Abstract: We give a counterexample to the following assertion from article I.E. Filippov and V.S. Mokeychev. The Least Root of a Continuous Function. Lobachevskii Journal of Mathematics, 2018, V. 39, No 2, P. 200–203: for every ε > 0 and every function g(τ, ξ) ∈ ℝ, ξ ∈ [a, b], continuous on a compact set Ω ⊂ ℝn and such that g(τ, a) · g(τ, b) < 0, there exist a function gε(τ, ξ) for which the least root ξ(τ) of the equation gε(τ, ξ) = 0 depends continuously on τ if g − gε C < ε. PubDate: 2018-11-01

Abstract: We consider the L2-critical nonlinear Schrödinger equation with an inhomogeneous damping coefficient a(x). We prove the global existence of the solution in H1(Rd) and we give the minimal time of the blow up for some initial data. PubDate: 2018-11-01

Abstract: We propose the conditions for a continuous function to be projection-convex, i.e. f(λp+ (1 − λ)q) ≤ λf(p) + (1 − λ)f(q) for any projections p and q and any real λ ∈ (0, 1). Also we obtain the characterization of projections commutativity and the characterization of trace in terms of equalities for non-flat functions. PubDate: 2018-11-01

Abstract: The purpose of this paper is to solve the spectral pollution. We suggest a modern method based on generalized spectral techniques, where we show that the propriety L is hold with norm convergence. In addition, we prove that under collectively compact convergence the proprieties U and L are hold. We describe the theoretical foundations of the method in details, as well as illustrate its effectiveness by numerical results. PubDate: 2018-11-01

Abstract: Slater introduced the point-addition operation on graphs to classify 4-connected graphs. The Γ-extension operation on binary matroids is a generalization of the point-addition operation. In this paper, we obtain necessary and sufficient conditions to preserve k-connectedness of a binary matroid under the Γ-extension operation. We also obtain a necessary and sufficient condition to get a connected matroid from a disconnected binary matroid using the Γ-extension operation. PubDate: 2018-11-01

Abstract: In this paper we study the topology of the Liouville foliation for the integrable case of Euler’s equations on the Lie algebra so(4) discovered by I.V. Komarov, which is a generalization of the Kovalevskaya integrable case in rigid body dynamics. We generalize some results by A.V. Bolsinov, P.H. Richter, and A.T. Fomenko about the topology of the classical Kovalevskaya case. We also show how the Fomenko–Zieschang invariant can be calculated for every admissible curve in the image of the momentum map. PubDate: 2018-11-01

Abstract: In this paper, a new generalization of Ostrowski type integral inequality for mappings of bounded variation is obtained and the quadrature formula is also provided. PubDate: 2018-11-01

Abstract: Let Γ be a closed Jordan curve on the complex plane dividing it onto domains D+ and D−, ∞ ∈ D−. The Hölder space Hv (Γ) is the space of functions satisfying the Hölder condition with exponent ν on Γ, and \(H^+_\nu(\Gamma),\;H^{-}_\nu(\Gamma)\) are its subspaces consisting of functions analytically extendable into D+ and D− relatively. We study intersection and sum of these subspaces for nonsmooth and non-rectifiable curves. PubDate: 2018-11-01

Abstract: The well known pure algebraic concept of group grading arises naturally in considering the crossed products, especially in the context of irreversible dynamical systems. In the paper some general aspects concerning group graded systems and related algebras are considered. In particular, a functional description of a C*-algebra associated with an Abelian group graded system is presented. PubDate: 2018-11-01

Abstract: The height filtration on the stack of formal groups \(\mathcal{M}\) FG is well known. We explore analogous filtration on a set of morphisms of formal group laws, which extends to the stack \(\mathcal{M}\) FG. It is correctly defined colimit object for this filtration which can be identified with the colimit \(\mathcal{M}\) FG,∞. As a corollary we prove explicitly density of additive formal group in any group law. PubDate: 2018-11-01

Abstract: In this paper, we consider three transformation groups of the Lobachevskii plane that are generated by the group of all motions and one-parameter transformation groups, which preserve an elliptic, a hyperbolic or a parabolic bundle of straight lines of this plane, respectively. It is proved that each of these groups acts 3-transitively on the Lobachevskii plane. The transformation groups and their generalizations can be applied an research of quasi-conformal mappings of the Lobachevskii space, in the special theory of relativity and in the fractal geometry. PubDate: 2018-11-01

Abstract: Some effects in the α-convex theory of the univalent functions are discussed in the light of the uniqueness problem for the critical point of the conformal radius. PubDate: 2018-11-01

