Abstract:
We review the theory of relaxational kinetics of superfluid turbulence--a tangle of quantized vortex lines--in the limit of very low temperatures when the motion of vortices is conservative. While certain important aspects of the decay depend on whether the tangle is non-structured, like the one in the Kibble-Zurek picture, or essentially polarized, like the one that emulates the Richardson-Kolmogorov regime of classical turbulence, there are common fundamental features. In both cases, there exists an asymptotic range in the wavenumber space where the energy flux is supported by the cascade of Kelvin waves (kelvons)--precessing distortions propagating along the vortex filaments. At large enough wavenumbers, the Kelvin-wave cascade is supported by three-kelvon elastic scattering. At T=0 the dissipative cutoff of the Kelvin-wave cascade is due to the emission of phonons, in which an elementary process converts two kelvons with almost opposite momenta into one bulk phonon. Along with the standard set of conservation laws, a crucial role in the theory is played by the fact of integrability of the local induction approximation (LIA) controlled by the parameter \Lambda = \ln (\lambda/a_0), with \lambda the characteristic kelvon wavelength and a_0 the vortex core radius. While excluding a straightforward onset of the pure three-kelvon cascade, the integrability of LIA does not plug the cascade because of the availability of the kinetic channels associated with vortex line reconnections. We argue that the crossover from Richardson-Kolmogorov to the Kelvin-wave cascade is due to eventual dominance of local induction of a single line over the collective induction of polarized eddies, which causes the breakdown of classical-fluid regime and gives rise to a reconnection-driven inertial range.

Abstract:
The paper presents possibilities of creating wax founding models by means of CPX3000 device. The device is used for Rapid Prototypingof models made of foundry wax in an incremental process. The paper also presents problems connected with choosing technologicalparameters for incremental shaping which influence the accuracy of created models. Issues connected with post-processing are alsodescribed. This process is of great importance for obtaining geometrically correct models. The analysis of parameters of cleaning models from supporting material is also presented. At present CPX3000 printer is the first used in Poland device by 3D Systems firm for creating wax models. The printer is at The Faculty of Mechanical Engineering at Rzeszów University of Technology.

Abstract:
The paper presents an analysis incremental methods of creating wax founding models. There are two methods of Rapid Prototypingof wax models in an incremental process which are more and more often used in industrial practice and in scientific research.Applying Rapid Prototyping methods in the process of making casts allows for acceleration of work on preparing prototypes. It isespecially important in case of element having complicated shapes. The time of making a wax model depending on the size and the appliedRP method may vary from several to a few dozen hours.

Abstract:
The article presents analysis of geometrical precision of casting form made by means of 3DP method. Three dimentional printing is a universal method of rapid prototyping which can be used to make tools – castings forms as a Rapid Tooling method. By means of this method in direct incremental process a casting form of spur gear was created. Precision of creating the form by 3DP method depends on different factors. Technological factors depending on machine operator include: the thickness of the layer and placing the model in working space. The precision of creating the model also depends on preparing the printer for work: the condition and calibration of printing heads, the condition of the printing unit slide guides and preparing the working space. Three dimentional printer Z510 Spectrum was prepared for work in a way assuring the greatest precision of created models. Technological parameters responsible for precision were set on maximum values. The aim of the research was defining the precision of casting form generated by 3DP Rapid Prototyping Method. The research was made by means of coordinate measuring machine Wenzel LH87. The measuring machine software was used to compare the outcome of the measurement to nominal model 3D-CAD. The problem of tool precision of casting forms generated by Rapid Tooling is rarely considered in literature covering rapid prototyping and casting technologies. That is why the research presented in this article isan original work in the technological and practical aspect.

Abstract:
In Polonia, a partire dal 2009/2010, i docenti della scuola pubblica possono utilizzare manuali didattici per l’insegnamento delle lingue solo se approvati dal Ministero e accompagnati da un programma. Il lavoro svolto da D. Kozik ha l’obiettivo, partendo dal manuale Affresco Italiano, di essere guida e strumento per la pianificazione di percorsi e la produzione di attività didattiche per l’insegnamento/apprendimento dell’italiano LS. Per la stesura sono stati presi in considerazione sia le indicazioni del Quadro Comune Europeo di riferimento sia i suggerimenti di alcuni sillabi per l’italiano L2/LS e da questo confronto è nato uno strumento flessibile e rigoroso che il Ministero polacco ha approvato. La versione integrale in lingua polacca è a disposizione in Intenet e sarà presto pubblicata.

