# «Matematike i informacione tehnologije Математические и информационные технологии Mathematical and Informational Technologies MIT 2009 August, 27 - ...»

Belov Yu.Ya., Siberian Federal University, Krasnoyarsk Frolenkov I.V., Siberian Federal University, Krasnoyarsk An iden ca on problems of the coecients of the parabolic equa ons In the report iden ca on problems of unknown coecients for the two dimensional and mul dimensional parabolic equa ons in case of given Cau chy data are considered. The local existence theorem and the theorem of uniqueness of the solu on for a iden ca on problem of two coecients in classes of the smooth limited func ons for the mul dimensional semilinear parabolic equa on with non-linearity of enough general view are proved. The case of the unknown factors standing at a nonlinear member and func on of a source, and a two-dimensional case of the unknown factors standing at a deriva ve on me and a nonlinear member is considered. The existence and uniqueness of the solu on are proved and es ma ons of stability by the ini al data for solu on of iden ca on problems of coecients at lower terms in the parabolic equa on are obtained. The mul dimensional inverse problems for the parabolic equa on with the ellip c operator in the right part which coecients depend on all spa al variables and have a special ap pearance in the case of enough smooth ini al data are considered. For the proof of existence of the solu on the weak approxima on method is used.

This method is a spli ng method of the equa on at the dieren al level, and was named so by N.N. Yanenko.

Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 Blaunstein N., Ben-Gurion University of the Negev, Beer-Sheva Modeling of Radio Propaga on in the Land-Satellite Link through the Stor m me Ionosphere This paper presents the intensity and phase uctua ons dependence on the degree of ionospheric plasma perturba ons occur during magne c storm based on experiments by GPS monitoring of the ionosphere. During this nat ural phenomenon, anomalous absorp on caused by decrease of the total electronic content, and fast fading of GPS radio signals caused by genera on of plasma small-scale irregulari es are observed experimentally. In order to present the eect of sca ering caused by plasma irregulari es generated during magne c storm, 2-D phase-screen model is introduced. A sa sfacto ry explana on of fading phenomena observed experimentally is presented based on the corresponding theore cal framework. It was found that during magne c storm, when experimentally observed devia ons of plasma density in the perturbed ionosphere can be changed at 10%-20%, the corresponding small-scale and moderate-scale plasma density irregulari es in the storm me F region yield strong fast fading of VHF/UHF radio signals with sucient signal intensity uctua ons (up to 10%) and phase uctua ons (up to hun dreds radians), which nally can signicantly decrease the spectral eciency, capacity and signal data rate in mul path land-satellite communica on link with fading passing through the perturbed ionosphere.

Bogdanovic Z., Faculty of organiza onal sciences, Belgrade Radenkovic B., Faculty of organiza onal sciences, Belgrade Barac D., Faculty of organiza onal sciences, Belgrade Despotovic M., Faculty of organiza onal sciences, Belgrade Crea ng adap ve moodle-centric courses using business intelligence This paper describes a method for crea ng adap ve Moodle courses based on learning styles using business intelligence techniques and tools. Building an eec ve e-learning framework depends on nding adequate means for discovering users’ interests, preferences, mo va on and needs. Data mining and its techniques are discussed as the most appropriate and sophis cated tools for swi ly determining students’ learning styles and classica on into groups. Each group a ended an adapted Moodle course. The evalua on of the system showed that students achieved be er results with higher level of sa sfac on when a ending courses adapted to learning styles. An experi ment was conducted within the distance educa on system of Laboratory for E-Business, Faculty of Organiza onal Sciences in Belgrade.

Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 Bozinovic M., Faculty of Economics, Kosovska Mitrovica Mathema cal model of monopoly compe on Essence of monopoly compe on consists in the way that, oer and demand are being specied by only one compe tor on the market. In this case, there is no chance of increasing numbers of bidders and goods which is oered on the market, could’t have an own replacement. Considering this new condi ons, market price is result of oer and demand opera ng law. Therefore, if consumers want to pay an actual price, shopping power will be shown up as limited factor for price increasing.

Bychkov I.V., IDSTU SB RAS, Irkutsk Gachenko A.S., IDSTU SB RAS, Irkutsk Ruzhnikov G.M., IDSTU SB RAS, Irkutsk Fereferov E.S., IDSTU SB RAS, Irkutsk Khmelnov A.E., IDSTU SB RAS, Irkutsk Contemporary informa on technologies: applica on in regional and municipal projects Solving priority problems of regional socio-economic development and eleva on of eciency of ac vity of the regional and municipal authori es (RMAs) necessitates development of a exible system of informa on-analy cal sup port, which is grounded on a set of problem-oriented databases character ized by diverse formats [1]. Such an objec ve shall employ all the known contemporary informa on technologies.

The systems to be developed shall allow the user to conduct modeling socio economic processes, execute mul variant simula on and goal-oriented com puta ons intended for es ma ng the development of the territory, analyze the inuence of macroeconomic indicators on the situa on in the region.

In this connec on, the technologies allowing one to automate the process of elabora on of complex informa on-analy cal systems, which would aid to increase the level of substan a on and validity of decisions made by RMAs, are of denite interest.

Within the frames of the priority direc on of fundamental research conduct ed by Siberian Branch of RAS “Basic and Technological Problems of Informa on, Telecommunica on and Computa onal Systems”, ISDCT has developed (i) methods for development of corpora ve systems intended to provide support of making management decisions, (ii) contemporary informa on technologies intended for intelligent forma on and selec on of decisions, processing spa ally distributed data and mul dimensional analysis of the data (OLAP), (iii) geoinforma on technologies, what has allowed to conduct development of research and applied projects at a qualita vely higher level.

Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 Cvejic S., Faculty of science and mathema cs, Kosovska MItrovica Lekic M., Faculty of science and mathema cs, Kosovska MItrovica Dimitrovski D., Faculty of science and mathema cs, Skopje Proper es of coecients of analy cal periodic func ons If func on f (x) is analy cal, then it can be presented by convergent ex ponen al sequence which, due to its convergence (d’Alember’s crite rium), can be dieren ated and integrated, member by member and as a rule it has Taylor’s coecients. However, in this work we have de termined the proper es of coecient sequence when func on is ana ly cal, but also periodic with period. We have also shown that for the periodic func on the coecient sequence has the following form ( k ) ( ) ( k ) (2 ) ( k ) (n ) ak k! k! k!

In this way we have obtained innite number of Taylor’s formulae which are valid near the points 0, 2,…,n.

Dairbayeva G., Al-Farabi Kazakh Na onal University, Almaty Gradient methods of solving Ill-Posed Cauchy problem Let be a bounded simply connected domain in R = {(x,y)} with a con nu ous piece-smooth boundary =. Let be divided into two connected parts 1 2, 1 2.

Consider the following problem u 0, (x,y), (1) u f ( x, y ), ( x, y ) 1, (2) u 0. (3) n The problem (1)-(3) is ill-posed according to Hadamard. The solu on is unique, but it is not stable with respect to a small perturba ons of the func on f. In this connec on we use the solu ons of the stable boundary prob lems for the same dieren al equa on (1) instead of solving the ill-posed problem (1)-(3). Such idea was proposed by Kabanikhin S.I. and Karchevskiy A. L. [1], and developed in [2].

Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 As a well-posed problem for (1)-(3), for instance, the Neumann problem for the ini al Laplace equa on in the domain may be used, which requires knowledge of boundary values of a normal deriva ve of the solu on on the whole boundary. Though according to the condi on (3), we are only given boundary condi ons on a part of the boundary. That is why it is necessary to associate boundary values of the ini al func on f with the boundary values of the normal deriva ve of the solu on on the addi onal part of the bound ary that is quite a dis nct problem.

Researching proper es of the operator connec ng f with the above men oned boundary values of the normal deriva ve of the solu on and its con jugate operator, allows to use varia onal method to look for an approximate solu on of the ini al problem (1)-(3}.

Analogous approach for other problems may be found in [2].

In this paper jus ca on of the use of the conjugate gradient method is given for solving the problem (1)-(.3) and its convergence.

References:

1. Kabanikhin S.I., Karchevskiy A.L. Op miza onal method for solving the Cauchy problem for an ellip c equa on// J. Inv. III - Posed Problems. 1995. Vol. 3, N 1.

