In this second paper, we prove another necessity Theorem about the topological origin of phase transitions. The Main Theorem of the present paper is proved by crucially resorting to the Main Theorem of paper I. However, the new Theorem has a much broader validity domain because it is proved under the generic condition of existence of critical points of the potential VN . In fact, on the basis o...

we consider the transitive linear maps on the operator algebra $b(x)$for a separable banach space $x$. we show if a bounded linear map is norm transitive on $b(x)$,then it must be hypercyclic with strong operator topology. also we provide a sot-transitivelinear map without being hypercyclic in the strong operator topology.

Let M be a smooth compact manifold (maybe with boundary, maybe disconnected) of any dimension d ≥ 1. Let m be some (smooth) volume probability measure in M. Let C(M,M) be the set of C maps M → M, endowed with the C topology. Given f ∈ C(M,M), we say that μ is an acim for f if μ is an f -invariant probability measure which is absolutely continuous with respect to m. Theorem 1. The set R of C map...

In this paper, the topology dynamic of Gnutella is studied through phase space. The dynamic changes in peer degree are studied as a time series in two dimensional phase space which is defined as the number of connected leaves and the number of connected ultras. The reported degrees are concentrated in three special Software related regions that we named as Ultra Stable Region, Leaf Stable Regio...

Topology construction and topology maintenance are significant sub-problems of topology control. Spanning tree based algorithms for topology control are basically transmission range based type construction algorithms. The construction of an effective backbone, however, is indirectly related to the placement of nodes. Also, the dependence of network reliability on the communication path undertak...

A topological quasi-variety Q T ∼ ) := IScP + ∼ generated by a finite algebra ∼ with the discrete topology is said to be standard if it admits a canonical axiomatic description. Drawing on the formal language notion of syntactic congruences, we prove that Q T ∼ ) is standard provided that the algebraic quasi-variety generated by ∼ is a variety, and that syntactic congruences in that variety are...

The knowledge of 3-dimensional virus structures is essential in understanding the mechanism of viral pathogenesis. It also provides insights to the stabilizing mechanisms of a nano-sized particle, since many viruses are less than 100 nanometers in diameter. This paper reports the results towards the development of a scalable parallel code for structural prediction of virus particles through ab ...

In this proposed paper, multicarrier sinusoidal pulse width modulation (M-SPWM) method is implemented for design of 15 level reduced switches inverter topology. This topology generates output-voltage with suitablelswitching production using M-SPWM and altered voltages are attained distinction modulationlindex. The split inductor used to diminish the harmoniclcontent flatted output current. type...

We give a thorough overview of the different notions for order convergence that are found in literature and provide systematic comparison associated topologies. As an application this study we prove result related to topology on von Neumann algebras, complementing started Chetcuti et al. (Stud. Math. 230:95-120, 2015). show every atomic algebra (not necessarily \(\sigma \)-finite) restriction b...

In this article we established the concept of multi-continuity in minimal structure spaces (in short $\mathscr{M}$ space) and notion product space multiset topological space. Continuity between $\mathscr{M}$-space, generalized topology ideal spaces. We have investigated some basic properties $\mathscr{M}$–continuity space, such as composition $\mathscr{M}$–continuous functions, functions etc.