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Mathematical modelling of HIV/AIDS transmission under treatment structured by age of infectionEjigu, Amsalework Ayele 03 1900 (has links)
Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2011. / Includes bibliography. / ENGLISH ABSTRACT: This thesis takes into account the different levels of infectiousness of the human immunodeficiency
virus (HIV) infected individuals throughout their period of infection. Infectiousness
depends on the time since infection. It is high shortly after the infection occurs and
then much lower for several years, and thereafter a higher plateau is reached before the acquired
immunodeficiency syndrome (AIDS) phase sets in. In line with this, we formulated
a mathematical model which is structured according to the age of infection. To understand
the dynamics of the disease, we first discuss and analyse a simple model in which the age
of infection is not considered, but progression of the HIV-AIDS transmission is taken into
consideration by introducing three stages of infection. Analysis of these models tells us
that the disease can be eradicated from the population only if on average one infected
individual infects less than one person in his or her infectious period, otherwise the disease
persists. To investigate the reduction of the number of infections caused by a single infectious
individual to less than one, we introduce different treatment strategies for a model
which depends on the age of infection, and we analyse it numerically. Current strategies
amount to introducing treatment only at a late stage of infection when the infected individual
has already lived through most of the infectious period. From our numerical results,
this strategy does not result in eradication of the disease, even though it does reduce the
burden for the individual. To eradicate the disease from the population, everyone would
need to be HIV tested regularly and undergo immediate treatment if found positive. / AFRIKAANSE OPSOMMING: Hierdie tesis hou rekening met die verskillende aansteeklikheidsvlakke van die menslike
immuniteitsgebreksvirus (MIV) deur besmette individue gedurende hulle aansteeklikheidstydperk.
Die graad van aansteeklikheid hang af van die tydperk sedert infeksie. Dit is
hoog kort nadat die infeksie plaasvind en daarna heelwat laer vir etlike jare, en dan volg
n hoer plato voordat uiteindelik die Verworwe-Immuniteitsgebreksindroom (VIGS) fase
intree. In ooreenstemming hiermee, formuleer ons n wiskundige model van MIV-VIGSoordrag
met n struktureer waarin die tydperk sedert infeksie bevat is. Om die dinamika
van die siekte te verstaan, bespreek en analiseer ons eers n eenvoudige model sonder inagneming
van die tydperk sedert infeksie, terwyl die progressie van MIV-VIGS-oordrag egter
wel in ag geneem word deur die beskouing van drie stadiums van infeksie. Analise van die
modelle wys dat die siekte in die bevolking slegs uitgeroei kan word as elke besmette mens
gemiddeld minder as een ander individu aansteek gedurende die tydperk waarin hy of sy
self besmet is, anders sal die siekte voortduur. Vir die ondersoek oor hoe om die aantal
infeksies per besmette individu tot onder die waarde van een te verlaag, beskou ons verskeie
behandelingsstrategiee binne die model, wat afhang van die tydperk sedert infeksie, en ondersoek
hulle numeries. Die huidige behandelingstrategiee kom neer op behandeling slegs
gedurende die laat sta- dium van infeksie, wanneer die besmette individu reeds die grootste
deel van die aansteeklikheidsperiode deurleef het. Ons numeriese resultate toon dat hierdie
strategie nie lei tot uitroeiing van die siekte nie, alhoewel dit wel die las van die siekte vir
die individu verminder. Om die siekte binne die bevolking uit te roei, sou elkeen gereeld
vir MIV getoets moes word en indien positief gevind, dadelik met behandeling moes begin.
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Implementation of cell clustering in cellular automataAdams, Roxane 03 1900 (has links)
Thesis (MSc (Mathematical Sciences)) University of Stellenbosch, 2011. / ENGLISH ABSTRACT: Cellular Automata (CA) have become a popular vehicle to study complex dynamical
behaviour of systems. CA can be used to model a wide variety of physical,
biological, chemical and other systems. Such systems typically consist of subparts
that change their state independently, based on the state of their immediate surroundings
and some generally shared laws of change.
When the CA approach was used to solve the LEGO construction problem, the best
solution was found when using a variant of CA allowing for the clustering of cells.
The LEGO construction problem concerns the optimal layout of a set of LEGO
bricks. The advantages found for using the CA method with clustering in this case
are the ease of implementation, the significantly smaller memory usage to previously
implemented methods, and its trivial extension to construct multicoloured LEGO
sculptures which were previously too complex to construct.
In our research we propose to explore the definitions of clustering in CA and investigate
the implementation and application of this method. We look at the ant
sorting method described by Lumer and Faieta, and compare the implementation
of this algorithm using regular CA as well as the clustering variation. The ant
sorting model is a simple model, in which ants move randomly in space and pick
up and deposit objects on the basis of local information. / AFRIKAANSE OPSOMMING: Sellulêre Outomate (SO) het ’n populêre metode geword om die komplekse dinamiese
gedrag van sisteme bestudeer. SO kan gebruik word om ’n groot verskeidenheid
fisiese, biologiese, chemiese en ander tipe sisteme te modelleer. Sulke sisteme bestaan
tipies uit subafdelings wat, gebaseer op die status van hulle omgewing en ’n
paar algemene gedeelde reëls van verandering, hulle status onafhanklik verander.
Met die gebruik van die SO benadering om the LEGO konstruksieprobleem op te
los, is die beste oplossing bereik deur gebruik te maak van ’n variant van SO, waar
selle saamgroepeer kan word. Die LEGO konstruksieprobleem behels die optimale
uitleg van ’n stel LEGO blokkies. In hierdie geval is die voordele van die SO
met sel groepering die maklike implementasie, ’n beduidende kleiner geheuegebruik
teenoor voorheen geïmplementeerde metodes, en die triviale uitbreiding daarvan om
gekleurde LEGO beelde wat voorheen te kompleks was, te kan bou.
In ons ondersoek verken ons die definisies van selgroepering in SO en ondersoek die
implementasie en toepassing van die metode. Ons kyk na die miersorteringsmetode
beskryf deur Lumer en Faieta, en vergelyk die implementasie van hierdie algoritme
deur gewone SO asook die groeperingsvariasie te gebruik. Die miersorteringsmodel
is ’n eenvoudige model waarin miere lukraak in ’n omgewing beweeg en voorwerpe
optel of neersit volgens plaaslike inligting.
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On non-archimedean dynamical systemsJoyner, Sheldon T 12 1900 (has links)
Thesis (MSc) -- University of Stellenbosch, 2000. / ENGLISH ABSTRACT: A discrete dynamical system is a pair (X, cf;) comprising a non-empty set X and a map
cf; : X ---+ X. A study is made of the effect of repeated application of cf; on X, whereby points
and subsets of X are classified according to their behaviour under iteration. These subsets
include the JULIA and FATOU sets of the map and the sets of periodic and preperiodic
points, and many interesting questions arise in the study of their properties.
Such questions have been extensively studied in the case of complex dynamics, but much
recent work has focussed on non-archimedean dynamical systems, when X is projective
space over some field equipped with a non-archimedean metric. This work has uncovered
many parallels to complex dynamics alongside more striking differences.
In this thesis, various aspects of the theory of non-archimedean dynamics are presented,
with particular reference to JULIA and FATOU sets and the relationship between good
reduction of a map and the empty JULIA set. We also discuss questions of the finiteness
of the sets of periodic points in special contexts. / AFRIKAANSE OPSOMMING: 'n Paar (X, <jJ) bestaande uit 'n nie-leë versameling X tesame met 'n afbeelding <jJ: X -+ X
vorm 'n diskrete dinamiese sisteem. In die bestudering van so 'n sisteem lê die klem op
die uitwerking op elemente van X van herhaalde toepassing van <jJ op die versameling.
Elemente en subversamelings van X word geklasifiseer volgens dinamiese kriteria en op
hierdie wyse ontstaan die JULIA en FATOU versamelings van die afbeelding en die versamelings
van periodiese en preperiodiese punte. Interessante vrae oor die eienskappe van
hierdie versamelings kom na vore.
In die geval van komplekse dinamika is sulke vrae reeds deeglik bestudeer, maar onlangse
werk is op nie-archimediese dinamiese sisteme gedoen, waar X 'n projektiewe ruimte is
oor 'n liggaam wat met 'n nie-archimediese norm toegerus is. Hierdie werk het baie
ooreenkomste maar ook treffende verskille met die komplekse dinamika uitgewys.
