Preliminary Survey of Retrograde Velocities Required for Insertion Into Low-Altitude Lunar Orbits

Closed lunar orbits are envisaged in lunar mission programs. The study described herein was undertaken to obtain an appreciation of the relevant fuel consumption requirements. The retrograde impulses necessary for establishing the orbits were assumed to occur at the point of closest approach of the main earth-moon trajectory; this point, designated as the arrival position, was restricted to a lunar altitude of 5,000 nautical miles or less. The orientation of the arrival position vector relevant to any coplanar radius vector is not constrained, however, and similarly the scalar value of the arrival velocity is unrestrained. Since the arrival altitude is restricted to 5,000 nautical miles or less, the perturbing accelerations of the earth and sun are sufficiently small that the vehicle and moon essentially comprise an isolated two-body system; this is discussed in the report. Retrograde velocities are determined for any required pericynthion position. If the pericynthion orientation requirement is relaxed then a smaller retrograde velocity is in some cases possible. A comparison between minimum retrograde velocities and retrograde velocities necessary for stipulated pericynthion positions is given. Arrival velocities are correlated with feasible earth departure conditions. The equations developed for determining retrograde velocities for desired pericynthion positions are considered useful for estimating essential data for the preliminary planning of lunar missions. Some graphical representation is included herein for immediate familiarization with possible conditions

Association between individual level characteristics and take-up of a Minimum Income Guarantee for Pensioners: Panel Data Analysis using data from the British Household Panel survey 1999–2002

\ua9 2024 The AuthorsA Minimum Income Guarantee (MIG) ensures people have a minimum amount of income for essentials such as healthy food, housing, health care, social and digital networks to support health and well-being. MIGs could be a useful tool to reduce inequalities. A MIG will only be effective if those who are eligible take it up. The aim of this paper is to explore how individual characteristics were associated with take-up of a MIG for pensioners (aged 60+ for women and aged 65+ for men) in England. The data used is from the British Household Panel Survey including 9430 observations from 1893 people, from 1999 to 2002. We estimated a random effects logistic regression. Results show that women were less likely to claim than men (OR ranging from 0.17 [95% CI 0.10–0.29]-0.73 [95% CI 0.40–1.34]), and couples were less likely to claim (OR ranging from 0.04 [95% CI 0.03–0.06]-0.01 [95%CI 0.01–0.02]) than single person households. People with better mental health (OR 1.05 95% CI 1.02–1.08), older pensioners (75+) (OR ranging from 1.98 [95% CI 1.52–2.59]-2.81 [95%CI 2.16–3.67]), those who were registered disabled (OR 4.03 95% CI 2.50–6.52), and those with no formal qualification (OR ranging from 1.74 [95%CI 0.93–3.26]-2.07 [95% CI 1.22–3.51]) were more likely to claim. Understanding who is likely to claim MIGs is important to avoid social security policy inadvertently increasing inequalities

Multidimensional Gaussian sums arising from distribution of Birkhoff sums in zero entropy dynamical systems

A duality formula, of the Hardy and Littlewood type for multidimensional Gaussian sums, is proved in order to estimate the asymptotic long time behavior of distribution of Birkhoff sums $S_n$ of a sequence generated by a skew product dynamical system on the $\mathbb{T}^2$ torus, with zero Lyapounov exponents. The sequence, taking the values $\pm 1$, is pairwise independent (but not independent) ergodic sequence with infinite range dependence. The model corresponds to the motion of a particle on an infinite cylinder, hopping backward and forward along its axis, with a transversal acceleration parameter $\alpha$. We show that when the parameter $\alpha /\pi$ is rational then all the moments of the normalized sums $E((S_n/\sqrt{n})^k)$, but the second, are unbounded with respect to n, while for irrational $\alpha /\pi$, with bounded continuous fraction representation, all these moments are finite and bounded with respect to n.Comment: To be published in J. Phys.

Branes, U-folds and hyperelliptic fibrations

We construct a class of supersymmetric vacua of type IIB string theory describing systems of three- and seven-branes non-perturbatively completed by brane instantons. The vacua are specified by a set of holomorphic functions defined over a complex plane up to non-trivial U-duality monodromies around the brane locations. In the simplest setting, the solutions can be seen as a generalization of F-theory elliptic fibrations, where the torus fiber is replaced by a genus two Riemann surface with periods encoding the information on the axio-dilaton, the warp factor and the NS-NS and R-R fluxes.Comment: 49 pages, including 22 pages of Appendix, 2 figures. Minor change

Statistical Mechanics of Elastica on Plane as a Model of Supercoiled DNA-Origin of the MKdV hierarchy-

In this article, I have investigated statistical mechanics of a non-stretched elastica in two dimensional space using path integral method. In the calculation, the MKdV hierarchy naturally appeared as the equations including the temperature fluctuation.I have classified the moduli of the closed elastica in heat bath and summed the Boltzmann weight with the thermalfluctuation over the moduli. Due to the bilinearity of the energy functional,I have obtained its exact partition function.By investigation of the system,I conjectured that an expectation value at a critical point of this system obeys the Painlev\'e equation of the first kind and its related equations extended by the KdV hierarchy.Furthermore I also commented onthe relation between the MKdV hierarchy and BRS transformationin this system.Comment: AMS-Tex Us

Fecal Microbiota in Premature Infants Prior to Necrotizing Enterocolitis

Intestinal luminal microbiota likely contribute to the etiology of necrotizing enterocolitis (NEC), a common disease in preterm infants. Microbiota development, a cascade of initial colonization events leading to the establishment of a diverse commensal microbiota, can now be studied in preterm infants using powerful molecular tools. Starting with the first stool and continuing until discharge, weekly stool specimens were collected prospectively from infants with gestational ages ≤32 completed weeks or birth weights≤1250 g. High throughput 16S rRNA sequencing was used to compare the diversity of microbiota and the prevalence of specific bacterial signatures in nine NEC infants and in nine matched controls. After removal of short and low quality reads we retained a total of 110,021 sequences. Microbiota composition differed in the matched samples collected 1 week but not <72 hours prior to NEC diagnosis. We detected a bloom (34% increase) of Proteobacteria and a decrease (32%) in Firmicutes in NEC cases between the 1 week and <72 hour samples. No significant change was identified in the controls. At both time points, molecular signatures were identified that were increased in NEC cases. One of the bacterial signatures detected more frequently in NEC cases (p<0.01) matched closest to γ-Proteobacteria. Although this sequence grouped to the well-studied Enterobacteriaceae family, it did not match any sequence in Genbank by more than 97%. Our observations suggest that abnormal patterns of microbiota and potentially a novel pathogen contribute to the etiology of NEC

Decline in Diarrhea Mortality and Admissions after Routine Childhood Rotavirus Immunization in Brazil: A Time-Series Analysis

A time series analysis by Manish Patel and colleagues shows that the introduction of rotavirus vaccination in Brazil is associated with reduced diarrhea-related deaths and hospital admissions in children under 5 years of age