Vol 39, No 9 (2018)

Scalability of computations in the FlowVision CFD software on the Angara-C1 cluster equipped with the Angara interconnect is studied. Different test problems with 260 thousand, 5.5 million and 26.8 million computational cells are considered. Computations in FlowVision are performed using a new solver of linear systems based on the algebraic multigrid (AMG) method. It is shown that the the special FlowVision’s Dynamic balancing technology significantly improves performance of computations if features of the problem lead to the non-uniform loading of CPUs. The Angara-C1 cluster demonstrates excellent performance and scalability characteristics comparable with its analogues based on the 4X FDR Infiniband interconnect.

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.

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.

We propose a linear time and linear space algorithm that constructs a minimal (in the total cost) sequence of operations required to transform a directed graph consisting of disjoint cycles into any graph of the same type. The following operations are allowed: double-cut-and-join of vertices and insertion or deletion of a connected fragment of edges; the latter two operations have the same cost. We present a complete proof that the algorithm finds the corresponding minimum. The problem is a nontrivial particular case of the general problem of transforming a graph into another, which in turn is an instance of a hard optimization problem in graphs. In this general problem, which is known to be NP-complete, each vertex of a graph is of degree 1 or 2, edges with the same name may repeat unlimitedly, and operations belong to a well-known list including the above-mentioned operations. We describe our results for the general problem, but the proof is given for the cyclic case only.

The work is devoted to the organization of high performance computing in the solution of multiscale problems of gas dynamics relevant for the implementation of modern nanotechnologies. The base of the presented computing technology is a multiscale two-level approach that combines calculations at macro- and microlevels. The approach makes it possible to study micro- and nanoflows of a gaseous medium under conditions of complex geometry of technical systems used in the production cycle in order to obtain new nanomaterials and nanocoatings. Within the framework of the approach a system of the quasigasdynamic (QGD) equations and a system of the molecular dynamics (MD) equations are considered as two basic mathematical models. These models are aggregated using the method of splitting by physical processes and scales. The QGD system is solved by the finite volume method on grids of arbitrary type. The MD equations are solved according to the Verlet integration. In view of the complexity of the problem a high performance computing is used for realization of the approach. Parallel implementation of the approach is based on the methods of domain decomposition and functional parallelism and is oriented towards the use of computer systems with hybrid architecture. The implementation uses MPI, OpenMP and CUDA technologies. Testing of the developed approach and parallel tool was performed using the example of the problem of spraying the nanoparticles on a substrate. Numerical experiments confirm the effectiveness of the developed computing technology.

The graph anomaly detection problem occurs in many application areas and can be solved by spotting outliers in unstructured collections of multi-dimensional data points, which can be obtained by graph analysis algorithms. We implement the algorithm for the small community analysis and the approximate LOF algorithm based on Locality-Sensitive Hashing, apply the algorithms to a real world graph and evaluate scalability of the algorithms. We use Apache Spark as one of the most popular Big Data frameworks.

In this paper, we consider a problem-solving technique of the texture changing of an object in a photograph. The task in hand is relevant in the field of intelligent image processing and has a number of practical applications. The solutions to this problem have been proposed in a number of works devoted to the neural network style transfer approach, but they have a number of limitations. Examples of the limitations are as follows: the texture transfer selectivity absence (the image is changed entirely), the target texture distortion with the heterogeneity of the original one, the initial illumination distortion of the object, and the absence of the photographic realism of the resulting image.

To solve the problems mentioned above, in this paper we propose a sequential image processing with the use of several neural networks types: segmental, stylizing and generative-adversarial (GAN) ones. The reliable transfer problem of an object illumination is proposed to be solved by the joint work of GAN and methods that do not use the neural network approach.

In the context of this paper we developed an algorithm that allows solving the texture transferring task with completely or partially elimination of the listed problems of classical methods. Its high quality of work is shown with the maintaining productivity acceptable for common use. Demonstration of the algorithm is performed on the task of a virtual furniture dust covers fitting (sofas, armchairs). In addition to the algorithm itself, this work includes an enumeration of some heuristics and limitations stated during its implementation and application.

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.

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.

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.

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(R^d) and we give the minimal time of the blow up for some initial data.

