Operator pencils on the algebra of densities

In this paper we continue to study equivariant pencil liftings and differential operators on the algebra of densities. We emphasize the role that the geometry of the extended manifold plays. Firstly we consider basic examples. We give a projective line of diff($M$)-equivariant pencil liftings for first order operators, and the canonical second order self-adjoint lifting. Secondly we study pencil liftings equivariant with respect to volume preserving transformations. This helps to understand the role of self-adjointness for the canonical pencils. Then we introduce the Duval-Lecomte-Ovsienko (DLO)-pencil lifting which is derived from the full symbol calculus of projective quantisation. We use the DLO-pencil lifting to describe all regular proj-equivariant pencil liftings. In particular the comparison of these pencils with the canonical pencil for second order operators leads to objects related to the Schwarzian. Within this paper the question of whether the pencil lifting factors through a full symbol map naturally arises.Comment: 23 pages, LaTeX file Small corrections are mad

Operator pencil passing through a given operator

Let $\Delta$ be a linear differential operator acting on the space of densities of a given weight \lo on a manifold $M$. One can consider a pencil of operators \hPi(\Delta)=\{\Delta_\l\} passing through the operator $\Delta$ such that any \Delta_\l is a linear differential operator acting on densities of weight \l. This pencil can be identified with a linear differential operator \hD acting on the algebra of densities of all weights. The existence of an invariant scalar product in the algebra of densities implies a natural decomposition of operators, i.e. pencils of self-adjoint and anti-self-adjoint operators. We study lifting maps that are on one hand equivariant with respect to divergenceless vector fields, and, on the other hand, with values in self-adjoint or anti-self-adjoint operators. In particular we analyze the relation between these two concepts, and apply it to the study of \diff(M)-equivariant liftings. Finally we briefly consider the case of liftings equivariant with respect to the algebra of projective transformations and describe all regular self-adjoint and anti-self-adjoint liftings.Comment: 32 pages, LaTeX fil

Perceived stress and emotional social support among women who are denied or receive abortions in the United States: a prospective cohort study.

BackgroundExamining women's stress and social support following denial and receipt of abortion furthers understanding of the effects of unwanted childbearing and abortion on women's well-being. This study investigated perceived stress and emotional social support over time among women who were denied wanted abortions and who received abortions, and compared outcomes between the groups.MethodsThe Turnaway Study is a prospective cohort study of women who sought abortions at 30 abortion facilities across the United States, and follows women via semiannual phone interviews for five years. Participants include 956 English or Spanish speaking women aged 15 and over who sought abortions between 2008 and 2010 and whose gestation in pregnancy fit one of three groups: women who presented up to three weeks beyond a facility's gestational age limit and were denied an abortion; women presenting within two weeks below the limit who received an abortion; and women who received a first trimester abortion. The outcomes were modified versions of the Perceived Stress Scale and the Multidimensional Scale of Perceived Social Support. Longitudinal mixed effects models were used to assess differences in outcomes between study groups over 30 months.ResultsWomen denied abortions initially had higher perceived stress than women receiving abortions near gestational age limits (1.0 unit difference on 0-16 scale, P = 0.003). Women receiving first-trimester abortions initially had lower perceived stress than women receiving abortions near gestational age limits (0.6 difference, P = 0.045). By six months, all groups' levels of perceived stress were similar, and levels remained similar through 30 months. Emotional social support scores did not differ among women receiving abortions near gestational limits versus women denied abortions or women having first trimester abortions initially or over time.ConclusionsSoon after being denied abortions, women experienced higher perceived stress than women who received abortions. The study found no longer-term differences in perceived stress or emotional social support between women who received versus were denied abortions

Apollo experience report guidance and control systems: Primary guidance, navigation, and control system development

The primary guidance, navigation, and control systems for both the lunar module and the command module are described. Development of the Apollo primary guidance systems is traced from adaptation of the Polaris Mark II system through evolution from Block I to Block II configurations; the discussion includes design concepts used, test and qualification programs performed, and major problems encountered. The major subsystems (inertial, computer, and optical) are covered. Separate sections on the inertial components (gyroscopes and accelerometers) are presented because these components represent a major contribution to the success of the primary guidance, navigation, and control system

Risk of violence from the man involved in the pregnancy after receiving or being denied an abortion.

