Na ovaj način čvor vektori B-splajn ploha određuju temeljne funkcije zajedno s kontrolnim točkama te oblik plohe. U nekoliko članaka (vidi na primjer 4 i 5) proučavale su se operacije na čvorovima i ...njihov utjecaj na obilk krivulja. Izračuni mogu biti izvedeni vrlo efikasno ako su temeljne funkcije i vektor funkcije B-splajn plohe prikazane u matričnom obliku (vidi 1 i 6). U našem posljednjem radu 2 saželi smo metode operacija na čvorovima i odgovarajućih izračuna u matričnom obliku. Također, razvili smo algoritam za izravno klizanje čvorova, tj. pokazali smo kako čvor može biti premješten u jednom
koraku umjesto da uvodimo novu vrijednost čvora, a zatim
uklanjanjem starog iz čvor vektora.
U ovom članku analiziramo utjecaj mijenjanja intervala
čvorova na Gaussovu zakrivljenost u zadanoj točki B- splajn plohe. Prikazujemo algoritam za deformaciju B-splajn plohe tako da prolazi kroz zadanu točku sa zadanom Gaussovom zakrivljenošću. Rezultat ove deformacije kaže da kugla zadanog radijusa dira preoblikovanu plohu u zadanoj točki s jednakim Gaussovim zakrivljenostima. Ista
situacija događa se u primjenama kad je alat kuglama uguran u plohu tijekom procesa.
S ciljem da postignemo numerički stabilna i efikasna rješenja, osim premještanja vrijednosti čvora, u nasem algoritmu koristimo samo jednadžbe linearne interpolacije.
Dijagnostika i posebno liječenje pneumonija,
unatoč stalnomu napretku, i danas su praćeni brojnim
kontroverzama. Algoritmi (hrvatski: postupnik, smjernice)
daju sažete preporuke o brojnim praktičnim ...problemima
pri dijagnosticiranju i liječenju pneumonija. Na izradu i
provedbu smjernica utječu brojni i različiti čimbenici koji se
bitno razlikuju u pojedinim sredinama. Moderni algoritmi za
zbrinjavanje pneumonija, osim izbora antibiotika, propisuju i
dijagnostičke postupke, kriterije za hospitalizaciju i duljinu
liječenja, prijelaz s parenteralnog na peroralni način primjene
antibiotika, preventivne mjere itd.
Najpoznatiji algoritmi (nekoliko američkih, kanadski,
britanski, Europskog udruženja za plućne bolesti) temelje se
na empirijskom liječenju pneumonija. Danas je općeprihvaćen
stav da u inicijalnom empirijskom liječenju treba primijeniti
antibiotik koji dobro djeluje na Streptococcus pneumoniae i
na atipične uzročnike. Za ambulantno liječenje ovi algoritmi
preporučuju makrolide, doksiciklin ili nove (respiratorne)
fl uorokinolone, a za hospitalizirane bolesnike betalaktamski
antibiotik u kombinaciji s makrolidom ili fl uorokinolonski
antibiotik s dobrim učinkom na pneumokoka. Danas je
uobičajena preporuka da se liječenje težih pneumonija
započinje u bolnici parenteralnom primjenom antibiotika, a
nakon stabilizacije stanja bolesnika prelazi se na peroralnu
primjenu (switch therapy).
Respektirajući brojne čimbenike koji utječu na zbrinjavanje
pneumonija u nas i polazeći od zatečenog stanja, uključujući
već tradicionalno kliničko razvrstavanje pneumonija na
bakterijske i atipične, za učinkovito i racionalno liječenje
pneumonija valja izraditi i prihvatiti vlastite smjernice na
nacionalnoj razini. U članku se daje prijedlog smjernica za
liječenje pneumonija.
Depresivni poremećaj jedan je od najčešćih
psihičkih poremećaja današnjice koji je u kontinuiranome
porastu od početka prošlog stoljeća. Epidemiološke studije
pokazuju da svaka peta žena i svaki ...deseti muškarac tijekom
života iskuse barem jednu ozbiljnu depresivnu epizodu. Osim
što je praćena gubitkom životne radosti, prema podacima
SZO, ona je i najčešći uzrok radne nesposobnosti u svijetu.