P. 21-46.

2. Kabanikhin S.I. Inverse and ill-Posed Problems. Novosibirsk: The Siberian scien c publishing house, 2008.

Dimitrovski D., Faculty of Science and Mathema cs, Skopje Vujakovic J., Faculty of Science and Mathema cs, Kosovska Mitrovica Rajovic M.., Faculty of Science and Mathema cs, Kosovska Mitrovica ON LOCATION OF ZEROS OF SECOND ORDER COMPLEX DIFFERENTIAL EQUATIONS (Comparison of R. Nevanlinna’s method of assessment of solu ons number with classical theorem on loca on of Sturm’s zeros of real dieren al equa ons) For second order real dieren al equa on y Ax y 0 in, so called, period of Sturm, form 1806 to 1826, the rst qualita ve theorems on numbers of zero solu ons y x in dependence of A x and a, b posi ve interval where Ax 0, have been established. At that me the concept of itera on were not known enough (it has been strictly introduced in 1860.), so at that me the loca on of zeros could not be precisely determined, Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 according to Sturm.

Later, the appearance of group theory on dieren al equa on enabled an exact approach to loca on of zero oscilla on. However, this has not been the best solu on since the oscilla ons are the fundamental natural phenomena related to the Newton’s law, while the method based on group theory was too dicult for such an elementary issue. So, the problem of loca on of zeros, and of courses the number of zeros, remain unsolved un l the me and forthcoming wave of new mathema cs did not push this issue at the corner of mathema cal science.

Recently, we are going back to the problem of zeros of Sturm’s equa on (1), and naturally we are looking for analogy to Sturm’s zeros of real dieren al equa on (1), if we are observing the complex dieren al equa on of oscilla on d 2w A z w d z which is corresponding to 1 only for z x i y x, y 0. Of course that does not have to be an equa on of some oscilla on (that is certain only for z x i y, y 0 and Ax 0 ), and (2) is also called complex dieren al equa on of oscilla ons. Due to historical con nuity the equa on (2) can have several possibili es of solu on varie es.

This paper will show various ways of bringing down the equa on (2) to the system of second order par al equa ons, and than to one simple dieren al equa on of order IV that further could be brought down to the two simple second order equa on of Sturm, given by (1).

Therefore, the ques on is rela on between two milestones in the qualita ve theory of dieren al equa ons:

Sturm’s theorem on the number of zeros Nevanlinna’s theorem on assessment of growth and rang.

Dolicanin C., State University of Novi Pazar, Novi Pazar Nikolic V., State University of Novi Pazar, Novi Pazar Radojkovic M., State University of Novi Pazar, Novi Pazar Mathema cal models and applica on of numerical methods in solving a phenomenon of the theory of thin plates The term thin plate implied a elas c body with cylindrical or prisma c shape of small thicknes in rela on to other two dimensions. The basic dependences between geometrical and physical proper es come to mostly to se ng up Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 of rela ons between stress and strain condi ons, which has been described by dieren al equa ons, simple and par al. Methods used for solving of es tablished equa ons, with respect of outline and ini al condi ons, may be classied in analy cal and numerical. In case of complex and big construc on systems subjected to the arbitrary loads, including a complex boundary condi on s, solving of dieren al equa ons by analy cal methods is almost impossible. Then the solu on is applica on of numerical methods. One of the basic numerical methods is Finite Dierence Method (FDM) based on replacing of dieren al equa ons with corresponding dierence equa ons.

Using of this method, the problem come to solving of system of paired alge braic equa ons, making the problem more easier for solving. In this paper, besides FDM, is also used Finite Element Method (FEM) for considera on of this phenomenon in at isotropic eld, respec vely at thin plates with dif ferent boundary condi ons and loadings. In the end, more comments and farther direc ons of inves ga ons are given.

Fedotov A.M., NSU, Novosibirsk Informa on resource interga on problems The given report to development of the technology buildings of the distrib uted integrable systems of the processing, keeping and issues informa on resource on base opened specica on of the models data.

The model of “virtual environment for interchange of the results of scien c researches” would be discussed – the enterprise or regional informa on system, which integrates the systems for scien c research and organiz ing ac vity. Its dis nc ve feature are: complex support of scien c ac vity, orienta on at various categories of users such as graduates, researchers, managers, secretaries, etc.

The researches that generalize applying of introduced technology for us ing at regional-scaled applica ons was done. Func oning to intellectual informa onal systems in terms of informa cs was described, the needs for informa on of scien c society explored.

Technological approach for exchanging catalogized data and integra ng informa onal systems was tested while crea ng new and modifying exist ing systems for storing and exchanging bibliographical records. Another important result is crea ng of unied informa onal space for researching in environmental science.

Models, procedures and interfaces of registra on the poli cian of the con trol of access in a control system of access to the distributed informa on Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 resources (CSADIR) are developed. Comple on created before prototype CSADIR for research of model of the distributed management by access is in addi on spent. Thus, condi ons for transi on to performance of a follow ing stage of works under the project pre-produc on opera on of the test monitoring system of access to resources and the analysis of this opera on will be which primary goal are created.

Fedotova Z.I., ICT SB RAS, Novosibirsk Khakimzyanov G.S., ICT SB RAS, Novosibirsk The nonlinear dispersive equa ons of shallow water on a rota ng sphere In the paper the nonlinear dispersive equa ons of a shallow water on a rotat ing sphere are derived. The received equa ons are completely nonlinear. The opportunity of a moveable bo om surface is taken into account. The new model will be useful to the descrip on of long waves (tsunami) over vast la tudinal and longitudinal direc ons of water areas during long me.

Fionov A., Siberian State University of Telecommunica ons and Informa cs, Novosibirsk Ryabko B., Siberian State University of Telecommunica ons and Informa cs, Novosibirsk Informa on-Theore c Methods for Solving Steganography Problem Сегодня в сфере защиты информации велик интерес к проблемам сте ганографии, т.е. (говоря упрощённо) методам внедрения скрытой ин формации в файлы, и стегоанализу, т.е. методам выявления скрытой информации. Оба эти направления развиваются параллельно и взаим но обогащают друг друга. Несмотря на достигнутый прогресс, всё еще остаётся большое поле для исследований как путей повышения стойко сти стегосистем, так и увеличения разрешающей способности методов стегоанализа. В настоящем докладе представлены результаты, получен ные авторами в течение нескольких последних лет совместно с их аспи рантами и магистрантами на основе применения идей и методов теории информации, прежде всего, универсального кодирования источников.

Ранее эти идеи с успехом были применены для построения просто реа лизуемых идеальных шифров, а также для криптоанализа генераторов псевдослучайных последовательностей и блоковых шифров, см. [1].

Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 Рассмотрим вначале суть теоретико-информационного подхода к зада чам стеганографии. В одной из первых работ в этой области [2] было вве дено понятие совершенной стегосистемы, т.е. такой системы внедрения данных, для которой в принципе не возможно создать алгоритм выявле ния факта наличия скрытой информации. При построении совершенной стегосистемы контейнер рассматривается как сообщение, порождён ное вероятностным источником, а (зашифрованные) данные, которые необходимо внедрить – как последовательность равновероятных и не зависимых нулей и единиц. Необходимо так внедрить данные, чтобы вероятностная структура контейнера осталась той же самой. Тогда за полненный контейнер становится сообщением того же источника, что и пустой, поэтому невозможно сказать, присутствует скрытая информация или нет. Впервые конструкция совершенной стегосистемы для источни ков конечной памяти с неизвестной статистикой была предложена в [3].

Эта конструкция основывается на идеях нумерационного кодирования и в простейшем случае может быть пояснена следующим примером. Рас смотрим источник без памяти над алфавитом {a,b}. Допустим, источник породил сообщение aaba. Мы не знаем вероятности появления этого сообщения, однако с уверенностью можем сказать, что она та же самая, что и для сообщений baaa, abaa и aaab, т.к. они содержат одинаковое число букв a и b. Все эти четыре сообщения принадлежат одному клас су эквивалентности – классу равновероятных сообщений для данного источника. Теперь мы можем скрыть два бита информации, используя отображение 00 aaab, 01 aaba, 10 abaa, 11 baaa. Как видим, скрываемая информация – это просто номер в лексикографически упо рядоченном множестве равновероятных сообщений. Таким образом, чтобы скрыть информацию, нужно решить задачу денумерации для за данного сообщения и типа источника. Извлечение скрытой информации выполняется путём определения номера сообщения, т.е. решения зада чи нумерации. Авторами построены эффективные методы нумерации и денумерации для широкого класса источников, включая марковские источники произвольного порядка.

