering.
9. M. Konstantinov, K. Yanev and G. Pelova. New bi-proportional methods
for the Bulgarian parliamentary elections.
Conf. AMEE - 2010,
AIP Conf. Proc., 36th Int.
CP1293, pp. 243-252, Sozopol, 2010.
Ðåçþìå: Åäèí íåäîñòàòúê íà ñúùåñòâóâàùèòå áè-ïðîïîðöèîíàëíè
ñèñòåìè íà áúëãàðñêàòà èçáèðàòåëíà ñèñòåìà å ãîëåìèÿò áðîé íåìî-
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íîòîííîñòè (ïàðòèéíè ëèñòè ñ ïî-ìàëúê áðîé ãëàñîâå ïðîèçâåæäàò
ïî-ãîëÿì áðîé ìàíäàòè, îòêîëêîòî ïàðòèéíè ëèñòè ñ ïî-ãîëÿì áðîé
ãëàñîâå) ïðè ðàçïðåäåëÿíåòî íà ìàíäàòè. Ïðåäëàãàíè ñà ðàçëè÷íè
ñõåìè çà îòñòðàíÿâàíå íà òîçè ôåíîìåí. Â òàçè ðàáîòà ïðåäëàãàìå
äâà íîâè ìåòîäà: 1) óãîëåìÿâàíå íà èçáèðàòåëíèòå ðàéîíè è 2) âúâåæäàíå íà íîâ èçáèðàòåëåí ðàéîí çà áðîåíå íà ãëàñîâåòå, ïîäàäåíè
â ÷óæáèíà. Ïî òîçè íà÷èí áðîÿò íà íåñúîòâåòñòâèÿòÿ ÷óâñòâèòåëíî
ñå ðåäóöèðà.
Abstract: A disadvantage of the existing bi-proportional system for
the Bulgarian parliamentary elections is the large number of discordances
(a party list with less votes gets more seats than a party list with more
votes) in the seat distributions. Dierent schemes has been proposed to
deal with this phenomenon. In this paper we propose two new methods:
1) augmentation of the electoral regions and 2) introduction of a new
electoral region for accounting the votes cast abroad. In this way the
number of discordances may be vastly reduced.
10. M. M. Konstantinov and G. B. Pelova. Autonomous generalized SturmLiouville problems: Numerical Solution by MATLAB. First International
Conf. EPU: Education, Science, Innovations - 2011, pp. 201 - 205,
Pernik, 2011.
Ðåçþìå: Ðàçãëåäàíî å ÷èñëåíîòî ðåøàâàíå íà îáîáùåíàòà çàäà÷à
íà Ùóðì-Ëþâèë çà ñîáñòâåíèòå ñòîéíîñòè íà ñèñòåìè åä îò àâòîíîìíè îáèêíîâåíè äèôåðåíöèàëíè óðàâíåíèÿ. Ðåøåíèåòî å ïîëó÷åíî â ñðåäàòà íà ñèñòåìàòà ÌÀÒËÀÁ, êàòî å èçïîëçâàíà ôóíêöèÿòà
ìàòðè÷íà åêñïîíåíòà.
Abstract: The numerical solution of a generalized Sturm-Liouville
eigenvalue problem for high order systems of autonomous ordinary
dierential equations is considered. The solution is obtained in MATLAB
environment using the matrix exponential function associated to the
given system.
11. Ã. Á. Ïåëîâà. Ðåøàâàíå íà ãåîìåòðè÷íè çàäà÷è ñ MATLAB.Ïúðâà
ìåæäóíàðîäíà êîíôåðåíöèÿ íà ÅÏÓ: Îáðàçîâàíèå, íàóêà, èíîâàöèè - 2011, ñòð. 190 - 193, Ïåðíèê, 2011.
Ðåçþìå: Ðàçãëåäàíè ñà íÿêîè àñïåêòè íà îáó÷åíèåòî ïî àíàëèòè÷íà è äèôåðåíöèàëíà ãåîìåòðèÿ ñ ïîìîùòà íà ïðîãðàìíàòà ñèñòåìà MATLAB. Ñïåöèàëíî âíèìàíèå å îòäåëåíî íà ãðàôè÷íîòî
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ïðåäñòàâÿíå íà èíôîðìàöèÿòà ãðàôèêè íà êðèâè è ïîâúðõíèíè.
Ðàçðàáîòåíè ñà ïðîãðàìè çà ïðåñìÿòàíå íà êîíêðåòíè çàäà÷è, êàòî
ñà èçïîëçóâàíè âúçìîæíîñòèòå íà ñèñòåìà MATLAB çà äèàëîãîâ
ðåæèì ïðè îáìåíà íà äàííè.
