Counting master integrals: Integration by parts vs. functional equations

We illustrate the usefulness of functional equations in establishing relationships between master integrals under the integration-by-parts reduction procedure by considering a certain two-loop propagator-type diagram as an example.Comment: 8 pages, 1 figur

Functional equations for one-loop master integrals for heavy-quark production and Bhabha scattering

The method for obtaining functional equations, recently proposed by one of the authors, is applied to one-loop box integrals needed in calculations of radiative corrections to heavy-quark production and Bhabha scattering. We present relationships between these integrals with different arguments and box integrals with all propagators being massless. It turns out that functional equations are rather useful for finding imaginary parts and performing analytic continuations of Feynman integrals. For the box master integral needed in Bhabha scattering, a new representation in terms of hypergeometric functions admitting one-fold integral representation is derived. The hypergeometric representation of a master integral for heavy-quark production follows from the functional equation.Comment: 14 pages, 3 figure

Simple energy barrier for component mixture of natural gases

This paper investigates the ability of a test molecule to overcome the energy barrier being in the gap between spherical nanoparticles. Three particles make a primitive structural element of composite porous material. The ability of molecules to converge with nanoparticles and then to move through more powerful repulsion field defines the filtration properties of porous materials. This paper presents the investigation of carbon nanoparticles and molecules of helium and methane bombarding them. Calculations proved that methane molecules can not get through three particles if the gap equals to 3.5 nm. For helium molecules this value makes 1.02 nm. These gaps remain the same when the size of nanoparticles increases. Therefore filters for helium separated from natural gas are to have nanopores within the range from 1.02 nm to 3.5 nm

Comprehensive assessment of deformation of rigid reinforcing system during convergence of mine shaft lining in unstable rocks

Operation of vertical mine shafts in complex mining and geological conditions is associated with a number of features. One of them is a radial displacement of the concrete shaft lining, caused by the influence of mining pressure on the stress-strain state of the mine workings. A rigid reinforcing system with shaft buntons fixed in the concrete lining thus experiences elastoplastic deformations, their value increases with time. It results in deviation of conductors from design parameters, weakening of bolt connections, worsening of dynamic properties of geotechnical system “vehicle – reinforcing”, increase of wear rate of reinforcing system elements, increase of risks for creating an emergency situation. The article offers a comprehensive assessment of displacements of characteristic points of the bunton system based on approximate engineering relations, numerical modeling of the deformation process of the bunton system and laser measurements of the convergence of the inner surface of the concrete shaft lining. The method was tested on the example of the reinforcing system of the skip-cage shaft of the potash mine. Displacement of the characteristic points of the reinforcing system is determined by the value of radial displacements of the surface of the concrete shaft lining. Evaluation of the radial displacements was made using monitoring measurements and profiling data. The results obtained make it possible to justify the need and timing of repair works. It is shown that the deterioration of the reinforcing system at different levels occurs at different rates, defined, among other things, by mechanical properties of the rock mass layers located at a given depth

14-(2,3-Dichloro­phen­yl)-9,10-dimethyl­benzimidazo[1,2-a]benzo[f][1,8]naphthyridine-6-carbonitrile

In the title compound, C27H16Cl2N4, the benzimidazo[1,2-a]benzo[f][1,8]naphthyridine system is nearly planar (r.m.s. deviation for all non-H atoms = 0.033 Å). The dichloro­phenyl substituent is rotated by −67.5 (2)° from this plane. In the crystal structure, mol­ecules form stacks along the crystallographic (100) direction due to π–π stacking inter­actions with a centroid–centroid distance of 3.4283 (9) Å

Finding new relationships between hypergeometric functions by evaluating Feynman integrals

Several new relationships between hypergeometric functions are found by comparing results for Feynman integrals calculated using different methods. A new expression for the one-loop propagator-type integral with arbitrary masses and arbitrary powers of propagators is derived in terms of only one Appell hypergeometric function F_1. From the comparison of this expression with a previously known one, a new relation between the Appell functions F_1 and F_4 is found. By comparing this new expression for the case of equal masses with another known result, a new formula for reducing the F_1 function with particular arguments to the hypergeometric function _3F_2 is derived. By comparing results for a particular one-loop vertex integral obtained using different methods, a new relationship between F_1 functions corresponding to a quadratic transformation of the arguments is established. Another reduction formula for the F_1 function is found by analysing the imaginary part of the two-loop self-energy integral on the cut. An explicit formula relating the F_1 function and the Gaussian hypergeometric function _2F_1 whose argument is the ratio of polynomials of degree six is presented.Comment: 14 pages, 3 figure

Genome Sequencing and Comparative Analysis of Saccharomyces cerevisiae Strains of the Peterhof Genetic Collection

The Peterhof genetic collection of Saccharomyces cerevisiae strains (PGC) is a large laboratory stock that has accumulated several thousands of strains for over than half a century. It originated independently of other common laboratory stocks from a distillery lineage (race XII). Several PGC strains have been extensively used in certain fields of yeast research but their genomes have not been thoroughly explored yet. Here we employed whole genome sequencing to characterize five selected PGC strains including one of the closest to the progenitor, 15V-P4, and several strains that have been used to study translation termination and prions in yeast (25-25-2V-P3982, 1B-D1606, 74-D694, and 6P-33G-D373). The genetic distance between the PGC progenitor and S288C is comparable to that between two geographically isolated populations. The PGC seems to be closer to two bakery strains than to S288C-related laboratory stocks or European wine strains. In genomes of the PGC strains, we found several loci which are absent from the S288C genome; 15V-P4 harbors a rare combination of the gene cluster characteristic for wine strains and the RTM1 cluster. We closely examined known and previously uncharacterized gene variants of particular strains and were able to establish the molecular basis for known phenotypes including phenylalanine auxotrophy, clumping behavior and galactose utilization. Finally, we made sequencing data and results of the analysis available for the yeast community. Our data widen the knowledge about genetic variation between Saccharomyces cerevisiae strains and can form the basis for planning future work in PGC-related strains and with PGC-derived alleles.PBD acknowledges the Russian Foundation for Basic Research (www.rfbr.ru) for grant 14-04-31265. OVT and SGIV acknowledge the Russian Foundation for Basic Research for grant 15-29-02526. JVS acknowledges the Russian Science Foundation (www.rscf.ru) for grant 14-50-00069 and the Saint-Petersburg State University for grant 1.38.426.2015. PBD, AGM, EAR, and JVS acknowledge the Saint-Petersburg State University for research grant 1.37.291.2015. PBD and OVT acknowledge the Saint-Petersburg City Committee on Science and High School (knvsh.gov.spb.ru/) for grants 15404 and 15919, respectively. PBD, AGM, JVS, and SGIV acknowledge the Saint-Petersburg State University for research grant 15.61.2218.2013. PBD acknowledges the Saint-Petersburg State University for research grant 1.42.1394.2015

Magnetic Dirac semimetal state of (Mn,Ge)Bi2_2Te4_4

For quantum electronics, the possibility to finely tune the properties of magnetic topological insulators (TIs) is a key issue. We studied solid solutions between two isostructural Z$_2$ TIs, magnetic MnBi$_2$Te$_4$ and nonmagnetic GeBi$_2$Te$_4$, with Z$_2$ invariants of 1;000 and 1;001, respectively. For high-quality, large mixed crystals of Ge$_x$Mn$_{1-x}$Bi$_2$Te$_4$, we observed linear x-dependent magnetic properties, composition-independent pairwise exchange interactions along with an easy magnetization axis. The bulk band gap gradually decreases to zero for $x$ from 0 to 0.4, before reopening for $x>0.6$, evidencing topological phase transitions (TPTs) between topologically nontrivial phases and the semimetal state. The TPTs are driven purely by the variation of orbital contributions. By tracing the x-dependent $6p$ contribution to the states near the fundamental gap, the effective spin-orbit coupling variation is extracted. As $x$ varies, the maximum of this contribution switches from the valence to the conduction band, thereby driving two TPTs. The gapless state observed at $x=0.42$ closely resembles a Dirac semimetal above the Neel temperature and shows a magnetic gap below, which is clearly visible in raw photoemission data. The observed behavior of the Ge$_x$Mn$_{1-x}$Bi$_2$Te$_4$ system thereby demonstrates an ability to precisely control topological and magnetic properties of TIs

Site- and spin-dependent coupling at the highly ordered h-BN/Co(0001) interface

Using photoelectron diffraction and spectroscopy, we explore the structural and electronic properties of the hexagonal boron nitride (h-BN) monolayer epitaxially grown on the Co(0001) surface. Perfect matching of the lattice parameters allows formation of a well-defined interface where the B atoms occupy the hollow sites while the N atoms are located above the Co atoms. The corrugation of the h-BN monolayer and its distance from the substrate were determined by means of R-factor analysis. The obtained results are in perfect agreement with the density functional theory (DFT) predictions. The electronic structure of the interface is characterized by a significant mixing of the h-BN and Co states. Such hybridized states appear in the h-BN band gap. This allows to obtain atomically resolved scanning tunneling microscopy (STM) images from the formally insulating 2D material being in contact with ferromagnetic metal. The STM images reveal mainly the nitrogen sublattice due to a dominating contribution of nitrogen orbitals to the electronic states at the Fermi level. We believe that the high quality, well-defined structure and interesting electronic properties make the h-BN/Co(0001) interface suitable for spintronic applications.L.V.Ya. acknowledges the RSF (Grant No. 16-42-01093). A.V.T., V.O.S., K.A.B., O.Yu.V., and D.Yu.U. acknowledge St. Petersburg State University for research Grant No. 11.65.42.2017. M.V.K. and I.I.O. acknowledge the RFBR (Grant No. 16-29-06410). C.L. acknowledges the DFG (Grant Nos. LA655-17/1 and LA655-19/1).Peer reviewe