Small values ofn 2α (mod 1)

Dedicated to Professor Wolfgang Schmidt on the occasion of his sixtieth birthday     

Synthesis of substituted 3-arylpiperidines and 3-arylpyrrolidines by radical 1,4 and 1,2-aryl migrations

A route to 3-arylpiperidines and 3-arylpyrrolidines involving radical 1,4- and 1,2-aryl migrations has been explored. For the piperidines, the first route requires a xanthate addition to an N-allylarylsulfonamide, followed by acetylation and treatment with lauroyl peroxide to give the corresponding 1,4-aryl transfer product. This compound can be converted into the desired piperidine derivative following acidic hydrolysis. For the second approach to piperidines, addition of an α-keto xanthate to olefins of type 14 causes 1,2-aryl migration leading to an α,β-unsaturated ester, which can be converted into a piperidine by the action of ammonia or a primary amine and sodium cyanoborohydride. Substituted 3-arylpyrrolidines can be obtained by simply starting with an α-amido substituted xanthate.     

Investigations of Passive Flow Control Devices for Vertical Axis Wind Turbines

The purpose of these investigations is to study the possibilities to improve performances of a typical vertical axis wind turbines (VAWT), of Darrieus-type, using passive devices (mounted “on” or “inside” the blades of VAWT) to control dynamic flow separation (dynamic stall phenomenon). The passive devices considered for investigations are the Gurney flap, the slot or thin channel, and the turbulence promoters. Studies are performed numerically using computational fluid dynamics and where it is possible the results are compared with existent experimental or numerical data. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Theoretical analysis of steady state genetic algorithms

Evolutionary Algorithms, also known as Genetic Algorithms in a former terminology, are probabilistic algorithms for optimization, which mimic operators from natural selection and genetics. The paper analyses the convergence of the heuristic associated to a special type of Genetic Algorithm, namely the Steady State Genetic Algorithm (SSGA), considered as a discrete-time dynamical system non-generational model. Inspired by the Markov chain results in finite Evolutionary Algorithms, conditions are given under which the SSGA heuristic converges to the population consisting of copies of the best chromosome.     

The logic of justified belief,explicit knowledge,and conclusive evidence

We present a complete, decidable logic for reasoning about a notion of completely trustworthy (“conclusive”) evidence and its relations to justifiable (implicit) belief and knowledge, as well as to their explicit justifications. This logic makes use of a number of evidence-related notions such as availability, admissibility, and “goodness” of a piece of evidence, and is based on an innovative modification of the Fitting semantics for Artemov?s Justification Logic designed to preempt Gettier-type counterexamples. We combine this with ideas from belief revision and awareness logics to provide an account for explicitly justified (defeasible) knowledge based on conclusive evidence that addresses the problem of (logical) omniscience.     

PLQP & Company: Decidable Logics for Quantum Algorithms

We introduce a probabilistic modal (dynamic-epistemic) quantum logic PLQP for reasoning about quantum algorithms. We illustrate its expressivity by using it to encode the correctness of the well-known quantum search algorithm, as well as of a quantum protocol known to solve one of the paradigmatic tasks from classical distributed computing (the leader election problem). We also provide a general method (extending an idea employed in the decidability proof in Dunn et al. (J. Symb. Log. 70:353–359, 2005)) for proving the decidability of a range of quantum logics, interpreted on finite-dimensional Hilbert spaces. We give general conditions for the applicability of this method, and in particular we apply it to prove the decidability of PLQP.     

Cluster analysis of an Ising-Preisach interacting particle system

The paper deals with the analysis of clusters' size in diverse magnetization states of a system of ferromagnetic particles organized in a perfect 2D array with all the anisotropy axes perpendicular to the plane (perpendicular medium) following the evolution of the clusters in correlation with various parameters like applied field or interaction strength. We present numerical simulations for a two-level Ising-type model each magnetic entity being characterized by a Stoner-Wohlfarth nonlinear energy barrier and a rectangular hysteresis loop (Ising-Preisach hysteron). In the simulations we took into account, the long-range inter-particle magnetostatic interactions in an attempt to mimic as accurately as possible with a still simple model, materials like Bit-Patterned media that are now considered as good candidates for the magnetic memories of the future.     

Differential forms on arithmetic jet spaces

We study derivations and differential forms on the arithmetic jet spaces of smooth schemes, relative to several primes. As applications, we give a new interpretation of arithmetic Laplacians, and we discuss the de Rham cohomology of some specific arithmetic jet spaces, especially arithmetic jet spaces of linear tori, elliptic curves, and Kummer surfaces.