Sve navedeno navodi nas na zaključak da se radi o javnozdravstvenom
problemu. S druge strane, do unatrag desetak
godina smatralo se da je liječenje depresije isključivo u
domeni psihijatra, no s obzirom na raširenost poremećaja
danas su prva linija u liječenju liječnici primarne zdravstvene
zaštite i obiteljski liječnici. Sukladno tomu potrebne su i praktične
smjernice liječenja, kao putokaz u svakodnevnom radu.
Učenje i poučavanje algoritama sortiranja je vrlo zahtjevno kako za učitelja tako i za učenike. Problem može biti još veći kada se nastava u cijelosti provodi u online okruženju što je bio slučaj u ...Republici Hrvatskoj od sredine ožujka do kraja školske godine 2019/20 zbog COVID-19 pandemije. Korištenje alata za vizualizaciju može pomoći u spuštanju razine apstrakcije pri poučavanju složenih koncepata kako bi učenici lakše razumjeli rad algoritama. U svrhu ispitivanja utjecaja korištenja alata za vizualizaciju tijekom online nastave provedeno je istraživanje u travnju i svibnju 2020. godine u dva treća razreda (n=52) jedne Prirodoslovno-matematičke gimnazije. U eksperimentalnoj grupi koristili smo alate za vizualizaciju VisuAlgo i Python Tutor za poučavanje algoritama sortiranja i implementaciju istih u Pythonu. Osim toga su ispitani i stavovi učenika o aktualnom provođenju online nastave U ovom radu su opisani provedba i rezultati navedenog istraživanja.
The Algorithmic Beauty of Plants Hanan, J. S; Prusinkiewicz, Przemyslaw; Fracchia, F. D ...
Springer eBooks,
1991, 1990.
eBook, Book
Odprti dostop
The beauty of plants has attracted the attention of mathematicians for Mathematics centuries. Conspicuous geometric features such as the bilateral sym and beauty metry of leaves, the rotational ...symmetry of flowers, and the helical arrangements of scales in pine cones have been studied most exten sively. This focus is reflected in a quotation from Weyl 159, page 3, "Beauty is bound up with symmetry. " This book explores two other factors that organize plant structures and therefore contribute to their beauty. The first is the elegance and relative simplicity of developmental algorithms, that is, the rules which describe plant development in time. The second is self-similarity, char acterized by Mandelbrot 95, page 34 as follows: When each piece of a shape is geometrically similar to the whole, both the shape and the cascade that generate it are called self-similar. This corresponds with the biological phenomenon described by Herman, Lindenmayer and Rozenberg 61: In many growth processes of living organisms, especially of plants, regularly repeated appearances of certain multicel lular structures are readily noticeable. . . . In the case of a compound leaf, for instance, some of the lobes (or leaflets), which are parts of a leaf at an advanced stage, have the same shape as the whole leaf has at an earlier stage. Thus, self-similarity in plants is a result of developmental processes. Growth and By emphasizing the relationship between growth and form, this book form follows a long tradition in biology.
Provider: - Institution: - Data provided by Europeana Collections- This thesis treats the problem of the network coverage in randomly deployed
wireless sensor networks. Placing the nodes ...quasi-randomly is often the only
way of deploying the network in geographically inaccessible regions. This way
of deployment is often present in military applications. In military
applications, high quality of the network coverage is usually a primary goal,
despite the fact that the nodes cannot be placed manually in the optimal
positions where they would all together provide the highest coverage, a
certain degree of robustness, and redundancy, by using the minimum number of
nodes. Bearing in mind that this kind of installation is usually realized by
using artillery or the aircrafts, before approaching the energy, security,
and reliability optimization, it is important for the application to meet the
basic functionality, i. e., it is important for the values of the basic
parameters that provide a certain degree of the network coverage and
connectivity for a given area of interest to be assessed. The area of
interest can be a region of any shape. In military applications, it is
usually the region of size 5-20km2. If the aim is for the whole area to be
covered, we deal with the area coverage. Another usual example of the
appliance of the wireless sensor networks in military applications is related
to the detection of intruders while attempting to cross the line between two
regions. In this case, we deal with the barrier coverage. This thesis covers
the modeling of the stochastic implementation of the wireless sensor
networks, the analysis of the area and the barrier coverage, as well as the
methods for improving the barrier coverage by using mobile nodes or robots.
