On finite groups with disconnected prime graph

All finite simple nonabelian groups that have the same prime graph as a Frobenius group or a 2-Frobenius group are found. © 2013 Pleiades Publishing, Ltd

Minimal Committee Problem for Inconsistent Systems of Linear Inequalities on the Plane

A representation of an arbitrary system of strict linear inequalities in R^n as a system of points is proposed. The representation is obtained by using a so-called polarity. Based on this representation an algorithm for constructing a committee solution of an inconsistent plane system of linear inequalities is given. A solution of two problems on minimal committee of a plane system is proposed. The obtained solutions to these problems can be found by means of the proposed algorithm.Comment: 29 pages, 2 figure

Interpretation of contradictory images by means of systems of linear inequalities

We consider the problem of interpretation of three-dimensional images from their flat projections up to the set of visible faces. For projections of convex polyhedra, we present an interpretation algorithm based on maximal feasible subsystems of a certain infeasible system of linear inequalities modeling the visibility requirement for faces. A number of model examples are given; in particular, the algorithm is applied to the interpretation of the Necker cube. © 2013 Pleiades Publishing, Ltd

Design and Goedel theorems

Рассматриваются математические модели восприятия текстов, основанные на распознавании образов и математической логике, а также на пределах формализации.The mathematical models are proposed, described the perception processes through pattern recognition and mathematical logics, and limits of formalization

Unsolved Problems in Group Theory. The Kourovka Notebook

This is a collection of open problems in group theory proposed by hundreds of mathematicians from all over the world. It has been published every 2-4 years in Novosibirsk since 1965. This is the 19th edition, which contains 111 new problems and a number of comments on about 1000 problems from the previous editions.Comment: A few new solutions and references have been added or update

Observation of the decay Bc→J/ψK+K−π+B_c \rightarrow J/\psi K^+ K^- \pi^+

The decay $B_c\rightarrow J/\psi K^+ K^- \pi^+$ is observed for the first time, using proton-proton collisions collected with the LHCb detector corresponding to an integrated luminosity of 3fb$^{-1}$. A signal yield of $78\pm14$ decays is reported with a significance of 6.2 standard deviations. The ratio of the branching fraction of \B_c \rightarrow J/\psi K^+ K^- \pi^+ decays to that of $B_c \rightarrow J/\psi \pi^+$ decays is measured to be $0.53\pm 0.10\pm0.05$, where the first uncertainty is statistical and the second is systematic.Comment: 18 pages, 2 figure

Measurements of the branching fractions of B+→ppK+ decays

The branching fractions of the decay B+ → pp̄K+ for different intermediate states are measured using data, corresponding to an integrated luminosity of 1.0 fb-1, collected by the LHCb experiment. The total branching fraction, its charmless component Mpp̄ < 2.85 GeV/c2 and the branching fractions via the resonant cc̄ states η c(1S) and ψ(2S) relative to the decay via a J/ψ intermediate state are [Equation not available: see fulltext.] Upper limits on the B + branching fractions into the η c(2S) meson and into the charmonium-like states X(3872) and X(3915) are also obtained

Observation of J/ψpJ/\psi p resonances consistent with pentaquark states in Λb0→J/ψK−p{\Lambda_b^0\to J/\psi K^-p} decays

Observations of exotic structures in the $J/\psi p$ channel, that we refer to as pentaquark-charmonium states, in $\Lambda_b^0\to J/\psi K^- p$ decays are presented. The data sample corresponds to an integrated luminosity of 3/fb acquired with the LHCb detector from 7 and 8 TeV pp collisions. An amplitude analysis is performed on the three-body final-state that reproduces the two-body mass and angular distributions. To obtain a satisfactory fit of the structures seen in the $J/\psi p$ mass spectrum, it is necessary to include two Breit-Wigner amplitudes that each describe a resonant state. The significance of each of these resonances is more than 9 standard deviations. One has a mass of $4380\pm 8\pm 29$ MeV and a width of $205\pm 18\pm 86$ MeV, while the second is narrower, with a mass of $4449.8\pm 1.7\pm 2.5$ MeV and a width of $39\pm 5\pm 19$ MeV. The preferred $J^P$ assignments are of opposite parity, with one state having spin 3/2 and the other 5/2.Comment: 48 pages, 18 figures including the supplementary material, v2 after referee's comments, now 19 figure

Observation of the decay B+c→Bºsπ+

The result of a search for the decay B+c→Bºsπ+ is presented, using the Bºs→Ds-π+ and Bºs→J/ψϕ channels. The analysis is based on a data sample of pp collisions collected with the LHCb detector, corresponding to an integrated luminosity of 1  fb-1 taken at a center-of-mass energy of 7 TeV, and 2  fb-1 taken at 8 TeV. The decay B+c→Bºsπ+ is observed with significance in excess of 5 standard deviations independently in both decay channels. The measured product of the ratio of cross sections and branching fraction is [σ(Bc+)/σ(Bºs)]×B(Bc+→Bºsπ+)=[2.37±0.31 (stat)±0.11 (syst)-0.13+0.17(τBc+)]×10-3, in the pseudorapidity range 2<η(B)<5, where the first uncertainty is statistical, the second is systematic, and the third is due to the uncertainty on the Bc+ lifetime. This is the first observation of a B meson decaying to another B meson via the weak interaction