We use combinatorial methods and permutation groups to classify homogeneous boolean functions. The property of symmetry of a boolean function limits the size of the function’s class. We exhaustively searched for all boolean functions on V6. We found two interesting classes of degree 3 homogeneous boolean functions: the first class is degree 3 homogeneous bent boolean functions; and the second i...

Introduction 2 1. Shimura curves 6 1.1. Modular interpretation 6 1.2. Integral models 13 1.3. Reductions of models 17 1.4. Hecke correspondences 18 1.5. Order R and its level structure 25 2. Heegner points 29 2.1. CM-points 29 2.2. Formal groups 34 2.3. Endomorphisms 37 2.4. Liftings of distinguished points 40 3. Modular forms and L-functions 43 3.1. Modular forms 44 3.2. Newforms on X 49 3.3. ...

Let G be a group. Two elements x, y are said to be z-equivalent if their centralizers are conjugate in G. The class equation of G is the partition of G into conjugacy classes. Further decomposition of conjugacy classes into z-classes provides an important information about the internal structure of the group, cf. [8] for the elaboration of this theme. Let I(Hn) denote the group of isometries of...

In this thesis we study relation liftings in the context of coalgebraic modal logic. In the first part of the thesis we look for conditions on relation liftings that can be used to define a notion of bisimilarity between states in coalgebras, such that two states are bisimilar if and only if they are behaviorally equivalent. We show that this is the case for relation liftings that are lax exten...

Let G be an Abelian group and let μ : A → G and ν : B → G be finitely additive measures (charges) defined on fields A and B of subsets of a set X. It is assumed that μ and ν agree on A∩B, i.e. they are consistent. The existence of common extensions of μ and ν is investigated, and conditions on A and B facilitating such extensions are given. 0. Introduction. We consider the following problem: Le...

We employ a forcing approach to extending Boolean algebras. A link between some forcings and some cardinal functions on Boolean algebras is found and exploited. We find the following applications: 1) We make Fedorchuk’s method more flexible, obtaining, for every cardinal λ of uncountable cofinality, a consistent example of a Boolean algebra Aλ whose every infinite homomorphic image is of cardin...