1,655,677 research outputs found
A Real Nullstellensatz for Matrices of Non-Commutative Polynomials
This article extends the classical Real Nullstellensatz to matrices of
polynomials in a free -algebra \RR\axs with .
This result is a generalization of a result of Cimpri\vc, Helton, McCullough,
and the author.
In the free left \RR\axs-module \RR^{1 \times \ell}\axs we introduce
notions of the (noncommutative) zero set of a left \RR\axs-submodule and of a
real left \RR\axs-submodule. We prove that every element from \RR^{1 \times
\ell}\axs whose zero set contains the intersection of zero sets of elements
from a finite subset S \subset \RR^{1 \times \ell}\axs belongs to the
smallest real left \RR\axs-submodule containing . Using this, we derive a
nullstellensatz for matrices of polynomials in \RR\axs.
The other main contribution of this article is an efficient, implementable
algorithm which for every finite subset S \subset \RR^{1 \times \ell}\axs
computes the smallest real left \RR\axs-submodule containing . This
algorithm terminates in a finite number of steps. By taking advantage of the
rigid structure of \RR\axs, the algorithm presented here is an improvement
upon the previously known algorithm for \RR\axs
Impact of changing US cigarette smoking patterns on incident cancer: Risks of 20 smoking-related cancers among the women and men of the NIH-AARP cohort
Background: Historically, US women started smoking at a later age than men and had lower relative risks for smoking-related cancers. However, more recent birth cohorts of women and men have similar smoking histories and have now reached the high-risk age for cancer. The impact of these changes on cancer incidence has not been systematically examined. Methods: Relative risks (RR), 95% confidence intervals (CI) and attributable fractions were calculated for cigarette smoking and incidence of 20 smoking-related cancers in 186 057 women and 266 074 men of the National Institutes of Health-AARP cohort, aged 50 to 71 years in 1995 and followed for 11 years. Results: In the cohort, which included participants born between 1924 and 1945, most women and men started smoking as teenagers. RRs for current vs never smoking were similar in women and men for the following cancers: lung squamous-cell (RR women: 121.4, 95% CI: 57.3–257.4; RR men:114.6, 95% CI: 61.2–214.4), lung adenocarcinoma (RR women: 11.7, 95% CI: 9.8–14.0; RR men: 15.6, 95% CI: 12.5–19.6), laryngeal (RR women: 37.0, 95% CI: 14.9–92.3; RR men: 13.8, 95% CI: 9.3–20.2), oral cavity-pharyngeal (RR women:4.4, 95% CI: 3.3–6.0; RR men: 3.8, 95% CI: 3.0–4.7), oesophageal squamous cell (RR women: 7.3, 95% CI: 3.5–15.5; RR men: 6.2, 95% CI: 2.8–13.7), bladder (RR women: 4.7, 95% CI: 3.7–5.8; RR men: 4.0, 95% CI: 3.5–4.5), colon (RR women: 1.3, 95% CI: 1.2–1.5; RR men: 1.3, 95% CI: 1.1–1.4), and at other sites, with similar attributable fractions. Conclusions: RRs for current smoking and incidence of many smoking-related cancers are now similar in US women and men, likely reflecting converging smoking patterns
Singular Liouville fields and spiky strings in \rr^{1,2} and SL(2,\rr)
The closed string dynamics in \rr^{1,2} and SL(2,\rr) is studied within
the scheme of Pohlmeyer reduction. In both spaces two different classes of
string surfaces are specified by the structure of the fundamental quadratic
forms. The first class in \rr^{1,2} is associated with the standard lightcone
gauge strings and the second class describes spiky strings and their conformal
deformations on the Virasoro coadjoint orbits. These orbits correspond to
singular Liouville fields with the monodromy matrixes . The first class
in SL(2,\rr) is parameterized by the Liouville fields with vanishing chiral
energy functional. Similarly to \rr^{1,2}, the second class in SL(2,\rr)
describes spiky strings, related to the vacuum configurations of the
SL(2,\rr)/U(1) coset model.Comment: 37 p. 6 fi
The RR Lyrae Distance Scale
We review seven methods of measuring the absolute magnitude M_V of RR Lyrae
stars in light of the Hipparcos mission and other recent developments. We focus
on identifying possible systematic errors and rank the methods by relative
immunity to such errors. For the three most robust methods, statistical
parallax, trigonometric parallax, and cluster kinematics, we find M_V (at
[Fe/H] = -1.6) of 0.77 +/- 0.13, 0.71 +/- 0.15, 0.67 +/- 0.10. These methods
cluster consistently around 0.71 +/- 0.07. We find that Baade-Wesselink and
theoretical models both yield a broad range of possible values (0.45-0.70 and
0.45-0.65) due to systematic uncertainties in the temperature scale and input
physics. Main-sequence fitting gives a much brighter M_V = 0.45 +/- 0.04 but
this may be due to a difference in the metallicity scales of the cluster giants
and the calibrating subdwarfs. White-dwarf cooling-sequence fitting gives 0.67
+/- 0.13 and is potentially very robust, but at present is too new to be fully
tested for systematics. If the three most robust methods are combined with
Walker's mean measurement for 6 LMC clusters, V_{0,LMC} = 18.98 +/- 0.03 at
[Fe/H] = -1.9, then mu_{LMC} = 18.33 +/- 0.08.Comment: Invited review article to appear in: `Post-Hipparcos Cosmic Candles',