We study the Dirichlet problem with continuous boundary data in simply connected domains D of the complex plane for the semi-linear partial differential equations whose linear part has the divergent form. We prove that if a Jordan domain D satisfies the so-called quasihyperbolic boundary condition, then the problem has regular (continuous) weak solutions whose first generalized derivatives by Sobolev are integrable in the second degree. We give a suitable example of a Jordan domain with the quasihyperbolic boundary condition that fails to satisfy both the well-known (A)-condition and the outer cone condition. We also extend these results to some non-Jordan domains in terms of the prime ends by Caratheodory. The proofs are based on our factorization theorem established earlier. This theorem allows us to represent solutions of the semilinear equations in the form of composition of solutions of the corresponding quasilinear Poisson equation in the unit disk and quasiconformal mapping of D onto the unit disk generated by the measurable matrix function of coefficients. In the end we give applications to relevant problems of mathematical physics in anisotropic inhomogeneous media.

Let Γ be a closed Jordan curve on the complex plane dividing it onto domains D⁺ and D₋, ∞ ∈ D⁻. The Hölder space H_v (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.

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.

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.

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.

Let p(z) be a polynomial of degree n and for α ∈ C, let D_αp(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.

Let R be a ring and n a fixed non-negative integer. In this paper, n-weak cotorsion modules are introduced and studied. A right R-module N is called n-weak cotorsion module if \(Ext^1_R(F,N)=0\) for any right R-module F with weak flat dimension at most n. Also some characterizations of rings with finite super finitely presented dimensions are given.

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 g_ε(τ, ξ) for which the least root ξ(τ) of the equation g_ε(τ, ξ) = 0 depends continuously on τ if ||g − g_ε||C < ε.

In 1998, R. Downey in his review paper outlined a research agenda for the study and description of sufficient conditions for computable representability of linear orderings, namely, the problem of describing order properties P such that, for any low linear ordering Limplies that, the feasibility of the condition P(L) implies that L has a computable presentation. This paper is a part of the research program initiated by R. Downey. It is shown in the paper that any low linear ordering whose factor order (in other words, condensation) is η (the order type of naturally ordered natural numbers) has a computable presentation via a 0—computable isomorphism if this ordering does not contain a strongly η-like infinite interval. A countable linear ordering is said to be strongly η-like if there exists some natural number k such that each maximal block of the ordering is of cardinality no more than k. It is also proved that the above result does not hold for a 0—computable isomorphism instead of the 0—computable one. Namely, we construct a low linear ordering L with condensation η and without strongly η-like infinite interval so that L has no computable presentation via a 0— computable isomorphism.

High-order accurate finite element schemes for a fourth-order ordinary differential equation with degenerate coefficients on the boundary are constructed. The method for solving the problem is based on multiplicative and additive-multiplicative separation of singularities. For right-hand sides of the given class of smoothness, an optimal convergence rate is proved.

An elastic homogeneous isotropic half-space filled with the Cosserat medium has been considered. The deformed state is characterized by independent displacement and rotation vectors. At the initial time and at infinity, there are no perturbations.On the boundary of a half-space, normal displacements are given. All components of the stress–strain state are supposed to be limited. A cylindrical coordinate system with an axis directed inward to the half-space has been used. With axial symmetry, the resolving system of equations includes three hyperbolic equations with respect to the scalar potential and the nonzero components of the vector potential and the rotation vector. The components of displacement vectors, rotation angle, stress tensors, and stress moments are related to potentials by known relationships. The solution of the problem has been sought in the form of generalized convolutions of a given displacement with corresponding superficial influence functions. These functions have been constructed using a Hankel transform with respect to the radius and a Laplace transform with respect to time. All images have three terms. The first of these terms corresponds to the tension–compression wave, and the remaining two are determined by the associated shear and rotation waves. The originals of the first components have been found accurately through successive inversion of transforms. For the remaining terms, we have used expansion in power series in a small parameter characterizing the relation between shear and rotation waves. The images of the first two coefficients of these series have been found. The corresponding originals have been determined by successive inversion of transforms. Examples of calculations of the regular components of the influence function of a granular composite of aluminum shot in an epoxy matrix have been given.