Some results on partial difference sets and partial geometries

This thesis shows results on 3 different problems involving partial difference sets (PDS) in abelian groups, and uses PDS to study partial geometries with an abelian Singer group. First, the last two undetermined cases of PDS on abelian groups with k ≤ 100, both of order 216, were shown not to exist. Second, new parameter bounds for k and ∆ were found for PDS on abelian groups of order p^n , p an odd prime, n odd. A parameter search on p^5 in particular was conducted, and only 5 possible such cases remain for p \u3c 250. Lastly, the existence of rigid type partial geometries with an abelian Singer group are examined; existence is left undetermined for 11 cases with α ≤ 200. This final study led to the determination of nonexistence for an infinite class of cases which impose a negative Latin type PDS

The combinatorics of binary arrays

This paper gives an account of the combinatorics of binary arrays, mainly concerning their randomness properties. In many cases the problem reduces to the investigation on difference sets.postprin

Dva-ločno-tranzitivni dvo-valentni digrafi določenih redov

The topic of this paper is digraphs of in-valence and out-valence 2 that admit a 2-arc-transitive group of automorphisms. We classify such digraphs that satisfy certain additional conditions on their order. In particular, a classification of those with order ▫$kp$▫ or ▫$kp^{2}$▫ where ▫$k leq 14$▫ and ▫$p$▫ is a prime can be deduced from the results of this paper.Tema tega članka so digrafi vhodne in izhodne valence 2, ki dopuščajo 2-ločno-tranzitivno grupo avtomorfizmov. Klasificiramo takšne digrafe, ki zadoščajo določenim dodatnim pogojem glede njihovega reda. Tako je npr. mogoče s pomočjo rezultatov tega članka klasificirati tiste, ki imajo red ▫$kp$▫ ali ▫$kp^{2}$▫, kjer je ▫$k leq 14$▫ in je ▫$p$▫ praštevilo

Automatic Calculation of supersymmetric Renormalization Group Equations and Self Energies

SARAH is a Mathematica package for studying supersymmetric models. It calculates for a given model the masses, tadpole equations and all vertices at tree-level. Those information can be used by \SARAH to write model files for CalcHep/CompHep or FeynArts/FormCalc. In addition, the second version of SARAH can derive the renormalization group equations for the gauge couplings, parameters of the superpotential and soft-breaking parameters at one and two-loop level. Furthermore, it calculates the one-loop self energies and the one-loop corrections to the tadpoles. SARAH can handle all N=1 SUSY models whose gauge sector is a direct product of SU(N) and U(1) gauge groups. The particle content of the model can be an arbitrary number of chiral superfields transforming as any irreducible representation with respect to the gauge groups. To implement a new model, the user has just to define the gauge sector, the particle, the superpotential and the field rotations to mass eigenstates.Comment: 32 pages, some typoes corrected, matches published versio

Supersymmetric Branes on AdS_5 x Y^{p,q} and their Field Theory Duals

We systematically study supersymmetric embeddings of D-brane probes of different dimensionality in the AdS_5xY^{p,q} background of type IIB string theory. The main technique employed is the kappa symmetry of the probe's worldvolume theory. In the case of D3-branes, we recover the known three-cycles dual to the dibaryonic operators of the gauge theory and we also find a new family of supersymmetric embeddings. The BPS fluctuations of dibaryons are analyzed and shown to match the gauge theory results. Supersymmetric configurations of D5-branes, representing domain walls, and of spacetime filling D7-branes (which can be used to add flavor) are also found. We also study the baryon vertex and some other embeddings which break supersymmetry but are nevertheless stable.Comment: LaTeX, 2 figures, 54 pages; v2: discussions sharpened at several points, new subsection and references adde