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Let $(G,\{\rho_0, \rho_1, \rho_2\})$ be a string C-group of order $4p^m$ with type $\{k_1, k_2\}$ for $m \geq 2$, $k_1, k_2\geq 3$ and $p$ be an odd prime. Let $P$ be a Sylow $p$-subgroup of $G$. We prove that $G \cong P \rtimes (\mathbb{Z}_2 \times \mathbb{Z}_2)$, $d(P)=2$, and up to duality, $p \mid k_1, 2p \mid k_2$. Moreover, we show that if $P$ is abelian, then $(G,\{\rho_0, \rho_1, \rho_2\})$ is tight and hence known. In the case where $P$ is nonabelian, we construct an infinite family of string C-group with type $\{p, 2p\}$ of order $4p^m$ where $m \geq 3$., Comment: arXiv admin note: text overlap with arXiv:2107.02925

We construct four infinite families of chiral $3$-polytopes of type $\{4, 8\}$, with $1024m^4$, $2048m^4$, $4096m^4$ and $8192m^4$ automorphisms for every positive integer $m$, respectively. The automorphism groups of these polytopes are solvable groups, and when $m$ is a power of $2$, they provide examples with automorphism groups of order $2^n$ where $n \geq 10$. (On the other hand, no chiral polytopes of type $\{4, 8\}$ exist for $n \leq 9$.) In particular, our families give a partial answer to a problem proposed by Schulte and Weiss in [Problems on polytopes, their groups, and realizations, {\em Period. Math. Hungar.} 53 (2006), 231-255] and a problem proposed by Pellicer in [Developments and open problems on chiral polytopes, {\em Ars Math. Contemp} 5 (2012), 333-354]., Comment: 11pges,1 figures. arXiv admin note: substantial text overlap with arXiv:1912.03398

GRB 221009A is the brightest gamma-ray burst ever detected since the discovery of this kind of energetic explosions. However, an accurate measurement of the prompt emission properties of this burst is very challenging due to its exceptional brightness. With joint observations of \textit{Insight}-HXMT and GECAM-C, we made an unprecedentedly accurate measurement of the emission during the first $\sim$1800 s of GRB 221009A, including its precursor, main emission (ME, which dominates the burst in flux), flaring emission and early afterglow, in the hard X-ray to soft gamma-ray band from $\sim$ 10 keV to $\sim$ 6 MeV. Based on the GECAM-C unsaturated data of the ME, we measure a record-breaking isotropic equivalent energy ($E_{\rm iso}$) of $\bf \sim 1.5 \times 10^{55}$ erg, which is about eight times the total rest-mass energy of the Sun. The early afterglow data require a significant jet break between 650 s and 1100 s, most likely at $\sim950$ s from the afterglow starting time $T_{AG}$, which corresponds to a jet opening angle of $\sim {0.7^\circ} \ (\eta_\gamma n)^{1/8}$, where $n$ is the ambient medium density in units of $\rm cm^{-3}$ and $\eta_\gamma$ is the ratio between $\gamma$-ray energy and afterglow kinetic energy. The beaming-corrected total $\gamma$-ray energy $E_{\gamma}$ is $\sim 1.15 \times10^{51} \ (\eta_\gamma n)^{1/4}$ erg, which is typical for long GRBs. These results suggest that this GRB may have a special central engine, which could launch and collimate a very narrowly beamed jet with an ordinary energy budget, leading to exceptionally luminous gamma-ray radiation per unit solid angle. Alternatively, more GRBs might have such a narrow and bright beam, which are missed by an unfavorable viewing angle or have been detected without distance measurement., Comment: Submitted to National Science Review. This paper is under press embargo, contact the corresponding author for details

As a new member of GECAM mission, GECAM-C (also named High Energy Burst Searcher, HEBS) was launched onboard the SATech-01 satellite on July 27th, 2022, which is capable to monitor gamma-ray transients from $\sim$ 6 keV to 6 MeV. As the main detector, there are 12 gamma-ray detectors (GRDs) equipped for GECAM-C. In order to verify the GECAM-C GRD detector performance and to validate the Monte Carlo simulations of detector response, comprehensive on-ground calibration experiments have been performed using X-ray beam and radioactive sources, including Energy-Channel relation, energy resolution, detection efficiency, SiPM voltage-gain relation and the non-uniformity of positional response. In this paper, the detailed calibration campaigns and data analysis results for GECAM-C GRDs are presented, demonstrating the excellent performance of GECAM-C GRD detectors., Comment: third version

