Subresultants in multiple roots: an extremal case

We provide explicit formulae for the coefficients of the order-d polynomial subresultant of (x-\alpha)^m and (x-\beta)^n with respect to the set of Bernstein polynomials \{(x-\alpha)^j(x-\beta)^{d-j}, \, 0\le j\le d\}. They are given by hypergeometric expressions arising from determinants of binomial Hankel matrices.Comment: 18 pages, uses elsart. Revised version accepted for publication at Linear Algebra and its Application

EORTC (30885) randomised phase III study with recombinant interferon alpha and recombinant interferon alpha and gamma in patients with advanced renal cell carcinoma. The EORTC Genitourinary Group.

In the treatment of renal cell carcinoma both complete (CRs) and partial remissions (PRs) have been obtained using recombinant (r) interferon alpha (IFN-alpha), with response rates ranging from 0 to 31% (mean 16%). rIFN-gamma is a potent immunostimulating agent, but the clinical experience of its use is limited and results are conflicting. In a phase II study with the combination of rIFN-alpha 2c (Boehringer Ingelheim) and rIFN-gamma (Genentech, supplied by Boehringer Ingelheim) in 31 eligible patients, a response rate of 25% was recorded. Based on this observation a randomised phase III study was initiated to investigate the possible advantage of the addition rIFN-gamma to rIFN-alpha 2c treatment. Treatment consisted of rIFN-alpha 2c 30 micrograms m-2 = 10 x 10(6) IU m-2 s.c. twice weekly in arm A and the same dose of rIFN-alpha combined with rIFN-gamma 100 micrograms m-2 = 2 x 10(6) IU m-2 in arm B. Eligibility criteria included documented progression of disease; patients with bone lesions only and overt central nervous system metastases were excluded. Between November 1988 and September 1990, 102 patients were entered into the study. An interim analysis showed a response in 7/53 (13%) patients (two CRs and five PRs) in the rIFN-alpha 2c monotherapy arm and in 2/45 (4%) (one CR and one PR) patients in the combination arm. This difference was not statistically significant (P = 0.17). The probability of missing an eventual 10% advantage for the combination is 0.001. The numbers are insufficient to rule out a negative effect of the addition of rIFN-gamma. The dose intensity of IFN-alpha 2c for the two treatment arms was the same. The addition of rIFN-gamma does not improve the response rate of rIFN-alpha 2c monotherapy. A possible detrimental effect cannot be excluded

1400 Liter 1.8K Test Facility

A double bath superfluid helium dewar has been constructed and operated at Fermilab`s Magnet Test Facility. The 1.8 K portion of the dewar is sized to contain a superconducting magnet up to 0.5 meters in diameter and 4 meters long in a vertical orientation in 0.12 MPa pressurized superfluid. The dewar can also provide a subcooled Helium I environment for tests; the entire temperature range from 4.4 K to 1. 8 K at 0.12 MPa is available. This paper describes the system design, lambda plate, heat exchanger, and performance

ISO observations of far-infrared rotational emission lines of water vapor toward the supergiant star VY Canis Majoris

We report the detection of numerous far-infrared emission lines of water vapor toward the supergiant star VY Canis Majoris. A 29.5 - 45 micron grating scan of VY CMa, obtained using the Short Wavelength Spectrometer (SWS) of the Infrared Space Observatory (ISO) at a spectral resolving power of approximately 2000, reveals at least 41 spectral features due to water vapor that together radiate a total luminosity ~ 25 solar luminosities. In addition to pure rotational transitions within the ground vibrational state, these features include rotational transitions within the (010) excited vibrational state. The spectrum also shows the doublet Pi 1/2 (J=5/2) <-- doublet Pi 3/2 (J=3/2) OH feature near 34.6 micron in absorption. Additional SWS observations of VY CMa were carried out in the instrument's Fabry-Perot mode for three water transitions: the 7(25)-6(16) line at 29.8367 micron, the 4(41)-3(12) line 31.7721 micron, and the 4(32)-3(03) line at 40.6909 micron. The higher spectral resolving power of approximately 30,000 thereby obtained permits the line profiles to be resolved spectrally for the first time and reveals the "P Cygni" profiles that are characteristic of emission from an outflowing envelope.Comment: 11 pages (inc. 2 figures), LaTeX, uses aaspp4.sty, accepted for publication in ApJ Letter

