For an infinity of number rings we express stable motivic invariants in terms topological data determined by the complex numbers, real and finite fields. We use this to extend Morel's identification endomorphism ring sphere with Grothendieck-Witt quadratic forms deeper base schemes.

We theoretically study skyrmion lattices realized in a Kondo lattice model on triangular lattice, focusing the phase, ellipticity, and angle of constituent multiple-$Q$ waves. Analyzing numerical data obtained previous [Ozawa R, Hayami S Motome Y 2017 Phys. Rev. Lett. 118 147205], we extract these parameters for two types with number $1$ $2$. show that topological transition between driven by a...

The area of graph theory (GT) is rapidly expanding and playing a significant role in cheminformatics, mostly mathematics chemistry to develop different physicochemical, chemical structure, their properties. manipulation study graphical details are made feasible by using numerical structure invariant. Investigating these characteristics topological indices (TIs) possible the discipline mathemati...

We introduce several series of novel ZE-isomerism descriptors derived directly from two-dimensional molecular topology. These descriptors make use of a quantity named ZE-isomerism correction, which is added to the vertex degrees of atoms connected by double bonds in Z and E configurations. This approach is similar to the one described previously for topological chirality descriptors (Golbraikh,...

The Lieb-Schultz-Mattis theorem and its higher-dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy excitations, spontaneously break some symmetries, or exhibit topological order with anyonic excitations. We establish a connection between these constraints and...

the padmakar-ivan (pi) index is a wiener-szeged-like topological index which reflectscertain structural features of organic molecules. the pi index of a graph g is the sum of alledges uv of g of the number of edges which are not equidistant from the vertices u and v. inthis paper we obtain the second and third extremals of catacondensed hexagonal systems withrespect to the pi index.

We present a picture of confinement based on representation of quarks as pointlike topological defects. The topological charge carried by quarks and confined in hadrons is explicitly constructed in terms of Yang-Mills variables. In 2+1 dimensions we are able to construct a local complex scalar field V (x), in terms of which the topological charge is Q = − i 4π d 2 xǫ ij ∂ i (V * ∂ i V − c.c.). ...