BackgroundIntimate partner violence is common among women having abortions, with between 6% and 22% reporting recent violence from an intimate partner. Concern about violence is a reason some pregnant women decide to terminate their pregnancies. Whether risk of violence decreases after having an abortion, remains unknown.MethodsData are from the Turnaway Study, a prospective cohort study of women seeking abortions at 30 facilities across the U.S. Participants included women who: presented just prior to a facility's gestational age limit and received abortions (Near Limit Abortion Group, n = 452), presented just beyond the gestational limit and were denied abortions (Turnaways, n = 231), and received first trimester abortions (First Trimester Abortion Group, n = 273). Mixed effects logistic regression was used to assess the relationship between receiving versus being denied abortion and subsequent violence from the man involved in the pregnancy over 2.5 years.ResultsPhysical violence decreased for Near Limits (adjusted odds ratios (aOR), 0.93 per month; 95% Confidence Interval (CI) 0.90, 0.96), but not Turnaways who gave birth (P < .05 versus Near Limits). The decrease for First Trimesters was similar to Near Limits (P = .324). Psychological violence decreased for all groups (aOR, 0.97; CI 0.94, 1.00), with no differential change across groups.ConclusionsPolicies restricting abortion provision may result in more women being unable to terminate unwanted pregnancies, potentially keeping them in contact with violent partners, and putting women and their children at risk

Deep Radio Imaging of Globular Clusters and the Cluster Pulsar Population

We have obtained deep multifrequency radio observations of seven globular clusters using the Very Large Array and the Australia Telescope Compact Array. Five of these, NGC 6440, NGC 6539, NGC 6544, NGC 6624 and Terzan 5 had previously been detected in a shallower survey for steep spectrum radio sources in globular clusters (Fruchter and Goss 1990). The sixth, the rich globular cluster, Liller 1, had heretofore been undetected in the radio, and the seventh, 47 Tucanae, was not included in our original survey. High resolution 6 and 20 cm images of three of the clusters, NGC 6440, NGC 6539, NGC 6624 reveal only point sources coincident with pulsars which have been discovered subsequent to our first imaging survey. 21 and 18 cm images reveal several point sources within a few core-radii of the center of 47 Tuc. Two of these are identified pulsars, and a third, which is both variable and has a steep spectrum, is also most likely a pulsar previously identified by a pulsed survey. However, the 6, 20 and 90 cm images of NGC 6544, Liller 1 and Terzan 5 display strong steep-spectrum emission which cannot be associated with known pulsars. The image of the rich cluster Terzan 5 displays numerous point sources within $30''$, or 4 core radii of the cluster center. The density of these objects rises rapidly toward the core, where an elongated region of emission is found. The brightest individual sources, as well as the extended emission, possess the steep spectra expected of pulsars. Furthermore, the flux distribution of the sources agrees well with the standard pulsar luminosity function. The total luminosity and number of objects observed suggest that Terzan 5 contains more pulsars than any other Galactic globular cluster.Comment: 33 pages, 6 Postscript figures; Accepted for publication in the Astrophysical Journal; abstract abridged. PDF version also available at http://nemesis.stsci.edu/~fruchter/fg99/fg99.pd

Partition Function Zeros of a Restricted Potts Model on Lattice Strips and Effects of Boundary Conditions

We calculate the partition function $Z(G,Q,v)$ of the $Q$-state Potts model exactly for strips of the square and triangular lattices of various widths $L_y$ and arbitrarily great lengths $L_x$, with a variety of boundary conditions, and with $Q$ and $v$ restricted to satisfy conditions corresponding to the ferromagnetic phase transition on the associated two-dimensional lattices. From these calculations, in the limit $L_x \to \infty$, we determine the continuous accumulation loci ${\cal B}$ of the partition function zeros in the $v$ and $Q$ planes. Strips of the honeycomb lattice are also considered. We discuss some general features of these loci.Comment: 12 pages, 12 figure

Molecular Clock on a Neutral Network

The number of fixed mutations accumulated in an evolving population often displays a variance that is significantly larger than the mean (the overdispersed molecular clock). By examining a generic evolutionary process on a neutral network of high-fitness genotypes, we establish a formalism for computing all cumulants of the full probability distribution of accumulated mutations in terms of graph properties of the neutral network, and use the formalism to prove overdispersion of the molecular clock. We further show that significant overdispersion arises naturally in evolution when the neutral network is highly sparse, exhibits large global fluctuations in neutrality, and small local fluctuations in neutrality. The results are also relevant for elucidating the topological structure of a neutral network from empirical measurements of the substitution process.Comment: 10 page