1,241 research outputs found

    Canonical bases of invariant polynomials for the irreducible reflection groups of types E6, E7, and E8

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    Given a rank n irreducible finite reflection group W, the W-invariant polynomial functions defined in R^n can be written as polynomials of n algebraically independent homogeneous polynomial functions, p_1(x),...,p_n(x), called basic invariant polynomials. Their degrees are well known and typical of the given group W. The polynomial p_1(x) has the lowest degree, equal to 2. It has been proved that it is possible to choose all the other n−1 basic invariant polynomials in such a way that they satisfy a certain system of differential equations, including the Laplace equations △p_a(x)=0, a=2,...,n, and so are harmonic functions. Bases of this kind are called canonical. Explicit formulas for canonical bases of invariant polynomials have been found for all irreducible finite reflection groups, except for those of types E_6, E_7 and E_8. Those for the groups of types E_6, E_7 and E_8 are determined in this article

    Universality in orbit spaces of compact linear groups

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    If {p_1(x), ..., p_q(x)} is a minimal integrity basis of the ideal of polynomial invariants of a compact coregular linear group G, the orbit map p=(p_1(x) .... ,p_q(x)):R^n->R^q, yields a diffeomorphic image S = p(R^n) \subset R^q of the orbit space R^n/G. Starting from this fact, we point out some properties which are common to the orbit spaces of all the compact coregular linear groups of transformations of R^n. In particular we show that a contravariant metric matrix P(p) can be defined in the interior of S, as a polynomial function of (p_1, ...,p_q). We prove that the matrix P(p), which characterizes the set S, as it is positive semi-definite only for p \in S, can be determined as a solution of a canonical differential equation, which, for every compact coregular linear group, depends only on the number q and on the degrees of the elements of the minimal integrity bases. This allows to determine all the isomorphism classes of the orbit spaces of the compact coregular linear groups through a determination of the equivalence classes of the corresponding matrices P(p). For q<3 (orbit spaces with dimensions < 3), the solutions P(p) of the canonical equation are explicitly determined and the number of their equivalence classes is shown to be finite. It is also shown that, with a convenient choice of the minimal integrity basis, the polynomial matrix elements of P(p) have only integer coefficients. Arguments are given in favour of the conjecture that our conclusions hold true for all values of q. Our results are relevant and lead to universality properties in the physics of spontaneous symmetry breaking

    Oral contraceptives and cervical neoplasia: pooled information from retrospective and prospective epidemiologic studies

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    A positive association between the use of oral contraceptives and the risk of cervical neoplasia has been suggested by different sources. This paper examines epidemiologic evidence on this issue through pooled computation of relative risks emerging from 21 studies, subdivided into three main categories: studies based on routine cytologic screening programs, case-control investigations and prospective studies. The pooled estimates of the relative risks for ever vs never use of oral contraceptives were broadly similar and slightly above unity (1.4 from cytologic screening programs, 1.1 from case-control and 1.4 from prospective studies). The risk increased with duration of use and, generally, lower relative risk estimates derived from the older studies, necessarily based on short-term use of oral contraceptives. A particularly limited increase in risk was apparent from case-control investigations. Furthermore, when allowance was made for the major covariates (mostly indicators of sexual habits), a noticeable decrease in the excess risk was evident. In conclusion, although statistical significance of moderate differences in risk can be obtained by pooling data from several studies, a risk of the magnitude of that for the association between oral contraceptives and cervical neoplasia may well be due to bias and confounding. In addition, since sexual behavior only indicates the probability of having been exposed to some sexually transmitted agent (most likely human papilloma virus), the greatest additional contribution may come from a case-control study in which adjustment for such exposure is possible

    Joint effects of family history and adult life dietary risk factors on colorectal cancer risk

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    Background. We analyzed the joint effects of family history of colorectal cancer and adult life dietary risk factors on colorectal cancer risk. Methods. We used data from a case-control study conducted in northern Italy between 1985 and 1992, including 1584 cases with colorectal cancer and 2879 controls. We created an adult life dietary risk factor score. Results. Among subjects with family history of colorectal cancer, those in the lowest risk score tertile were not at elevated risk of colorectal cancer (odds ratio = 1.2; 95% confidence interval = 0.7-2.1), whereas those in the highest score tertile were at increased risk (odds ratio = 5.5; 95% confidence interval = 3.5-8.7). Conclusions. These findings indicate that the expression of familial susceptibility can be substantially modified by adult life risk factors. RI Fernandez, Esteve/A-9750-200

    Natural history of atypical and equivocal melanocytic lesions in children: An observational study of 19 cases

