On the stationary flows of viscous,incompressible and heat-conducting fluids

We consider a boundary-value problem describing the motion of viscous, incompressible and heat-conducting fluids in a bounded domain in ?³. We admit non-homogeneous boundary conditions, the appearance of exterior forces and heat sources. Our aim is to prove the existence of a solution of the problem in Sobolev spaces.     

On Minimal Projections in l∞(n)

 In this paper we present an estimate of the relative projection constant for a particular class of subspaces of of codimension two. In some cases the exact value of will be calculated. Also Theorem 2.5 from [11] will be generalized.     

ContinuousK-theory

We study arithmetical properties of homotopy groups of thel-adic completion of Quillen'sK-theory space of number field, with a view on the Dwyer-Friedlander comparison map into étaleK-theory. The relation of these groups toK-theory is a complete analogy to the relation of continuous étale cohomology to étale cohomology. We identify the torsion subgroup of the resulting term with the subgroup of divisible elements inK _2n (F). We prove that this term is sent isomorphically into étaleK-theory, giving some further evidence for the Lichtenbaum-Quillen conjectures.     

Attenuation and modal dispersion models for spatially multiplexed co-propagating helical optical channels in step index fibers: Comment

We comment on a recent paper [J Opt Laser Technol 43 (2011) 430–436] in which the authors introduce dispersion and attenuation models of spatially multiplexed channels in step index multimode fibers. We consider the theoretical explanation of the model given in the paper incorrect.     

Real-World Data Difficulty Estimation with the Use of Entropy

In the era of the Internet of Things and big data, we are faced with the management of a flood of information. The complexity and amount of data presented to the decision-maker are enormous, and existing methods often fail to derive nonredundant information quickly. Thus, the selection of the most satisfactory set of solutions is often a struggle. This article investigates the possibilities of using the entropy measure as an indicator of data difficulty. To do so, we focus on real-world data covering various fields related to markets (the real estate market and financial markets), sports data, fake news data, and more. The problem is twofold: First, since we deal with unprocessed, inconsistent data, it is necessary to perform additional preprocessing. Therefore, the second step of our research is using the entropy-based measure to capture the nonredundant, noncorrelated core information from the data. Research is conducted using well-known algorithms from the classification domain to investigate the quality of solutions derived based on initial preprocessing and the information indicated by the entropy measure. Eventually, the best 25% (in the sense of entropy measure) attributes are selected to perform the whole classification procedure once again, and the results are compared.     

Einstein-Hopf drag,Doppler shift of thermal radiation and blackbody drag: Three perspectives on quantum friction

The thermal friction force acting on an atom moving relative to a thermal photon bath has recently been calculated on the basis of the fluctuation-dissipation theorem. The thermal fluctuations of the electromagnetic field give rise to a drag force on an atom provided one allows for dissipation of the field energy via spontaneous emission. The drag force exists if the atomic polarizability has a nonvanishing imaginary part. Here, we explore alternative derivations. The damping of the motion of a simple harmonic oscillator is described by radiative reaction theory (result of Einstein and Hopf), taking into account the known stochastic fluctuations of the electromagnetic field. Describing the excitations of the atom as an ensemble of damped harmonic oscillators, we identify the previously found expressions as generalizations of the Einstein-Hopf result. In addition, we present a simple explanation for blackbody friction in terms of a Doppler shift of the thermal radiation in the inertial frame of the moving atom: The atom absorbs blue-shifted photons from the front and radiates off energy in all directions, thereby losing energy. The original plus the two alternative derivations provide for additional confirmation of an intriguing quantum friction effect, and leave no doubt regarding its existence.     

Critical circle maps near bifurcation

We estimate harmonic scalings in the parameter space of a one-parameter family of critical circle maps. These estimates lead to the conclusion that the Hausdorff dimension of the complement of the frequency-locking set is less than 1 but not less than 1/3. Moreover, the rotation number is a Hölder continuous function of the parameter.Partially supported by KBN grant Iteracje i Fraktale #210909101.Partially supported by NSF Grant #DMS-9206793 and the Sloan Research Fellowship.     

Analysis of nanopore arrangement and structural features of anodic alumina layers formed by two-step anodizing in oxalic acid using the dedicated executable software

Anodic porous alumina layers were fabricated by a two-step self-organized anodization in 0.3 M oxalic acid under various anodizing potentials ranging from 30 to 60 V at two different temperatures (10 and 17 ^°C). The effect of anodizing conditions on structural features and pore arrangement of AAO was investigated in detail by using the dedicated executable publication combined with ImageJ software. With increasing anodizing potential, a linear increase of the average pore diameter, interpore distance, wall thickness and barrier layer thickness, as well as a decrease of the pore density, were observed. In addition, the higher pore diameter and porosity values were obtained for samples anodized at the elevated temperature, independently of the anodizing potential. A degree of pore order was investigated on the basis of Delaunay triangulations (defect maps) and calculation of pair distribution or angle distribution functions (PDF or ADF), respectively. All methods confirmed that in order to obtain nanoporous alumina with the best, hexagonal pore arrangement, the potential of 40 V should be applied during anodization. It was confirmed that the dedicated executable publication can be used to a fast and complex analysis of nanopore arrangement and structural features of nanoporous oxide layers.     

On the Ehrenfeucht–Mycielski sequence

We introduce the inverted prefix tries (a variation of suffix tries) as a convenient formalism for stating and proving properties of the Ehrenfeucht–Mycielski sequence [A. Ehrenfeucht, J. Mycielski, A pseudorandom sequence—how random is it? American Mathematical Monthly 99 (1992) 373-375]. We also prove an upper bound on the position in the sequence by which all strings of a given length will have appeared; our bound is given by the Ackermann function, which, in light of experimental data, may be a gross over-estimate. Still, it is the best explicitly known upper bound at the moment. Finally, we show how to compute the next bit in the sequence in a constant number of operations.