Spitzer/IRS spectroscopy of high mass precursors to planetary nebulae

We present Spitzer/IRS observations of a small sample of heavily obscured IRAS sources displaying both the infrared and OH maser emission characteristic of OH/IR stars on the asymptotic giant branch (AGB), but also radio continuum emission typical of ionized planetary nebulae (PNe), the so-called OHPNe. Our observations show that their mid-infrared spectra are dominated by the simultaneous presence of strong and broad amorphous silicate absorption features together with crystalline silicate features, originated in their O-rich circumstellar shells. Out of the five sources observed, three of them are clearly non-variable at infrared wavelengths, confirming their post-AGB status, while the remaining two still show strong photometric fluctuations, and may still have not yet departed from the AGB. One of the non-variable sources in the sample, IRAS 17393-2727, displays a strong [Ne II] nebular emission at 12.8 microns, indicating that the ionization of its central region has already started. This suggests a rapid evolution from the AGB to the PN stage. We propose that these heavily obscured OHPNe represent the population of high mass precursors to PNe in our Galaxy.Comment: To appear in The Astrophysical Journal Letters (scheduled in the 2007 September 1 issue

Sylvester-t' Hooft generators of sl(n) and sl(n|n), and relations between them

Among the simple finite dimensional Lie algebras, only sl(n) possesses two automorphisms of finite order which have no common nonzero eigenvector with eigenvalue one. It turns out that these automorphisms are inner and form a pair of generators that allow one to generate all of sl(n) under bracketing. It seems that Sylvester was the first to mention these generators, but he used them as generators of the associative algebra of all n times n matrices Mat(n). These generators appear in the description of elliptic solutions of the classical Yang-Baxter equation, orthogonal decompositions of Lie algebras, 't Hooft's work on confinement operators in QCD, and various other instances. Here I give an algorithm which both generates sl(n) and explicitly describes a set of defining relations. For simple (up to center) Lie superalgebras, analogs of Sylvester generators exist only for sl(n|n). The relations for this case are also computed.Comment: 14 pages, 6 figure

The partially alternating ternary sum in an associative dialgebra

The alternating ternary sum in an associative algebra, $abc - acb - bac + bca + cab - cba$, gives rise to the partially alternating ternary sum in an associative dialgebra with products $\dashv$ and $\vdash$ by making the argument $a$ the center of each term: $a \dashv b \dashv c - a \dashv c \dashv b - b \vdash a \dashv c + c \vdash a \dashv b + b \vdash c \vdash a - c \vdash b \vdash a$. We use computer algebra to determine the polynomial identities in degree $\le 9$ satisfied by this new trilinear operation. In degrees 3 and 5 we obtain $[a,b,c] + [a,c,b] \equiv 0$ and $[a,[b,c,d],e] + [a,[c,b,d],e] \equiv 0$; these identities define a new variety of partially alternating ternary algebras. We show that there is a 49-dimensional space of multilinear identities in degree 7, and we find equivalent nonlinear identities. We use the representation theory of the symmetric group to show that there are no new identities in degree 9.Comment: 14 page

Alternative antiretroviral monitoring strategies for HIV-infected patients in east Africa: opportunities to save more lives?

<p>Abstract</p> <p>Background</p> <p>Updated World Health Organization guidelines have amplified debate about how resource constraints should impact monitoring strategies for HIV-infected persons on combination antiretroviral therapy (cART). We estimated the incremental benefit and cost effectiveness of alternative monitoring strategies for east Africans with known HIV infection.</p> <p>Methods</p> <p>Using a validated HIV computer simulation based on resource-limited data (USAID and AMPATH) and circumstances (east Africa), we compared alternative monitoring strategies for HIV-infected persons newly started on cART. We evaluated clinical, immunologic and virologic monitoring strategies, including combinations and conditional logic (e.g., only perform virologic testing if immunologic testing is positive). We calculated incremental cost-effectiveness ratios (ICER) in units of cost per quality-adjusted life year (QALY), using a societal perspective and a lifetime horizon. Costs were measured in 2008 US dollars, and costs and benefits were discounted at 3%. We compared the ICER of monitoring strategies with those of other resource-constrained decisions, in particular earlier cART initiation (at CD4 counts of 350 cells/mm³rather than 200 cells/mm³).</p> <p>Results</p> <p>Monitoring strategies employing routine CD4 testing without virologic testing never maximized health benefits, regardless of budget or societal willingness to pay for additional health benefits. Monitoring strategies employing virologic testing conditional upon particular CD4 results delivered the most benefit at willingness-to-pay levels similar to the cost of earlier cART initiation (approximately $2600/QALY). Monitoring strategies employing routine virologic testing alone only maximized health benefits at willingness-to-pay levels (>$4400/QALY) that greatly exceeded the ICER of earlier cART initiation.</p> <p>Conclusions</p> <p>CD4 testing alone never maximized health benefits regardless of resource limitations. Programmes routinely performing virologic testing but deferring cART initiation may increase health benefits by reallocating monitoring resources towards earlier cART initiation.</p