Search results for "topological [string]"

THE TOPOLOGY OF BASIN BOUNDARIES IN A CLASS OF THREE-DIMENSIONAL DYNAMICAL SYSTEMS

1996

We will develop new methods to determine the topology of the basin boundary in a class of three-dimensional dynamical systems. One approach is to approximate the basin boundary by backward integration. Unfortunately, there are dynamical systems where it is hard to approximate the basin boundary by a numerical backward integration algorithm. We will introduce topological methods which will provide new information about the structure of the basin boundary. The topological invariants which we will use can be numerically computed.

Topological Insulators from a Chemist’s Perspective

2012

Topology and chemistry are deeply entangled subjects, whichmanifests in the way chemists like to think and approachproblems. Although not at first glance, topology allows thecategorizationoffundamentalinherentpropertiesofthehugenumber of different chemical compounds, carving out theunique features of a class of materials of different complexity,a topic which Turro worked out in his treatise on geometricaland topological thinking in chemistry.

Hypergraph functor and attachment

2010

Using an arbitrary variety of algebras, the paper introduces a fuzzified version of the notion of attachment in a complete lattice of Guido, to provide a common framework for the concept of hypergraph functor considered by different authors in the literature. The new notion also gives rise to a category of variable-basis topological spaces which is a proper supercategory of the respective category of Rodabaugh.

On closures of discrete sets

2018

The depth of a topological space $X$ ($g(X)$) is defined as the supremum of the cardinalities of closures of discrete subsets of $X$. Solving a problem of Mart\'inez-Ruiz, Ram\'irez-P\'aramo and Romero-Morales, we prove that the cardinal inequality $|X| \leq g(X)^{L(X) \cdot F(X)}$ holds for every Hausdorff space $X$, where $L(X)$ is the Lindel\"of number of $X$ and $F(X)$ is the supremum of the cardinalities of the free sequences in $X$.

K-theory of function rings

1990

AbstractThe ring R of continuous functions on a compact topological space Xwith values in R or C is considered. It is shown that the algebraic K-theory of such rings with coefficients in ZkZ, k any positive integer, agrees with the topological K-theory of the underlying space X with the same coefficient rings. The proof is based on the result that the map from Rδ (R with discrete topology) to R (R with compact-open topology) induces a natural isomorphism between the homologies with coefficients in ZkZ of the classifying spaces of the respective infinite general linear groups. Some remarks on the situation with X not compact are added.

Topology Inference and Signal Representation Using Dictionary Learning

2019

This paper presents a Joint Graph Learning and Signal Representation algorithm, called JGLSR, for simultaneous topology learning and graph signal representation via a learned over-complete dictionary. The proposed algorithm alternates between three main steps: sparse coding, dictionary learning, and graph topology inference. We introduce the “transformed graph” which can be considered as a projected graph in the transform domain spanned by the dictionary atoms. Simulation results via synthetic and real data show that the proposed approach has a higher performance when compared to the well-known algorithms for joint undirected graph topology inference and signal representation, when there is…

Floquet engineering of magnetism in topological insulator thin films

2023

Dynamic manipulation of magnetism in topological materials is demonstrated here via a Floquet engineering approach using circularly polarized light. Increasing the strength of the laser field, besides the expected topological phase transition, the magnetically doped topological insulator thin film also undergoes a magnetic phase transition from ferromagnetism to paramagnetism, whose critical behavior strongly depends on the quantum quenching. In sharp contrast to the equilibrium case, the non-equilibrium Curie temperatures vary for different time scale and experimental setup, not all relying on change of topology. Our discoveries deepen the understanding of the relationship between topology…

Prediction of Weak Topological Insulators in Layered Semiconductors

2012

We report the discovery of weak topological insulators by ab initio calculations in a honeycomb lattice. We propose a structure with an odd number of layers in the primitive unit-cell as a prerequisite for forming weak topological insulators. Here, the single-layered KHgSb is the most suitable candidate for its large bulk energy gap of 0.24 eV. Its side surface hosts metallic surface states, forming two anisotropic Dirac cones. Though the stacking of even-layered structures leads to trivial insulators, the structures can host a quantum spin Hall layer with a large bulk gap, if an additional single layer exists as a stacking fault in the crystal. The reported honeycomb compounds can serve as…

Heusler Compounds—A Material Class With Exceptional Properties

2011

The class of Heusler compounds, including the XYZ and the X2YZ compounds, has not only an endless number of members, but also a vast variety of properties can be found in this class of materials, ranging from semiconductors, half-metallic ferromagnets, superconductors, and topological insulators to shape memory alloys. With this review article, we would like to provide an overview of Heusler compounds, focusing on their structure, properties, and potential applications.

2021

The bosonic analogs of topological insulators have been proposed in numerous theoretical works, but their experimental realization is still very rare, especially for spin systems. Recently, two-dim...