Probability theory is an important tool of modeling randomness in a practical problem. But besides randomness, in the real world, there exists other kind of uncertainties such as impreciseness or vagueness. Set-valued functions are employed to model the impreciseness in applied field such as in Economics, control theory (see for example [1]). Integrals of set-valued functions have been received...

As every high-school graduate knows, animals are classified into two large groups ñ those that have vertebrae and those that do not. What every high-school graduate should also know (but probably doesnít) is that the vertebrates are further divided into jawless (Agnatha) and jawed (Gnathostomata). The jawed vertebrates are distinguished not only by the possession of jaws, but also by a suite of...

Resumé / Ðåçþìå In this thesis we propose state-dependent importance sampling heuristics to estimate the probability of population overflow in queuing networks. These heuristics capture state-dependence along the boundaries (when one or more queues are almost empty) which is crucial for the asymptotic efficiency of the change of measure. The approach does not require difficult (and often intrac...

We study the mixing property for the skew product F : TdˆTl Ñ Td ˆ Tl given by F px, yq “ pTx, y ` τpxqq, where T : Td Ñ Td is a C8 uniformly expanding endomorphism, and the fiber map τ : Td Ñ Tl is a C8 map. We apply the semiclassical analytic approach to get the dichotomy: either F mixes exponentially fast or τ is an essential coboundary. In the former case, the Koopman operator p F of F has ...

An extremum principle was postulated by Horne, Finkelstein, Shull, Zeilinger, and Bernstein in order to derive the physically allowable parameters for sinusoidal standing waves governing a neutron in a crystal which is immersed in a strong external magnetic field: `̀ the expectation value of the total potential á V ñ is an extremum .’’ We show that this extremum principle can be obtained from th...

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Throughout the text, Γ will be a metric graph; that is, a finite one-dimensional CW-complex with a metric on it. We can also describe Γ with combinatorial data, by giving a graph G “ pV,Eq with a length function E Ñ Rą0 on the edges. Such a weighted graph will be called a graph representation of Γ. We will assume that such a graph representation has no loops (if it does, we add a vertex somewhe...