Abstract: Some aspects of solving problems connected to the education
of the subjects Analytical and Dierential Geometry are considered.
Special attention is paid to the graphics of curves and surfaces. Programs
for calculating concrete problems are developed by using the opportunities
given by MATLAB for digital regime of data exchange.
12. Ì. Êîíñòàíòèíîâ, Ï. Ïåòêîâ, Â. Òîäîðîâ, Â. Ïàøåâà, Ì. Òîäîðîâ,
Ã. Ïåëîâà, Þ. Áîíåâà. Äèñêóñèÿ Íîâ êóðñ ïî ìàòåìàòèêà çà òåõíè÷åñêèòå óíèâåðñèòåòè.
Ìàòåìàòèêà è ìàò. îáðàçîâàíèå, 2011,
40 Ïðîëåòíà Êîíô. ÑÌÁ,
ñòð. 147 - 150, Áîðîâåö, 2011.
Ðåçþìå: Â òàçè äèñêóñèÿ ñå ðàçãëåæäàò îñíîâíèòå ïðîáëåìè íà
ïðåïîäàâàíåòî íà ìàòåìàòèêà â òåõíè÷åñêèòå óíèâåðñèòåòè.
Abstract: This discussion covers the basic problems of teaching mathematics
at the technical universities.
13. G. Pelova and J. Boneva. The Theory of Probability with MATLAB.
Second International Conf. EPU: Education, Science, Innovations 2012, Pernik, 2012, to appear.
Ðåçþìå: Ðàçãëåäàíè ñà íÿêîè àñïåêòè ïðè ðåøàâàíåòî íà çàäà÷è
îò òåîðèÿ íà âåðîÿòíîñòèòå. Ðàçðàáîòåíè ñà ïðîãðàìè çà ïðåñìÿòàíå íà êîíêðåòíè çàäà÷è êàòî ñà èçïîëçâàíè âúçìîæíîñòèòå íà
ñèñòåìàòà MATLAB çà îáìåí íà äàííè.
Abstract: Some aspects of solving problems connected to the theory of
probability are considered. Programs for calculating concrete problems
are developed by using the opportunities given by MATLAB for digital
regime of data exchange.
14. M. Konstantinov, K. Yanev, G. Pelova and J. Boneva. Optimization
Problems in the Bulgarian Electoral System.
Int. Conf. AMEE - 2013,
AIP Conf. Proc., 39th
Sozopol, 2013, to appear.
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Ðåçþìå: Â òàçè ðàáîòà ñà ðàçãëåäàíè íÿêîëêî îïòèìèçàöèîííè
çàäà÷è, ñâúðçàíè ñ áè-ïðîïîðöèîíàëíè ñèñòåìè íà áúëãàðñêàòà èçáèðàòåëíà ñèñòåìà. Ïðåäñòàâåíè ñà ÷èñëåíè åêñïåðèìåíòè ñ äàííè
îò ðåàëíè èçáîðè. Ïî òîçè íà÷èí ïîðåäèöà îò ïðåäèøíè èçñëåäâàíèÿ íà àâòîðèòå å äîðàçâèòà.
Abstract: In this paper we consider several optimization problems
for the Bulgarian bi-proportional electoral systems. Experiments with
data from real elections are presented. In this way a series of previous
investigations of the authors is further developed.
15. Ã. Á. Ïåëîâà.ÀÍÀËÈÒÈ×ÍÀ
Ñ MATLAB.
È ÄÈÔÅÐÅÍÖÈÀËÍÀ ÃÅÎÌÅÒÐÈß
Åëåêòðîííî ó÷åáíî ïîñîáèå, ïóáëèêóâàíî íà àäðåñ:
http://www.uacg.bg/lebank/att_4042.pdf
Àíîòàöèÿ: Ó÷åáíîòî ïîñîáèå å ïðåäíàçíà÷åíî äà çàïîçíàå ñòóäåíòèòå ñ îñíîâíèòå âúçìîæíîñòè íà ñèñòåìàòà MATLAB çà íÿêîè ñïåöèôè÷íè ïðèëîæåíèÿ ïðè ðåøàâàíå íà çàäà÷è ïî àíàëèòè÷íà è äèôåðåíöèàëíà ãåîìåòðèÿ. Òî ïðåäîñòàâÿ íà ÷èòàòåëÿ ãëåäíà òî÷êà,
ñúîáðàçåíà ñ âúçìîæíîñòèòå íà ñúâðåìåííèòå êîìïþòúðíè òåõíîëîãèè, âêëþ÷èòåëíî çà èçïúëíåíèå íà ðåäèöà òåõíè÷åñêè îïåðàöèè
ïðè ðåøàâàíåòî íà ïðèëîæíè çàäà÷è.
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