The Sorting Index and Permutation Codes

In the combinatorial study of the coefficients of a bivariate polynomial that generalizes both the length and the reflection length generating functions for finite Coxeter groups, Petersen introduced a new Mahonian statistic $sor$, called the sorting index. Petersen proved that the pairs of statistics $(sor,cyc)$ and $(inv,rl\textrm{-}min)$ have the same joint distribution over the symmetric group, and asked for a combinatorial proof of this fact. In answer to the question of Petersen, we observe a connection between the sorting index and the B-code of a permutation defined by Foata and Han, and we show that the bijection of Foata and Han serves the purpose of mapping $(inv,rl\textrm{-}min)$ to $(sor,cyc)$. We also give a type $B$ analogue of the Foata-Han bijection, and we derive the quidistribution of $(inv_B,{\rm Lmap_B},{\rm Rmil_B})$ and $(sor_B,{\rm Lmap_B},{\rm Cyc_B})$ over signed permutations. So we get a combinatorial interpretation of Petersen's equidistribution of $(inv_B,nmin_B)$ and $(sor_B,l_B')$. Moreover, we show that the six pairs of set-valued statistics $\rm (Cyc_B,Rmil_B)$, $\rm(Cyc_B,Lmap_B)$, $\rm(Rmil_B,Lmap_B)$, $\rm(Lmap_B,Rmil_B)$, $\rm(Lmap_B,Cyc_B)$ and $\rm(Rmil_B,Cyc_B)$ are equidistributed over signed permutations. For Coxeter groups of type $D$, Petersen showed that the two statistics $inv_D$ and $sor_D$ are equidistributed. We introduce two statistics $nmin_D$ and $\tilde{l}_D'$ for elements of $D_n$ and we prove that the two pairs of statistics $(inv_D,nmin_D)$ and $(sor_D,\tilde{l}_D')$ are equidistributed.Comment: 25 page

X-ray Diagnostics of Grain Depletion in Matter Accreting onto T Tauri Stars

Recent analysis of high resolution Chandra X-ray spectra has shown that the Ne/O abundance ratio is remarkably constant in stellar coronae. Based on this result, we point out the utility of the Ne/O ratio as a discriminant for accretion-related X-rays from T Tauri stars, and for probing the measure of grain-depletion of the accreting material in the inner disk. We apply the Ne/O diagnostic to the classical T Tauri stars BP Tau and TW Hya--the two stars found to date whose X-ray emission appears to originate, at least in part, from accretion activity. We show that TW Hya appears to be accreting material which is significantly depleted in O relative to Ne. In constrast, BP Tau has an Ne/O abundance ratio consistent with that observed for post-T Tauri stars. We interpret this result in terms of the different ages and evolutionary states of the circumstellar disks of these stars. In the young BP Tau disk (age 0.6 Myr) dust is still present near the disk corotation radius and can be ionized and accreted, re-releasing elements depleted onto grains. In the more evolved TW Hya disk (age 10 Myr), evidence points to ongoing coagulation of grains into much larger bodies, and possibly planets, that can resist the drag of inward-migrating gas, and accreting gas is consequently depleted of grain-forming elements.Comment: 13 pages, 1 Figure, ApJ Letters, in pres

Powering Anomalous X-ray Pulsars by Neutron Star Cooling

Using recently calculated analytic models for the thermal structure of ultramagnetized neutron stars, we estimate the thermal fluxes from young ($t\sim 1000$ yr) ultramagnetized ($B \sim 10^{15}$ G) cooling neutron stars. We find that the pulsed X-ray emission from objects such as 1E 1841-045 and 1E 2259+586 as well as many soft-gamma repeaters can be explained by photon cooling if the neutron star possesses a thin insulating envelope of matter of low atomic weight at densities $\rho < 10^{7}-10^{8}$ g/cm$^3$. The total mass of this insulating layer is $M \sim 10^{-11}-10^{-8} M_\odot$.Comment: 8 pages, 1 figure, to appear in Ap.J. Letters (one reference entry corrected, no other changes

Pengembangan Tortila Berkalsium sebagai Alternatif Pangan Diet Casein Free-Gluten Free pada Industri Kecil dengan Metode Value Engineering

The number of people with autism increased 56% in 1998 – 2013, and it was a global problem. People with autism need special treatments and CFGF diet (casein free, gluten free) was one of those treatments. That's why, the development The calcium content was expected to substitute the calcium from dairy consumption, which shouldn't be consumed by people with autism. The method used in this product development was value engineering which separated in three steps: information, creativity, and analysis steps. Respectively, this research was also further completed with chemical The goal of this research was to design some product implemented in small scale industry. Respondends and panelist in this research were consisted of students and teachers. They acted as the market of the product, especially as a part of general society. This product were designed to provide CFGF snack for people with autism, and those who need CFGF diet. But this product was not limited to that market, it can be consumed by general society not only for people with autism, hence the students and teachers were used. The research showed that the best concept was a product produced with to get 200 grams of dough. This product concept was also designed to be packed in big size gusset packaging materials and the chips was triangle-shaped with size of feasible to be produced in small scale industry

A multi-color fast-switching microfluidic droplet dye laser

We describe a multi-color microfluidic dye laser operating in whispering gallery mode based on a train of alternating droplets containing solutions of different dyes; this laser is capable of switching the wavelength of its emission between 580 nm and 680 nm at frequencies up to 3.6 kHz -— the fastest among all dye lasers reported; it has potential applications in on-chip spectroscopy and flow cytometry

Effects of exoplanetary gravity on human locomotor ability

At some point in the future, if mankind hopes to settle planets outside the Solar System, it will be crucial to determine the range of planetary conditions under which human beings could survive and function. In this article, we apply physical considerations to future exoplanetary biology to determine the limitations which gravity imposes on several systems governing the human body. Initially, we examine the ultimate limits at which the human skeleton breaks and muscles become unable to lift the body from the ground. We also produce a new model for the energetic expenditure of walking, by modelling the leg as an inverted pendulum. Both approaches conclude that, with rigorous training, humans could perform normal locomotion at gravity no higher than 4 $g_{\textrm{Earth}}$.Comment: 12 pages, 4 figures, to be published in The Physics Teache

Deeper Chandra Follow-up of Cygnus TeV Source Perpetuates Mystery

A 50 ksec Chandra observation of the unidentified TeV source in Cygnus reported by the HEGRA collaboration reveals no obvious diffuse X-ray counterpart. However, 240 Pointlike X-ray sources are detected within or nearby the extended TeV J2032+4130 source region, of which at least 36 are massive stars and 2 may be radio emitters. That the HEGRA source is a composite, having as counterpart the multiple point-like X-ray sources we observe, cannot be ruled out. Indeed, the distribution of point-like X-ray sources appears non-uniform and concentrated broadly within the extent of the TeV source region. We offer a hypothesis for the origin of the very high energy gamma-ray emission in Cyg OB2 based on the local acceleration of TeV range cosmic rays and the differential distribution of OB vs. less massive stars in this association.Comment: Substantially revised version; incorporates referee suggestions & expanded discussio