Under the initial assumptions and approximations, the conditions for an
expected degree of the specific types of coverage are given for those types
of coverage whose quality can be expressed in terms of the expected detection
probability. But, regarding the strong barrier coverage, instead of assessing
the coverage quality, only the information on barrier coverage creation can
be derived, i.e., a strong barrier coverage can either be accomplished or not
accomplished. According to the theoretical results from literature, it can be
concluded that the full barrier coverage can be achieved almost always if the
very strict conditions are met. These conditions, however, are hard to be
provided. Therefore, in this thesis, two algorithms for creating the full
barrier coverage, by filling the network breaks with mobile nodes or by using
robots, in the situations where these conditions are not met, are proposed.
In order for the algorithms to be implemented, a simulator is developed.
According to the rules defined in algorithms, the simulator determines the
number of breaks, the position and the appropriate number of additionally
needed nodes for the strong barrier coverage to be provided. The simulator
functionality is verified by using the theoretically derived results for the
area coverage and the weak barrier coverage. Instead of using the fully
mobile network, in order to make the price of the network more flexible, the
hybrid networks are considered in this thesis. The proposed algorithms for
improving the strong barrier coverage can be executed in centralized or
distributed manner. To mend the barrier gaps, either mobile nodes (that fill
the gaps and become part of the network just as same as the other stationary
nodes) or mobile robots (that place the stationary nodes into the appropriate
positions) can be used. Algorithms for moving the mobile devices in hybrid
networks are also proposed. Bearing in mind some of the development trends in
system and software engineering, related to improving the efficiency of the
development process by using the appropriate methodologies and machine-based
identification of the data structures, in this thesis, the description of the
technical solution is given in the context of CMMI (Capability Maturity Model
Integration) while the most important aspects of the automatic identification
of the position and the sensing characteristics of the nodes are presented by
using the methodologies of the conceptual modeling.- U ovoj tezi se razmatra problem pokrivenosti bežičnim senzorskim mrežama u
slučaju stohastičkog razmeštaja čvorova u određenom regionu od interesa.
Stohastički razmeštaj čvorova je jedini način instalacije mreže u situacijama
kada je pristup terenu otežan ili nemoguć. Tipični primeri ovog načina
instalacije nalaze se u oblasti vojnih primena. U vojnim aplikacijama,
najčešće je potrebno obezbediti dobru pokrivenost regiona od interesa
senzorskim poljem, bez obzira na činjenicu što se senzori ne mogu manuelno
smestiti u optimalnim pozicijama gde je pokrivenost maksimalna pri minimalnom
broju senzorskih čvorova i pri određenom nivou robusnosti i redundatnosti
mreže. Štaviše, ovakav vid instalacije se može realizovati uglavnom samo
upotrebom artiljerije ili avijacije te je, u ovim uslovima, pre nego što se
pristupi optimizaciji mreže po pitanju potrošnje energije, sigurnosti i
pouzdanosti, potrebno odrediti fundamentalne parametre pri kojima se može
postići osnovna funkcionalnost mreže, odnosno određeni stepen pokrivenosti
područja od interesa i potrebna konektivnost. Područje od interesa može biti
region bilo kojeg oblika. U vojnim aplikacijama, to je najčešće geografsko
područje površine od 5 do 20 . Ako je cilj očitavanje veličina iz čitavog
regiona, govorimo o pokrivenosti regiona. Drugi čest slučaj primene
senzorskih mreža u vojnim aplikacijama, odnosi se na obezbeđivanje određene
linije između dva regiona po pitanju prelaska neprijateljskih vojnih trupa sa
jednog regiona na drugi. U ovom slučaju se govori o pokrivenosti barijere. U
ovoj tezi se vrši modeliranje i analiza stohastičke implementacije bežičnih
senzorskih mreža da bi se, u okviru modela, izvršila evaluacija pokrivenosti
regiona kao i evaluacija i poboljšanje pokrivenosti senzorskom barijerom
korišćenjem mobilnih čvorova ili robota. U ovom pravcu se, pod određenim
početnim pretpostavkama i aproksimacijama, daju uslovi za postizanje
očekivanog nivoa određenog tipa pokrivenosti kao i određivanje uticaja
fundamentalnih parametara mreže na kvalitet pokrivenosti za one tipove
pokrivenosti gde se kvalitet može izraziti u pogledu očekivane verovatnoće
detekcije objekata ili događaja. Međutim, kada je u pitanju sigurna senzorska
barijera, ona može postojati ili ne postojati. U tom smislu se ne može
govoriti o stepenu kvaliteta pokrivenosti već samo o verovatnoći postojanja
jakih (ili sigurnih) senzorskih barijera. Na osnovu teorijskih izvedbi iz
literature, može se zaključiti da je sigurno postojanje jake senzorske
barijere moguće ostvariti samo pod određenim strogim uslovima instalacije.
Međutim, kako su ti uslovi praktično teško ostvarivi, u ovom radu se predlažu
dva algoritma za dopunjavanje mreže koristeći mobilne čvorove ili robote u
uslovima kada nisu zadovoljeni strogi uslovi postojanja jakih senzorskih
barijera. Za implementaciju algoritma se razvija simulator kojim se određuje
pozicija i broj dodatnih mobilnih čvorova potrebnih da bi se u svakoj
situaciji sa velikom verovatnoćom formirala jaka senzorska barijera.
Funkcionalnost simulatora se verifikuje korišćenjem teorijski izvedenih
rezultata za pokrivenost regiona i pokrivenost slabom senzorskom barijerom.
Umesto korišćenja potpuno mobilnih mreža (koje su manje fleksibilne u pogledu
troškova realizacije mreže), ovde se koriste hibridne mreže, gde se
predloženi algoritmi za određivanje pozicija i broja dodatnih čvorova mogu
praktički realizovati na centralizovan ili distribuiran način. Za
dopunjavanje mreže se mogu koristiti mobilni čvorovi (koji se kreću do
određene tačke, a zatim izvršavaju istu funkciju kao i svi ostali statički
čvorovi) ili roboti (koji nose određeni broj fiksnih čvorova i pozicioniraju
ih u određenim tačkama mreže). U okviru teze se takođe predlažu algoritmi za
pomeranje ovih uređaja u cilju ostvarivanja sigurnih senzorskih barijera.
Uzevši u obzir neke trendove razvoja u sistemskom i softverskom inženjerstvu,
koji se odnose na povećanje efikasnosti razvoja rešenja koristeći
odgovarajuće modele unapređivanja procesa i na metodologiju mašinskog
prepoznavanja podatkovnih struktura, u ovoj tezi se daje opis razvoja rešenja
u kontekstu integracionog modela sazrevanja procesa a najvažniji aspekti
procesa automatskog prepoznavanja pozicija i osnovnih funkcionalnih
karakteristika čvorova u zavisnosti od okolnosti instalacije se opisuje kroz
metode konceptualnog modeliranja.- All metadata published by Europeana are available free of restriction under the Creative Commons CC0 1.0 Universal Public Domain Dedication. However, Europeana requests that you actively acknowledge and give attribution to all metadata sources including Europeana
Provider: - Institution: - Data provided by Europeana Collections- The twentieth century has been marked by the expansion and development of new
computer applications as well as sophisticated ...electronic devices for various
purposes. Low cost of computer components, Internet availability, continuous
development and improvement of the network access, development of services
that enable the widest range of options and compulsory education in the field
of computer literacy, have generated billions of users worldwide. Nowadays,
the market of telecommunications users’ devices and services, is extremely
rich and it is constantly increasing, and being modified by more complex
applicationes and devices. Among the large number of services, users are
offered by highly sophisticated multimedia services that work in real time,
interacting with one or more users. They have the oportunity to create and
distribute multimedia content, to stream audio and video files, to create
video conferences, chats, working with distributed databases, etc. Mobile
devices now allow realization of almost all of the integrated users’ service
and functionalities, which until recently have been realized by special
devices. Today we have the possibility of receiving TV signals on mobile
devices, access to web and mail servers and services, as well as access to
specialized services and information. Concerning very active market
competition, and the fact that providers always want to offer new and better
products, continuous development is inevitable, combined with constant
improvement and application of new technological solutions. All above
mentioned services are based on transfer of large amounts of information, and
on that way they are constantly increasing the density of traffic in
communication networks. Modern services require network structure with higher
bandwidth ranges, larger number of alternative paths, fast transfer, low
delays etc. On the other hand, users expect high quality services, fast
access to networks, the guarantee of certain quality and quick response
systems. Bearing this in mind, it is clear that the structure and quality of
communication network permanently needs to grow and improve. In addition,
ongoing evaluation of devices and algorithms for routing providing reliable
and solid communication is needed.. Today, there are a large number of
scientific papers aimed to improve the quality of signal transmission. With
the increase of complexity of demands, the need for more sophisticated tools,
that can offer better performances exists. One such group of tools is based