Although the two-dimensional electron gas (2DEG) in (001) Zn$_{1-x}$Mg$_x$O/ZnO heterostructures has been discovered for about twenty years, the origin of the 2DEG is still inconclusive. In the present letter, the formation mechanisms of 2DEG near the interfaces of (001) Zn$_{1-x}$Mg$_x$O/ZnO heterostructures were investigated via the first-principles calculations method. It is found that the polarity discontinuity near the interface can neither lead to the formation of 2DEG in devices with thick Zn$_{1-x}$Mg$_{x}$O layers nor in devices with thin Zn$_{1-x}$Mg$_{x}$O layers. For the heterostructure with thick Zn$_{1-x}$Mg$_{x}$O layers, the oxygen vacancies near the interface introduce a defect band in the band gap, and the top of the defect band overlaps with the bottom of the conduction band, leading to the formation of the 2DEG near the interface of the device. For the heterostructure with thin Zn$_{1-x}$Mg$_{x}$O layers, the absorption of hydrogen atoms, oxygen atoms, or OH groups on the surface of Zn$_{1-x}$Mg$_{x}$O film plays a key role for the formation of 2DEG in the device. Our results manifest the sources of 2DEGs in Zn$_{1-x}$Mg$_x$O/ZnO heterostructures on the electronic structure level., Comment: 6 pages, 6 figures

Ta-doped SnO$_2$ films with high conductivity and high optical transparency have been successfully fabricated using rf-sputtering method and their electrical transport properties have been investigated. All films reveal degenerate semiconductor (metal) characteristics in electrical transport properties. For the thick films ($t\sim 1\,\mu \rm{m}$ with $t$ being the thickness) deposited in pure argon, the electron-phonon scattering alone cannot explain the temperature dependent behaviors of resistivity, the interference effect between electron-phonon and electron-impurity scattering should be considered. For the $t\lesssim 36$ nm films, both conductivity and the Hall coefficient show linear relation with the logarithm of temperature ($\ln T$) from $\sim$100 K down to liquid helium temperature. The $\ln T$ behaviors of conductivity and Hall coefficient cannot be explained by the Altshuler-Aronov type electron-electron interaction effect, but can be quantitatively interpreted by the electron-electron interaction effects in the presence of granularity. Our results not only provide strong supports for the theoretical results on the electron-phonon-impurity interference effect, but also confirm the validity of the theoretical predictions of charge transport in granular metals in strong coupling regime., Comment: 7 pages and 6 figures

Realtime trigger and localization of bursts are the key functions of GECAM, which is an all-sky gamma-ray monitor launched in Dec 10, 2020. We developed a multifunctional trigger and localization software operating on the CPU of the GECAM electronic box (EBOX). This onboard software has the following features: high trigger efficiency for real celestial bursts with a suppression of false triggers caused by charged particle bursts and background fluctuation, dedicated localization algorithm optimized for short and long bursts respetively, short time latency of the trigger information which is downlinked throught the BeiDou satellite navigation System (BDS). This paper presents the detailed design and deveopment of this trigger and localization software system of GECAM, including the main functions, general design, workflow and algorithms, as well as the verification and demonstration of this software, including the on-ground trigger tests with simulated gamma-ray bursts made by a dedicated X-ray tube and the in-flight performance to real gamma-ray bursts and magnetar bursts., Comment: Draft, comments welcome

In this paper, we construct an infinite families of group $G$ of order $4p^m$ which can be an automorphism group of some regular polytope with type $\{p, 2p\}$, where $m \geq 3$ and $p$ is an odd prime. For $p=3$, our polytopes are the regular toroidal maps $\{3, 6\}$., Comment: 10pages. arXiv admin note: text overlap with arXiv:2001.02945

In [Problems on polytopes, their groups, and realizations, Periodica Math. Hungarica 53 (2006) 231-255] Schulte and Weiss proposed the following problem: {\em Characterize regular polytopes of orders $2^np$ for $n$ a positive integer and $p$ an odd prime}. In this paper, we first prove that if a $3$-polytope of order $2^np$ has Schl\"afli type $\{k_1, k_2\}$, then $p \mid k_1$ or $p \mid k_2$. This leads to two classes, up to duality, for the Schl\"afli type, namely Type (1) where $k_1=2^sp$ and $k_2=2^t$ and Type (2) where $k_1=2^sp$ and $k_2=2^tp$. We then show that there exists a regular $3$-polytope of order $2^np$ with Type (1) when $s\geq 2$, $t\geq 2$ and $n\geq s+t+1$ coming from a general construction of regular $3$-polytopes of order $2^n\ell_1\ell_2$ with Schl\"afli type $\{2^s\ell_1,2^t\ell_2\}$ where both $\ell_1$ and $\ell_2$ are odd. Furthermore, for $p=3$ and $n \geq 7$, we show that there exists a regular 3-polytope of order $3\cdot2^n$ with type $\{6,2^s\}$ if and only if $2\leq s \leq n-2$ and $s \neq n-3$. For Type (2), we prove that there exists a regular $3$-polytope of order $2^n\cdot 3$ with Schl\"afli type $\{6, 6\}$ when $n \ge 5$ coming from a general construction of regular $3$-polytopes of Schl\"afli type $\{6,6\}$ with orders $192m^3$, $384m^3$ or $768m^3$, for any positive integer $m$., Comment: 17pages