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    Digital dermoscopy follow-up helps to identify patterns of change typical of common atypical nevi and early melanoma and improves the follow-up of patients with atypical nevi. We report the morphologic changes observed over time in 19 atypical or equivocal acquired melanocytic nevi that underwent dermoscopic follow-up. Two observers retrospectively examined digitalized dermoscopic images of 19 atypical melanocytic nevi from 15 children and young adults (median age 12 years, range 3-26 years). The images were assessed for global dermoscopic patterns at baseline and after a median 25-month (range 6-138 mos) follow-up. Ten (52.6%) nevi changed and nine (47.4%) retained a stable dermoscopic pattern. Of the 10 changing lesions, 2 of 4 homogeneous nevi evolved into a reticular pattern and 2 into a mixed pattern; 1 of 2 nevi with a mixed pattern evolved into a homogeneous nevus and 1 into a regressing nevus; 1 of 2 nevi with "other" patterns, such as negative pigment network and peppering throughout the lesion, evolved into a mixed nevus and 1 into a regressing nevus; 1 globular nevus evolved into a mixed pattern; and 1 starburst nevus evolved into a homogeneous nevus. The most striking results of our study were that atypical nevi can evolve into common nevi or they can regress, as documented by long-term dermoscopic follow-up. In children and young adults, dermoscopic follow-up of atypical nevi might be a valid alternative to surgical excision and enables us to achieve new insights into the natural history of these nevi

    Genital and urinary tract diseases and prostate cancer risk

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    The objectives of this study were to investigate whether venereal diseases, prostatic and urinary infections, and other selected conditions of the genital and urinary tracts may have a role in the development of prostate cancer. We analysed data from a hospital-based case-control study conducted between 1985 and 1992 in Italy, including 280 cases of prostatic cancer and 689 controls, hospitalized for acute, non-neoplastic, non-genital or urinary tract conditions. We calculated odds ratios and 95% confidence intervals using unconditional multiple logistic regression. The odds ratios of prostate cancer were 0.64 for history of selected venereal diseases, 0.53 for prostatitis, 0.67 for benign prostatic hyperplasia, 1.53 for urinary tract stones and 1.76 for cystitis. No relationship, however, was observed for cystitis &rt; 5 years before prostate cancer. The present study, based on satisfactorily reproducible information on medical history, did not found any association between genital and urinary tract diseases and prostate cancer risk. European Journal of Cancer Prevention 15:254-257 (c) 2006 Lippincott Williams & Wilkins

    MEAL FREQUENCY AND RISK OF COLORECTAL-CANCER

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    The relation between meal frequency and the risk of colorectal cancer was investigated in a case-control study conducted in North Italy on 889 cases of colon cancer, 581 cases of rectal cancer, and 2475 controls admitted to hospital for acute, nonneoplastic, or digestive disorders. As compared to individuals who reported 2 or fewer meals per day, the multivariate colon cancer odds ratios were 1.7 [95% confidence interval (95% CI), 1.5-2.1] for 3, and 1.9 (95% CI, 1.1-3.3) for 4 meals or more. Corresponding rectal cancer odds ratios were 1.4 (95% CI, 1.1-1.7) for 3, and 1.9 (95% CI, 1.1-3.5) for 4 meals or more. The direct trends in risk of colorectal cancer with frequency of eating were not substantially modified by allowance for various dietary and nondietary potential confounding factors, including an approximate measure of total energy intake, and did not show significant effect modification across strata of age, sex, education, and other major risk covariates. A role of meal frequency in the etiology of colorectal cancer is biologically plausible, since when a meal is eaten, the gallbladder contracts and releases bile acids. Thus, eating patterns can influence the enterohepatic circulation and, consequently, the exposure time of intestinal mucosa to bile acids

    The effectiveness of continuing education in postoperative pain management: a follow up study

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    BACKGROUND: Studies still report high levels of postoperative pain. Inadequate treatment of patients experiencing pain is often due to lack of understanding of pain. METHODS: The objective of this study was to assess the effectiveness of a course on "pain," evaluated by a pretest-posttest design, with a questionnaire mailed to the 168 participants in February 2005. The course consisted of seven sessions held from October 2002 to June 2003 in a public hospital in Udine, Italy. This hospital has 710 beds and more than 30,000 admissions a year. The course, included in the "pain-free hospital" national objective, consisted of lectures, discussions, and role playing. RESULTS: Of the 10 test questions participants answered, seven showed a significant difference between the posttest taken at the end of the course and the posttest taken after 18 months. CONCLUSION: It is believed that knowledge is progressively lost if refresher courses are not held on a regular basi
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