In hierdie tesis word daar ondersoek oor verskeie aspekte van die teorie van nie-archimediese
dinamika ingestel, in besonder met betrekking tot die JULIA en FATOU versamelings en
die verband tussen goeie reduksie van 'n afbeelding en die leë JULIA versameling. Vrae
oor die eindigheid van versamelings van periodiese punte in spesiale kontekste word ook
aangebied.
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Ternary interpolatory subdivisionVan der Walt, Maria Dorothea 12 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Subdivision is an important and e cient tool for rendering smooth curves and
surfaces in computer graphics, by repeatedly applying a subdivision (re ning)
scheme to a given set of points. In the literature, attention has been mostly
restricted to developing binary subdivision schemes. The primary emphasis of
this thesis is on ternary subdivision, and in particular on the interpolatory case.
We will derive a symmetric ternary interpolatory subdivision scheme for the
rendering of curves, satisfying analogous properties to the Dubuc-Deslauriers
binary scheme. Explicit construction methods, as well as a corresponding
convergence analysis, will be presented. Graphical illustrations of the results
will also be provided. / AFRIKAANSE OPSOMMING: Subdivisie bied 'n belangrike en doeltre ende metode om gladde krommes
en oppervlakke in rekenaargra ka te genereer. Hierdie metode behels dat 'n
subdivisieskema (of verfyningskema) herhaaldelik toegepas word op 'n gegewe
versameling punte. In die literatuur word daar hoofsaaklik gefokus op die ont-
wikkeling van bin^ere subdivisieskemas. In hierdie tesis word die klem gel^e op
tern^ere subdivisieskemas, en in die besonder op interpolerende skemas. Ons sal
'n simmetriese tern^ere interpolerende subdivisieskema, wat analo e eienskappe
as di e van die Dubuc-Deslauriers bin^ere skema bevredig, ontwikkel, om krom-
mes te lewer. Eksplisiete konstruksiemetodes en ooreenkomstige konvergensie-
analise, asook gra ese illustrasies van die resultate, sal getoon word.
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Investigating credit based mechanisms for enhancing performance in wireless ad hoc networksGoldberg, Ariel Shei 12 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: This thesis explores two key aspects of wireless ad hoc networks. The first aspect concerns the topic of stimulating cooperation between nodes in a wireless ad hoc network. The functionality of a wireless ad hoc network depends entirely on the willingness of nodes to relay messages on behalf of other nodes. Network functionality depends on ensuring cooperation between nodes, so that each node benefits from continued participation in the network. This suggests an important question: how can cooperation among individual nodes be managed to improve overall wireless ad hoc network performance?
The second aspect explored in this thesis concerns the concept of optimal resource utilisation. Wireless ad hoc networks are characterised by limited bandwidth and energy resources, which facilitates deployment in situations in which traditional infrastructure based networks are not practical. This suggests another important question: how can the use of the limited energy and bandwidth resources of wireless ad hoc networks be optimised?
This research relies on the concept of a credit-based market economy. Nodes in simulated ad hoc networks use credits to pay for the cost of sending their own traffic and earn credits by forwarding traffic on behalf of other nodes. We show that a credit-based market economy approach can be employed to stimulate and regulate cooperation between nodes in a wireless ad hoc network. We show that this approach can be implemented in a simple decentralised manner and that it has several variants depending on which node is considered to be paying for the service, what the price of each service should be and how we route packets around the network using information derived from the credit-based economy.
This thesis demonstrates that several variants of a credit-based scheme can be implemented in a packet based simulator and that these variants result in the stable operation of the network and improve the overall performance. The credit-based mechanisms also show significant improvement to network performance in resource constrained conditions and represent an effective means for optimising limited energy and bandwidth resource. The effectiveness of the credit-based mechanisms increases as the load on the networks increases. / AFRIKAANSE OPSOMMING: Hierdie tesis ondersoek twee belangrike aspekte van draadlose ad hoc-netwerke. Die eerste aspek het betrekking op die onderwerp van 'n stimulerende samewerking tussen die nodusse in 'n draadlose ad hoc-netwerk. Dat die network funksioneer hang daarvan af om samewerking tussen die nodusse te verseker sodat elke nodus voordeel put uit voortgesette deelname in die netwerk. Dit dui op 'n belangrike vraag: Hoe kan die samewerking tussen die individuele nodusse bestuur word om die prestasie van 'n draadlose ad hoc-netwerk te verbeter?
