Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds

Let M be a smooth compact and simply-connected manifold with simply-connected boundary \(\partial M\), r be a fixed odd natural number. We consider f, a \(C^1\) self-map of M, preserving \(\partial M\). Under the assumption that the dimension of M is at least 4, we define an invariant \(D_r(f;M,\partial M)\) that is equal to the minimal number of r-periodic points for all maps preserving \(\partial M\) and \(C^1\)-homotopic to f. As an application, we give necessary and sufficient conditions for a reduction of a set of r-periodic points to one point in the \(C^1\)-homotopy class.     

Measurements of CP-violating asymmetries in B0-->a1+/-(1260)pi-/+ decays

We present measurements of CP-violating asymmetries in the decay B(0)-->a(1)(+/-)(1260)pi(-/+) with a(1)(+/-)(1260)-->pi(-/+)pi(+/-)pi(+/-). The data sample corresponds to 384x10(6) BB[over ] pairs collected with the BABAR detector at the PEP-II asymmetric B factory at SLAC. We measure the CP-violating asymmetry A(CP)(a(1)pi)=-0.07+/-0.07+/-0.02, the mixing-induced CP violation parameter S(a(1)pi)=0.37+/-0.21+/-0.07, the direct CP violation parameter C(a(1)pi)=-0.10+/-0.15+/-0.09, and the parameters DeltaC(a(1)pi)=0.26+/-0.15+/-0.07 and DeltaS(a(1)pi)=-0.14+/-0.21+/-0.06. From these measured quantities we determine the angle alpha(eff)=78.6 degrees +/-7.3 degrees.     

The imprints of superstatistics in multiparticle production processes

We provide an update of the overview of imprints of Tsallis nonextensive statistics seen in a multiparticle production processes. They reveal an ubiquitous presence of power law distributions of different variables characterized by the nonextensivity parameter q > 1. In nuclear collisions one additionally observes a q-dependence of the multiplicity fluctuations reflecting the finiteness of the hadronizing source. We present sum rules connecting parameters q obtained from an analysis of different observables, which allows us to combine different kinds of fluctuations seen in the data and analyze an ensemble in which the energy (E), temperature (T) and multiplicity (N) can all fluctuate. This results in a generalization of the so called Lindhard’s thermodynamic uncertainty relation. Finally, based on the example of nucleus-nucleus collisions (treated as a quasi-superposition of nucleon-nucleon collisions) we demonstrate that, for the standard Tsallis entropy with degree of nonextensivity q < 1, the corresponding standard Tsallis distribution is described by q′ = 2 − q > 1.     

Multiple solutions and corresponding power output of a nonlinear bistable piezoelectric energy harvester

We examine multiple responses of a vibrational energy harvester composed of a verticalbeam and a tip mass. The beam is excited horizontally by a harmonic inertial force whilemechanical vibrational energy is converted to electrical power through a piezoelectricpatch. The mechanical resonator can be described by single or double well potentialsdepending on the gravity force from the tip mass. By changing the tip mass we examine theappearance of various solutions and their basins of attraction. Identification ofparticular solutions of the energy harvester is important as each solution may provide adifferent level of power output.     

Structural and optical properties of layers of pentacene formed by PLD method

Organic films fabrication offers the possibility of producing electronic devices of low weight, mechanical flexibility and low cost. One suitable material for organic film fabrigation which is the subject of the great interest is pentacene, because it is characterized by the large carrier mobility (∼1 cm²/Vs). In this work, the growth of pentacene layers using pulse laser deposition (PLD) on different substrates (glass/ITO, Si) is described and various processing parameters are investigated. Two pulsed YAG:Nd³⁺ laser wavelengths were used for the ablation of the PLD target: the first harmonic at 1064 nm aGn:dNdth3+e second at 532 nm. The structure of the layers formed was examined using SEM and RHEED methods. The results were compared with results of optical spectroscopy studies. It will be shown that layers deposed using second harmonics have a higher quality than those for first harmonic. The other PLD parametersalso have a strong influence on the structure quality of layers.      

An Air Permeability Study of Anisotropic Glass Wool Fibrous Products

This article reports an experimental study of the permeability of fibrous porous media based on air flow. Two glass wools have been analyzed in three different flow directions to evaluate their anisotropic structure. The usual flow theories such as Darcy’s law, valid for granular materials, have been shown to apply also to these fibrous media which is a more complex structure (fiber arrangement, high porous media,…). The intrinsic permeabilities and the anisotropic factors have been determined from an air permeability measurement based on a standard test for industrial fabrics. The experimental results have been compared to different models, showing the limits of some simplistic models when applied to our highly porous structures. One model, Kyan’s model based on the flow around submerged objects, was, however, found to agree with our experimental data. This study also demonstrates the interesting use of an experimental technique, which is air permeability measurement (water permeability is not adapted), in the investigation of flow phenomena in a fibrous medium.     

Transition to chaos and escape phenomenon in two-degrees-of-freedom oscillator with a kinematic excitation

We study the dynamics of a two-degrees-of-freedom (two-DOF) nonlinear oscillator representing a quarter-car model excited by a road roughness profile. Modeling the road profile by means of a harmonic function, we derive the Melnikov criterion for a system transition to chaos or escape. The analytically obtained estimations are confirmed by numerical simulations. To analyze the transient vibrations, we used recurrences.     

Filippov Lemma for certain second order differential inclusions

In the paper we give an analogue of the Filippov Lemma for the second order differential inclusions with the initial conditions y(0) = 0, y??(0) = 0, where the matrix A ?? ? ^d×d and multifunction is Lipschitz continuous in y with a t-independent constant l. The main result is the following: Assume that F is measurable in t and integrably bounded. Let y ₀ ?? W ^2,1 be an arbitrary function fulfilling the above initial conditions and such that where p ₀ ?? L ¹[0, 1]. Then there exists a solution y ?? W ^2,1 to the above differential inclusions such that a.e. in [0, 1], .     

On-Line Chain Partitions of Orders: A Survey

On-line chain partition is a two-player game between Spoiler and Algorithm. Spoiler presents, point by point, a partially ordered set. Algorithm assigns incoming points (immediately and irrevocably) to the chains which constitute a chain partition of the order. The value of the game for orders of width w is a minimum number val(w) such that Algorithm has a strategy using at most val(w) chains on orders of width at most w. There are many recent results about variants of the general on-line chain partition problem. With this survey we attempt to give an overview over the state of the art in this field. As particularly interesting aspects of the article we see: