Formation of the macroscopically-infinite hydrogen-bonded water network in various aqueous systems occurs via 3D percolation transition when the probability of finding a spanning water cluster exceeds 95%. As a result, in a wide interval of water content below the percolation threshold, rarefied quasi-2D water networks span over the mesoscopic length scale. Formation and topology of spanning wa...

Fix a one-dimensional group variety G with Euler–characteristic χ(G) = 0, and a quasi–projective variety Y , both defined over C. For any f ∈ Hom(Y, G) and constructible sheaf F on Y , we construct an invariant cF (f) ∈ G, which provides substantial information about the topology of the fiber–structure of f and the structure of F along the fibers of f . Moreover, cF : Hom(Y,G)→ G is a group hom...

Let M be a hyperbolic 3–manifold, namely a complete 3–dimensional Riemannian manifold of constant curvature −1, such that the fundamental group π1 (M) is finitely generated. A fundamental subset of M is its convex core CM , defined as the smallest non-empty closed convex subset ofM . The boundary ∂CM of this convex core is a surface of finite topological type, and its geometry was described by ...

Novel 3-level GTO inverter topology is presented. This new power circuit includes many advantages comparing with the conventional 3-level GTO inverter. The main advantages are snubberless and good device utilization by employing dual quasi-resonant dc-link which guarantees the complete zero voltage switching of the inverter GTO's. This 3-level GTO inverter can be operated with lower switching l...

Wind energy is a leader area of application for variable-speed generators operating on the constant grid frequency. This paper depicts the power quality enhancement in wind power system using permanent magnet synchronous generator (PMSG) and Quasi Z-source Inverter. The PMSG is connected to the power network by means of a quasi z-source inverter (qZSI). The PMSG are used by these technologies d...

We present old and new characterizations of core spaces, alias worldwide web spaces, originally defined by the existence of supercompact neighborhood bases. The patch spaces of core spaces, obtained by joining the original topology with a second topology having the dual specialization order, are the so-called sector spaces, which have good convexity and separation properties and determine the o...

For a locally quasi-convex (lqc) abelian group G, we describe all compatible lqc topologies on G and apply this result to the Mackey problem for groups. We characterize groups which are or admit topology provide characterization of two whose product is Mackey. convex spaces

We study theoretically analog multi-terminal Josephson junctions formed by gapped superfluids created upon resonant pumping of cavity exciton-polaritons. the $p$-like bands a 5-terminal junction in 4D parameter space superfluid phases acting as quasi-momenta. find 4/6 Weyl points 3D subspaces with preserved/broken time-reversal symmetry. link real topology (vortices) to one (Weyl points). deriv...

A classical result in the theory of Hopf algebras concerns the uniqueness and existence of inte-grals: for an arbitrary Hopf algebra, the integral space has dimension ≤ 1, and for a finite dimensional Hopf algebra, this dimension is exaclty one. We generalize these results to quasi-Hopf algebras and dual quasi-Hopf algebras. In particular, it will follow that the bijectivity of the antipode fol...