Abstract:
We reveal the connection of the recent numerical observations of Krstulovic and Brachet [arXiv:1007.4441] with the general theory of relaxation kinetics of the strongly non-equilibrium Bose-Einstein condensates.

Abstract:
Let $m^*(n)$ be the minimum number of edges in an $n$-uniform simple hypergraph that is not two colorable. We prove that $m^*(n)=\Omega(4^n/\ln^2(n))$. Our result generalizes to $r$-coloring of $b$-simple uniform hypergraphs. For fixed $r$ and $b$ we prove that a maximum vertex degree in $b$-simple $n$-uniform hypergraph that is not $r$-colorable must be $\Omega(r^n /\ln(n))$. By trimming arguments it implies that every such graph has $\Omega((r^n /\ln(n))^{b+1/b})$ edges. For any fixed $r \geq 2$ our techniques yield also a lower bound $\Omega(r^n/\ln(n))$ for van der Waerden numbers $W(n,r)$.

Abstract:
Numerous programs exist for identifying regions of homology or collinearity between two genomes, including PipMaker [1,2], MUMmer [3,4], FORRepeats [5], REPuter [6,7], ADHoRe [8], GRIMM [9,10], BLASTZ [11] and PatternHunter [12]. Of course, not all of these serve the same needs. Programs designed to identify homologous regions by making sequence alignments (such as PipMaker and BLASTZ) may excel at accurately finding high-quality short alignments, but not at piecing together and reporting larger genomic-scale homologies. Programs designed to work with nucleotide data may not work with peptide data, or raw positional information such as marker positions. With increasing numbers of genomes being sequenced, it is becoming a more frequent task to identify very large, often multi-megabase, corresponding regions between two genomes. These are frequently interrupted by insertions, deletions, or small inversions in one or both genomes, but can nevertheless be considered to have recognizable common ancestry and genomic context, and to show approximate collinearity in gene order. These large chromosomal regions that are similar in content and organization are frequently referred to as synteny blocks [4,10,13-15] or, in the case of a comparison of a genome to itself, segmental duplications [16-19].Here we report two new programs, DiagHunter and GenoPix2D, which are distributed together, and may be used together or separately to explore comparative genomic data at genome-wide or single-gene scales. DiagHunter has several strengths for large-scale collinearity prediction: it is cross-platform (Windows, Unix, Linux, OS X, and others, requiring Perl and the GD module); it can easily and quickly handle large amounts of new genomic data; it can operate on protein, nucleotide, marker, or other data types; it includes BioPerl and Tcl/Tk-based scripts for processing various input data formats; and it generates simple text output consisting of lists of gene or nucleotide sequence or mar

Abstract:
We show that Monte Carlo sampling of the Feynman diagrammatic series (DiagMC) can be used for tackling hard fermionic quantum many-body problems in the thermodynamic limit by presenting accurate results for the repulsive Hubbard model in the correlated Fermi liquid regime. Sampling Feynman's diagrammatic series for the single-particle self-energy we can study moderate values of the on-site repulsion ($U/t \sim 4$) and temperatures down to $T/t=1/40$. We compare our results with high temperature series expansion and with single-site and cluster dynamical mean-field theory.

Abstract:
A key observable in strongly interacting resonant Fermi gases is the contact parameter C, which governs both the pair correlation function at short distances and the momentum distribution at large momenta. The temperature dependence of C was recently measured at unitarity, where existing theoretical predictions differ substantially. We report accurate data for the contact and the momentum distribution in the normal phase of the unitary gas, obtained by Bold Diagrammatic Monte Carlo. In our scheme, C is extracted from the pair correlation function, while the C/k^4 tail of the momentum distribution, being built in at the analytical level, is free of k-dependent noise.