In this thesis, we use string diagrams to study the theory of Hopf algebras in the context of Categorical Quantum Mechanics. First, we treat the theory of representations of a Hopf algebra diagrammatically. The category of representations of a quasitriangular Hopf algebra Rep(H) is a braided tensor category and can be understood as a process theory of particles in Topological Quantum theory. We...

the geometric-arithmetic index is another topological index was defined as2 deg ( )deg ( )( )deg ( ) deg ( )g guv eg gu vga gu v  , in which degree of vertex u denoted by degg (u). wenow define a new version of ga index as 4( )2 ε ( )ε ( )( )ε ( ) ε ( )g ge uv e g g gu vga g  u v , where εg(u) isthe eccentricity of vertex u. in this paper we compute this new topological index for twogr...

Topological insulators are materials with a bulk band gap, but with topologically protected, spin polarized surface states with Dirac dispersion. Bi2Te3 is such a topological insulator with a single Dirac cone at the center of the Brillouin zone. ARPES studies have shown that the Fermi surface of Bi2Te3 changes from a circle to a hexagon, and then to a hexagram, when moving away from the Dirac ...

the capability of academic articles to be cited in the future using a topological analysis of citation networks. The basic idea is that articles that will have many citations were in a " similar " position topologically in the past. To validate this hypothesis, we investigated the correlation between future times cited and three measures of centrality: clustering centrality, closeness cen-trali...

Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices are invariants of the topology of graphs associated with molecular structure of nanomaterials to correlate certain physicochemical properties like bo...

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...

A new definition of boundedness of linear order-homomorphisms (LOH)in $L$-topological vector spaces is proposed. The new definition iscompared with the previous one given by Fang [The continuity offuzzy linear order-homomorphism, J. Fuzzy Math. 5 (4) (1997)829$-$838]. In addition, the relationship between boundedness andcontinuity of LOHs is discussed. Finally, a new uniform boundednessprincipl...

We numerically investigate the surface states of a strong topological insulator in the presence of strong electron-electron interactions. We choose a spherical topological insulator geometry to make the surface amenable to a finite size analysis. The single-particle problem maps to that of Landau orbitals on the sphere with a magnetic monopole at the center that has unit strength and opposite s...

We present a study of the surface reactivity of a Pd/Bi2Te3 thin film heterostructure. The topological surface states from Bi2Te3, being delocalized and robust owing to their topological natures, were found to act as an effective electron bath that significantly enhances the surface reactivity of palladium in the presence of two oxidizing agents, oxygen and tellurium respectively, which is cons...

This paper presents a novel algorithm, called Radial Sector Coding (RSC), for Translation, Rotation and Scale invariant character recognition. Translation invariance is obtained using Center of Mass (CoM). Scaling invariance is achieved by normalizing the features of characters. To obtain most challenging rotation invariance, RSC searches a rotation invariant Line of Reference (LoR) by exploiti...