Braiding structures on formal Poisson groups and classical solutions of the QYBE

If is a quasitriangular Lie bialgebra, the formal Poisson group can be given a braiding structure. This was achieved by Weinstein and Xu using purely geometrical means, and independently by the authors by means of quantum groups. In this paper we compare these two approaches. First, we show that the braidings they produce share several similar properties (in particular, the construction is functorial); secondly, in the simplest case (G=SL₂) they do coincide. The question then rises of whether they are always the same this is positively answered in a separate paper.     

A family of affine quantum group invariant integrable extensions of the Hubbard Hamiltonian

We construct a family of spin chain Hamiltonians, which have the affine quantum group symmetry . Their eigenvalues coincide with the eigenvalues of the usual spin chain Hamiltonians, but have the degeneracy of levels, corresponding to the affine . The space of states of these spin chains is formed by the tensor product of the fully reducible representations of the quantum group.

The fermionic representations of the constructed spin chain Hamiltonians show that we have obtained new extensions of the Hubbard Hamiltonians. All of them are integrable and have the affine quantum group symmetry. The exact ground state of such type of model is presented, exhibiting superconducting behavior via the η-pairing mechanism.     

Poincaré-Invariant Markov Processes and Gaussian Random Fields on Relativistic Phase Space

We give a complete characterization, including a Lévy–Itô decomposition, of Poincaré-invariant Markov processes on , the relativistic phase space in 1+1 spacetime dimensions. Then, by means of such processes, we construct Poincaré-invariant Gaussian random fields, and we prove a no-go theorem for the random fields corresponding to Brownian motions on .     

Normalized intensity correlation function of single-mode laser system driven by colored cross-correlation noises

Considering a single-mode laser system with cross-correlated additive colored noise and multiplicative colored noise, we study the effects of correlation among noises on the normalized intensity correlation function C(s).C(s) is derived by means of the projection operator method.     

Some Quantum-like Hopf Algebras which Remain Noncommutative when q = 1

Starting with only three of the six relations defining the standard (Manin) GL _q (2), we try to construct a quantum group. The antipode condition requires some new relations, but the process stops at a Hopf algebra with a Birkhoff–Witt basis of irreducible monomials. The quantum determinant is group-like but not central, even when q = 1. So, the two Hopf algebras constructed in this way are not isomorphic to the Manin GL _q (2), all of whose group-like elements are central. Analogous constructions can be made starting with the Dipper–Donkin version of GL _q (2), but these turn out to be included in the two classes of Hopf algebras described above.     

Ultrafast X‐ray imaging of laser–metal additive manufacturing processes

The high‐speed synchrotron X‐ray imaging technique was synchronized with a custom‐built laser‐melting setup to capture the dynamics of laser powder‐bed fusion processes in situ. Various significant phenomena, including vapor‐depression and melt‐pool dynamics and powder‐spatter ejection, were captured with high spatial and temporal resolution. Imaging frame rates of up to 10 MHz were used to capture the rapid changes in these highly dynamic phenomena. At the same time, relatively slow frame rates were employed to capture large‐scale changes during the process. This experimental platform will be vital in the further understanding of laser additive manufacturing processes and will be particularly helpful in guiding efforts to reduce or eliminate microstructural defects in additively manufactured parts.     

Effect of MgO additive on the high-frequency properties of Z-type hexaferrites

MgO was introduced into low-temperature sintered Z-type hexaferrites in order to improve their high-frequency electromagnetic properties. In the doped samples the major Z-type phase coexists with a small amount of W-type magnetoplumbite phase. The addition of MgO causes a decrease of the average grain size and an increase of the magnetocrystalline anisotropy (K₁) and the saturation magnetization (M_s) with the increment of K₁ being larger than that of M_s. These factors result in a reduce of the initial permeability. Also, the samples with MgO additive exhibit higher Q-factor and dc resistivity. Furthermore, the introduction of MgO can decrease the dielectric constant and improve the dielectric loss tangent of the samples by reducing the electronic transition in octahedral site (B-site) between Fe²⁺ and Fe³⁺ ions.     

Large single crystal diamond grown in FeNiMnCo-S-C system under high pressure and high temperature conditions

Large diamonds have successfully been synthesized from FeNiMnCo-S-C system at temperatures of 1255-1393 ℃and pressures of 5.3-5.5 GPa.Because of the presence of sulfur additive,the morphology and color of the large diamond crystals change obviously.The content and shape of inclusions change with increasing sulfur additive.It is found that the pressure and temperature conditions required for the synthesis decrease to some extent with the increase of S additive,which results in left down of the V-shape region.The Raman spectra show that the introduction of additive sulfur reduces the quality of the large diamond crystals.The x-ray photoelectron spectroscopy(XPS) spectra show the presence of S in the diamonds.Furthermore,the electrical properties of the large diamond crystals are tested by a four-point probe and the Hall effect method.When sulfur in the cell of diamond is up to 4.0 wt.%,the resistance of the diamond is 9.628×10~5 Ω·cm.It is shown that the large single crystal samples are n type semiconductors.This work is helpful for the further research and application of sulfur-doped semiconductor large diamond.     

Examples of Twisted Cyclic Cocycles from Covariant Differential Calculi

For two covariant differential *-calculi, the twisted cyclic cocycle associated with the volume form is represented in terms of commutators for some self-adjoint operator and some *-representation of the underlying *-algebra.