Boundary values of analytic functions

It is known that a complex — valued continuous functionS(x) as well as a Schwartz distribution on the real axis can be extended in the complex plane minus the support ofS to an analytic function?(z). In the case of a continuous function the jump of?(z) on the real axis represents exactlyS(x): $$\mathop {\lim }\limits_{\varepsilon \to 0 + } [\hat S(x + i\varepsilon ) - \hat S(x - i\varepsilon )] = S(x)$$ . We call regular a pointx on the support ofS such that \(\mathop {\lim }\limits_{\varepsilon \to 0 + } [\hat S(x + i\varepsilon ) - \hat S(x - i\varepsilon )]\) exists. Conditions are found for the existence of regular points on the support of a distribution. It is possible to call this limit (if this exists) the valueS(x) of the distributionS in the pointx. Properties of this type occur in the theory of dispersion relations.     

Cyclic Hilbert Spaces and Connes’ Embedding Problem

Let M be a II ₁-factor with trace τ, the finite dimensional subspaces of L ²(M, τ) are not just common Hilbert spaces, but they have an additional structure. We introduce the notion of a cyclic linear space by taking these additional properties as axioms. In Sect. 3 we formulate the following problem: “does every cyclic Hilbert space embed into L ²(M, τ), for some M?”. An affirmative answer would imply the existence of an algorithm to check Connes’ embedding Conjecture. In Sect. 4 we make a first step towards the answer of the previous question.     

A numerical investigation on the dynamic stall of a vertical axis wind turbine

In the last years, for home user, the wind turbine with vertical axis (VAWT) began to be more attractive due benefits in exploitation. In terms of aerodynamics, when the wind speed approaches the speed of operation (low value of tip speed ratio -TSR) the blade airfoil exceeds the critical angle of incidence for static conditions. Angle of incidence varies quickly across blade and the blade works in dynamic stall condition. The goal of the present work is to investigate the two-dimensional dynamic stall phenomenon around the NACA 0012 airfoil at relatively low Reynolds. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Unsteady Flow and its Influence to Aerodynamic and Aeroacoustic of VAWT's

A study is reported of the influence of unsteady flow on the aerodynamics and aeroacoustics of vertical axis wind turbines by numerical simulation. The combination of aerodynamic predictions with a discrete vortex method and aeroacoustic predictions based on Ffowcs Williams-Hawkings equation is used to achieve this goal. The numerical results show that unsteady flow of the turbine has a significant influence on the turbine aerodynamics and can lead to a decrease in generated noise as compared to the conventional horizontal axis wind turbine at the similar aerodynamic performance. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimization strategy based on genetic algorithms and neural networks applied to a polymerization process

The article presents a simple and general methodology, especially destined to the optimization of complex, strongly nonlinear systems, for which no extensive knowledge or precise models are available. The optimization problem is solved by means of a simple genetic algorithm, and the results are interpreted both from the mathematical point of view (the minimization of the objective function) and technological (the estimation of the achievement of individual objectives in multiobjective optimization). The use of a scalar objective function is supported by the fact that the genetic algorithm also computes the weights attached to the individual objectives along with the optimal values of the decision variables. The optimization strategy is accomplished in three stages: (1) the design and training of the neural model by a new method based on a genetic algorithm where information about the network is coded into the chromosomes; (2) the actual optimization based on genetic algorithms, which implies testing different values for parameters and different variants of the algorithm, computing the weights of the individual objectives and determining the optimal values for the decision variables; (3) the user's decision, who chooses a solution based on technological criteria. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Generalized (anti) Yetter-Drinfeld modules as components of a braided T-category

If H is a Hopf algebra with bijective antipode and α, β ∈ Aut _Hopf (H), we introduce a category , generalizing both Yetter-Drinfeld modules and anti-Yetter-Drinfeld modules. We construct a braided T-category having all the categories as components, which, if H is finite dimensional, coincides with the representations of a certain quasitriangular T-coalgebra DT(H) that we construct. We also prove that if (α, β) admits a so-called pair in involution, then is isomorphic to the category of usual Yetter-Drinfeld modules . Research partially supported by the programme CERES of the Romanian Ministry of Education and Research, contract no. 4-147/2004.     

Surface hydrophobicity modulates the operation of actomyosin-based dynamic nanodevices

We studied the impact of surface hydrophobicity on the motility of actin filaments moving on heavy-meromyosin (HMM)-coated surfaces. Apart from nitrocellulose (NC), which is the current standard for motility assays, all materials tested are good candidates for microfabrication: hydrophilic and hydrophobic glass, poly(methyl methacrylate) (PMMA), poly(tert-butyl methacrylate) (PtBuMA), and a copolymer of O-acryloyl acetophenone oxime with a 4-acryloyloxybenzophenone (AAPO). The most hydrophilic (hydrophilic glass, contact angle 35 degrees) and the most hydrophobic (PtBuMA, contact angle 78 degrees) surfaces do not maintain the motility of actin filaments, presumably because of the low density of adsorbed HMM protein or its high levels of denaturation, respectively. The velocity of actin filaments presents higher values in the middle of this "surface hydrophobicity motility window" (NC, PMMA), and a bimodal distribution, which is more apparent at the edges of this motility window (hydrophobic glass and AAPO). A molecular surface analysis of HMM and its S1 units suggests that the two very different, temporally separated conformations of the HMM heads could exacerbate the surface-modulated protein behavior, which is common to all microdevices using surface-immobilized proteins. An explanation for the above behavior proposes that the motility of actin filaments on HMM-functionalized surfaces is the result of the action of three populations of motors, each in a different surface-protein conformation, that is, HMM with both heads working (high velocities), working with one head (low velocities), and fully denatured HMM (no motility). It is also proposed that the molecularly dynamic nature of polymer surfaces amplifies the impact of surface hydrophobicity on protein behavior. The study demonstrates that PMMA is a good candidate for the fabrication of future actomyosin-driven dynamic nanodevices because it induces the smoothest motility of individual nano-objects with velocities comparable with those obtained on NC.     

The Distribution of the Free Path Lengths in the Periodic Two-Dimensional Lorentz Gas in the Small-Scatterer Limit

We study the free path length and the geometric free path length in the model of the periodic two-dimensional Lorentz gas (Sinai billiard). We give a complete and rigorous proof for the existence of their distributions in the small-scatterer limit and explicitly compute them. As a corollary one gets a complete proof for the existence of the constant term in the asymptotic formula of the KS entropy of the billiard map in this model, as conjectured by P. Dahlqvist.In memory of Walter Philipp