How to assess and report the performance of a stochastic algorithm on a benchmark problem: mean or best result on a number of runs?

Some authors claim that reporting the best result obtained by a stochastic algorithm in a number of runs is more meaningful than reporting some central statistic. In this short note, we analyze and refute the main argument brought in favor of this statement.     

Differentiators and the geometry of polynomials

In 1959, Davis introduced the concept of a differentiator of an operator on a finite-dimensional Hilbert space. We prove that every such operator possesses a differentiator. We also use the theory of differentiators to solve several problems in the geometry of polynomials. For instance, we answer in the affirmative a twenty year old unsolved conjecture of Schoenberg, a related conjecture of Katsoprinakis and a fifty year old unsolved conjecture of De Bruijn and Springer.     

Isotopic production cross sections of residues in reactions induced by relativistic heavy ions with protons and deuterons

The isotopic production cross sections of heavy residues in relativistic heavy-ion collisions have been investigated in inverse kinematics. The primary reaction products were fully identified in mass and atomic number prior to beta decay using the fragment separator FRS. The huge collection of data obtained helps in the understanding of the two main reaction mechanisms involved: fragmentation and fission. These data provide basic information for future radioactive ion beam facilities and for technical applications like intense neutron sources by means of spallation targets.     

A non-isothermal Ginzburg–Landau model in superconductivity: Existence,uniqueness and asymptotic behaviour

In this paper we study a Ginzburg–Landau model which describes the behaviour of a superconducting material including thermal effects. We extend the traditional formulation of the problem, by introducing the temperature as an additional state variable. Accordingly, together with the Gor’kov–Eliashberg system, we introduce an evolution equation for the absolute temperature. We examine in detail the case which allows only variations of the concentration of superconducting electrons and of the temperature, neglecting the electromagnetic field. For this problem existence and uniqueness of the solution are shown. Finally we analyze the asymptotic behaviour of the solutions, proving that the system possesses a global attractor.     

New fir laser lines and frequency measurements from optically pumped13CD3OH3

We report the discovery of 57 new fir laser lines from¹³CD₃OH molecule optically pumped by a waveguide CO₂ laser of 300 MHz tunability. For all lines, precise frequency offset measurements between the CO₂ line center and the center of the absorbing¹³CD₃OH line were performed using the transferred Lamb-Dip technique. We have also measured directly the frequency of seven FIR laser lines by heterodyning with already known laser lines. We present a complete list of all known laser lines (134) and frequency measurements (24) for this molecule.Work supported by CNPq, FAPESP, FAEP-Brasil, and CNR-Italia     

Holographic dark energy and the universe expansion acceleration

By incorporating the holographic principle in a time-depending Λ-term cosmology, new physical bounds on the arbitrary parameters of the model can be obtained. Considering then the dark energy as a purely geometric entity, for which no equation of state has to be introduced, it is shown that the resulting range of allowed values for the parameters may explain both the coincidence problem and the universe accelerated expansion, without resorting to any kind of additional structures.     

Implementation of recycling routes for scanning probe microscopy tips.

In this work, effective, yet simple, recycling mechanisms for used scanning probe microscopy (SPM) tips were implemented. Comprising a tip profile characterization methodology and specific cleaning procedures, which decontaminate SPM tips whether the contamination nature is known or not, such routes were optimized during numerous tests with brand new, previously used, and already discarded categories of SPM tips. The results show that if the used tip suffered contamination only, but no physical damages, during its scanning lifetime, it becomes readily available for reutilization after the cleansing process, characterizing a recycling route. On the other hand, if the tip went through wear and breakages during its utilization, it still can be decontaminated, but may not be directly reutilized due to its inadequate physical profile. Nevertheless, the methodology developed in this work may yet be applied as part of a more complex recycling route.     

Polynomial Stability to Three-Dimensional Magnetoelastic Waves

In this work we show that the energy associated to the linear three-dimensional magneto-elastic system decays polynomially to zero as time goes to infinity, provided the initial data is smooth enough.     

A purely algebraic characterization of the hyperreal numbers

The hyperreal numbers of nonstandard analysis are characterized in purely algebraic terms as homomorphic images of a suitable class of rings of functions.