on application of models and mechanisms that exist in highly intelligent
entities, is artificial intelligence. Its special sub-group consists of tools
based on the principles of the human brain, in terms of stimulus detection,
transmission, storage, and decision-making process. This scientific
discipline is realized through artificial neural networks. This dissertation
presents capabilities of artificial neural networks, their comparative
advantages over standard computing devices, and clasifies them in relation to
a number of criteria. Special emphasis is given on recurrent neural networks
as a very important artificial neural networks. They show very good results
in solving of complex optimization problems. As a prominent representative of
this group of networks Hopfield neural network is considered here. This type
of network has been chosen for solving of the transport problems, dealt with
in this dissertation. The dissertation examines in detail the creation of a
mathematical model of Hopfield's neural network and the capabilities of its
hardware implementation. Special attention has been paid to defining of the
Energy function, which plays a key role in the Hopfield neural network
implementation. Given the proper choice of energy function, the relations
that define the general convergence of energy functions were handled and
analyzed the conditions for the stability of the network. Since this network
can be used for solving complex optimization problems, we point out the
possibility of false situations that may arise in its implementation.
Starting from the general model of Hopfield's neural network, its application
in solving of the Traveling salesman problem, as well as modifications that
were implemented by other authors with the goal of finding of the shortest
path, all relationships that describe a given network are explained. These
have been used later on as a basis for further modifications introduced by
this thesis. In connection to the requirements described for improving of the
quality of a routing protocol, in this dissertation, a modified model of
Hopfield's neural network designed for dynamic multicast routing in packet
traffic is shown. The problems in the distribution and routing of multimedia
content were defined, and based on defined transfer preconditions the
existing algorithms and methods that are currently used are described here.
The primary problem in multicast routing is multicast tree establishment, and
the solution based on the Hopfield's neural network is proposed here. In
order to fit the proposed solution with the real conditions, the
multicriteria optimization of five different network parameters with the
description of obtainig of the multicast path in a network of arbitrary
topology is explained. The results were compared with results available in
the literature. By analyzing a number of different criteria, the obtained
results show a better or at least the same quality of the final solution then
others. In addition, we analyzed the performance of a number of solutions
(operation speed, the required number of iterations, the probability of
blocking, scalable solutions, etc.). The dissertation proposes a new way of
determining of the optimal number of iterations in the Hopfield neural
network implementation. In this way a logic of minimizing of the required
number of iterations and network operation time is derived. It is shown that
the results are significantly better than similar ones in literature. Since
the proposed solution is given regarding the routing information in computer
networks, the algorithms for routing in optical networks were analyzed, too.
Having in mind the existence of increased number of communication networks
and that it goes towards the optical fiber technology implementation,
particularly demanding conditions are imposed to algorithms for routing of
the optical signal. The dissertation proposes a new algorithm for routing and
wavelength assignment in all-optical networks. This solution shows all of the
stages in the creation of models, modifications of the original topology of
optical networks, creating a modified energy function of Hopfield's neural
network and usage of the same one in optical routing problem. The proposed
solution allows a high degree of scalability and adaptability to the real
limitations in certain optical networks. We have further analyzed the results
of the additional proposed model that solves the problem of routing phase
(within the routing algorithm and assignment of wavelengths), while for the
allocation of wavelengths we have used the described standardized algorithms.
