Cheban loops

Left Cheban loops are loops that satisfy the identity x(xy.z) = yx.xz. Right Cheban loops satisfy the mirror identity {(z.yx)x = zx.xy}. Loops that are both left and right Cheban are called Cheban loops. Cheban loops can also be characterized as those loops that satisfy the identity x(xy.z) = (y.zx)x. These loops were introduced in Cheban, A. M. Loops with identities of length four and of rank three. II. (Russian) General algebra and discrete geometry, pp. 117-120, 164, "Shtiintsa", Kishinev, 1980. Here we initiate a study of their structural properties. Left Cheban loops are left conjugacy closed. Cheban loops are weak inverse property, power associative, conjugacy closed loops; they are centrally nilpotent of class at most two.Comment: 6 page

Holddown arm release mechanism used on Saturn vehicles

With the development of the Saturn launch vehicle, it became mandatory to develop a system for restraining the vehicle until after all checks and engine thrust buildup were completed. The basic Saturn I holddown arm constrains the vehicle by clamping it between a fixed support and a movable jaw. The jaw is on a link pinned to rotate sufficiently to release the vehicle. There are three links in the jaw (restraining) system arranged so that with a small force provided by a pneumatic separator mechanism, the large loads of the vehicle can be restrained. Design details discussed are the link system, the separator, adjustments, and the energy absorber. The function of preloading is discussed. The secondary release system is described. Finally, the design differences between the Saturn I and the Saturn V arm are described

A survey of the UK benefit system

This paper describes all the main benefits in the UK system, giving details of rates and allowances, as well as numbers and types of claimants and levels of expenditure

Using chiral perturbation theory to extract the neutron-neutron scattering length from pi- d -> n n gamma

The reaction pi- d -> n n gamma is calculated in chiral perturbation theory so as to facilitate an extraction of the neutron-neutron scattering length (a_nn). We include all diagrams up to O(Q^3). This includes loop effects in the elementary pi- p -> gamma n amplitude and two-body diagrams, both of which were ignored in previous calculations. We find that the chiral expansion for the ratio of the quasi-free (QF) to final-state-interaction (FSI) peaks in the final-state neutron spectrum converges well. Our third-order calculation of the full spectrum is already accurate to better than 5%. Extracting a_nn from the shape of the entire pi- d -> n n gamma spectrum using our calculation in its present stage would thus be possible at the +-0.8 fm level. A fit to the FSI peak only would allow an extraction of a_nn with a theoretical uncertainty of +-0.2 fm. The effects that contribute to these error bars are investigated. The uncertainty in the $nn$ rescattering wave function dominates. This suggests that the quoted theoretical error of +-0.3 fm for the most recent pi- d -> n n gamma measurement may be optimistic. The possibility of constraining the nn rescattering wave function used in our calculation more tightly--and thus reducing the error--is briefly discussed.Comment: 35 pages, 14 eps figures, references and figure added, discussions of errors extended and clarified, improved conclusions, typos corrected, to be published in PR

Poverty and Inequality in the UK: 2008

In this Commentary, we assess the changes to average incomes, inequality and poverty that have occurred under the first 10 years of the Labour government, with a particular focus on the changes that have occurred in the latest year of data. This analysis is based upon the latest figures from the DWP's Households Below Average Income (HBAI) series, published on 10 June 2008 (Department for Work and Pensions, 2008c). The HBAI series takes household income as its measure of living standards and is derived from the Family Resources Survey, a survey of around 28,000 households in the United Kingdom that asks detailed questions about income from a range of sources

Herschel observations in the ultracompact HII region Mon R2: Water in dense photon-dominated regions (PDRs)