A. Heck & F. Caputo (Eds), Kluwer Academic Publ., Dordrecht, in press. 21
pages including 1 table; uses Kluwer's crckapb.sty LaTeX style file, enclose
Strategies to improve retention in randomised trials: a Cochrane systematic review and meta-analysis
Objective: To quantify the effect of strategies to improve retention in randomised trials.<p></p>
Design: Systematic review and meta-analysis.<p></p>
Data sources Sources searched: MEDLINE, EMBASE, PsycINFO, DARE, CENTRAL, CINAHL, C2-SPECTR, ERIC, PreMEDLINE, Cochrane Methodology Register, Current Controlled Trials metaRegister, WHO trials platform, Society for Clinical Trials (SCT) conference proceedings and a survey of all UK clinical trial research units.<p></p>
Review: methods Included trials were randomised evaluations of strategies to improve retention embedded within host randomised trials. The primary outcome was retention of trial participants. Data from trials were pooled using the fixed-effect model. Subgroup analyses were used to explore the heterogeneity and to determine whether there were any differences in effect by the type of strategy.<p></p>
Results: 38 retention trials were identified. Six broad types of strategies were evaluated. Strategies that increased postal questionnaire responses were: adding, that is, giving a monetary incentive (RR 1.18; 95% CI 1.09 to 1.28) and higher valued incentives (RR 1.12; 95% CI 1.04 to 1.22). Offering a monetary incentive, that is, an incentive given on receipt of a completed questionnaire, also increased electronic questionnaire response (RR 1.25; 95% CI 1.14 to 1.38). The evidence for shorter questionnaires (RR 1.04; 95% CI 1.00 to 1.08) and questionnaires relevant to the disease/condition (RR 1.07; 95% CI 1.01 to 1.14) is less clear. On the basis of the results of single trials, the following strategies appeared effective at increasing questionnaire response: recorded delivery of questionnaires (RR 2.08; 95% CI 1.11 to 3.87); a ‘package’ of postal communication strategies (RR 1.43; 95% CI 1.22 to 1.67) and an open trial design (RR 1.37; 95% CI 1.16 to 1.63). There is no good evidence that the following strategies impact on trial response/retention: adding a non-monetary incentive (RR=1.00; 95% CI 0.98 to 1.02); offering a non-monetary incentive (RR=0.99; 95% CI 0.95 to 1.03); ‘enhanced’ letters (RR=1.01; 95% CI 0.97 to 1.05); monetary incentives compared with offering prize draw entry (RR=1.04; 95% CI 0.91 to 1.19); priority postal delivery (RR=1.02; 95% CI 0.95 to 1.09); behavioural motivational strategies (RR=1.08; 95% CI 0.93 to 1.24); additional reminders to participants (RR=1.03; 95% CI 0.99 to 1.06) and questionnaire question order (RR=1.00, 0.97 to 1.02). Also based on single trials, these strategies do not appear effective: a telephone survey compared with a monetary incentive plus questionnaire (RR=1.08; 95% CI 0.94 to 1.24); offering a charity donation (RR=1.02, 95% CI 0.78 to 1.32); sending sites reminders (RR=0.96; 95% CI 0.83 to 1.11); sending questionnaires early (RR=1.10; 95% CI 0.96 to 1.26); longer and clearer questionnaires (RR=1.01, 0.95 to 1.07) and participant case management by trial assistants (RR=1.00; 95% CI 0.97 to 1.04).<p></p>
Conclusions: Most of the trials evaluated questionnaire response rather than ways to improve participants return to site for follow-up. Monetary incentives and offers of monetary incentives increase postal and electronic questionnaire response. Some strategies need further evaluation. Application of these results would depend on trial context and follow-up procedures.<p></p>
On Coarse Spectral Geometry in Even Dimension
Let be the involution of the Roe algebra \Roe{\RR} which is
induced from the reflection \RR\to\RR; x\mapsto -x. A graded Fredholm module
over a separable -algebra gives rise to a homomorphism
\tilde{\rho}:A\to\Roe{\RR}^\sigma to the fixed-point subalgebra. We use this
observation to give an even-dimensional analogue of a result of Roe. Namely, we
show that the -theory of this symmetric Roe algebra is
K_0(\Roe{\RR}^\sigma)\cong\ZZ, K_1(\Roe{\RR})=0, and that the induced map
\tilde{\rho}_*:K_0(A) \to \ZZ on -theory gives the index pairing of
-homology with -theory
Nonlinear asteroseismology of RR Lyrae
The observations of the Kepler space telescope revealed that fundamental-mode
RR Lyrae stars may show various radial overtones. The presence of multiple
radial modes may allow us to conduct nonlinear asteroseismology: comparison of
mode amplitudes and frequency shifts between observations and models. Here we
report the detection of three radial modes in the star RR Lyr, the eponym of
the class, using the Kepler short cadence data: besides the fundamental mode,
both the first and the ninth overtones can be derived from the data set. RR
Lyrae shows period doubling, but switches occasionally to a state where a
pattern of six pulsation cycles repeats instead of two. We found hydrodynamic
models that show the same three modes and the period-six state, allowing for
comparison with the observations.Comment: 5 pages, 4 figures, accepted for publication in ApJ Letter
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