A class of finite pp-groups and the normalized unit groups of group algebras

Let $p$ be a prime and $\mathbb{F}_p$ be a finite field of $p$ elements. Let $\mathbb{F}_pG$ denote the group algebra of the finite $p$-group $G$ over the field $\mathbb{F}_p$ and $V(\mathbb{F}_pG)$ denote the group of normalized units in $\mathbb{F}_pG$. Suppose that $G$ is a finite $p$-group given by a central extension of the form $$1\longrightarrow \mathbb{Z}_{p^n}\times \mathbb{Z}_{p^m} \longrightarrow G \longrightarrow \mathbb{Z}_p\times \cdots\times \mathbb{Z}_p \longrightarrow 1$$ and $G'\cong \mathbb{Z}_p$, $n, m\geq 1$ and $p$ is odd. In this paper, the structure of $G$ is determined. And the relations of $V(\mathbb{F}_pG)^{p^l}$ and $G^{p^l}$, $\Omega_l(V(\mathbb{F}_pG))$ and $\Omega_l(G)$ are given. Furthermore, there is a direct proof for $V(\mathbb{F}_pG)^p\bigcap G=G^p$

Four field coupled dynamics for a micro resonant gas sensor

In a micro resonant gas sensor, the electrostatic excitation is used widely. For a micro resonant gas sensor with electrostatic excitation, four physical fields are involved. In this paper, for the micro resonant gas sensor, the four-field coupled dynamics equation is proposed. It includes mechanical force field, chemical density field, electrostatic force field, and the van der Waals force field. Using the method of multiple scales, the coupled dynamics equation is resolved. The effects of the four physical fields on the natural frequencies for the micro resonant gas sensor are investigated. Results show that the effects of the Van der Waals force on the natural frequencies of the micro resonant gas sensor depend on the mechanical parameters and the bias voltages; the sensitivity of the natural frequencies to the gas adsorption depends on the mechanical parameters, the bias voltages, and the Van der Waals force

Three-dimensional Turbulent Reconnection within Solar Flare Current Sheet

Solar flares can release coronal magnetic energy explosively and may impact the safety of near-earth space environments. Their structures and properties on macroscale have been interpreted successfully by the generally-accepted two-dimension standard model invoking magnetic reconnection theory as the key energy conversion mechanism. Nevertheless, some momentous dynamical features as discovered by recent high-resolution observations remain elusive. Here, we report a self-consistent high-resolution three-dimension magnetohydrodynamical simulation of turbulent magnetic reconnection within a flare current sheet. It is found that fragmented current patches of different scales are spontaneously generated with a well-developed turbulence spectrum at the current sheet, as well as at the flare loop-top region. The close coupling of tearing-mode and Kelvin-Helmholtz instabilities plays a critical role in developing turbulent reconnection and in forming dynamical structures with synthetic observables in good agreement with realistic observations. The sophisticated modeling makes a paradigm shift from the traditional to three-dimension turbulent reconnection model unifying flare dynamical structures of different scales.Comment: 15 pages, 8 figure, accepted for publication in ApJ

Molecular Simulation of Hyperbranched Polyester

A new types of hyperbranched polyester was synthesized by the 2,2-bis(hydroxymethyl) propionic acid as an AB2-type monomer and glycerol as the core moiety. Molecular weights were confirmed by Gel Permeation Chromatography. Acid values were titrated by KOH. The hydroxy value was obtained by titration. Furthermore, we calculate logarithmic value of acid value, hydroxy value, and molecular weight, respectively, and the simulation model curves were obtained. Based on the simulation model curves, we establish the empirical equation of the relationship of molecular weight, acid value and hydroxy value

Valley-polarized quantum anomalous Hall effect in van der Waals heterostructures based on monolayer jacutingaite family materials

We numerically study the general valley polarization and anomalous Hall effect in van der Waals (vdW) heterostructures based on monolayer jacutingaite family materials Pt$_{2}$AX$_{3}$ (A = Hg, Cd, Zn; X = S, Se, Te). We perform a systematic study on the atomic, electronic, and topological properties of vdW heterostructures composed of monolayer Pt$_{2}$AX$_{3}$ and two-dimensional ferromagnetic insulators. We show that four kinds of vdW heterostructures exhibit valley-polarized quantum anomalous Hall phase, i.e., Pt$_{2}$HgS$_{3}$/NiBr$_{2}$, Pt$_{2}$HgSe$_{3}$/CoBr$_{2}$, Pt$_{2}$HgSe$_{3}$/NiBr$_{2}$, and Pt$_{2}$ZnS$_{3}$/CoBr$_{2}$, with a maximum valley splitting of 134.2 meV in Pt$_{2}$HgSe$_{3}$/NiBr$_{2}$ and sizable global band gap of 58.8 meV in Pt$_{2}$HgS$_{3}$/NiBr$_{2}$. Our findings demonstrate an ideal platform to implement applications on topological valleytronics