Characterizing W2,pW^{2,p}~submanifolds by pp-integrability of global curvatures

We give sufficient and necessary geometric conditions, guaranteeing that an immersed compact closed manifold $\Sigma^m\subset \R^n$ of class $C^1$ and of arbitrary dimension and codimension (or, more generally, an Ahlfors-regular compact set $\Sigma$ satisfying a mild general condition relating the size of holes in $\Sigma$ to the flatness of $\Sigma$ measured in terms of beta numbers) is in fact an embedded manifold of class $C^{1,\tau}\cap W^{2,p}$, where $p>m$ and $\tau=1-m/p$. The results are based on a careful analysis of Morrey estimates for integral curvature--like energies, with integrands expressed geometrically, in terms of functions that are designed to measure either (a) the shape of simplices with vertices on $\Sigma$ or (b) the size of spheres tangent to $\Sigma$ at one point and passing through another point of $\Sigma$. Appropriately defined \emph{maximal functions} of such integrands turn out to be of class $L^p(\Sigma)$ for $p>m$ if and only if the local graph representations of $\Sigma$ have second order derivatives in $L^p$ and $\Sigma$ is embedded. There are two ingredients behind this result. One of them is an equivalent definition of Sobolev spaces, widely used nowadays in analysis on metric spaces. The second one is a careful analysis of local Reifenberg flatness (and of the decay of functions measuring that flatness) for sets with finite curvature energies. In addition, for the geometric curvature energy involving tangent spheres we provide a nontrivial lower bound that is attained if and only if the admissible set $\Sigma$ is a round sphere.Comment: 44 pages, 2 figures; several minor correction

Recent Labour Market Trends in the Visegrad Group Countries

The large declines in the Slovak and Czech employment appeared because the countries' GDPs grew smaller while real wages grew bigger. Shorter working hours and limitations on labour productivity that the two countries introduced could not reverse the unfavourable employment trends that occurred during economic downturn.Duże spadki zatrudnienia w Słowacji i Czechach były związane ze słabym wzrostem PKB i silnym wzrostem płac realnych. Redukcje czasu pracy i wydajności pracy nie były w stanie odwrócić niekorzystnych tendencji w zatrudnieniu

Featured Snippets Results in Google Web Search: An Exploratory Study

In this paper authors analyzed 163412 keywords and results with featured snippets collected from localized Polish Google search engine. A method-ology for retrieving data from Google search engine was proposed in terms of obtaining necessary data to study featured snippets. It was observed that almost half of featured snippets (48%) is taken from result on first ranking position. Furthermore, some correlations between prepositions and the most often appearing content words in keywords was discovered. Results show that featured snippets are often taken from trustworthy websites like e.g., Wikipedia and are mainly presented in form of a paragraph. Paragraph can be read by Google Assistant or Home Assistant with voice search. We conclude our findings with discussion and research limitations.Comment: 10 pages, 6 tables, accepted to conference ICMarktech'1

Structural and optical properties of as-grown and annealed Alq3 thin films

International audienc

Improved Unsteady RANS Models Applied to Jet Transverse to a Pipe Flow

An unsteady RANS model is developed in order to simulate the complex situations involving both free and bounded flows. This model tuned to catch coherent flow structures is developed both in the k-ε and k-l approaches. The full 3D geometry of a round jet exiting from a reservoir into a pipe has been computed. Periodic conditions are applied in order to compare with an experiments consisting of eight jets exiting in a cross pipe flow. Improvement has been obtained with this URANS turbulence model compared to RANS and good agreement compared with experiments has been obtained. Unsteady phenomena are reproduced by the model and provide more insight into the physical properties of the flow and of the transport of a passive scalar

