In this thesis/project we give necessary and sufficient conditions for both the Weak Law and the Generalized Weak Law of Large Numbers (GWLLN) to hold. To achieve our goals we rely on Pitman’s work on the characteristic function as well as Kolmogorov’s concept of generalized mathematical expectation. We also emphasize that the GWLLN is related to what physicists call the Quantum Zeno Effect.

We consider a generalized hyperelastic-rod wave equation (or generalized Camassa– Holm equation) describing nonlinear dispersive waves in compressible hyperelastic rods. We establish existence of a strongly continuous semigroup of global weak solutions for any initial data from H1(R). We also present a “weak equals strong”uniqueness result.

It is well known that MTL satisfies the finite embeddability property. Thus MTL is complete w.r.t. the class of all finite MTL-chains. In order to reach a deeper understanding of the structure of this class, we consider the extensions of MTL by adding the generalized contraction since each finite MTL-chain satisfies a form of this generalized contraction. Simultaneously, we also consider extens...

The automata-theoretic approach to model checking requires two basic ingredients: a translation from logic to automata, and an algorithm for checking language emptiness. LTL model checking has traditionally been based on (generalized) Büchi automata. Weak alternating automata provide an attractive alternative because there is an elegant and linear-time translation from LTL. However, due to thei...

This paper provides a direct equivalence proof for minimax solutions of A.I. Subbotin and generalized weak solutions in the sense of idempotent analysis. It is shown that the Hamilton-Jacobi equation Vt+H(t, x,DxV ) = 0 (with the Hamiltonian H(t, x, s) concave in s), considered in the context of minimax generalized solutions, is linear w.r.t. ⊕ = min and ̄ = +. This leads to a representation fo...