The Component Diagnosability of General Networks

The processor failures in a multiprocessor system have a negative impact on its distributed computing efficiency. Because of the rapid expansion of multiprocessor systems, the importance of fault diagnosis is becoming increasingly prominent. The [Formula: see text]-component diagnosability of [Formula: see text], denoted by [Formula: see text], is the maximum number of nodes of the faulty set [Formula: see text] that is correctly identified in a system, and the number of components in [Formula: see text] is at least [Formula: see text]. In this paper, we determine the [Formula: see text]-component diagnosability of general networks under the PMC model and MM[Formula: see text] model. As applications, the component diagnosability is explored for some well-known networks, including complete cubic networks, hierarchical cubic networks, generalized exchanged hypercubes, dual-cube-like networks, hierarchical hypercubes, Cayley graphs generated by transposition trees (except star graphs), and DQcube as well. Furthermore, we provide some comparison results between the component diagnosability and other fault diagnosabilities.

Linguistic peculiarities of text component of the creolized Internet memes

The object of this research is the text component of Internet meme as a signifier of special type. The subject of this research is the peculiarities of text captions to the images posted in the Russian-speaking and English-speaking segments of the Internet. The authors dwell on such aspects as the syntactic, theme-rhematic, and orthographic peculiarities of the text component of Internet memes. Special attention is given to the problem of intentional misspellings in text captions. In most cases, namely the text actualizes the image; the memes usually involve film stills, drawings, and photo images, and text captions turn these images into the relevant Internet memes. The main conclusions lies in determination of the peculiarities of the text part of creolized Internet memes on all linguistic levels. Due to the specificities of Internet memes, the texts usually represent short sentences. The syntactic structure of used phrases often resembles a marked construction, and in a number of instances with intentional misspellings. The novelty of this research lies in the analysis of Internet memes from the perspective of linguistics. Although there are Russian and foreign research dedicated to semiotic and communicative components of the Internet memes, as well as their evolution and transformations, the analysis of linguistic component is carried out for the first time.

Measurement of the tensor analyzing power T20 for the reaction γd → pnπ0

This paper presents new results for the [Formula: see text]-component of the tensor analyzing power of the reaction [Formula: see text] in the photon energy range of [Formula: see text]. The experimental statistics accumulated in 2013 at the VEPP-3 accelerator-storage complex is used. The reaction events are identified by the coincidence registration of the proton and two [Formula: see text]-quanta from the decay of the neutral pion. To determine the [Formula: see text]-component, the asymmetry of the yields with respect to the change of sign of the tensor polarization of the deuterium target is measured. The experimental results are compared with the theoretical calculations in which the MAID 2007 model is used as the elementary pion–nucleon photoproduction amplitude and contributions from the pion–nucleon and nucleon–nucleon rescattering are taken into account.

Tied links in various topological settings

Tied links in [Formula: see text] were introduced by Aicardi and Juyumaya as standard links in [Formula: see text] equipped with some non-embedded arcs, called ties, joining some components of the link. Tied links in the Solid Torus were then naturally generalized by Flores. In this paper, we study this new class of links in other topological settings. More precisely, we study tied links in the lens spaces [Formula: see text], in handlebodies of genus [Formula: see text], and in the complement of the [Formula: see text]-component unlink. We introduce the tied braid monoids [Formula: see text] by combining the algebraic mixed braid groups defined by Lambropoulou and the tied braid monoid, and we formulate and prove analogues of the Alexander and the Markov theorems for tied links in the 3-manifolds mentioned above. We also present an [Formula: see text]-move braid equivalence for tied braids and we discuss further research related to tied links in knot complements and c.c.o. 3-manifolds. The theory of tied links has potential use in some aspects of molecular biology.

Note on Reliability Analysis of Cartesian Product of Networks for Components

Connectivity is a critical parameter which can measure the reliability of networks. Let [Formula: see text] be a vertex set of [Formula: see text]. If [Formula: see text] has at least [Formula: see text] components, then [Formula: see text] is a [Formula: see text]-component cut of [Formula: see text]. The [Formula: see text]-component connectivity [Formula: see text] of [Formula: see text] is the vertex number of a smallest [Formula: see text]-component cut. Cartesian product of graphs is a useful method to construct a large network. We will use Cauchy–Schwarz inequality to determine the component connectivity of Cartesian product of some graphs.

On the solvability of graded Novikov algebras

We show that the right ideal of a Novikov algebra generated by the square of a right nilpotent subalgebra is nilpotent. We also prove that a [Formula: see text]-graded Novikov algebra [Formula: see text] over a field [Formula: see text] with solvable [Formula: see text]-component [Formula: see text] is solvable, where [Formula: see text] is a finite additive abelean group and the characteristic of [Formula: see text] does not divide the order of the group [Formula: see text]. We also show that any Novikov algebra [Formula: see text] with a finite solvable group of automorphisms [Formula: see text] is solvable if the algebra of invariants [Formula: see text] is solvable.