Не все контейнеры, используемые в практической стеганографии, на пример, цифровые фотографии, можно точно описать некоторым слу чайным процессом. Однако построение приближённой вероятностной модели этих контейнеров часто оказывается полезным. Такая вероят ностная модель (явная или неявная) строится, например, при сжатии графических файлов. Мы предлагаем использовать вероятностные мо дели для решения задач стеганографии. В этом случае внедряемое со общение перекодируется таким образом, чтобы кодовые символы под чинялись тем же распределениям вероятностей, что и заменяемые ими символы в контейнере. Быстрые методы кодирования, обеспечивающие в точности заданные вероятности появления кодовых символов, пред Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 ложены в [4]. Иногда целесообразно использовать методы, приближён но решающие эту задачу, например, арифметическое декодирование.

Нами построен алгоритм внедрения информации в растровые изобра жения, учитывающий статистику младших бит цветовых составляющих в некотором окружающем контексте. Экспериментальные исследова ния алгоритма показали его заметное преимущество в стойкости по от ношению к известным аналогам: увеличение стойкости на 15–40 % на случайной выборке файлов и на 95 % на «удобных» файлах (с плавными переходами цветов) по отношению к известным программам HIDE4PGP и STEGOTOOLS.

Применение идей теории информации для решения задач стегоанали за основывается на теоретическом фундаменте, построенном в [5, 6]. В этих работах было показано, как можно использовать методы универ сального кодирования для эффективного решения многих задач мате матической статистики. Для стегоанализа графических файлов, в част ности, важно уметь решать задачу выявления степени статистической зависимости младших бит цветовых составляющих или частотных коэф фициентов от остальной информации в файле. Дело в том, что при вне дрении информации эта статистическая связь искажается или теряется вовсе. Наиболее успешная практическая реализация этих идей была выполнена при построении системы стегоанализа BMP-файлов [7], а за тем и JPEG-файлов. Основная идея состоит в сравнении степеней сжатия полученного файла и этого же файла с различным уровнем внедрения в него случайных данных. Если разность степеней сжатия превышает некоторый порог, делается вывод о наличии в полученном файле скры той информации. В результате экспериментальных исследований на выборке из 1000 файлов было установлено, что ошибка первого рода (пустой контейнер принимается как заполненный) не превосходит 1 %.

При уровне внедрения информации 40 % и выше ошибка второго рода (заполненный контейнер признаётся пустым) не превосходит 2 %. Со вокупность этих показателей лучше, чем у известных методов, таких как STEGDETECT.

Литература 1. Рябко Б. Я., Фионов А. Н. Криптографические методы защиты информации. М.: Горячая линия-Телеком, 2005. 229 с.

2. Cachin С. An informa on-theore c model of steganography // Lecture Notes in Computer Science (Proc. 2nd Informa on Hiding Workshop). Springer Verlag, 1998.

V. 1525. P. 306–318.

3. Ryabko B., Ryabko D. Informa on-theore c approach to steganographic systems // IEEE Inter-na onal Symposium on Informa on Theory. Nice, France, 2007. P.

2461–2464.

4. Fionov A., Ryabko B. Simple ideal steganographic systems for containers with known sta s cs // XI Interna onal Symposium on Problems of Redundancy. St. Petersburg, July 2–6, 2007. P. 184–188.

5. Ryabko B., Astola J. Universal codes as a basis for me series tes ng // Sta s cal Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 Methodology. 2006. V. 3. P. 375–397.

6. Ryabko B, Astola J. Universal codes as a basis for nonparametric tes ng of serial independence for me series // Journal of Sta s cal Planning and Inference. 2006.

V. 136, N. 12. P. 4119–4128.

7. Zhilkin M., Melentsova N., Ryabko B. Data compression based method of reveal ing hidden in-forma on in steganographic systems // XI Interna onal Symposium on Problems of Redun-dancy. St.-Petersburg, July 2–6, 2007. P. 42–44.

Gajic Lj., University of Novi Sad, Novi Sad A xed point theorem for mappings with a concrac ve iterate at a point on D*-metric spaces The concept of D* -metric space introduced by S. Sedghi et al. seems to be more appropriate in xed point theory then S. Gahler and B. C. Dhage deni ons of distance for three (or more) points. In this paper I am going to prove a xed point theorem for self-mappings with contrac ve iterate at a point on closed subset of D*-metric space. At the end a common xed point theorem for sequence of self-mappings on D*-metric space will be proved. Let us re call that func on T X: X with property: for any x in X there exists n=n(x) in N such that any y,z in X D*(Tnx,Tny,Tnz) qD*(x,y,z), q in [0,1), we say that T has a contrac ve iterate at a point.

Gavrilov A., Ins tute of Thermophysics of SB RAS, Krasnoyarsk Dekterev A., Ins tute of Thermophysics of SB RAS, Krasnoyarsk Numerical simula on of unsteady cavita ng ow over hydrofoil Modeling of the cavita ng turbulent ow over hydrofoil NACA6602-12% in 2D statement at various angles of a ack and cavita ng numbers has been carried out. Modeling of cavita ng turbulent ow is carried out within the framework of homogeneous approxima on for the two-phase medium. For the purpose of vapor phase transfer descrip on a number of models ap proved for the problems of cavita ng ow around streamline bodies (blades, hydrofoils) is chosen. Two-phase turbulent ow modeling is based on the non-sta onary formula on of the RANS approach. For the closure of Reyn olds averaged equa ons dissipa ve models of turbulence are used: modied high-Reynolds k-epsilon model and two-layer k-omega Menter model. Basing Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 on the operator-spli ng techniques for non-steady form of con nuity and ow equa on, there is proposed the scheme of the Douglas-Rachford type for problems with strong coupling between pressure and density elds. The numerical implementa on of this scheme is performed as a predictor-correc tor procedure similar to SIMPLEC algorithm. The simula on of ows over a number of axisymmetric cylindrical bodies and a planar hydrofoil at various cavita on numbers has been performed for the purpose of cavita on models and numerical methods verica on. The numerical modeling of the cavitat ing turbulent ow over the hydrofoil has predicted a development of the self oscilla ng mode. On the rear side of hydrofoil near to a head part the vapor cavity is formed. In the tail of cavity the re-entrant jet is observed, resul ng in the separa on of vapor cavi es and development of the bubbly ow mode.

The obtained numerical results are compared to available experimental data for the pressure eld distribu on, Strouhal number and the maximal length of the a ached vapor cavity.

Golushko S.K., ICT SB RAS, Novosibirsk Golushko K.S, ICT SB RAS, Novosibirsk On certain statements of inverse problems in mechanics of composite plates and shells and methods of a solu on thereof Тонкостенные изделия типа пластин и оболочек являются важнейши ми элементами многих современных конструкций атомной эне ргетики, авиационной, космической и машиностроительной техники, глубоководных аппаратов, строительной индустрии.

При анализе работоспособности и надежности таких конструкций, их экономической эффективности первостепенное значение имеют расчеты их прочности, жесткости, обеспечения минимального веса и стоимости.

Высокие удельные прочностные характеристики традиционных материалов (сталей, алюминиевых, магниевых и титановых сплавов) достигли своего предела и возможности их дальнейшего прогресса невелики. Значительное повышение требований к современным конструкциям, заставило использовать при их изготовлении новые композиционные материалы. Принцип армирования высокопрочными и высокомодульными волокнами открыл пути к практически нео граниченному совершенствованию современных композитных ко нструкций, сочетающих высокие показатели прочности, жесткости, на дежности с другими ценными качествами: относительно малым весом, регулируемыми свойствами электро и теплопроводности, высокой Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 стойкостью к агрессивным средам и т.п.

В работе рассматриваются некоторые новые постановки обратных задач механики тонкостенных однородных, слоистых и армированных пластин и оболочек. Обсуждаются возможные критерии рационального и оптимального проектирования однородных и гибридных конструкций.

Представлен оригинальный метод решения широкого класса за дач рационального проектирования композитных конструкций.

Исследован ряд конкретных задач рационального проектирования армированных оболочек, когда в качестве критериев рациональности выступают требования безмоментности и безызгибности напряженно деформированного состояния, равнонапряженности арматуры, посто янства удельной потенциальной энергии оболочки.

