Department of Mathematical Sciences

An algebraic framework for reasoning about privacy

Rajaona, Solofomampionona Forunat (Stellenbosch : University of Stellenbosch, 2016-03)

ENGLISH ABSTRACT: In this thesis, we study a formal programming language and algebraic tech-niques to analyse computational systems that considers data confidentiality and hidden computations. The reasoning techniques are ...

Parabolic curve fitting study subject to Joule heating in MHD thermally stratified mixed convection stagnation point flow of Eyring-Powell fluid induced by an inclined cylindrical surface

Rehman, Khalil-Ur; Malik, M. Y.; Makinde, O. D. (Elsevier, 2018)

The current analysis is carried out to envision the properties of magneto-hydrodynamic boundary layer stagnation point flow of Eyring-Powell (non-Newtonian) fluid induced by an inclined stretching cylindrical surface in ...

Quantifying multiple-site compositional turnover in an Afrotemperate forest, using zeta diversity

Hui, Cang; Vermeulen, Wessel; Durrheim, Graham (SpringerOpen, 2018)

Background: Species turnover is typically measured by partitioning diversity components into alpha and pairwise beta diversity. However, alpha and beta components cannot express the full spectrum of multiple-site ...

Growing and destroying Catalan–Stanley trees

Hack, Benjamin; Prodinger, Helmut (Discrete Mathematics and Theoretical Computer Science, 2018)

Stanley lists the class of Dyck paths where all returns to the axis are of odd length as one of the many objects enumerated by (shifted) Catalan numbers. By the standard bijection in this context, these special Dyck paths ...

Modeling top-down and bottom-up drivers of a regime shift in invasive aquatic plant stable states

Strange, Emily F.; Landi, Pietro; Hill, Jaclyn M.; Coetzee, Julie A. (Frontiers Media, 2019)

The evidence for alternate stable states characterized by dominance of either floating or submerged plant dominance is well established. Inspired by an existing model and controlled experiments, we conceptually describe a ...

Visibility problems related to skip lists

Prodinger, Helmut (Combinatorial Mathematics Society of Australasia, 2018)

For sequences (words) of geometric random variables, visibility problems related to a sun positioned in the north-west are considered. This leads to a skew version of such words. Various parameters are analyzed, such as ...

Euler Classes and Frobenius Algebras

Ranaivomanana, Valimbavaka Hosana (Stellenbosch : Stellenbosch University, 2019-04)

ENGLISH ABSTRACT : This thesis investigates the relationship between the handle element of the De Rham cohomology algebra of a compact oriented smooth manifold, thought of as a Frobenius algebra, and the Euler class of ...

Evolutionary fields can explain patterns of high-dimensional complexity in ecology

Wilsenach, James; Landi, Pietro; Hui, Cang (American Physical Society, 2017)

One of the properties that make ecological systems so unique is the range of complex behavioral patterns that can be exhibited by even the simplest communities with only a few species. Much of this complexity is commonly ...

Representing derivatives of Chebyshev polynomials by Chebyshev polynomials and related questions

Prodinger, Helmut (De Gruyter, 2017)

A recursion formula for derivatives of Chebyshev polynomials is replaced by an explicit formula. Similar formulae are derived for scaled Fibonacci numbers.

Hopf and Lie algebras in semi-additive varieties

Porst, Hans E. (Logical Methods in Computer Science, 2017)

We study Hopf monoids in entropic semi-additive varieties with an emphasis on adjunctions related to the enveloping monoid functor and the primitive element functor. These investigations are based on the concept of the ...

A duality theoretic perspective on recognisable languages

Rozanova, Julia (Stellenbosch : Stellenbosch University, 2019-04)

ENGLISH ABSTRACT : A connection between recognisable languages and profinite identities is established through the composition of two famous theorems: Eilenberg’s theorem and Reiterman’s theorem. In this work, we present ...

An error correction neural network for stock market prediction

Mvubu, Mhlasakululeka (Stellenbosch : Stellenbosch University, 2019-04)

ENGLISH ABSTRACT : Predicting stock market has long been an intriguing topic for research in different fields. Numerous techniques have been conducted to forecast stock market movement. This study begins with a review ...

Summations in Bernoulli's triangles via generating functions

Oliver, Kamilla; Prodinger, Helmut (University of Waterloo, 2017)

We revisit sums along straight lines of indices in Bernoulli triangles, and emphasize the use of generating functions as the appropriate tool. This leads to more direct and extended results, compared with a recent paper ...

Mathematical models of Ebola virus disease with socio-economic dynamics

Djiomba Njankou, Sylvie Diane (Stellenbosch : Stellenbosch University, 2019-04)

ENGLISH ABSTRACT : West Africa hosted the deadliest Ebola virus disease epidemic from 2013 to 2016 and one of the common characteristics of the affected countries is their status of being developing countries. Poor ...

Biocapacity optimization in regional planning

Guo, Jianjun; Yue, Dongxia; Li, Kai; Hui, Cang (Nature Research, 2017)

Ecological overshoot has been accelerating across the globe. Optimizing biocapacity has become a key to resolve the overshoot of ecological demand in regional sustainable development. However, most literature has focused ...

Investigating diffusion on networks with long-range interactions: application to object clustering using the generalised heat kernel invariants

Nanyanzi, Alice (Stellenbosch : Stellenbosch University, 2018-12)

ENGLISH ABSTRACT : Diffusion on networks is widely used to model dynamical processes on networks such as propagation of information through a social network for marketing purposes [79], spread of epidemics within a social ...