Baroque religious pilgrimages and decorations of printed pilgrimage guides

Pilgrimage guides belong to the most widely published types of religious literature in Bohemia and Moravia in the 17th and 18th centuries. During this period Baroque religiosity grew stronger and the Catholic Church sought to consolidate its position in the country, which inclined to the ideas of the Reformation. Religious pilgrimages, festivities and ceremonies along with the worship of saints and faith in miracles, served as promotional tools of the Catholic faith. In order to spread Marian Piety, Czech and Moravian printers published works written by the representatives of church elites. In their works they dealt with the history of pilgrimage sites related to the Virgin Mary. The prints were published in Latin and German. In addition to the treatise about the pilgrimage sites and miraculous healings, they included prayers, songs and recommendations as to how to behave during a pilgrimage. It was not only the text component which the reader found interesting; he/she was also impressed by the graphic design of the print. The book decoration consisted of vignettes, friezes, typographic ornaments, lines or clichés, which fulfi lled an aesthetic and practical function. The customers’ interest was stimulated by copper engraving illustrations and Baroque allegorical frontispieces depicting a Marian statue and miracle picture or by depiction of the concrete pilgrimage site in the form of a veduta. The authors included some of the important Czech illustrators and engravers who collaborated with famous foreign artists.

Strange star with Krori–Barua potential in the presence of anisotropy

In this paper, a well-behaved new model of anisotropic compact star in (3+1)-dimensional spacetime has been investigated in the background of Einstein’s general theory of relativity. The model has been developed by choosing [Formula: see text] component as Krori–Barua (KB) ansatz [Krori and Barua in J. Phys. A, Math. Gen. 8 (1975) 508]. The field equations have been solved by a proper choice of the anisotropy factor which is physically reasonable and well behaved inside the stellar interior. Interior spacetime has been matched smoothly to the exterior Schwarzschild vacuum solution and it has also been depicted graphically. Model is free from all types of singularities and is in static equilibrium under different forces acting on the system. The stability of the model has been tested with the help of various conditions available in literature. The solution is compatible with observed masses and radii of a few compact stars like Vela X-1, 4U [Formula: see text], PSR J[Formula: see text], LMC X [Formula: see text], EXO [Formula: see text].

Relation of Extra Edge Connectivity and Component Edge Connectivity for Regular Networks

Reliability of interconnection networks is important to design multiprocessor systems. The extra edge connectivity and component edge connectivity are two parameters for the reliability evaluation. The [Formula: see text]-extra edge connectivity [Formula: see text] is the cardinality of the minimum extra edge cut [Formula: see text] such that [Formula: see text] is not connected and each component of [Formula: see text] has at least [Formula: see text] vertices. The [Formula: see text]-component edge connectivity [Formula: see text] of a graph [Formula: see text] is the minimum edge number of a set [Formula: see text] such that [Formula: see text] is not connected and [Formula: see text] has at least [Formula: see text] components. In this paper, we find the relation of extra edge connectivity and component edge connectivity for regular networks. As an application, we determine the component edge connectivity of BC networks, [Formula: see text]-ary [Formula: see text]-cubes, enhanced hypercubes.

Mixed convective 3D flow of Maxwell nanofluid induced by stretching sheet: Application of Cattaneo-Christov theory

The present study invokes the application of Cattaneo-Christov theory for the thermal analysis in the buoyancy driven three dimensional flow of Maxwell nanofluid. The flow is induced above the vertical bidirectional stretching sheet. The phenomena of thermophoresis and Brownian diffusion of nanoparticles in the flow Maxwell liquid are deliberated with the help of Buongiorno model for nanofluid. The physical problem is formulated in the form of boundary layer partial differential equations (PDEs). Moreover, suitable ansatz for flow mechanism are employed to reduce the governing PDEs into the non-linear ordinary differential equations (ODEs). The flow mechanism of Maxwell fluid along with energy transport is analyzed in the form of homotopic solutions of the governing ODEs. The outcomes are presented graphically and discussed with physical explanation. The analysis revealed that both buoyancy and mixed convection parameters enhanced the [Formula: see text]-component of velocity field but declined the [Formula: see text]-component. Moreover, in assisting mode these two parameters also increased the thermal and solutal energy transport in nanofluid. It is noted that the thermophorectic force boosts up the thermal energy transport in the flow in the presence of thermal relaxation phenomenon. The validation of the present results are confirmed through tabular data with some previous studies.