A well known result due to Ankeny and Rivlin [1] states that if p(z) = ∑n v=0 avz v is a polynomial of degree n satisfying p(z) 6= 0 for |z| < 1 then for R ≥ 1 max |z|=R |p(z)| ≤ R n + 1 2 max |z|=1 |p(z)|. It was proposed by late Professor R.P. Boas, Jr. to obtain an inequality analogous to this inequality for polynomials having no zeros in |z| < K, K > 0. In this paper, we obtain some results...

Dietary intervention with serum-derived bovine immunoglobulins protects barrier 1 function in a mouse model of colitis 2 Anna Pérez-Bosque*, PhD; Lluïsa Miró*, PhD; Mònica Maijó, PhD; Javier Polo, PhD; Joy 3 Campbell, PhD; Louis Russell, PhD; Joe Crenshaw, PhD; Eric Weaver, PhD; Miquel 4 Moretó, Prof. 5 Departament de Fisiologia, Facultat de Farmàcia and Institut de Recerca en Nutrició i 6 Segu...

Many number-theoretic algorithms rely on a result of Ankeny, which states that if the Extended Riemann Hypothesis (ERH) is true, any nontrivial multiplicative subgroup of the integers modulo m omits a number that is 0(log m). This has been generalized by Lagañas. Montgomery, and Odlyzko to give a similar bound for the least prime ideal that does not split completely in an abelian extension of n...

An error in the program for verifying the Ankeny-Artin-Chowla (AAC) conjecture is reported. As a result, in the case of primes p which are ≡ 5 mod 8, the AAC conjecture has been verified using a different multiple of the regulator of the quadratic field Q(√p) than was meant. However, since any multiple of this regulator is suitable for this purpose, provided that it is smaller than 8p, the main...

1 Kuschner WG, Gruenewald DA, Clum N, et al. Implementation of ICU palliative care guidelines and procedures. Chest 2009; 135:26–32 2 Truog RD, Campbell ML, Curtis JR, et al. Recommendations for end-of-life care in the intensive care unit: a consensus statement by the American College of Critical Care Medicine. Crit Care Med 2008; 36: 953–963 3 Miller FG, Truog RD. Rethinking the ethics of vita...

ABSTRACTIs Kuhn’s notion of exemplar applicable to ongoing biomedical sciences? Many philosophers may be skeptical because cases are mostly from physics and chemistry. However, how do test the above (non-)applicability directly? We will use examples illustrate a scientometric approach integrated history philosophy science (SciHPS) argue that SciHPS can provide an empirical basis empirically rev...

using the mean-value theorem for integrals we tried to solved the nonlinear integral equations of hammerstein type . the mean approach is to obtain an initial guess with unknown coefficients for unknown function y(x). the procedure of this method is so fast and don&apos;t need high cpu and complicated programming. the advantages of this method are that we can applied for those integral equation...