Gourary M M., IPPM RAS, Moscow Rusakov S. G., IPPM RAS, Moscow Stempkovsky A.L., IPPM RAS, Moscow Ulyanov S. L., IPPM RAS, Moscow Zharov M.M., IPPM RAS, Moscow Numerical Aspects of Adap ve Harmonic Balance Method in Circuit Simu la on The Harmonic Balance (HB) is the powerful and ecient method of steady state analysis in many prac cal simula on problems in par cular in nonlinear automa c control systems, in electrical simula on and others. HB is the fre quency-domain technique of nonlinear simula on and it has well known ad vantages in comparison with me-domain steady-state simula on. In par c ular, applying to simula on of nonlinear radio frequency (RF) circuits it nds solu ons eciently for problems with widely separated me constants and also with mul tone excita on. However, though the conven onal HB method is well suited for weakly and mildly nonlinear problems it has essen al limi ta ons for analysis of strong nonlinear circuits. Actually the each variable is presented by a truncated Fourier series, resul ng in a system of equa ons of order ORD=(2K+1)N, where K is the number of terms in the Fourier series (harmonics) and N is the number of state variables in the analyzed circuit. To obtain desired accuracy highly nonlinear problems require a large number of harmonics, which may increase the size of the system to be solved beyond prac cal limits. Therefore the problem of solving of large dimension system is the key computa onal problem of the HB technique. New techniques are required to extend the Harmonic Balance method for solving strong nonlin ear problems. New computa onal approach - Adap ve HB Analysis (AHBA Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 approach) is discussed. The approach is based on adjus ng the order of HB problems by adapta on to nonlinearity degree. The suggested adap ve har monic balance analysis is intended to reduce computa onal eorts for HB large problems during simula on process due to automa c varying number of harmonics. The main purposes of AHBA approach are the following:

- de velop computa onal schemes that support reducing HB problems by adapta on to nonlinearity degree;

- reduce computa onal eorts for solving large dimension HB problems with large number of rela vely small entries. The de veloped computa onal procedures are based on Krylov subspace techniques.

Jainakov A., Ins tute Physics, Bishkek Ashirbaev B.Y., Ins tute Physics, Bishkek Analy cal design of linear regulator on singular perturba ons In ar cle is considered sta onary singularly pertubed opera ng system. Of fered the way of designing of linear regulator based on method of mo on separa on and characteris cs of Grama operator. The results were obtained:

controlling, which provides passing the system from ini al state to the nal state, possesses the decomposi on, and it can be deter mined in dierent scales of me by vectors, which belongs to the area of values corresponding to inverse operators Grama;

matrixes-operator Grama - an symmetric and depending on me of moving the prepared subsystems, have the dierent scales of inte gra on area;

for operated sta onary system with slow and quick mo on is con structed the linear regulator, consis ng of two sub regulators, which provide the transla on of system from any point in space to the origin of coordinate system moreover under their ac on are apart adjusted (on rate of ac on depending on me) dierent phase mo on of the system Jainakov A., Ins tute Physics, Bishkek Numerical analysis of electric arc by the relaxa on method In this work a mathema cal model is proposed, in the basis of which there is a total nonsta onary system of magnetogasdynamic equa ons. Produc on of the steady-state condi on of gas ow and gas hea ng with electric arc in a channel by the relaxa on /pseudoviscosity method is inves gated. This Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 model and the developed algorithm and program of calcula on may be used for studies of nonsta onary processes related to connec on and interrup on of arcs, transient processes and use of alterna ng current sources. Besides, this computa on method allows to study stability of sta onary solu on pro duced by the relaxa on method.

Kamalova G.A., Ins tute of Mathema cs, Almaty Ramazanova G.Y., Ins tute of Mathema cs, Almaty Numerical modeling of interac on of solid par cles with a gas ow In the present work the injec on of two-phase gas-dispersed ows (air-solid par cles) are simulated. For the solu on of the problem the Euler-Lagrange approaches is used. The mechanism of an interchange of gases with par cles is studied.

Karepova E.D., Ins tute of Computa onal Modelling SB RAS, Krasnoyarsk Malyshev A.V., Ins tute of Computa onal Modelling SB RAS, Krasnoyarsk Shaidurov V.V., Ins tute of Computa onal Modelling SB RAS, Krasnoyarsk Research of eciency of parallel realiza on of FEM for boundary problem of shallow water equa ons In this work eciency of some parallel realiza ons of an algorithm for the numerical solu on of a boundary-value problem for the shallow water equa ons which were performed with the help of the MPI library for C language is compared. The rst approach is based on the decomposi on of a com puta onal domain without overlapping subdomains, the second approach is based on the decomposi on with shady sides. Theore cal es mates of accel era on for the parallel algorithm are given. Numerical results for a model grid and nonstructured grid for the Okhotsk sea are presented. Results concern ing accelera on of computa ons depending on the number of processes, the type of communica on realiza on, and the method of the decomposi on of a computa onal domain are presented.

Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 Kazakov A.L., Ins tute of System Dynamics and Contriol Theory SB RAS, Irkutsk Generalized Cauchy problem for the descrip on of complicated gas ow with shock waves A study of the ows with singulari es, including shock waves, is on the mod ern problems of gas dynamics. Mathema cal descrip on of such ows one can transform to generalized Cauchy problem (GKP) for the system of PDEs.

A dierence in the GKP from the Cauchy problem in tradi onal se ng lies in fact that ini al (boundary) condi ons are given not on one, but on two or on various surfaces. The number of surfaces does not exceed the number of independent variables. The number of condi ons coincides with the number unknown func ons. Existence and uniqueness theorems of GKP in a class of analy c func ons are proved. The proved theorems are used for mathema cal descrip on of various gas ows with shock waves.

Kevkic T.S., Faculty of Science and Mathema cs, Kosovska Mitrovica Petkovic D.M., Faculty of Science and Mathema cs, Kosovska Mitrovica Some analy cal solu on of nonlinear poisson equa on for inversion layer of mos structure In this paper, some analy cal solu ons of the nonlinear Poisson equa on for inversion layer of MOS structure are presented. These solu ons are based on smoothing func ons and parameters than on physical approximate expres sions available in the weak and strong inversion. On this way an explicit sur face poten al versus gate voltage rela ons in the case of strong inversion in semiconductor are derived. Comparison with numerical data shows that the solu on gives good approxima ons of poten al for MOS structure. These so lu ons can be applied to es mate classical and quantum mechanical density of carriers of nanoscale MOSFETs.

Khabakhpasheva T.I., Lavrentyev Ins tute of Hydrodynamic, Novosibirsk Entry and exit of an elas c shell on a thin layer of the water The paper is concerned with a problem of elas c shell fall down onto a thin layer of an ideal incompressible liquid. The shell ini ally touches the liquid free surface at a single point and then penetrates the liquid layer. The prob lem is coupled because the liquid ow, the shape of the elas c shell and the geometry of the contact region between the body and the liquid must be Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 determined simultaneously. The 2D-problem of a circular cylindrical shell impact and axisymmetrical case were considered before by the method of matched asympto c expansions for analyzes of liquid ow. This method was developed by Korobkin (1995) for the case of the at rigid body penetrate onto a the thin layer of the liquid. The structural analysis is based on the nor mal-mode method. Strain- me histories of the inner surface of the spherical shell are of par cular interest. At the present study velocity of the interac on is small and eects of gravity taken into account. It is allow us to considered not only exit, but also exit of shell from the water layer under the buoyancy forces.

Kobalinsky M.В., Siberian Federal University, Krasnoyarsk Sibgatulin V.G., Siberian Federal University, Krasnoyarsk Simonov K.V., Siberian Federal University, Krasnoyarsk Peretokin S.A., Siberian Federal University, Krasnoyarsk Hudoberdin I.R., Siberian Federal University, Krasnoyarsk Krasnoramenskaja T.G., Siberian Federal University, Krasnoyarsk Informa on technology for the geodynamic risks es ma on Research is directed on sa sfac on of increasing volumes of building in dif cult geodynamic condi ons, taking into account development of the mar ket of the real estate, for the purpose of decrease in geodynamic risks, with reference to territory of Krasnoyarsk region. As a result of researches the informa on technology which components are the analysis of the data of geomonitoring about adverse geodynamic factors, se lement modules of an es ma on сотрясаемости грунтов, and also the account of geodynamic risk at a cadastral both market es ma on of the ground areas and real estate insurance is developed. Working out of the GIS-SCHEME of division into dis tricts of Krasnoyarsk on degree of geodynamic danger, razlomno-blokovomu to a structure and neotectonic movements is carried out by carrying out of tool geophysical researches. Bases of records axelerogramms, which allows to create the rynochno-a rac ve informa on for the building companies are created. Points of supervision of geomonitoring have been placed on pro les from known pointed zones Altai Sayansk seismoac ve area in a direc on to Krasnoyarsk for recep on axelerogramms and characteris cs of a enua on of seismic uctua ons with distance. Within the limits of the specied researches it is developed informa on-methodical maintenance for the ac count of geodynamic factors at a cadastral both market es ma on of the ground areas and real estate insurance.

Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 Kosogorov O.M., St. Petersburg State University, St. Petersburg Makarov A.A., St. Petersburg State University, St. Petersburg Spline wavelet decomposi on and parallel compression Splines and wavelets are extensively applied to designing ecient algorithms for processing of digital data ows. If spline spaces on a rening sequence of grids are embedded in each other, the chain of embedded spaces decom poses into a direct sum of wavelet spaces, and basis func ons with minimum support length are given, then a wavelet decomposi on of the correspond ing data ow can be constructed, which substan ally reduces computa onal expenditures. Moreover, by using non-uniform grids, it is possible to improve approxima on without complica ng computa ons. Thus, we can split the ini al data ow so as to dis nguish main and rening data ows. This allows us to compress the input digital signal and transmit the main data ow at higher speed;

the rening ow can be transmi ed only fragmentarily, depending on needs. We regard spline wavelet decomposi on of B-spline spaces for ar bitrary rening of non-uniform grids. Thus a new algorithm for compression (decomposi on formulas) and decompression (reconstruc on formulas) of digital data ows is developed. Numerical simula on results of compression of model digital data ows are done. Mul processor systems or mul core processors give the best t to spline wavelet spli ng of digital ows: every ow processing can appoint to one of processors (cores). Even two cores ap preciably increase compressing and decompressing of digital signals. Parallel forms of decomposi on and reconstruc on formulas are done.

Lempert A. A., Ins tute of System Dynamics and Contriol Theory SB RAS, Irkutsk Gornov A.Yu., Ins tute of System Dynamics and Contriol Theory SB RAS, Irkutsk Algorithm of stochas c approxima on of set of a ainability for controlled system on plane Algorithm of the internal approxima ons construc on for the a ainability set of controlled system with parallelepiped limita ons for two-dimensional systems Is considered. Algorithm is based on the method of stochas c ap proxima on, which includes the genera on procedure of the collec on of func ons, which can cover suciently ghtly the set of admissible controls, and integra on method of system under selected control. As the class of ap proxima ng controls, the random relay func ons with random number of switching are used. To inves gate the proper es of proposed algorithm, the collec on of test problems is developed. Carried out comparisons with re Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 sults of other authors conrm the tness for work of proposed method. We give some results of computational experiments.

Ljajko E., Faculty of Science and Mathema cs, Kosovska Mitrovica Pavlicic Z., Faculty of Science and Mathema cs, Kosovska Mitrovica Geogebra and high school analy c geometry instruc on All modern versions of educa onal so ware simply a ract high school teach ers as well as their students to apply them in the process of teaching/learning mathema cs. GeoGebra oers extraordinary high possibili es to modernize the process of teaching/learning analy c geometry in high schools. Never theless, how ecient is such a process? How much eort should teachers and students invest in the process to combine GeoGebra and mathema cs in a meaningful manner? Does such an eort pay o? In this ar cle we try to an swer these and other similar ques ons. Our source of informa on was an ex perimental instruc on we held in technical school “Nikola Tesla” in Leposavi, Serbia. Results of earlier researches in this eld (dr. Dragoslav Herceg, – 2008 dr. Radivoje Stojkovi, 2003 – 2006) were used while organizing and carrying out the instruc on process. GeoGebra was embedded in the ana ly c geometry instruc on using appropriate dynamic worksheets. There are shown in the ar cle some of the worksheets used as well as possible ways to organize and perform such a process of teaching/ learning, ways to organize an appropriate classroom and advantages and disadvantages of the process.

Lyamina V.A., IGM SB RAS, Novosibirsk Zolnikov I.D., IGM SB RAS, Novosibirsk Korolyuk A.Yu., CSBG SB RAS, Novosibirsk Dobretcov N.N., IGM SB RAS, Novosibirsk Smolentcev B.A., ISA SB RAS, Novosibirsk Glushkova N.V., IGM SB RAS, Novosibirsk Mapping and monitoring of heterogeneous landscapes by methods of GIS and RS The complex technology of mapping and monitoring of heterogeneous land scapes with use of methods of remote sensing and geoinforma on modeling is presented. Development and approba on of complex technology was pro Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 vided on etalon polygone “Kasmalinsky forest”, wich represents complex of pinery and grassy landscapes of south-western part of Altay region. Strip for ests of steppe area of Ob-Irtysh interriver are unique natural phenomenon.

They form a series of north-east extended stripes, occupying troughs. Such landscapes have complex spa al structure of soil-plant cover, that makes them a rac ve for heterogeneous landscape analysis on dierent hierarchic levels.

Proposed technology is realized for images of all scales (MODIS, Landsat, QuickBird) and for all ecosystem levels in the same way. This technology al lows to analyze heterogeneous landscapes with complex spa al structure by methods of GIS and RS. It is based on using geodatabases, including geology geomorphologic, soils and botanic data normalized to the interdisciplinary standard. This technology includes image processing of the dierent spa al resolu on by methods of supervised classica ons, and also density analy sis of territorial heterogeneity with use of grid models (with applica on of so ware packages ENVI and ArcGIS). Alloca on of landscapes on the basis of image processing and geoinforma on modelling allows to map not only homogeneous, but also heterogeneous land ecosystems and also to conduct monitoring of their dynamics.

The work was made in frameworks of project “Development complex indica on system of deser ca on processes and es ma on of modern ecosys tems condi on of Siberia and Central Asia”, and supported by RFBR (##09 05-00732, 08-04-00055) Lyubashevskaya I.V., Lavrentyev Ins tute of Hydrodynamics SB RAS, Novosibirsk Banshchikova I.A., Lavrentyev Ins tute of Hydrodynamics SB RAS, Novosibirsk Deforma on of plates from alloys with dierent proper es on tension and compression at creep The results of calcula ons received by using various techniques in one- and twodimensional statements for a problem of torsion of a square plate at the high temperature with taking into account dierent resistance of a materi al to tension and compression at creep are submi ed. Kinema c and sta c statements of a problem are considered also. Calcula on for materials with dierent resistance at creep by using the standard nite-elements packages is problema c enough, but such programs can be used for an es ma on of the received decisions. Comparison of numerical results and experimental data of curvature of a plate for two aluminium alloys is executed. It is shown Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 not taking into account of real proper es of creep at the decision of applied problems of details shaping and forecas ng of their further exploita on can result in essen al mistakes which can reach one order and more.

Madzhara T., Ins tute for System Dynamics and Control Theory SB RAS, Irkutsk Adap ve technology for the numerical solu on of the op mal control problems with the computa onal peculiari es В докладе рассмотрен класс задач оптимального управления с вычис лительными особенностями, описаны подходы, позволяющие успешно находить оптимальные решения. В целях автоматизации процесса ре шения таких задач разработан интеллектуальный динамический плани ровщик - компонент программного комплекса, имитирующий действия эксперта при работе с программным комплексом в диалоговом режи ме. Представлена формальная модель эксперта, на основании которой разработан планировщик, приведена архитектура программного ком плекса, учитывающая возможность решения задач рассматриваемого класса. Работоспособность разработанного программного комплекса проверена на пакете тестовых задач и ряде модельных прикладных за дач из области биохимии и аэродинамики.

Mandak A., Teacher-training Faculty of Prizren, Leposavic On construc on weighted projec ve plane of order 4 and (2, 4 – 1)-quasig roup We introduce a no on of weighted projec ve planes which is a generaliza on of usual projec ve planes. We prove that a Frobenius group G of order operates on a projec ve plane P of order 4 as a colinea on group. Using this opera on the plane P may be constructed. A weighted projec ve plane P’ of order 4 is equivalent to a totally symmetric (2, 4 – 2)-quasigroup.

Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 Martysevich U.V., Ins tute of Geology and Mineralogy for SB RAS, Novosibirsk Boldyrev I.I., Ins tute of Geology and Mineralogy for SB RAS, Novosibirsk Dobretsov N.N., Ins tute of Geology and Mineralogy for SB RAS, Novosibirsk Mul spectral satellite data correc on and preprocessing techniques for simula ng of geological and landscape condi ons Despite great achievements in Earth remote sensing techniques so far vi sual image interpreta on based on knowledge of decoding indica ons of considering objects is applying most of me then using mul spectral data for geological purposes. Recogni on of rock types on mul spectral satellites images of cross-country areas and areas with presence of vegeta on is dif cult. A empt of integrated solu on of research of natural rock outcropping components specicity in spectral characteris c of satellite images includ ing inuence of landscape and vegeta on is undertaken in presented ar cle.

