The hyperplanes of the U (4)(3) near hexagon

Combining theoretical arguments with calculations in the computer algebra package GAP, we are able to show that there are 27 isomorphism classes of hyperplanes in the near hexagon for the group U (4)(3). We give an explicit construction of a representative of each class and we list several combinatorial properties of such a representative

The hyperplanes of the glued near hexagon Q(5,2) ⊗ Q(5,2)

With the aid of the computer algebra system GAP, we show that the glued near hexagon Q(5, 2) circle times Q(5, 2) has 16 isomorphism classes of hyperplanes. We give at least one explicit construction for a representative of each isomorphism class and we list several properties of such a representative

Instanton Geometry and Quantum A-infinity structure on the Elliptic Curve

We first determine and then study the complete set of non-vanishing A-model correlation functions associated with the ``long-diagonal branes'' on the elliptic curve. We verify that they satisfy the relevant A-infinity consistency relations at both classical and quantum levels. In particular we find that the A-infinity relation for the annulus provides a reconstruction of annulus instantons out of disk instantons. We note in passing that the naive application of the Cardy-constraint does not hold for our correlators, confirming expectations. Moreover, we analyze various analytical properties of the correlators, including instanton flops and the mixing of correlators with different numbers of legs under monodromy. The classical and quantum A-infinity relations turn out to be compatible with such homotopy transformations. They lead to a non-invariance of the effective action under modular transformations, unless compensated by suitable contact terms which amount to redefinitions of the tachyon fields.Comment: 24 pages, 6 figures, LaTeX2

Designing a mobile application interface to support mid-career professionals in creating better financial futures

South Africans borrow more and save less than other nations (Discovery Bank, 2018). One reason is a lack of financial knowledge. If a mobile application could guide individuals to modify their financial habits slightly by spending less and saving more, they could dramatically improve their financial future. When designing visualisation systems such as a mobile application interface, users' qualitative design feedback and quantitative usability evaluation are both important and complementary. The benefit of usability feedback in software development is undisputed. The importance of qualitative design feedback from users however, seems to be controversial in Science. Gathering users' qualitative design feedback, ahead of usability evaluation, can have a substantial impact on downstream development costs. The researcher used design as a tool for thinking (imagining new possibilities) and communicating (sharing ideas). The purpose was to clarify ways in which a mobile application interface could support users in making better financial decisions and creating better financial futures for themselves and consequently for society. A user centred design (UCD) approach was followed, emphasising design before development, with a strong focus on user involvement in all three phases, namely requirements gathering, design and evaluation. A primary client archetype for mid-career professionals was developed, split into two personas, Alan and Zoe, based on personality and self-rated motivational attributes which were used in an unconventional way to inspire two parallel, diverse designs. In early design stages, before an idea is well formed, producing multiple contrasting designs in parallel and qualitative design feedback from users is beneficial to establishing utility (solving the right problem), tapping into users' domain knowledge, improving the quality of the design and reducing fixation on one idea. Once the concept has been socialised and evolved sufficiently with users' input, converging on one final design and testing usability (solving the problem in the right way) become more important. This research offers two refinements of the UCD process guidelines for the benefit of researchers and practitioners