Context. Monoceros R2, at a distance of 830 pc, is the only ultracompact Hii region (UC H_(II)) where the photon-dominated region (PDR) between the ionized gas and the molecular cloud can be resolved with Herschel. Therefore, it is an excellent laboratory to study the chemistry in extreme PDRs (G_0 > 10^5 in units of Habing field, n > 10^6 cm^9−3)). Aims. Our ultimate goal is to probe the physical and chemical conditions in the PDR around the UC H_(II) Mon R2. Methods. HIFI observations of the abundant compounds ^(13)CO, C^(18)O, o-H_2^(18)O, HCO^+, CS, CH, and NH have been used to derive the physical and chemical conditions in the PDR, in particular the water abundance. The modeling of the lines has been done with the Meudon PDR code and the non-local radiative transfer model described by Cernicharo et al. Results. The ^(13)CO, C^(18)O, o-H^(18)_2O, HCO^+ and CS observations are well described assuming that the emission is coming from a dense (n = 5 × 10^6 cm^(−3), N(H_2) > 10^(22) cm^(−2)) layer of molecular gas around the H_(II) region. Based on our o-H^(18)_2O observations, we estimate an o-H_2O abundance of ≈2 × 10^(−8). This is the average ortho-water abundance in the PDR. Additional H^(18)_2O and/or water lines are required to derive the water abundance profile. A lower density envelope (n ~ 10^5 cm^(−3), N(H_2) = 2−5 × 10^(22) cm^(−2)) is responsible for the absorption in the NH 1_1 → 0_2 line. The emission of the CH ground state triplet is coming from both regions with a complex and self-absorbed profile in the main component. The radiative transfer modeling shows that the ^(13)CO and HCO^+ line profiles are consistent with an expansion of the molecular gas with a velocity law, v_e = 0.5 × (r/R_(out))^(−1) km s^(−1), although the expansion velocity is poorly constrained by the observations presented here. Conclusions. We determine an ortho-water abundance of ≈2 × 10^(−8) in Mon R2. Because shocks are unimportant in this region and our estimate is based on H^(18)_2O observations that avoids opacity problems, this is probably the most accurate estimate of the water abundance in PDRs thus far

Poverty and inequality in the UK: 2009

In this Commentary, we assess the changes to average incomes, inequality and poverty that have occurred since Labour came to power in 1997, with a particular focus on the changes that have occurred in the latest year of data. This analysis is based upon the latest figures from the DWP's Households Below Average Income (HBAI) series, published on 7 May 2009 (Department for Work and Pensions, 2009). The HBAI series takes household income as its measure of living standards, and is derived from the Family Resources Survey, a survey of around 25,000 households in the United Kingdom that asks detailed questions about income from a range of sources

The molecular emission-line spectrum of IRC +10216 between 330 and 358 GHz

We have conducted a spectral line survey of IRC + 10216 using the Caltech Submillimeter Observatory to an average sensitivity of ≾95 mK. A deconvolution algorithm has been used to derive the continuous single-sideband spectrum from 330.2 to 358.1 GHz. A total of 56 spectral lines were detected of which 54 have been identified with 8 molecules and a total of 18 isotopomers. The observed lines are used to derive column densities and relative abundances for the detected species. Within this frequency range the spectral lines detected contribute the majority of the total flux emitted by IRC + 10216. We use the derived column densities and excitation temperatures to simulate the molecular line emission (assuming LTE) at frequencies up to 1000 GHz. The observed and simulated flux from line emission is compared to broadband total flux measurements and to dust emission assuming a power-law variation of the dust emissivity. We conclude that significant corrections for the line flux must be made to broadband flux measurements of IRC + 10216 at wavelengths longer than ~750 µm

Whistleblowing to regulators: are prescribed persons fit for purpose?

A study of 53 organisations designated as prescribed persons for whistleblowing purposes under Part IVA Employment Rights Act 1996 (ERA) revealed that a significant number of prescribed persons lacked essential knowledge and skills for the role, including certainty as to which organisations actually were prescribed persons. The report describes and analyses these shortcomings and offers recommendations for making the role of the prescribed person more effective