Abstract: It is well known that the lattice of closed subsets of any topological space is isomorphic to that of a T0-topological space. This result is extended to lattices of closed subsets with respect to arbitrary closure operator on a set. Also, we establish a one-to-one correspondence between closure operators which are both algebraic and topological on a given set X and pre-orders on X and prove that this correspondence induces a one-to-one correspondence between topological algebraic T0-closure operators on X and partial orders on X. PubDate: 2018-11-01

Abstract: We research an initial-boundary value problem with integral condition of the second kind in a rectangular domain for a hyperbolic equation with singular coefficient. The solution is obtained in the form of the Fourier–Bessel series. There are proved theorems on uniqueness, existence and stability of the solution. In order to prove the existence of solution of the non-local problem we obtain sufficient conditions for the convergence of the series in terms of the initial values. PubDate: 2018-11-01

Abstract: For the successful development of the astrophysics and, accordingly, for obtaining more complete knowledge of the Universe, it is extremely important to combine and comprehensively analyze information of various types (e.g., about charged cosmic particles, gamma rays, neutrinos, etc.) obtained by using divers large-scale experimental setups located throughout the world. It is obvious that all kinds of activities must be performed continually across all stages of the data life cycle to help support effective data management, in particular, the collection and storage of data, its processing and analysis, refining the physical model, making preparations for publication, and data reprocessing taking refinement into account. In this paper we present a general approach to construction and the architecture of a system to be able to collect, store, and provide users’ access to astrophysical data. We also suggest a new approach to the construction of a metadata registry based on the blockchain technology. PubDate: 2018-11-01

Abstract: Let p(z) be a polynomial of degree n and for α ∈ C, let Dαp(z):= np(z) + (α − z)p′(z) denote the polar derivative of the polynomial p(z) with respect to α. In this paper, we obtain certain integral inequalities concerning the polar derivative of a polynomial, which besides yielding some interesting results, also includes some well-known theorems as special cases. Moreover we refine some Zygmund type inequalities for the polar derivative of a polynomial and present compact generalizations of some prior results. PubDate: 2018-11-01

Abstract: New conditions are constructed for the critical point of the conformal radius (hyperbolic derivative) to be unique where the mapping function is holomorphic and locally univalent in the unit disk. We use an approach based on the uniqueness research of the univalence conditions depending on the additional parameters. Such a research has been carried out for the univalence criteria due to Singhs, Szapiel and some other mathematicians. PubDate: 2018-11-01

Abstract: The paper is devoted to the problem of constructing a predictive model in the high-dimensional feature space. The space is redundant, there is multicollinearity in the design matrix columns. In this case the model is unstable to changes in data or in parameter values. To build a stable model, the authors solve the dimensionality reduction problem for the feature space. It is proposed to use feature selection methods during parameter optimization process. The idea is to select the active set of model parameters which have to be optimized in the current optimization step. Quadratic programming feature selection is used to find the active set of parameters. The algorithm maximizes the relevance of model parameters to the residuals and makes them pairwise independent. Nonlinear regression and logistic regression models are investigated. We carried out the experiment to show how the proposed method works and compare it with other methods. The proposed algorithm achieves the less error and greater stability with comparison to the other methods. PubDate: 2018-11-01

Abstract: Large amount of data being generated at large scale facilities like European X-ray Free- Electron Laser (XFEL) requires new approaches for data processing and analysis. One of the most computationally challenging experiments at an XFEL is single-particle structure determination. In this paper we propose a new design for an integrated software platform which combines well-established techniques for XFEL data analysis with High Performance Data Analysis (HPDA) methods. In our software platform we use streaming data analysis algorithms with high performance computing solutions. This approach should allow analysis of the experimental dataflow in quasi-online regime. PubDate: 2018-11-01

Abstract: The paper is devoted to the development of a calculation technique for elasto-plastic solids with regard to finite strains. The kinematics of elasto-plastic strains is based on the multiplicative decomposition of the total deformation gradient into elastic and inelastic (plastic) components. The stress state is described by the Cauchy stress tensor. Physical relations are obtained from the equation of the second law of thermodynamics supplemented with a free energy function. The free energy function is written in an invariant form of the left Cauchy–Green elastic strain tensor. An elasto-plasticity model with isotropic strain hardening is considered. Based on an analog of the associated rule of plastic flows and the von Mises yield criterion, we develop the method of stress projection onto the yield surface (known as the radial return method) with an iterative refinement of the current stress-strain state. The iterative procedure is based on the introduction of additional virtual stresses to the resolving power equation. The constitutive relations for the rates and increments of the true Cauchy stresses are constructed. In terms of the incremental loading method, the variational equation is obtained on the basis of the principle of possible virtual powers. Spatial discretization is based on the finite element method; an octanodal finite element is used.We present the solution to the problem of tension of a circular bar and give a comparison with results of other authors. PubDate: 2018-11-01