Singular normal form for the Painlev\'e equation P1

We show that there exists a rational change of coordinates of Painlev\'e's P1 equation $y''=6y^2+x$ and of the elliptic equation $y''=6y^2$ after which these two equations become analytically equivalent in a region in the complex phase space where $y$ and $y'$ are unbounded. The region of equivalence comprises all singularities of solutions of P1 (i.e. outside the region of equivalence, solutions are analytic). The Painlev\'e property of P1 (that the only movable singularities are poles) follows as a corollary. Conversely, we argue that the Painlev\'e property is crucial in reducing P1, in a singular regime, to an equation integrable by quadratures

Methodological guidelines for the execution of laboratory work in the discipline «Basics of Digital Technologies» for undergraduate students of all NUWEE degree programmes of full-time and part-time forms of education. Module 2

Digital competence is a key competence of the fourth industrial revolution. Confident mastery and use of digital technologies for education, employment, work, leisure and participation in public life is critically important for every citizen of Ukraine. The aim of the course is to develop skills and abilities in such areas as: information and media literacy, communication and collaboration, creating digital content, protecting information in the digital environment, solving problems and lifelong learning. The course is based on the European conceptual framework of digital competences for EU citizens (DigComp 2.1.). The course "Basics of digital technologies" is divided into two content modules: 1. Digital technologies for working with text and data; 2. Creation and use of digital content. Mastering of each module is checked using test tasks in the Moodle environment. To successfully pass the course, the student must complete 15 laboratory works and pass two modules. Each laboratory work is evaluated in the range of 0-4 points. Each module - 0-20 points. To successfully pass the discipline, a student must score at least 60 points. The form of final control is an exam

Phase Diagram of the Spin-Orbital model on the Square Lattice

We study the phase diagram of the spin-orbital model in both the weak and strong limits of the quartic spin-orbital exchange interaction. This allows us to study quantum phase transitions in the model and to approach from both sides the most interesting intermediate-coupling regime and in particular the SU(4)-symmetric point of the Hamiltonian. It was suggested earlier by Li et al [Phys.Rev.Lett. vol. 81, 3527 (1999)] that at this point the ground state of the system is a plaquette spin-orbital liquid. We argue that the state is more complex. There is plaquette order, but it is anisotropic: bonds in one direction are stronger than those in the perpendicular direction. This order is somewhat similar to that found recently in the frustrated J_1-J_2 Heisenberg spin model.Comment: 8 pages, 4 Postscript figure

Structural and biophysical analysis of nuclease protein antibiotics

© 2016 The Author(s); published by Portland Press Limited on behalf of the Biochemical Society. Protein antibiotics (bacteriocins) are a large and diverse family of multidomain toxins that kill specific Gram-negative bacteria during intraspecies competition for resources. Our understanding of the mechanism of import of such potent toxins has increased significantly in recent years, especially with the reporting of several structures of bacteriocin domains. Less well understood is the structural biochemistry of intact bacteriocins and how these compare across bacterial species. Here, we focus on endonuclease (DNase) bacteriocins that target the genomes of Escherichia coli and Pseudomonas aeruginosa, known as E-Type colicins and S-Type pyocins, respectively, bound to their specific immunity (Im) proteins. First, we report the 3.2 Å structure of the DNase colicin ColE9 in complex with its ultra-high affinity Im protein, Im9. In contrast with Im3, which when bound to the ribonuclease domain of the homologous colicin ColE3 makes contact with the translocation (T) domain of the toxin, we find that Im9 makes no such contact and only interactions with the ColE9 cytotoxic domain are observed. Second, we report small-Angle X-ray scattering data for two S-Type DNase pyocins, S2 and AP41, into which are fitted recently determined X-ray structures for isolated domains. We find that DNase pyocins and colicins are both highly elongated molecules, even though the order of their constituent domains differs. We discuss the implications of these architectural similarities and differences in the context of the translocation mechanism of protein antibiotics through the cell envelope of Gram-negative bacteria

Comprehensive study of the magnetic stars HD 5797 and HD 40711 with large chromium and iron overabundances

We present the results of a comprehensive study of the chemically peculiar stars HD 5797 and HD 40711. The stars have the same effective temperature, Teff = 8900 K, and a similar chemical composition with large iron (+1.5 dex) and chromium (+3 dex) overabundances compared to the Sun. The overabundance of rare-earth elements typically reaches +3 dex. We have measured the magnetic field of HD 5797. The longitudinal field component Be has been found to vary sinusoidally between -100 and +1000 G with a period of 69 days. Our estimate of the evolutionary status of the stars suggests that HD 5797 and HD 40711, old objects with an age t \approx 5 \times 108 yr, are near the end of the core hydrogen burning phase.Comment: 26 pages, 5 Encapsulated Postscript figure

