114,698 research outputs found
Criteria of strong nearest-cross points and strong best approximation pairs
[EN] The concept of strong nearest-cross point (strong n.c. point) is introduced, which is the generalization of strong uniqueness of best approximation from a single point. The relation connecting to localization is discussed. Some criteria of strong n.c. points are given. The strong best approximation pairs are also studied.The corresponding author Jingshi Xu was supported by the NNSF (No. 60474070) of ChinaPan, W.; Xu, J. (2006). Criteria of strong nearest-cross points and strong best approximation pairs. Applied General Topology. 7(1):41-50. https://doi.org/10.4995/agt.2006.1931SWORD41507
Tris(ethylenediamine-κ2 N,N′)cobalt(III) aquatris(oxalato-κ2 O 1,O 2)indate(III)
In the cation of the title compound, [Co(C2H8N2)3][In(C2O4)3(H2O)], the CoIII atom is coordinated by six N atoms from three ethylenediamine molecules. The CoIII—N bond lengths lie in the range 1.956 (4)–1.986 (4) Å. In the anion, the InIII atom is seven-coordinated by six O atoms from three oxalate ligands and by a water molecule. The cations and anions are linked by extensive O—H⋯O and N—H⋯O hydrogen bonds, forming a supermolecular network
Permanence and almost periodic solution of a multispecies Lotka-Volterra mutualism system with time varying delays on time scales
In this paper, we consider the almost periodic dynamics of a multispecies
Lotka-Volterra mutualism system with time varying delays on time scales. By
establishing some dynamic inequalities on time scales, a permanence result for
the model is obtained. Furthermore, by means of the almost periodic functional
hull theory on time scales and Lyapunov functional, some criteria are obtained
for the existence, uniqueness and global attractivity of almost periodic
solutions of the model. Our results complement and extend some scientific work
in recent years. Finally, an example is given to illustrate the main results.Comment: 31page
Universal presence of time-crystalline phases and period-doubling oscillations in one-dimensional Floquet topological insulators
In this work, we reported a ubiquitous presence of topological Floquet time
crystal (TFTC) in one-dimensional periodically-driven systems. The rigidity and
realization of spontaneous discrete time-translation symmetry (DTS) breaking in
our model require necessarily coexistence of anomalous topological invariants
(0 modes and modes), instead of the presence of disorders or many-body
localization. We found that in a particular frequency range of the underlying
drive, the anomalous Floquet phase coexistence between zero and pi modes can
produce the period-doubling (2T, two cycles of the drive) that breaks the
spontaneously, leading to the subharmonic response (, half the drive
frequency). The rigid period-oscillation is topologically-protected against
perturbations due to both non-trivially opening of 0 and -gaps in the
quasienergy spectrum, thus, as a result, can be viewed as a specific "Rabi
oscillation" between two Floquet eigenstates with certain quasienergy splitting
. Our modeling of the time-crystalline 'ground state' can be easily
realized in experimental platforms such as topological photonics and ultracold
fields. Also, our work can bring significant interests to explore topological
phase transition in Floquet systems and to bridge the gap between Floquet
topological insulators and photonics, and period-doubled time crystals.Comment: 31 pages, 6 figures, 2 supplementary figure
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