Since Hopfield's neural network showed good results in the field of
multicriteria optimization in the domain of routing signal, we analyzed its
possible application of the modified model to solve more general transport
problems. The dissertation proposed solution for finding optimal alignment of
the new road junction, which is an integral part of business analysis and
transportation planning. Whereas it is necessary to analyze the influence of
geomorphologic features of the ground on construction of the route, and track
the impact of political, economic and environmental factors, the proposed
solution is based on multicriteria analysis of a number of factors
inconsistent with the effects differed. The proposed solution is tested in
real conditions on the ground of the Republic of Serbia, and it can be used
as an aid in conducting studies on new roads. All proposed solutions, or
models that can further improve the existing algorithms, are presented here.
They indicate that the use of Hopfield's neural network is justified in a
number of different types of problems that need solving multicriteria
optimization problems.- Dvadeseti vek je obeležen ekspanzijom u razvoju, proizvodnji i primeni
računara i sofisticiranih elektronskih uređaja najrazličitijih namena. Niska
cena računara, dostupnost Interneta, stalni razvoj i poboljšanja na nivou
pristupne mreže, razvoj servisa koji omogućavaju najširi spektar mogućnosti i
obavezno obrazovanje u domenu računarske pismenosti, stvorili su milijarde
korisnika na celom svetu. Danas na tržištu postoji izuzetno veliki broj
telekomunikacionih korisničkih uređaja i usluga koji se permanentno
povećavaju, usložnjavaju i modifikuju. Među velikim brojem korisničkih
servisa, korisnicima su na raspolaganju i vrlo sofisticirani multimedijalni
servisi koji rade u realnom vremenu i u interakciji sa jednim ili većim
brojem drugih korisnika (mogućnost kreiranja i distribucije multimedijalnog
sadržaja, streaming audio i video fajlova, video konferencije, četovi, rad sa
distribuiranim bazama podataka, itd.). Mobilni uređaji danas omogućavaju
realizaciju skoro svih integrisanih korisničkih funkcionalnosti i servisa,
koje su do skoro realizovali posebni uređaji. Danas imamo mogućnost prijema
TV signala na mobilnim uređajima, pristup web i mail serverima i servisima,
pristup specijalizovanim korisničkim servisima i informacijama i sl. Obzirom
da je prisutna vrlo aktivna tržišna konkurencija, i da davaoci usluga uvek
žele da ponude novi i bolji proizvod, to neminovno dovodi do stalnog razvoja,
usavršavanja i primene novih tehnoloških rešenja kod proizvođača. Svi
navedeni servisi svoj način rada baziraju na prenosu većeg broja informacija,
čime se gustina saobraćaja u komunikacionim mrežama s
Provider: - Institution: - Data provided by Europeana Collections- In this work some actual combinatorial optimization problems are investigated. Several different methods are suggested for solving ...the following NP hard problems: maximally balanced connected partition problem in graph, general maximally balanced problem with q partitions ( q ≥ 2), maximum set splitting problem and p-ary transitive reduction problem in digraphs. Together with investigation of combinatorial optimization methods for solving these problems, the applying of these problems in education is also considered in the dissertation. For solving each of these problems, metaheuristics are developed: variable neighborhood search is developed for each problem and genetic algorithm is used for solving p-ary transitive reduction problem in digraphs. For maximally balanced connected partition problem a mixed linear programming model is established, which enables to solve the problem exactly for the instances of lower dimensions. Achieved numerical results indicate the high level of reliability and usability of the proposed methods. Problems solved in this research are of a great interest both in theoretical and practical points of view. They are used in production, computer networks, engineering, image processing, biology, social sciences and also in various fields of applied mathematics and computer science. In this work the applying of some problems in educational issues is also considered. It is shown that approaches of finding maximally balanced connected partition in graph and finding maximum splitting of the