Dierent methods of satellite images topographic correc on are analyzed in the proceeding. Such as methods to minimize inuence eect of variable illu mina on of surface in visible and infrared spectral bands. And also were ana lyzed dierent techniques for suppression of vegeta ve spectral contribu on in areas with par al growth. Verica on and evalua on of satellite data spectral correc on results was done by example of test polygons with dierent typical landscapes with considera on of eld data: assessment of vegeta on ll, grain composi on, contents of forming minerals in rocks, illumina on. It was found that vegeta on type and illumina on range (for regions with compound relief) impact on reectance of rocks more than their grain and mineral composi on.

Technique of shadow suppression on satellite pictures may be used for stud ies of dierent landscape proper es: spectral and visual assessment of veg eta on proper es located on low illuminated mountainsides and modeling of landscape parts contribu ons (vegeta on, underlying surface, illumina on).

Topographic correc on is promising with respect to resolving of geological problems: satellite images classica on for geological subjects in mountain areas where iden cal rocks may have dierent reectance because of illumi na on dierences;

hidden tectonic structures recogni ons without demon stra on in relief.

Martyushov S.N., State Duma of Russian Federa on, Moscow Numerical simula on of shock wave dirac on on the body as the test for me accuracy of explisit algorithm At calcula ons of sta onary or slowly varying ow near a ying body the main a en on gives to increase the accuracy of the decision on spa al co Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 ordinates. Some mes large me step is used for achieving of sta onary de cision. The other situa on appears for numerical simula on of essen ally non-sta onary processes. So for dirac on of a shock wave on a ying body, there is the impulse of displacing forces genera ng non-sta onary forward and rotary movement of a body. Change of a trajectory, a direc on of move ment and speed in turn change value and the direc on and value of inuence to a body. There is a problem with a feedback. For such problems the error of calcula on on me coordinate is integrated at calcula on of integral charac teris cs of ow, rst of all works of displacing forces and, in consequence of it, sizes of displacement, a direc on of movement or a turn of a body. As the result absolutely dierent decisions can be received, depending on me ac curacy of algorithm. Dirac on of a shock wave on the free and xed sphere in a shock tube was numerically simulated. Two similar numerical algorithms were used: TVD schemes of Harten and Chakravarty. In the rst case the sec ond order of approxima on on me in a mul dimensional case was reached by spli ng of the operator of a step on symmetric sequence of operators of a step in coordinate direc ons. In the second case me approxima on of Run ge-Cu a of dierent orders of accuracy was used. Calcula ons were made on sequence of structured ellip c grads. Points of grid where condensed on the surface of sphere. The algorithm of grid construc on is based on the decision of system of Poisson equa ons. Results of calcula ons show essen al change of integral characteris cs of ow with increasing of decision accuracy.

Massel L.V., Energy Systems Ins tute named L.A. Melen ev SB RAS, Irkutsk Intera on of the distributed informa on resourses for the power engineer ing research Energy Systems Ins tute named Melen ev L.A. of SB RAS carry out research es of energy systems and fuel and energy complex (FEC). These researches are associated and have common informa on base. For the receiving of valid conclusions and recommenda ons prepared for the outside organiza ons was proposed virtual integra on of separate data bases and knowledge bas es. Knowledge bases are realized as ontology space joining some ontology’s of energy applied elds. Integra on is made in the bounds of informa on infrastructure included into IT-infrastructure of power engineering research.

In informa on infrastructure picked out three stratums: the rst stratum is metadata model of informa on infrastructure, the second is metadata stra Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 tum and the third is data stratum of IT-infrastructure. For the making of meta data model are used ontology’s. The objects of IT-infrastructure are described by metadata on the base of crea ng ontology. The program components of informa on infrastructure are divided on three logical levels: le system lev el, DBMS level and client level. In informa on infrastructure there are system and applied components. System components are Program core, Metadata base, File store, Administra ve program and Repository driver. Applied com ponents are Data retrieval program, File retrieval program, Web-applica on for the revision of Repository, SOAP-interface and others. The realiza on of all program components of informa on infrastructure made accordance with SOA concep on. The central component is Repository which was realized on the base of DBMS Firebird 1.5.2 and Microso SQL Server 2000/2005.

Mausumbekova S.D., Al- Farabi Kazakh Na onal University, Almaty Naimanova A. VNS Ins tute of mathema cs, Almaty Numerical modeling of a stremnilining two bodies in tandem in the air ow Численно моделируется процесс образования и взаимодействия вихрей при обтекании потоком воздуха двух тел, расположенных тандемом. Ис следовано влияния расстояний между препятствиями на вихреобразо вание. Определены расстояния между препятствиями, при которых про исходит интерференция завихренности (эффект резонанса).

Maximov V.V., St. Petersburg State University of Technology and Design, St. Petersburg Nudner I.S., Research Centre for Capital Construc on, St. Petersburg The interac on of gravity waves with the par ally permeable obstacles The interac on of surface waves with the mari me works having permeable members is considered. The waves of rela vely small height are studied. The liquid is ideal and incompressible, and its mo on has the poten al func on.

The theore cal problem is solved by the eigenfunc on expansion method.

The solu on is compared with the experimental data. The analysis shows the sa sfactory agreement.

Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 Mestrovic R., Faculty of Mari me Studies, Kotor Pavicevic Z., Faculty of Science and Mathema cs, Podgorica Topologies on the Privalov spaces with applica ons in the theory of Ban ach algebras We compare dierent topologies on the Privalov spaces of analy c func ons on the open unit disk in the complex plane. As an apllica on, we obtain the asympto c versions of some known theorems in the Theory of Banach Alge bras.

Mijajlovic Z., Faculty of Science and Mathema cs, Beograd Applica on of informa on science in digi za on of scien c and cultural heritage The aim of this paper is to present the eorts in the area of digi za on done by a group of Serbian scien sts from the Faculty of Mathema cs of the Uni versity of Belgrade, the Mathema cal ins tute and the Archeological ins tute of the Serbian Academy of Science and Art and since recently the Fac ulty of natural sciences of the University in Pris na, now situated in Kosovska Mitrovica. Goals are development of standards for digi za on, development of metadata, development of computer technologies, so ware and database specic for digi za on and scien c research of theore cal disciplines on which digi za on is founded. Our achievements include the Virtual library (h p://elib.ma.bg.ac.yu:8080/virlib) which includes several hundred old and rare books in mathema cal sciences wri en by Serbian authors and most of doctoral disserta ons in mathema cs, astronomy and mechanics wri en at the Belgrade University. There is also the e-library of Serbian math ema cal journals (h p://elib.mi.sanu.ac.rs) which contains, for example, the complete digi zed collec on (since 1932) of the leading and oldest Serbian mathema cal journal Publica ons de l’Ins tut Mathma que. These two projects are oriented towards Digital mathema cal library, a world project on which works many world ins tu ons. The nal aim of this project is the fulllment of a mathema cal dream of a digital archive containing all peer-re viewed mathema cal literature ever published, properly linked and validated (veried). Finally we men on the Electronic catalog of cultural monuments in Serbia h p://spomenicikulture.mi.sanu.ac.yu. It includes various data, in cluding GIS data, on more than 1000 most important monuments in Serbia (monasteries, archeological sites, historical sites etc).

Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 Milosavljevic S., Faculty of Economics, Kosovska Mitrovica Trajkovic S., Faculty of Science and Mathema cs, Kosovska Mitrovica M-commerce i savremene telekomunikacione tehnologije Mobile telecommunica ons is a link that connects people anywhere to be found. Voice and data over the mobile telecommunica on network enables the sending of informa on and perform transac ons on a new and unique way. They create a new business domain called mobile business or m-com merce, which is an expanded founda on of Internet e-business with many unique features built. As a basic pla orm, mobile telecommunica on net works play a crucial role in the mobile business today. Technical characteris cs of mobile telecommunica ons and their development is determined by the base for mobile business. In this paper we study and present the techni cal characteris cs of mobile telecommunica on technology of 1g network to 3G and beyond.

Milosevic H.M., Faculty of Science and Mathema cs, Kosovska Mitrovica Applica on of low-temperature plasma in steel-making converters With the use of numerical modeling an inves ga on of the process of the jet gunni ng of the walls of a steel-making converter is considered. By the jet gunni ng is meant the process of making an addi onal protec ve refractory coa ng on the basic lining of the walls of the steel-making converter with the aid of a system of two-phase jets transpor ng a so ened refractory material (magnesite) to the converter wall. The results of numerical modeling agree quite sa sfactorily with the experimental results in terms that the highest penetra on rate of par cles takes place in the region of high temperatures near the nozzle block axis into which the par cles migrate under the ac on of turbulent uctua ons of the carrying gas ow.