Die tweede aspek wat in hierdie tesis ondersoek word, behels die konsep van optimale hulpbronbenutting. Draadlose ad hoc-netwerke word gekenmerk deur beperkte bandwydte- en energie-hulpbronne, wat ontplooiing bewerkstellig in situasies waar tradisionele infrastruktuur-gebaseerde netwerke nie practise moontlik is nie. Dit dui op 'n ander belangrike vraag: Hoe kan die gebruik van die beperkte energie- en bandwydte-hulpbronne van draadlose ad hoc-netwerke optimaal bestuur word?
Hierdie navorsing berus op die konsep van 'n krediet-gebaseerde markekonomie. Nodusse in gesimuleerde ad hoc-netwerke gebruik krediete om te betaal vir die versending van hul eie verkeer en nodusse verdien krediete deur die verkeer van ander nodusse aan te stuur. Ons wys dat die benadering van 'n krediet-gebaseerde markekonomie gebruik kan word om die samewerking tussen die nodusse in 'n draadlose ad hoc-netwerk te stimuleer en te reguleer. Ons wys dat hierdie benadering geïmplementeer kan word op 'n eenvoudige gedesentraliseerde wyse. Ons ondersoek verskeie variasies van die benadering, na gelang van watter nodus oorweeg word om vir die diens te betaal, wat die prys van elke diens moet wees en hoe inligting afgelei van die krediet-gebaseerde ekonomie gebruik kan word om pakkies in die netwerk te roeteer.
Hierdie tesis toon dat verskeie variante van 'n krediet-gebaseerde skema geïmplementeer kan word in 'n netwerksimulator en dat hierdie variante die stabiele bedryf van en algehele verbetering in die prestasie van die network tot gevolg het. Die krediet-gebaseerde meganismes toon 'n beduidende
verbetering in hulpbronbenutting en netwerkprestasie in omgewings met beperkte hulpbronne en verteenwoordig 'n doeltreffende manier om die beperkte energie- en bandwydte-hulpbronne optimaal te benut. Laastens, die doeltreffendheid van die krediet-gebaseerde meganismes word verhoog as die las op die netwerke word verhoog.
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Fourier methods for pricing early-exercise options under levy dynamicsFadina, Tolulope Rhoda 12 1900 (has links)
Thesis(MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The pricing of plain vanilla options, including early exercise options, such as Bermudan
and American options, forms the basis for the calibration of financial models.
As such, it is important to be able to price these options quickly and accurately.
Empirical studies suggest that asset dynamics have jump components which can be
modelled by exponential Lévy processes. As such models often have characteristic
functions available in closed form, it is possible to use Fourier transform methods,
and particularly, the Fast Fourier Transform, to price such options efficiently. In
this dissertation we investigate and implement four such methods, dubbed the Carr-
Madan method, the convolution method, the COS method and the Fourier spacetime
stepping method. We begin by pricing European options using these Fourier
methods in the Black-Scholes, Variance Gamma and Normal Inverse Gaussian models.
Thereafter, we investigate the pricing of Bermudan and American options in
the Black-Scholes and Variance Gamma models. Throughout, we compare the four
Fourier pricing methods for accuracy and computational efficiency. / AFRIKAANSE OPSOMMING: Die prysbepaling van gewone vanilla opsies, insluitende opsies wat vroeg uitgeoefen
kan word, soos Bermuda-en Amerikaanse opsies, is grondliggend vir die kalibrering
van finansiële modelle. Dit is daarom belangrik dat die pryse van sulke opsies vinnig
en akkuraat bepaal kan word. Empiriese studies toon aan dat batebewegings
sprongkomponente besit, wat gemodelleer kan word met behulp van exponensiëele
Lévyprosesse. Aangesien hierdie modelle dikwels karakteristieke funksies het wat
beskikbaar is in geslote vorm, is dit moontlik om Fourier-transform metodes, en
in besonders die vinnige Fourier-transform, te gebruik om opsiepryse doeltreffend
te bepaal. In hierdie proefskrif ondersoek en implementeer ons vier sulke metodes,
genaamd die Carr-Madan metode, die konvolusiemetode, die COS-metode en die
Fourier ruimte-tydstap metode. Ons begin deur die pryse van Europese opsies
in die Black-Scholes, Gammavariansie (Engels: Variance gamma) en Normaal Invers
Gauss (Engels: Normal Inverse Gaussian)-modelle te bepaal met behulp van
die vier Fourier-metodes. Daarna ondersoek ons die prysbepaling van Bermuda-en
Amerikaanse opsies in die Black-Scholes en Gammavariansiemodelle. Deurlopend
vergelyk ons die vier Fourier-metodes vir akkuraatheid en berekeningsdoeltreffendheid.