Toward a Midisuperspace Quantization of LeMaitre-Tolman-Bondi Collapse Models

LeMa\^\i tre-Tolman-Bondi models of spherical dust collapse have been used and continue to be used extensively to study various stellar collapse scenarios. It is by now well-known that these models lead to the formation of black holes and naked singularities from regular initial data. The final outcome of the collapse, particularly in the event of naked singularity formation, depends very heavily on quantum effects during the final stages. These quantum effects cannot generally be treated semi-classically as quantum fluctuations of the gravitational field are expected to dominate before the final state is reached. We present a canonical reduction of LeMa\^\i tre-Tolman-Bondi space-times describing the marginally bound collapse of inhomogeneous dust, in which the physical radius, $R$, the proper time of the collapsing dust, $\tau$, and the mass function, $F$, are the canonical coordinates, $R(r)$, $\tau(r)$ and $F(r)$ on the phase space. Dirac's constraint quantization leads to a simple functional (Wheeler-DeWitt) equation. The equation is solved and the solution can be employed to study some of the effects of quantum gravity during gravitational collapse with different initial conditions.Comment: 9 pages, 1 figure, Latex file. Minor corrections made. A general solution of the constraints is presented. Revised version to appear in Phys. Rev.

The first WASP public data release

The WASP (wide angle search for planets) project is an exoplanet transit survey that has been automatically taking wide field images since 2004. Two instruments, one in La Palma and the other in South Africa, continually monitor the night sky, building up light curves of millions of unique objects. These light curves are used to search for the characteristics of exoplanetary transits. This first public data release (DR1) of the WASP archive makes available all the light curve data and images from 2004 up to 2008 in both the Northern and Southern hemispheres. A web interface () to the data allows easy access over the Internet. The data set contains 3 631 972 raw images and 17 970 937 light curves. In total the light curves have 119 930 299 362 data points available between them

Dark pair coherent states of the motion of a trapped ion

We propose a scheme for generating vibrational pair coherent states of the motion of an ion in a two-dimensional trap. In our scheme, the trapped ion is excited bichromatically by three laser beams along different directions in the X-Y plane of the ion trap. We show that if the initial vibrational state is given by a two-mode Fock state, the final steady state, indicated by the extinction of the fluorescence emitted by the ion, is a pure state. The motional state of the ion in the equilibrium realizes that of the highly-correlated pair coherent state.Comment: 14 pages, 3 figure

Structures of the Ultra-High-Affinity Protein-Protein Complexes of Pyocins S2 and AP41 and Their Cognate Immunity Proteins from Pseudomonas aeruginosa

© 2015 The Authors. Published by Elsevier Ltd. How ultra-high-affinity protein-protein interactions retain high specificity is still poorly understood. The interaction between colicin DNase domains and their inhibitory immunity (Im) proteins is an ultra-high-affinity interaction that is essential for the neutralisation of endogenous DNase catalytic activity and for protection against exogenous DNase bacteriocins. The colicin DNase-Im interaction is a model system for the study of high-affinity protein-protein interactions. However, despite the fact that closely related colicin-like bacteriocins are widely produced by Gram-negative bacteria, this interaction has only been studied using colicins from Escherichia coli. In this work, we present the first crystal structures of two pyocin DNase-Im complexes from Pseudomonas aeruginosa, pyocin S2 DNase-ImS2 and pyocin AP41 DNase-ImAP41. These structures represent divergent DNase-Im subfamilies and are important in extending our understanding of protein-protein interactions for this important class of high-affinity protein complex. A key finding of this work is that mutations within the immunity protein binding energy hotspot, helix III, are tolerated by complementary substitutions at the DNase-Immunity protein binding interface. Im helix III is strictly conserved in colicins where an Asp forms polar interactions with the DNase backbone. ImAP41 contains an Asp-to-Gly substitution in helix III and our structures show the role of a co-evolved substitution where Pro in DNase loop 4 occupies the volume vacated and removes the unfulfilled hydrogen bond. We observe the co-evolved mutations in other DNase-Immunity pairs that appear to underpin the split of this family into two distinct groups

Shapiro Effect as a Possible Cause of the Low-Frequency Pulsar Timing Noise in Globular Clusters

A prolonged timing of millisecond pulsars has revealed low-frequency uncorrelated noise, presumably of astrophysical origin, in the pulse arrival time (PAT) residuals for some of them. In most cases, pulsars in globular clusters show a low-frequency modulation of their rotational phase and spin rate. The relativistic time delay of the pulsar signal in the curved space time of randomly distributed and moving globular cluster stars (the Shapiro effect) is suggested as a possible cause of this modulation. Given the smallness of the aberration corrections that arise from the nonstationarity of the gravitational field of the randomly distributed ensemble of stars under consideration, a formula is derived for the Shapiro effect for a pulsar in a globular cluster. The derived formula is used to calculate the autocorrelation function of the low-frequency pulsar noise, the slope of its power spectrum, and the behavior of the $\sigma_z$ statistic that characterizes the spectral properties of this noise in the form of a time function. The Shapiro effect under discussion is shown to manifest itself for large impact parameters as a low-frequency noise of the pulsar spin rate with a spectral index of n=-1.8 that depends weakly on the specific model distribution of stars in the globular cluster. For small impact parameters, the spectral index of the noise is n=-1.5.Comment: 23 pages, 6 figure