set can be successfully used in course organization, which is verified on the concrete examples. Based on the objective indicators and professor's assessment, the techniques for the identifying the connections between the lessons, as well as the weights of the lessons are developed. Thus, whole course can be represented as a connected weighted graph, enabling the resolving of the lesson partition problem by mathematical approaches. By assigning the lessons into the appropriate categories (topics area) inside a iv course, a collection of subsets (corresponding to the topics) of the set of lessons is created. If we set the requirement that lessons should be split into two disjoint subsets (e.g. into the winter and summer semesters), in a way that corresponding topics are processed in both subsets, then the mathematical model of the requirement and its solution corresponds to the set splitting problem. By the developed models of course organization, from which the NP hard problems arise, in addition to the scientific contributions in the fields of mathematical programming and operational research, contributions in educational aspects are added, especially in the methodology of teaching mathematics and computer science.- U ovom radu se istražuju neki aktuelni problemi kombinatorne optimizacije. Analizirane su i predstavljene različite metode rješavanja sljedećih NP teških problema: problem pronalaženja maksimalne povezane particije, uopšteni problem pronalaženja maksimalno balansirane povezane particije u grafu sa q particija (q ≥ 2), problem pronalaženja podjele skupa na dvije particije i problem pronalaženja p-arne tranzitivne redukcije u digrafu. Zajedno sa istraživanjem metoda kombinatorne optimizacije, kojima se rješavaju navedeni problemi, u disertaciji se istražuje i mogućnost primjene nekih od navedenih problema kombinatorne optimizacije u organizaciji nastave. Za svaki od ovih problema prikazane su metaheuristike za njihovo rješavanje: metod promjenljivih okolina je razvijen za sva četiri problema, dok je za problem tranzitivne redukcije u digrafu razvijen i genetski algoritam. Za problem maksimalno balansirane povezane particije u grafu je razvijen i model mješovitog cjelobrojnog linearnog programiranja, koji omogućava pronalaženje tačnog rješenja za instance manjih dimenzija. Dobijeni eksperimentalni rezultati ukazuju na visoku upotrebnu vrijednost svih razvijenih metoda. Problemi koji su rješavani u ovom radu su od velikog teorijskog i praktičnog značaja. Koriste se u proizvodnji, oblastima računarskih mreža, inžežerstvu, obradi slika, biologiji, društvenim naukama, a takođe i u oblastima primijenjene matematike i računarstva. U radu je razmatrana primjena nekih od navedenih problema u organizaciji nastave. Pokazalo se da se pronalaženja maksimalno balansirane povezane particije u grafu i problem pronalaženja podjele skupa na dvije particije uspješno mogu primijeniti u ogranizaciji planova i programa, kako je to prikazano i na konkretnim primjerima. Razvijene su tehnike za načine povezivanja lekcija, kao i za određivanje njihovih težina, zasnovanih na objektivnim pokazateljima i subjektivnim procjenama profesora. Time je postignuto da se čitav kurs predstavi kao povezan težinski graf, što pruža mogućnost da se problem podjele lekcija unutar kursa posmatra i rješava kao matematički problem. Pridruživanjem lekcija odgovarajućim kategorijama (tematskim cjelinama) unutar jednog kursa, kreira se familija podskupova (tematskih cjelina) čitavog skupa lekcija. Ako pretpostavimo da lekcije kursa treba razbiti u dva disjunktna podskupa (na primjer na zimski i ljetnji semestar), tako da što više tematskih cjelina bude "pokriveno" u oba ta podskupa, tada se navedeni problem svodi na rješavanje problema maksimalne podjele skupa. Razvijenim modelima u organizaciji nastave, iz kojih nastaju NP teški problemi, ovom radu je, pored naučnog doprinosa u polju matematičkog programiranja i operacionih istraživanja, pridodat i doprinos iz oblasti metodologije nastavnog procesa, sa naglaskom na metodologiju nastave matematike i računarstva.- All metadata published by Europeana are available free of restriction under the Creative Commons CC0 1.0 Universal Public Domain Dedication. However, Europeana requests that you actively acknowledge and give attribution to all metadata sources including Europeana