Topological effects in the thermal properties of knotted polymer rings

The topological effects on the thermal properties of several knot configurations are investigated using Monte Carlo simulations. In order to check if the topology of the knots is preserved during the thermal fluctuations we propose a method that allows very fast calculations and can be easily applied to arbitrarily complex knots. As an application, the specific energy and heat capacity of the trefoil, the figure-eight and the $8_1$ knots are calculated at different temperatures and for different lengths. Short-range repulsive interactions between the monomers are assumed. The knots configurations are generated on a three-dimensional cubic lattice and sampled by means of the Wang-Landau algorithm and of the pivot method. The obtained results show that the topological effects play a key role for short-length polymers. Three temperature regimes of the growth rate of the internal energy of the system are distinguished.Comment: 7 pages, 12 figures, LaTeX + RevTeX. With respect to the first version, in the second version the text has been improved and all figures are now in black and whit

Studies of unicellular micro-organisms Saccharomyces cerevisiae by means of Positron Annihilation Lifetime Spectroscopy

Results of Positron Annihilation Lifetime Spectroscopy (PALS) and microscopic studies on simple microorganisms: brewing yeasts are presented. Lifetime of ortho - positronium (o-Ps) were found to change from 2.4 to 2.9 ns (longer lived component) for lyophilised and aqueous yeasts, respectively. Also hygroscopicity of yeasts in time was examined, allowing to check how water - the main component of the cell - affects PALS parameters, thus lifetime of o-Ps were found to change from 1.2 to 1.4 ns (shorter lived component) for the dried yeasts. The time sufficient to hydrate the cells was found below 10 hours. In the presence of liquid water an indication of reorganization of yeast in the molecular scale was observed. Microscopic images of the lyophilised, dried and wet yeasts with best possible resolution were obtained using Inverted Microscopy (IM) and Environmental Scanning Electron Microscopy (ESEM) methods. As a result visible changes to the surface of the cell membrane were observed in ESEM images.Comment: Nukleonika (2015

Compressive Sensing of Signals Generated in Plastic Scintillators in a Novel J-PET Instrument

The J-PET scanner, which allows for single bed imaging of the whole human body, is currently under development at the Jagiellonian University. The dis- cussed detector offers improvement of the Time of Flight (TOF) resolution due to the use of fast plastic scintillators and dedicated electronics allowing for sam- pling in the voltage domain of signals with durations of few nanoseconds. In this paper we show that recovery of the whole signal, based on only a few samples, is possible. In order to do that, we incorporate the training signals into the Tikhonov regularization framework and we perform the Principal Component Analysis decomposition, which is well known for its compaction properties. The method yields a simple closed form analytical solution that does not require iter- ative processing. Moreover, from the Bayes theory the properties of regularized solution, especially its covariance matrix, may be easily derived. This is the key to introduce and prove the formula for calculations of the signal recovery error. In this paper we show that an average recovery error is approximately inversely proportional to the number of acquired samples

Transparent amorphous zinc oxide thin films for NLO applications

This review focuses on the growth and optical properties of amorphous zinc oxide (ZnO) thin films. A high quality ZnO films fabricated by dip-coating (sol–gel) method were grown on quartz and glass substrates at temperature equal to 350 K. The amorphous nature of the films was verified by X-ray diffraction. Atomic Force Microscopy was used to evaluate the surface morphology of the films. The optical characteristics of amorphous thin films have been investigated in the spectral range 190–1100 nm. Measurement of the polarized optical properties was shows a high transmissivity (80–99%) and low absorptivity (<5%) in the visible and near infrared regions at different angles of incidence. Linear optical properties were investigated by classic and Time-Resolved Photoluminescence (TRPL) measurements. Photoluminescence spectrum exhibits a strong ultraviolet emission while the visible emission is very weak. An innovative TRPL technique has enabled the measurement of the photoluminescence decay time as a function of temperature. TRPL measurements reveal a multiexponential decay behavior typical for amorphous thin films. Second and third harmonic generation measurements were performed by means of the rotational Maker fringe technique using Nd:YAG laser at 1064 nm in picosecond regime for investigations of the nonlinear optical properties. The obtained values of second and third order nonlinear susceptibilities were found to be high enough for the potential applications in the optical switching devices based on refractive index changes. Presented spectra confirm high structural and optical quality of the investigated zinc oxide thin films