1. Propose a quantum mechanical model for the LC circuit and show that its (quantum) energy eigenvalues can be written in terms of the frequency ω = 1/ √ LC. 2. What is the meaning of the quantum eigenstates? [Hint: if you are not satisfied to find the quantum model by simple similarity with a very well-known model, consider ∂E ∂E that we have: = −Φ̇ and ̇ = Q, thus Φ and Q are generalized canoni...

Let A be the Cantor space of bi-infinite sequences in a finite alphabet A, and let σ be the shift map on A. A cellular automaton is a continuous, σ-commuting self-map Φ of A, and a Φ-invariant subshift is a closed, (Φ, σ)-invariant subset S ⊂ A. Suppose a ∈ A is S-admissible everywhere except for some small region we call a defect. It has been empirically observed that such defects persist unde...

Let & = (P, £, I) be a generalized quadrangle of order 5, s φ 1, having a flag (x, L) with χ and L regular. Then a generalized quadrangle SP = (Ρ',Β',Ι') of order s can be constructed. We say that &" is obtained by switching from & with respect to (je, L). Examples are given where ¥ £ &'\ e.g., starting from a T2(O) of Tits, with O an oval of PG(2, q), q even, with nucleus «, the GQ T2((O {*}) ...

In this paper, we propose generalizations of the de Bruijn’s identities based on extensions of the Shannon entropy, Fisher information and their associated divergences or relative measures. The foundation of these generalizations are the φ-entropies and divergences of the Csiszár’s class (or Salicrú’s class) considered within a multidimensional context, included the monodimensional case, and fo...

Recent results have shown that any closed operator A commuting with the backwards shift S∗ restricted to K u := H 2 ⊖ uH, where u is an inner function, can be realized as a Nevanlinna function of S∗ u := S ∗| K2 u , A = φ(S∗ u), where φ belongs to a certain class of Nevanlinna functions which depend on u. In this paper this result is generalized to show that given any contraction T of class C0(...

and Applied Analysis 3 The aim of this paper is to prove the equivalence of convergent results of above Ishikawa andMann iterations with errors for generalized asymptoticallyΦ-strongly pseudocontractive mappings without bounded range assumptions in uniformly smooth real Banach spaces. For this, we need the following concepts and lemmas. Definition 1.4 see 4 . The mapping T is called generalized...

For a continuous map f on a compact metric space we study the geometry and entropy of the generalized rotation set Rot(Φ). Here Φ = (φ1, ..., φm) is a m-dimensional continuous potential and Rot(Φ) is the set of all μ-integrals of Φ and μ runs over all f -invariant probability measures. It is easy to see that the rotation set is a compact and convex subset of R. We study the question if every co...

The goal of this poster is to draw attention to observational calculi, to explain their main features and to outline possibilities of their application in Semantic Web. Observational calculi were defined in the book [1] as a tool to answer the questions (i) Can computers formulate and verify scientific hypotheses? (ii) Can computers in a rational way analyze empirical data and produce a reasona...

The assumption in the main result of [2] is removed Let G be a Lie group which acts isometrically on a Riemannian manifold M . A section of the Riemannian G-manifold M is a closed submanifold Σ which meets each orbit orthogonally. In this situation the trace on Σ of the G-action is a discrete group action by the generalized Weyl group W (Σ) = NG(Σ)/ZG(Σ), where NG(Σ) := {g ∈ G : g.Σ = Σ} and ZG...

This paper is concerned with formal solutions to the lottery paradox on which high probability defeasibly warrants acceptance. It considers some recently proposed solutions of this type and presents an argument showing that these solutions are trivial in that they boil down to the claim that perfect probability is sufficient for rational acceptability. The argument is then generalized, showing ...