Milovanovic G., College of Computer Science, Beograd Numerical treatment of Fredholm integral equa ons In this lecture we introduce and discuss some numerical methods, based on new results of polynomial approxima on, for solving Fredholm integral equa ons of the second kind in the spaces of con nuous func ons equipped with Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 certain uniform weighted norms, where is the unknown func on, and are given func ons, is a weight func on, and is a nite interval or the real semi axis. Also, we men on some results for the Cauchy singular integral equa ons. The case we treat with the Jacobi weight and the case on half-line with the generalized Laguerre weight Assuming the con nuity of the kernel we use Nystrm methods and prove the stability, the convergence and the well condi oning of the corresponding matrices. Error es mates and numerical tests are also included.

Milovanovic G., Faculty of Electronic Engineering, Nis Spalevic M. M., Faculty of Science, Kragujevac Paunovic Lj., Teacher-training Faculty, Leposavic Error bounds of Gauss-Turn-Kronrod quadratures with Gori-Micchelli weight func ons for analy c func ons In this paper, Kronrod extensions of Chakalov-Popoviciu quadratures are in troduced. We study some cases of Chakalov-Popoviciu-Kronrod quadrature formula for a subclass of Gori-Micchelli weight func ons, as well as for the generalized Chebyshev weights. For the Gori-Micchelli weight func ons in the case of the Gauss-Turn-Kronrod quadratures we succeeded to nd very eec ve error bounds, for func ons analy c on confocal ellipses.

Minic G. S., Teachers faculty, Leposavic Vorkapic M., IHTM-CMTM, Belgrade Tanaskovic D., IHTM-CMTM, Belgrade ACQUISITION AND PROCESSING DATA AT THE MEASUREMENT RESISTANCE THERMOMETERS This paper will talk about the crea on of virtual instrumenta on for test, measurement and data acquisi on at the measurement resistance thermom eters with a Pt-100 sensor. In this way, engineers are given the opportunity to achieve the desired performance and accuracy in measurements. Virtu al instrument is a combina on of hardware and so ware elemenanta, and used to display the LABWindows/CVI program. This program contains all the necessary elements for the development of advanced applica ons for mea suring, tes ng and automa c control. The use of classical instruments that Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 monitor and measure the temperature bands have a need for automa on of data, which is realized in combina on with virtually instruments.

Mi c Z. D., Faculty of Technical Science, Kosovska Mitrovica Petkovic M. D., Faculty of Science and Mathema cs, Kosovska Mitrovica Characteriza on of heavy doped semiconductors using analy cal approxi ma on of Fermi integrals In heavy doped semiconductors the charge carriers have energy distribu on according Fermi-Dirac func on. Because that the carriers concentra on and electric eld and poten als in surface layers versus Fermi level rela ons are expressed as Fermi integrals. In this paper we are analyzed some analy cal approxima ons of Fermi integrals order of one half and tree half and their applicability for calcula on of carrier concentra ons and surface electric eld in heavy doped semiconductor. These results are also applicable on polycrystalline grains of polysilicon lms.

Moskvichev V.V., Presidium of Krasnoyarsk Scien c Center of SB RAS, Krasnoyarsk Applied problems in probabilis c risk-analysis of technical systems The study presents generaliza on of causes of failure and classica on of the limit states for complex technical systems (CTS). Proposed are models and algorithms for risk-analysis of CTS, and data base for applied problems solv ing. Calcula ons are based on probabilis c models of defects, crackresistance proper es, loading condi ons, and stress-strain and limit states. Assessment of structural risk is determined by the fracture probability of structure ele ments for a given type of limit state. Model calcula ons of risk-analysis are carried out for a number of CTS construc ons including components of nu clear and space engineering, pressure vessels and pipelines.

Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 Moskvicheva L.F, Ins tute of Computa onal Modeling, Krasnoyarsk Burov A.E., Ins tute of Computa onal Modeling, Krasnoyarsk Bogulskaya N.A., Ins tute of Computa onal Modeling, Krasnoyarsk Module structure of a master course “CAD and CAE systems” A teaching-methodical complex on «Computer Aided and Computer Aided Engineering Systems» has been developed as part of a master program for specialists in carrying and li ing machines, and technological complexes. The discipline is indented to provide students with fundamental knowledge on ap plica on of computer technologies in solving scien c and engineering prob lems, as well as to develop skills in modeling, design and analysis of technical objects, developing engineering documenta on. The course consists of three modules. The module “Computer technologies in solving research problems” deals with methods used for solving engineering tasks and elabora ng ex perimental data with means of MatLAB and MathCAD so ware. The module “Design and engineering in graphical CAD” teaches students how to use CAD technologies in design and analysis of li ing machines. Digital prototyping of items and engineering documenta on are developed using Autodesk Inven tor so ware. The module “Computer aided engineering analysis” provides in-depth understanding and prac cal skills required in design and analysis of technical objects. The training is based on applica on of ANSYS so ware. The main objec ves of the module are:

- fundamentals of mathema cal model ing, numerical methods used to iden fy and analyze engineering problems;

- nite elements methods in solid mechanics;

- analysis of stress and limits states of structural components.

Odalovic M.T., Faculty of Science and Mathema cs, Kosovska Mitrovica Petkovic D.M., Faculty of Science and Mathema cs, Kosovska Mitrovica A stochas c model of gamma-ray induced charge in silicon dioxide lms of mos transistors In this paper a stochas c model of gamma-ray irradia on eects on density of induced charge in silicon dioxide lms of MOS transistors is explained. In this model the we are assumed that both of irradia on traps crea on and charge genera on-recombina on are stochas c processes. For es ma ng gamma-ray induced charges spa ally distributed in silicon dioxide lms Mon te Carlo method was used. The developed model enables the gamma-ray induced threshold voltage shi determina on as a func on on gamma-ray doses. These results are compared with experimentally determined thresh Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 old voltage shi of gamma irradiated MOS transistors and sa sfactory agree ments are obtained.

Alexandros Leontitsis, University of Ioannina, Ioannina Epameinondas Lekkas, General Hospital of Preveza, Preveza Eugenia Toki, University of Ioannina, Ioannina Jenny Pange, University of Ioannina, Ioannina An approach on Cronbach’s alpha In this work we propose the prac cal use of the Cronbach’s alpha sta s cal signicance problem. This coecient measures the reliability of a ques onnaire’s answers. Many analy cal tests have been developed over the years which gave birth to very complicated formulas. A previously adopted simula on approach to the solu on of this problem takes advantage of the computa onal power in order to give exact results for the distribu on of the null hypothesis regarding this coecient. The applica on of this coecient may apply to sta s cal analysis of medical data.

Pavicevic Z., Faculty of Science and Mathema cs, Podgorica Hyperbolic geometry, curvilinear angles and points of porosity in inves ga on of boundary proper es of func ons The curvilinear angle in the open unit disk in the complex plane with the ver tex a is a region generated by the hyperbolic disk with the hyperbolic center at a point w and the hyperbolic radius r when w passes along Jordan curve that ends at a point a from the boundary of the disk. We inves gate possibili es for cover of region that arises by arc extension of curvilinear angle with the vertex a by curvilinear angles whose ver ces are points of the set E on the boundary of the unit disk for which the vertex a is not the point of porosity.

The obtained results can be used in the inves ga on of boundary proper es of arbitrary func on dened on the open unit disk.

Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 Pchelnikov D.V., Ins tute of Geology and Mineralogy for SB RAS, Novosibirsk Dobretsov N.N., Ins tute of Geology and Mineralogy for SB RAS, Novosibirsk Sladkih L.A., Data Recep on and Processing Center for West Siberian Region, Novosibirsk Crop forecas ng system based on object-oriented monitoring concept Crop yield forecas ng is very important task for agricultural development in Siberian region. Nowadays all informa on concerning arable lands usage in Russia is provided by farmers. Lack of reliable informa on points at the ne cessity of development of agriculture monitoring system based on remote data, which will be independent from the informa on provided by the farm ers. Since 2006 Novosibirsk Meteorological Survey has been developing ag riculture monitoring system for Novosibirsk and neighborhood regions. The EPIC crop yield forecas ng model is used as base model with some regional adapta on. This presenta on discusses usage of object-oriented GIS archi tecture, which is specially developed for motoring tasks, both automate data handling process and improve of measure parameters quan ty, as well as greater ability of system adapta on for local and regional condi ons. The main system component is the agriculture eld observa on model. This mod el is based on the observa on model abstrac on class, which uses dierent data exchange interfaces and allows using any dierent data sources includ ing satellite and meteorological data as well as eld observa ons. Supposed architecture doesn’t require ini al deni on of the agriculture eld geom etry. The only base loca on of the monitoring object is required. It allows star ng the monitoring having minimal informa on and then collec ng the required data in process.

