Nobel Lecture, presented on December 8, 2016, at Aula Magna, Stockholm University. This article describes the history and background of three discoveries cited in this Nobel Prize: The "TKNN" topological formula for the integer quantum Hall effect found by David Thouless and collaborators, the Chern insulator of quantum anomalous Hall effect, and its role in the later discovery of time-reversal invariant topological insulators, and the unexpected topological spin-liquid state of the spin-1 quantum antiferromagnetic chain, which provided an initial example of topological quantum matter. This article summarizes how these early beginnings have led to the exciting, and currently extremely active, field of "topological matter"., F. Duncan M. Haldane ; přeložil Ivan Gregora ; foto A. Mahmoud, Odile Belmontová., and Obsahuje bibliografii
Nobel Lecture, presented on December 8, 2016, at Aula Magna, Stockholm University. In his lecture F. J. M. Kosterlitz described theoretical discoveries of topological phase transitions and topological phases of matter, partially on behalf of the main researcher behind those discoveries, David Thouless, who was not able to give the talk. First, the history of the collaboration between Kosterlitz and Thouless was briefly described. Then, a summary of their contribution to applications of topology to classical Berezinskii-Kosterlitz-Thouless of BKT phase transition was described., John Michael Kosterlitz ; přeložil Ivan Gregora ; foto A. Mahmoud., and Obsahuje bibliografii
In this paper, we investigate the grouping behavior of multi-agent systems by exploiting the graph structure. We propose a novel algorithm for designing a network from scratch which yields the desired grouping in a network of agents utilizing a consensus-based algorithm. The proposed algorithm is shown to be optimal in the sense that it consists of the minimum number of links. Furthermore, we examine the effect of adding new vertices and edges to the network on the number of groups formed in the group consensus problem. These results can be further utilized by the network topology designer to restructure the network and achieve the desired grouping. Theoretical results are illustrated with simulation examples.
In this paper we investigate the relations between torsion classes of Specker lattice ordered groups and torsion classes of generalized Boolean algebras.
The contribution is a continuation of [2] which deals with analytic solution of torsion of a bar with simply connected profile, i.e. profile without holes. In this paper the case of multiply connected profile, i.e. profile with holes, is studied. The stress-strain analysis leads to the Airy stress function Φ. On boundary of each hole the function Φ has prescribed an unknown constant value completed with an integral condition. The mathematical model is also derived from the variational principle.
The second part of the paper contains solutions for the ring profile and for comparison also for incomplete ring profiles including the ‘broken‘ ring profile. The results are compared in tables and pictures. and Obsahuje seznam literatury
The contribution deals with strain-stress analysis of torsion of a non-circular bar. Mathematical model is exactly derived and solutions are introduced and visualised for cases of triangular, rectangular and some other profiles. and Obsahuje seznam literatury
We investigate the Zassenhaus conjecture regarding rational conjugacy of torsion units in integral group rings for certain automorphism groups of simple groups. Recently, many new restrictions on partial augmentations for torsion units of integral group rings have improved the effectiveness of the Luther-Passi method for verifying the Zassenhaus conjecture for certain groups. We prove that the Zassenhaus conjecture is true for the automorphism group of the simple group PSL(2, 11). Additionally we prove that the Prime graph question is true for the automorphism group of the simple group PSL(2, 13)., Joe Gildea., and Obsahuje seznam literatury
By a torsion of a general connection $\Gamma $ on a fibered manifold $Y\rightarrow M$ we understand the Frölicher-Nijenhuis bracket of $\Gamma $ and some canonical tangent valued one-form (affinor) on $Y$. Using all natural affinors on higher order cotangent bundles, we determine all torsions of general connections on such bundles. We present the geometrical interpretation and study some properties of the torsions.
One of the most important problems in communication network design is the stability of network after any disruption of stations or links. Since a network can be modeled by a graph, this concept is examined under the view of vulnerability of graphs. There are many vulnerability measures that were defined in this sense. In recent years, measures have been defined over some vertices or edges having specific properties. These measures can be considered to be a second type of measures. Here we define a new measure of the second type called the total accessibility. This measure is based on accessible sets of a graph. In our study we give the total accessibility number of well known graph models such as Pn, Cn, Km,n, W1,n, K1,n. We also examine this new measure under operations on graphs. A simple algorithm, which calculates the total accessibility number of graphs, is given. We observe that when any two graphs of the same size are compared in stability, it is inferred that the graph of higher total accessibility number is more stable than the other one. All the graphs considered in this paper are undirected, loopless and connected.
The objective of our study was to assess the influence of mechanical ventilation on healthy body organs. Fifteen piglets (aged 6 weeks, 19-27 kg) were anesthetized, instrumented, and divided into three groups: Group A - spontaneously breathing, group B - mechanically ventilated with tidal volume 6 ml/kg, and group C - ventilated with tidal volume 10 ml/kg for 12 hours. The parameters of lung, heart, liver and kidney functions neurohumoral regulation and systemic inflammatory reaction were recorded initially (time-1) and after 12 hours (time-12) of mechanical ventilation. At the onset of experiment (time-1) the levels of soluble adhesive molecules were higher (CAM; P<0.01), glomerular filtration index and free water clearance were lower (P<0.05) in both ventilated groups than in group A. Right ventricle myocardial performance index was higher (RIMP; P<0.05) in group C when compared with group A. Levels of CAM (P<0.05) and creatinine clearance (P<0.01) were higher, free water clearance was lower (P<0.05) in group C when compared to group B. At time-12 the RIMP (P<0.05) and levels of CAM were increased (P<0.01), creatinine clearance was decreased (P<0.05) in both ventilated groups compared to the same parameter at time-1. Ventilation index was higher (P<0.05), and hypoxemic index was lower (P<0.01) in group C when compared to group B. In conclusion, this study showed that mechanical ventilation induced changes compatible with early inflammatory response in healthy animals. Higher tidal volumes had detrimental effect on ventilatory parameters, reduced myocardial performance and potentiated adverse reaction of other organs., J. Kobr ... [et al.]., and Obsahuje bibliografii a bibliografické odkazy