Search results for "topological [string]"
showing 10 items of 213 documents
On two topological cardinal invariants of an order-theoretic flavour
2012
Noetherian type and Noetherian $\pi$-type are two cardinal functions which were introduced by Peregudov in 1997, capturing some properties studied earlier by the Russian School. Their behavior has been shown to be akin to that of the \emph{cellularity}, that is the supremum of the sizes of pairwise disjoint non-empty open sets in a topological space. Building on that analogy, we study the Noetherian $\pi$-type of $\kappa$-Suslin Lines, and we are able to determine it for every $\kappa$ up to the first singular cardinal. We then prove a consequence of Chang's Conjecture for $\aleph_\omega$ regarding the Noetherian type of countably supported box products which generalizes a result of Lajos S…
Nonlinear higher-order polariton topological insulator
2020
We address the resonant response and bistability of the exciton-polariton corner states in a higher-order nonlinear topological insulator realized with kagome arrangement of microcavity pillars. Such states are resonantly excited and exist due to the balance between pump and losses, on the one hand, and between nonlinearity and dispersion in inhomogeneous potential landscape, on the other hand, for pump energy around eigen-energies of corresponding linear localized modes. Localization of the nonlinear corner states in a higher-order topological insulator can be efficiently controlled by tuning pump energy. We link the mechanism of corner state formation with symmetry of the truncated kagome…
Existentially closed locally cofinite groups
1992
Let be a class of finite groups. Then a c-group shall be a topological group which has a fundamental system of open neighbourhoods of the identity consisting of normal subgroups with -factor groups and trivial intersection. In this note we study groups which are existentially closed (e.c.) with respect to the class Lc of all direct limits of c-groups (where satisfies certain closure properties). We show that the so-called locally closed normal subgroups of an e.c. Lc-group are totally ordered via inclusion. Moreover it turns out that every ∀2-sentence, which is true for countable e.c. L-groups, also holds for e.c. Lc-groups. This allows it to transfer many known properties from e.c. L-group…
Topological Space
2020
We introduce some formal definition of Topological Space in the the framework of the so-called classical mathematics.
Online Edge Flow Imputation on Networks
2022
Author's accepted manuscript © 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. An online algorithm for missing data imputation for networks with signals defined on the edges is presented. Leveraging the prior knowledge intrinsic to real-world networks, we propose a bi-level optimization scheme that exploits the causal dependencies and the flow conservation, respe…
Antiferromagnetic order competing with topological state in CexBi2−xTe3
2015
The topological surface states in three-dimensional topological insulators are easily tuned by chemical doping, especially by magnetic impurities. We prepared single crystals of CexBi2−xTe3 with various x (=0.04, 0.06, 0.08, 0.10, and 0.12). The obtained crystals were characterized by X-ray diffraction and scanning electron microscopy. The magnetic susceptibility data revealed that the Ce atoms are well substituted for Bi into Bi2Te3. From the Curie-Weiss fits, we observed that the effective magnetic moments μeff are close to 2.54 μB for free Ce ion, and the paramagnetic Curie-Weiss temperatures θp are negatively increased from 2.87 K to −59.3 K with increasing x. The magnetization data cle…
The Partial Inner Product Space Method: A Quick Overview
2010
Many families of function spaces play a central role in analysis, in particular, in signal processing (e.g., wavelet or Gabor analysis). Typical are spaces, Besov spaces, amalgam spaces, or modulation spaces. In all these cases, the parameter indexing the family measures the behavior (regularity, decay properties) of particular functions or operators. It turns out that all these space families are, or contain, scales or lattices of Banach spaces, which are special cases ofpartial inner product spaces(PIP-spaces). In this context, it is often said that such families should be taken as a whole and operators, bases, and frames on them should be defined globally, for the whole family, instead o…
Proposal to Detect Dark Matter using Axionic Topological Antiferromagnets
2019
Antiferromagnetically doped topological insulators (A-TI) are among the candidates to host dynamical axion fields and axion-polaritons; weakly interacting quasiparticles that are analogous to the dark axion, a long sought after candidate dark matter particle. Here we demonstrate that using the axion quasiparticle antiferromagnetic resonance in A-TI's in conjunction with low-noise methods of detecting THz photons presents a viable route to detect axion dark matter with mass 0.7 to 3.5 meV, a range currently inaccessible to other dark matter detection experiments and proposals. The benefits of this method at high frequency are the tunability of the resonance with applied magnetic field, and t…
Existence of zero-energy impurity states in different classes of topological insulators and superconductors and their relation to topological phase t…
2015
We consider the effects of impurities on topological insulators and superconductors. We start by identifying the general conditions under which the eigenenergies of an arbitrary Hamiltonian H belonging to one of the Altland-Zirnbauer symmetry classes undergo a robust zero energy crossing as a function of an external parameter which can be, for example, the impurity strength. We define a generalized root of \det H, and use it to predict or rule out robust zero-energy crossings in all symmetry classes. We complement this result with an analysis based on almost degenerate perturbation theory, which allows a derivation of the asymptotic low-energy behavior of the ensemble averaged density of st…
van der Waals heterostructures based on atomically-thin superconductors
2021
Van der Waals heterostructures (vdWHs) allow the assembly of high-crystalline two-dimensional (2D) materials in order to explore dimensionality effects in strongly correlated systems and the emergence of potential new physical scenarios. In this work, it is illustrated the feasibility to integrate 2D materials in-between 2D superconductors. Particularly, it is presented the fabrication and electrical characterization of vertical vdWHs based on air-unstable atomically-thin transition metal dichalcogenides formed by NbSe2/TaS2/NbSe2 stacks, with TaS2 being the insulator 1T-TaS2 or the metal 2H-TaS2. Phase transitions as 1T-TaS2 charge density wave and NbSe2 superconductivity are detected. An …