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Drinfeld modules and their application to factor polynomialsRandrianarisoa, Tovohery Hajatiana 12 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Major works done in Function Field Arithmetic show a strong analogy between
the ring of integers Z and the ring of polynomials over a nite eld Fq[T]. While
an algorithm has been discovered to factor integers using elliptic curves, the
discovery of Drinfeld modules, which are analogous to elliptic curves, made it
possible to exhibit an algorithm for factorising polynomials in the ring Fq[T].
In this thesis, we introduce the notion of Drinfeld modules, then we demonstrate
the analogy between Drinfeld modules and Elliptic curves. Finally, we
present an algorithm for factoring polynomials over a nite eld using Drinfeld
modules. / AFRIKAANSE OPSOMMING: 'n Groot deel van die werk wat reeds in funksieliggaam rekenkunde voltooi
is toon 'n sterk verband tussen die ring van heelgetalle, Z; en die ring van
polinome oor 'n eindige liggaam, F[T]: Terwyl daar alreeds 'n algoritme, wat
gebruik maak van elliptiese kurwes, ontwerp is om heelgetalle te faktoriseer,
het die ontdekking van Drinfeld modules, wat analoog is aan elliptiese kurwes,
dit moontlik gemaak om 'n algoritme te konstrueer om polinome in die ring
F[T] te faktoriseer.
In hierdie tesis maak ons die konsep van Drinfeld modules bekend deur sekere
aspekte daarvan te bestudeer. Ons gaan voort deur 'n voorbeeld te voorsien
wat die analoog tussen Drinfeld modules en elliptiese kurwes illustreer. Uiteindelik,
deur gebruik te maak van Drinfeld modules, bevestig ons hierdie analoog
deur die algoritme vir die faktorisering van polinome oor eindige liggame te
veskaf.
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An algebraic framework for reasoning about securityRajaona, Solofomampionona Fortunat 03 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Stepwise development of a program using refinement ensures that the program
correctly implements its requirements. The specification of a system is
“refined” incrementally to derive an implementable program. The programming
space includes both specifications and implementable code, and is ordered with
the refinement relation which obeys some mathematical laws. Morgan proposed a
modification of this “classical” refinement for systems where the confidentiality of
some information is critical. Programs distinguish between “hidden” and “visible”
variables and refinement has to bear some security requirement. First, we review
refinement for classical programs and present Morgan’s approach for ignorance pre-
serving refinement. We introduce the Shadow Semantics, a programming model
that captures essential properties of classical refinement while preserving the ignorance
of hidden variables. The model invalidates some classical laws which do
not preserve security while it satisfies new laws. Our approach will be algebraic,
we propose algebraic laws to describe the properties of ignorance preserving refinement.
