On σ\sigma-quasinormal subgroups of finite groups

Let $G$ be a finite group and $\sigma =\{\sigma_{i} | i\in I\}$ some partition of the set of all primes $\Bbb{P}$, that is, $\sigma =\{\sigma_{i} | i\in I \}$, where $\Bbb{P}=\bigcup_{i\in I} \sigma_{i}$ and $\sigma_{i}\cap \sigma_{j}= \emptyset$ for all $i\ne j$. We say that $G$ is $\sigma$-primary if $G$ is a $\sigma _{i}$-group for some $i$. A subgroup $A$ of $G$ is said to be: ${\sigma}$-subnormal in $G$ if there is a subgroup chain $A=A_{0} \leq A_{1} \leq \cdots \leq A_{n}=G$ such that either $A_{i-1}\trianglelefteq A_{i}$ or $A_{i}/(A_{i-1})_{A_{i}}$ is $\sigma$-primary for all $i=1, \ldots, n$, modular in $G$ if the following conditions hold: (i) $\langle X, A \cap Z \rangle=\langle X, A \rangle \cap Z$ for all $X \leq G, Z \leq G$ such that $X \leq Z$, and (ii) $\langle A, Y \cap Z \rangle=\langle A, Y \rangle \cap Z$ for all $Y \leq G, Z \leq G$ such that $A \leq Z$. In this paper, a subgroup $A$ of $G$ is called $\sigma$-quasinormal in $G$ if $L$ is modular and ${\sigma}$-subnormal in $G$. We study $\sigma$-quasinormal subgroups of $G$. In particular, we prove that if a subgroup $H$ of $G$ is $\sigma$-quasinormal in $G$, then for every chief factor $H/K$ of $G$ between $H^{G}$ and $H_{G}$ the semidirect product $(H/K)\rtimes (G/C_{G}(H/K))$ is $\sigma$-primary.Comment: 9 page

First Principles Study of Work Functions of Double Wall Carbon Nanotubes

Using first-principles density functional calculations, we investigated work functions (WFs) of thin double-walled nanotubes (DWNTs) with outer tube diameters ranging from 1nm to 1.5nm. The results indicate that work function change within this diameter range can be up to 0.5 eV, even for DWNTs with same outer diameter. This is in contrast with single-walled nanotubes (SWNTs) which show negligible WF change for diameters larger than 1nm. We explain the WF change and related charge redistribution in DWNTs using charge equilibration model (CEM). The predicted work function variation of DWNTs indicates a potential difficulty in their nanoelectronic device applications.Comment: 11 pages, 3 figures, to appear as rapid communication on Physical Review

TimeTrader: Exploiting Latency Tail to Save Datacenter Energy for On-line Data-Intensive Applications

Datacenters running on-line, data-intensive applications (OLDIs) consume significant amounts of energy. However, reducing their energy is challenging due to their tight response time requirements. A key aspect of OLDIs is that each user query goes to all or many of the nodes in the cluster, so that the overall time budget is dictated by the tail of the replies' latency distribution; replies see latency variations both in the network and compute. Previous work proposes to achieve load-proportional energy by slowing down the computation at lower datacenter loads based directly on response times (i.e., at lower loads, the proposal exploits the average slack in the time budget provisioned for the peak load). In contrast, we propose TimeTrader to reduce energy by exploiting the latency slack in the sub- critical replies which arrive before the deadline (e.g., 80% of replies are 3-4x faster than the tail). This slack is present at all loads and subsumes the previous work's load-related slack. While the previous work shifts the leaves' response time distribution to consume the slack at lower loads, TimeTrader reshapes the distribution at all loads by slowing down individual sub-critical nodes without increasing missed deadlines. TimeTrader exploits slack in both the network and compute budgets. Further, TimeTrader leverages Earliest Deadline First scheduling to largely decouple critical requests from the queuing delays of sub- critical requests which can then be slowed down without hurting critical requests. A combination of real-system measurements and at-scale simulations shows that without adding to missed deadlines, TimeTrader saves 15-19% and 41-49% energy at 90% and 30% loading, respectively, in a datacenter with 512 nodes, whereas previous work saves 0% and 31-37%.Comment: 13 page

Distinguishing technicolor models via tt-bar productions at polarized photon colliders

We study top quark pair productions at a polarized photon collider from an e(+)e(-) linear collider (LC) in various improved technicolor model, namely, the one-family walking technicolor model, the top-color-assisted technicolor model, and the top-color-assisted multiscale technicolor model. Recent constraint on the top-pion mass from the precision data of R(b) is considered. It is shown that, considering only the statistical errors, a polarized photon collider from a 500 GeV LC with an integrated luminosity of 500 inverse fb is sufficient for distinguishing the three improved technicolor models experimentally.Comment: 7 pages, 6 figures, to appear in Physical Review

Research on the drag reduction performance induced by the counterflowing jet for waverider with variable blunt radii

Waverider will endure the huge aero-heating in the hypersonic flow, thus, it need be blunt for the leading edge. However, the aerodynamic performance will decrease for the blunt waverider because of the drag hoik. How to improve the aerodynamic performance and reduce the drag and aero-heating is very important. The variable blunt radii method will improve the aerodynamic performance, however, the huge aero-heating and bow shock wave at the head is still serious. In the current study, opposing jet is used in the waverider with variable blunt radii to improve its performance. The three-dimensional coupled implicit Reynolds-averaged Navier-Stokes(RANS) equation and the two equation SST k–ω turbulence model have been utilized to obtain the flow field properties. The numerical method has been validated against the available experimental data in the open literature. The obtained results show that the L/D will drop 7–8% when R changes from 2 to 8. The lift coefficient will increase, and the drag coefficient almost keeps the same when the variable blunt radii method is adopted, and the L/D will increase. The variable blunt radii method is very useful to improve the whole characteristics of blunt waverider and the L/D can improve 3%. The combination of the variable blunt radii method and opposing jet is a novel way to improve the whole performance of blunt waverider, and L/D can improve 4–5%. The aperture as a novel way of opposing jet is suitable for blunt waverider and also useful to improve the aerodynamic and aerothermodynamic characteristics of waverider in the hypersonic flow. There is the optimal P0in/P0 that can make the detached shock wave reattach the lower surface again so that the blunt waverider can get the better aerodynamic performance

α\alpha-vacuum and inflationary bispectrum

In this paper, we discuss the non-Guassianity originated from the $\alpha$-vacuum on the CMB anisotropy. For $\alpha$-vacuum, there exist correlation between points in the acausal two patches of de Sitter spactime. Such kind of correlation can lead to large local form non-Guassianity in $\alpha$-vacuum. For the single field slow-roll inflationary scenario, the spacetime is in a quasi-de Sitter phase during the inflation. We will show that the $\alpha$-vacuum in this case will lead to non-Gaussianity with distinguished feature, of a large local form and a very different shape.Comment: 39 pages, 8 figures, references added, minor changes, accepted by Phys.Rev.