Time-dependent Schr\"odinger equations having isomorphic symmetry algebras. I. Classes of interrelated equations

In this paper, we focus on a general class of Schr\"odinger equations that are time-dependent and quadratic in X and P. We transform Schr\"odinger equations in this class, via a class of time-dependent mass equations, to a class of solvable time-dependent oscillator equations. This transformation consists of a unitary transformation and a change in the ``time'' variable. We derive mathematical constraints forthe transformation and introduce two examples.Comment: LaTeX, 18 pages, new format, edite

Natural Salinity Removal Processes in Reservoirs

A small but significant amount of salinity removal has been reported by various authors to occur in mainstem Colorado River reservoirs. Recalculation of some of these salinity budgets, together with a review of the data bases used, usggests taht removal has not often been conclusively demonstrated. Laboratory microcosm experiments and field data indicate that calcium carbonate precipitation, perhaps with some coprecipitation of magnesium carbonate, is the mechanism responsible for most of the salinity removal in Oneida Reservoir, Idaho. Coprecipitation processes (including ion exchange), coagulation, and bioassimilation do not appear to be important natural salinity removal mechanisms. Finally, loss of calcium, relative to monovalent cations, may decrease water quality for irrigation purposes through increasing the sodium adsorption ratio (SAR), despite a pross decrease in the TDS. The potential role of various reservoir operation options in managing natural salinity removal processes and the value of such removal is discussed

Gravitational Waves from Core Collapse Supernovae

We present the gravitational wave signatures for a suite of axisymmetric core collapse supernova models with progenitors masses between 12 and 25 solar masses. These models are distinguished by the fact they explode and contain essential physics (in particular, multi-frequency neutrino transport and general relativity) needed for a more realistic description. Thus, we are able to compute complete waveforms (i.e., through explosion) based on non-parameterized, first-principles models. This is essential if the waveform amplitudes and time scales are to be computed more precisely. Fourier decomposition shows that the gravitational wave signals we predict should be observable by AdvLIGO across the range of progenitors considered here. The fundamental limitation of these models is in their imposition of axisymmetry. Further progress will require counterpart three-dimensional models.Comment: 10 pages, 5 figure

Strategic verbal rehearsal in adolescents with mild intellectual disabilities: A multi-centre European study

Background: There is a long-held view that verbal short-term memory problems of individuals with intellectual disabilities (ID) might be due to a deficit in verbal rehearsal. However, the evidence is inconclusive and word length effects as indicator of rehearsal have been criticised. Aim & Method: The aim of this multi-site European study was to investigate verbal rehearsal in adolescents with mild ID (n=90) and a comparison group of typically developing children matched individually for mental age (MA, n=90). The investigation involved: (1) a word length experiment with non-verbal recall using pointing and (2) ‘self-paced’ inspection times to infer whether verbal strategies were utilised when memorising a set of pictorial items. Results: The word length effect on recall did not interact with group, suggesting that adolescents with ID and MA comparisons used similar verbal strategies, possibly phonological recoding of picture names. The inspection time data suggested that high span individuals in both groups used verbal labelling or single item rehearsal on more demanding lists, as long named items had longer inspection times. Conclusions: The findings suggest that verbal strategy use is not specifically impaired in adolescents with mild ID and is mental age appropriate, supporting a developmental perspective

Semi-Hard Scattering Unraveled from Collective Dynamics by Two-Pion Azimuthal Correlations in 158 A GeV/c Pb + Au Collisions

Elliptic flow and two-particle azimuthal correlations of charged hadrons and high-$p_T$ pions ($p_T>$ 1 GeV/$c$) have been measured close to mid-rapidity in 158A GeV/$c$ Pb+Au collisions by the CERES experiment. Elliptic flow ($v_2$) rises linearly with $p_T$ to a value of about 10% at 2 GeV/$c$. Beyond $p_T\approx$ 1.5 GeV/$c$, the slope decreases considerably, possibly indicating a saturation of $v_2$ at high $p_T$. Two-pion azimuthal anisotropies for $p_T>$ 1.2 GeV/$c$ exceed the elliptic flow values by about 60% in mid-central collisions. These non-flow contributions are attributed to near-side and back-to-back jet-like correlations, the latter exhibiting centrality dependent broadening.Comment: Submitted to Phys. Rev. Letters, 4 pages, 5 figure

Modeling core collapse supernovae in 2 and 3 dimensions with spectral neutrino transport

The overwhelming evidence that the core collapse supernova mechanism is inherently multidimensional, the complexity of the physical processes involved, and the increasing evidence from simulations that the explosion is marginal presents great computational challenges for the realistic modeling of this event, particularly in 3 spatial dimensions. We have developed a code which is scalable to computations in 3 dimensions which couples PPM Lagrangian with remap hydrodynamics [1], multigroup, flux-limited diffusion neutrino transport [2], with many improvements), and a nuclear network [3]. The neutrino transport is performed in a ray-by-ray plus approximation wherein all the lateral effects of neutrinos are included (e.g., pressure, velocity corrections, advection) except the transport. A moving radial grid option permits the evolution to be carried out from initial core collapse with only modest demands on the number of radial zones. The inner part of the core is evolved after collapse along with the rest of the core and mantle by subcycling the lateral evolution near the center as demanded by the small Courant times. We present results of 2-D simulations of a symmetric and an asymmetric collapse of both a 15 and an 11 M progenitor. In each of these simulations we have discovered that once the oxygen rich material reaches the shock there is a synergistic interplay between the reduced ram pressure, the energy released by the burning of the shock heated oxygen rich material, and the neutrino energy deposition which leads to a revival of the shock and an explosion.Comment: 10 pages, 3 figure

Positive Surgical Margins in the 10 Most Common Solid Cancers.

A positive surgical margin (PSM) following cancer resection oftentimes necessitates adjuvant treatments and carries significant financial and prognostic implications. We sought to compare PSM rates for the ten most common solid cancers in the United States, and to assess trends over time. Over 10 million patients were identified in the National Cancer Data Base from 1998-2012, and 6.5 million had surgical margin data. PSM rates were compared between two time periods, 1998-2002 and 2008-2012. PSM was positively correlated with tumor category and grade. Ovarian and prostate cancers had the highest PSM prevalence in women and men, respectively. The highest PSM rates for cancers affecting both genders were seen for oral cavity tumors. PSM rates for breast cancer and lung and bronchus cancer in both men and women declined over the study period. PSM increases were seen for bladder, colon and rectum, and kidney and renal pelvis cancers. This large-scale analysis appraises the magnitude of PSM in the United States in order to focus future efforts on improving oncologic surgical care with the goal of optimizing value and improving patient outcomes