Thus completing the laws proposed in. Moreover, we show
that the laws are sound in the Shadow Semantics. Finally, following the approach of Hoare and He for classical programs, we give a completeness result for the
program algebra of ignorance preserving refinement. / AFRIKAANSE OPSOMMING: Stapsgewyse ontwikkeling van ’n program met behulp van verfyning verseker dat
die program voldoen aan die vereistes. Die spesifikasie van ’n stelsel word geleidelik
”verfyn” wat lei tot ’n implementeerbare kode, en word georden met ‘n
verfyningsverhouding wat wiskundige wette gehoorsaam. Morgan stel ’n wysiging
van hierdie klassieke verfyning voor vir stelsels waar die vertroulikheid van
sekere inligting van kritieke belang is. Programme onderskei tussen ”verborgeën
”sigbare” veranderlikes en verfyning voldoen aan ’n paar sekuriteitsvereistes. Eers
hersien ons verfyning vir klassieke programme en verduidelik Morgan se benadering
tot onwetendheid behoud. Ons verduidelik die ”Shadow Semantics”, ’n programmeringsmodel
wat die noodsaaklike eienskappe van klassieke verfyning omskryf
terwyl dit die onwetendheid van verborge veranderlikes laat behoue bly. Die model
voldoen nie aan n paar klassieke wette, wat nie sekuriteit laat behoue bly nie,
en dit voldoen aan nuwe wette. Ons benadering sal algebraïese wees. Ons stel
algebraïese wette voor om die eienskappe van onwetendheid behoudende verfyning
te beskryf, wat dus die wette voorgestel in voltooi. Verder wys ons dat die wette konsekwent is in die ”Shadow Semantics”. Ten slotte, na aanleiding
van die benadering in vir klassieke programme, gee ons ’n volledigheidsresultaat
vir die program algebra van onwetendheid behoudende verfyning.
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Continuity of Drazin and generalized Drazin inversion in Banach algebrasBenjamin, Ronalda Abigail Marsha 03 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2013. / Please refer to full text to view abstract.
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Enumeration problems on latticesOcansey, Evans Doe 03 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: The main objective of our study is enumerating spanning trees (G) and perfect matchings
PM(G) on graphs G and lattices L. We demonstrate two methods of enumerating
spanning trees of any connected graph, namely the matrix-tree theorem and as a special
value of the Tutte polynomial T(G; x; y).
We present a general method for counting spanning trees on lattices in d 2 dimensions.
In particular we apply this method on the following regular lattices with d = 2:
rectangular, triangular, honeycomb, kagomé, diced, 9 3 lattice and its dual lattice to
derive a explicit formulas for the number of spanning trees of these lattices of finite sizes.
Regarding the problem of enumerating of perfect matchings, we prove Cayley’s theorem
which relates the Pfaffian of a skew symmetric matrix to its determinant. Using
this and defining the Pfaffian orientation on a planar graph, we derive explicit formula for
the number of perfect matchings on the following planar lattices; rectangular, honeycomb
and triangular.
For each of these lattices, we also determine the bulk limit or thermodynamic limit,
which is a natural measure of the rate of growth of the number of spanning trees (L)
and the number of perfect matchings PM(L).
An algorithm is implemented in the computer algebra system SAGE to count the
number of spanning trees as well as the number of perfect matchings of the lattices
studied. / AFRIKAANSE OPSOMMING: Die hoofdoel van ons studie is die aftelling van spanbome (G) en volkome afparings
PM(G) in grafieke G en roosters L. Ons beskou twee metodes om spanbome in ’n samehangende
grafiek af te tel, naamlik deur middel van die matriks-boom-stelling, en as ’n
spesiale waarde van die Tutte polinoom T(G; x; y).
Ons behandel ’n algemene metode om spanbome in roosters in d 2 dimensies af te
tel. In die besonder pas ons hierdie metode toe op die volgende reguliere roosters met
d = 2: reghoekig, driehoekig, heuningkoek, kagomé, blokkies, 9 3 rooster en sy duale
rooster. Ons bepaal eksplisiete formules vir die aantal spanbome in hierdie roosters van
eindige grootte.
Wat die aftelling van volkome afparings aanbetref, gee ons ’n bewys van Cayley se
stelling wat die Pfaffiaan van ’n skeefsimmetriese matriks met sy determinant verbind.
Met behulp van hierdie stelling en Pfaffiaanse oriënterings van planare grafieke bepaal
ons eksplisiete formules vir die aantal volkome afparings in die volgende planare roosters:
reghoekig, driehoekig, heuningkoek.
Vir elk van hierdie roosters word ook die “grootmaat limiet” (of termodinamiese limiet)
bepaal, wat ’n natuurlike maat vir die groeitempo van die aantaal spanbome (L) en die
aantal volkome afparings PM(L) voorstel.
’n Algoritme is in die rekenaaralgebra-stelsel SAGE geimplementeer om die aantal
spanboome asook die aantal volkome afparings in die toepaslike roosters af te tel.
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