Peregudin S.I., St. Petersburg State University, St. Petersburg Kholodova S.E., St. Petersburg State University, St. Petersburg About geostrophic mo ons in a rota ng spherical layer of a non-uniform electrically conduc ng uid Research of mechanisms of genera on of a magne c eld of the Earth owing to three-dimensional large-scale movement of the nonviscous, incompress ible, non-uniform ideally spending electrowire rota ng liquid concentrated in a liquid terrestrial kernel is conducted. The oered mathema cal model of inves gated physical process represents the closed system of the equa ons in the private deriva ves, consis ng of the equa ons of hydrodynamics tak ing into account rota on of the Earth, Lorentz’s force and the corresponding equa ons of magne c dynamics with necessary boundary condi ons. With Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 use of spherical co-ordinates and scales of func ons, suitable the analysis of mathema cal model is made for calcula on of three-dimensional move ments with the big me scale and spa al horizontal scale, comparable with radius of the Earth. The basic idea of the analysis consists in construc on of the scheme consecu ve approach in which geostrophe approach is the rst step. The specied method of the analysis allows, without being limited to heuris c reasonings, to deduce the general geostrophe equa ons describ ing movements as homogeneous, so and the stra ed electrowire rota ng liquid. The analy cal decision of system of the nonlinear equa ons in the private deriva ves, modelling geostrophe movement in a layer of the ideal electrowire stra ed rota ng liquid is received. The analysis of structure of the presented elds magne c hydrodynamics values allows to draw a con clusion on jus ce of a hypothesis of S.I.Braginsky about existence of strong changes in the thin layer of a terrestrial kernel adjoining border with a cloak.

Petkovic D., Faculty of Science and Mathema cs, Kosovska Mitrovica Arandjelovic I., Faculty of Science and Mathema cs, Kosovska Mitrovica On the convergence of diagonal approxima on In rst part of this talk we present some recent results on the convergence of Diagonal approxima ons obtained by A.A. Gonchar and E.A. Rahmanov.

Fulther we give solu on of one conjecture proposed by A.A. Gonchar. In the last sec on we prove some new results.

Petkovic D., Faculty of Science and Mathema cs, Kosovska Mitrovica Petrovic M., Faculty of Science and Mathema cs, Kosovska Mitrovica A truly third order nite volume schene on quadrilateral mesh A third order nite volume method on a quadrilateral mesh is presented. By using quadrangles instead of rectangles as a basic element of the mesh, full generaliza on is archived. This work holds on a simple but valuable conser va ve rule: inside a certain special domain (volume) the total amount of a contained quan ty (such as mass, energy, momentum) is preserved. Said in another way, the total quan ty in the volume doesn’t change except by ow (or due to the uxes) across the boundary of a domain. Ecient tools for Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 solving the conserva on laws are the nite volume methods. These methods are dealing with volumes (cells) and with averaged quan es within. In each of these cells we have exact conserva on. The dynamics of the average is determined by point values of the ux along the boundary. The aim is to ob tain a third order accurate numerical solu on. This gives a mo va on for the reconstruc on of the numerical ux by some known func ons (polynomial, hyperbolic, logarithmic). In this work local double logarithmic reconstruc on was used. The components needed for developing LDRD func ons are sec ond order approxima on to the rst deriva ves. These approxima ons are actually a crucial problem in this thesis and were solved specically according to mul dimensional numerical integra on theory.

Petrovic I., Higher Educa on Ins tu on for Electrical Engineering and Compu ng, Beograd Petrovic M., Higher Educa on Ins tu on for Electrical Engineering and Compu ng, Beograd Spalevic P., Higher Educa on Ins tu on for Electrical Engineering and Compu ng, Beograd Second order sta s cs of SC diversity system in the presence of fading In this paper second order sta s cs of SC (Selec on Combining) macrodi versity sistem’s in presece of varius clases of input feding of macrodiversity sistem’s are analized. Inputs of microdiversity sistem’s are varius combining of high speed and low speed feding that are modeled with Vabull, Nakagami – m, Raly and Rice distribu on. Macrodiversity SC sistem consist two micro diversity sistems and opserve signal selec on based on their averige outputs powers that is modeled with Gama distribu on. Gained results are applied in modeling and designing of wireless comunica on sistems, in den ing param eters of equivalent code chanel based on Marcovie model with nite number of states, as well as assessment of posibility package erors with nite lenght.

Petrovic I., Higher Educa on Ins tu on for Electrical Engineering and Compu ng, Beograd Stefanovic C., Higher Educa on Ins tu on for Electrical Engineering and Compu ng, Beograd Sekulovic N., Higher Educa on Ins tu on for Electrical Engineering and Compu ng, Beograd Petrovic M., Higher Educa on Ins tu on for Electrical Engineering and Compu ng, Beograd Stefanovic M., Higher Educa on Ins tu on for Electrical Engineering and Compu ng, Beograd Second order sta s cs of ra o of two random variables In this paper, joint probability density func on of ra o of two random vari ables and its rst deriva ve is determined. Furthermore, for ra o of two ran Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 dom variables, level crossing rate is derived. Random variables have Rayleigh, Rice, Nakagami-m and Weibull distribu on. Obtained results can be used for evalua on the performance of mobile telecommunica on systems opera ng over fading channels. Numerical results are presented to illustrate the pro posed mathema cal analysis.

Petrovic L., Faculty of Science and Mathema cs, Kosovska Mitrovica Stanojevic D., Faculty of Science and Mathema cs, Kosovska Mitrovica Dimitrijevic S. Faculty of Science and Mathema cs, Kosovska Mitrovica Sta s cal causality, weak solu ons and mar ngale problems of stochas c dieren al equa ons driven with brownian mo on The paper introduces a sta s cal concept of causality in con nuous me in ltered probability spaces which is based on Granger”-”s deni on of causal ity. Then, we consider Ito’s stochas c dieren al equa on driven with a pro cess of Brownian mo on and show the equivalence between some models of causality and weak uniqueness (for weak solu ons of stochas c dieren al equa ons). We also show that the given concept of causality is closely con nected to the extremal solu ons of mar ngale problem and stopped mar n gale problem.

Petrovic V. V., Higher Educa on Ins tu on for Electrical Engineering and Compu ng, Beograd Kine cs of sintering with mathema cal theory of Gropjanov Ceramic materials have been in use in many dierent areas of human wellbe ing for a very long me. Important domains in ceramic materials are those materials that are applied in electronics. Our research is focused on magne sium- tanate (MgTiO3). Most common way of obtaining this material is by using the process of sintering. During mechanical ac va on inorganic mate rials are grinded when grain size is being reduced. Crystal structure submits distor on and also change, what is leading in some systems to chemical re ac on and forma on of new compound. In this work we are explaining me chanical ac va on inuence on sintering kine cs in system MgO-TiO2 with mathema cal theory of Gropjanov. We no ced temperature drop and me reduc on needed for MgTiO3 sintering when dura on of mechanical ac va on is longer.

Kopaonik, 27.08 - 31.08.2009 Budva, 31.08. - 05.09.2009.

MIT 2009 Pikula M., Faculty of Philosophy, Istono Sarajevo Vladicic V., Faculty of Philosophy, Istono Sarajevo About structures on the set of triangles In this paper we consider possibility of introduc on algebraic structures on the set of triangles, each of triangles we will represent as element of R3, with x10, x20, x30, where present lenght sides of triangle.

Popovic Z., Faculty of Economics, Nis Bogdanovic S., Faculty of Economics, Nis Mathema cal modelling of capital reinsurance The main topic of this paper is the capital reinsurance of enterprises.The no on of capital reinsurance, its classica on as well as mathema cal models used in dening the reten on are discussed here.The models displayed in the paper are examined under the assump on that the ideal condi ons exist, which is,generally, not true in prac ce.Reinsurance denotes the reinsurance of capital i.e. insurance of insurance.Reinsurance represents the most e cient form of risk sharing among insurance companies.