The Padmakar-Ivan (PI) index is a Wiener-Szeged-like topological index which reflects certain structural features of organic molecules. The PI index of a graph G is the sum of all edges uv of G of the number of edges which are not equidistant from the vertices u and v. In this paper we obtain the second and third extremals of catacondensed hexagonal systems with respect to the PI index.

background: heat shock proteins (hsp) are highly conserved molecules with many immunological functions. they are highly immunogenic with important role in cancer immunotherapy and in vaccine development against infectious diseases. as adjuvant, hsp can augment the immunogenicity of weak antigens and can stimulate antigen presenting cells. although vaccines have been successful for many infectio...

A bstract In this work, we show that a critical point of 1d self-dual boundary phase transition between two gapped boundaries the ℤ N topological order can be described by mathematical structure called an enriched fusion category. The viewed as gappable non-chiral gapless order. theory 2d orders developed Kong and Zheng (arXiv:1905.04924 arXiv:1912.01760) tells us all macroscopic observables on...

By a topological ring we mean a ring X with a Hausdorff topology such that (x, y) 7→ x + y, x 7→ −x, (x, y) 7→ x · y are continuous. A morphism of topological rings is a continuous homomorphism of rings. An inverse system of topological rings is a family of topological rings Xi and a family of morphisms πi,j : Xi → Xj for i, j ∈ I with i ≥ j, such that when i ≥ j ≥ k, πi,k = πj,k ◦ πi,j . If Y ...

We investigate the possibility of realizing a disorder-induced topological Floquet spectrum in two-dimensional periodically driven systems. Such a state would be a dynamical realization of the topological Anderson insulator. We establish that a disorder-induced trivial-to-topological transition indeed occurs, and characterize it by computing the disorder averaged Bott index, suitably defined fo...

Graph topologies for nonlinear operators which admit coprime factorisations are defined w.r.t. a gain function notion of stability in a general normed signal space setting. Several metrics are also defined and their relationship to the graph topologies are examined. In particular, relationships between nonlinear generalisations of the gap and graph metrics, Georgiou-type formulae and the graph ...

We present a topological characterization for fuzzy regular languages: we show that there is a bijective correspondence between fuzzy regular languages and the set of all clopen fuzzy subsets with finite image in the induced fuzzy topological space of Stone space (Profinite space), and then we give a representation of closed fuzzy subsets in the induced fuzzy topological space via fuzzy regular...

Using the coupled wire construction, authors investigate a novel Abelian quantum Hall state that possesses symmetry-enriched topological order given combination of internal and spatial symmetry. This is termed ``nondiagonal'' due to its relation nondiagonal conformal field theory, characterized by quasiparticles with constrained motion, whose braiding statistics features marriage Laughlin \ensu...

We formulate a construction of type-I fracton models based on gauging planar subsystem symmetries topologically ordered two-dimensional layers that have been stacked in three ambient spatial dimensions. Via our construction, any defect an Abelian symmetry group symmetry-enriched topological order can be promoted to fracton. This allows us construct supporting chiral boundaries and fractons noni...

Dynamic Topological Logic provides a context for studying the confluence of the topological semantics for S4, based on topological spaces rather than Kripke frames; topological dynamics; and temporal logic. In the topological semantics for S4, 2 is interpreted as topological interior: thus S4 can be understood as the logic of topological spaces. Topological dynamics studies the asymptotic prope...