We construct two infinite families of locally toroidal chiral polytopes of type $\{4,4,4\}$, with $1024m^2$ and $2048m^2$ automorphisms for every positive integer $m$, respectively. The automorphism groups of these polytopes are solvable groups, and when $m$ is a power of $2$, they provide examples with automorphism groups of order $2^n$ where $n$ can be any integer greater than $9$. (On the other hand, no chiral polytopes of type $[4,4,4]$ exist for $n \leq 9$.) In particular, our two families give a partial answer to a problem proposed by Schulte and Weiss in [Problems on polytopes, their groups, and realizations, {\em Periodica Math.\ Hungarica\} 53 (2006), 231-255]., Comment: 10pages

In this letter, we discuss the possibility of non 0-0 atomic lines as the reference transitions to design a new atomic clock. The proposed clock operates in high C-field regime offering an interesting alternative to conventional clock based on 0-0 transition as the former can also eliminate the influence of the first-order Zeeman effect. Using the Breit-Rabi formula, we theoretically calculate the magnetically insensitive frequency and the corresponding C-field value for different alkali atom species. We also provide an estimate of the uncertainty of frequency shift to change of C-field. We show that a high C-field clock based on Cs: 3,-1 - 4,0, 3,0 - 4,-1, and 3,-1 - 4,-1, can achieve a bias of 10-14 with a C-field of 10-6 uncertainty. The free first-order Zeeman effect C-field for 3,-1 - 4,0 or 3,0 - 4,-1 transition is about one half that for 3,-1 - 4,-1 transition., Comment: 7 pages, 2 figures, and 1 table

For any positive integers $n, s, t, l$ such that $n \geq 10$, $s, t \geq 2$, $l \geq 1$ and $n \geq s+t+l$, a new infinite family of regular 3-hypertopes with type $(2^s, 2^t, 2^l)$ and automorphism group of order $2^n$ is constructed., Comment: 11. arXiv admin note: text overlap with arXiv:1604.03162

For each $d\geq 3$, $n \geq 10$, and $k_1, k_2, \ldots, k_{d-1}\geq 2$ with $k_1+k_2+\ldots+k_{d-1}\leq n-1$, we construct a regular $d$-polytope whose automorphism group is of order $2^n$ and whose Schl\"afli type is $\{2^{k_1},2^{k_2}, \ldots, 2^{k_{d-1}}\}$.

In this paper, we consider the possible types of regular maps of order $2^n$, where the order of a regular map is the order of automorphism group of the map. For $n \le 11$, M. Conder classified all regular maps of order $2^n$. It is easy to classify regular maps of order $2^n$ whose valency or covalency is $2$ or $2^{n-1}$. So we assume that $n \geq 12$ and $2\leq s,t\leq n-2$ with $s\leq t$ to consider regular maps of order $2^n$ with type $\{2^s, 2^t\}$. We show that for $s+t\leq n$ or for $s+t>n$ with $s=t$, there exists a regular map of order $2^n$ with type $\{2^s, 2^t\}$, and furthermore, we classify regular maps of order $2^n$ with types $\{2^{n-2},2^{n-2}\}$ and $\{2^{n-3},2^{n-3}\}$. We conjecture that, if $s+t>n$ with $s

We demonstrate a laser-based underwater transfer of radio frequency clock signal with a phase compensation technique. With this frequency transfer scheme, a 100 MHz signal has been transferred over 5 m underwater link. Timing jitter power spectral density, timing fluctuations and instabilities were all measured to evaluate the quality of the transferred frequency signal. The experimental results show the root-mean-square (RMS) timing fluctuations of the transferred frequency signal over 5 m underwater link with and without phase compensation are 2.1 ps and 9.6 ps within 5000 s, respectively. The relative fractional frequency instabilities are on the order of 5E-13 at 1 s and 7E-16 at 1000 s for phase-compensated link, and 2E-12 at 1 s and 7E-15 at 1000 sfor uncompensated link, respectively. The proposed frequency transfer scheme has a potential application that disseminating Cs and H-master clocks signal over the underwater transmission link since the stability of the transmission link is superior to these atomic clocks., Comment: 5 pages, 6 figures

We experimentally investigated Rabi resonance-based continuously frequency-tunable microwave (MW) magnetic field detection using a single hybrid vapor cell filled with cesium and rubidium atoms. The multispecies atomic systems, with their tunable abilities in transition frequencies, enabled this atomic sensing head to cover a broader detectable MW field scope compared to the use of a single metal atom. Here, we demonstrated the simultaneous observation of atomic Rabi resonance signals with 85Rb, 87Rb, and 133Cs in the same vapor cell. Using an experimentally feasible static magnetic field (DC field) below 500 Gauss, we realized a MW magnetic field strength detection with bandwidths of 4.8 GHz around 8.1 GHz. The use of these three atomic systems confined in a single vapor cell also enabled the establishment of an identical MW field with the help of DC field, allowing us to perform a perfect comparison for different applications that require the same electromagnetic environment. The results may be useful for the realization and application of many atomic detectors based on different physical principles., Comment: 10 pages, 7 figures