Bourgin-Yang version of the Borsuk-Ulam theorem for Z(pk)-equivariant maps

Let G = Z(pk) be a cyclic group of prime power order and let V and W be orthogonal representations of G with V-G = W-G = W-G = {0}. Let S(V) be the sphere of V and suppose f: S(V) -> W is a G-equivariant mapping. We give an estimate for the dimension of the set f(-1){0} in terms of V and W. This extends the Bourgin-Yang version of the Borsuk-Ulam theorem to this class of groups. Using this estimate, we also estimate the size of the G-coincidences set of a continuous map from S(V) into a real vector space W'.

On the zeros of polynomials: an extension of the Enestrom-Kakeya theorem

This paper presents an extension of the Enestrom-Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown (K, L) methods. The generalization relates to relaxing one of the inequalities on the coefficients of the polynomial. Two results concerning the zeros of polynomials will be proved, one of them providing a partial answer to a conjecture by Meneguette (1994)[6]. (C) 2011 Elsevier Inc. All rights reserved.

Kleiner's theorem for unitary representations of posets

A subspace representation of a poset S = {s(1), ..., S-t} is given by a system (V; V-1, ..., V-t) consisting of a vector space V and its sub-spaces V-i such that V-i subset of V-j if s(i) (sic) S-j. For each real-valued vector chi = (chi(1), ..., chi(t)) with positive components, we define a unitary chi-representation of S as a system (U: U-1, ..., U-t) that consists of a unitary space U and its subspaces U-i such that U-i subset of U-j if S-i (sic) S-j and satisfies chi 1 P-1 + ... + chi P-t(t) = 1, in which P-i is the orthogonal projection onto U-i. We prove that S has a finite number of unitarily nonequivalent indecomposable chi-representations for each weight chi if and only if S has a finite number of nonequivalent indecomposable subspace representations; that is, if and only if S contains any of Kleiner's critical posets. (c) 2012 Elsevier Inc. All rights reserved.

Exclusive breastfeeding protects against postpartum migraine recurrence attacks?

Objectives: To observe postpartum migraine recurrence among migraine sufferers before pregnancy, its classifications and associated factors and to compare women, who were exclusively breastfeeding, with those that used other forms of infant feeding. Methods: Out of 686 consecutively assisted women, at the first postnatal week, 266 were identified as migraine sufferers before pregnancy. Among those, one in five that were exclusively breastfeeding (53) and all the ones consecutively using others forms of infant feeding (40) were interviewed at the first and forth postpartum weeks. Results: After multivariable analysis, exclusive breastfeeding, no breastfeeding problems, and low income were associated with decrease in migraine recurrence at the first postpartum week. At the fourth week, exclusive breastfeeding continued to be a protective factor. Conclusions: A decrease in postpartum migraine recurrence seems to be another advantage of exclusive breastfeeding.

Regularity at infinity of real mappings and a Morse-Sard theorem

We prove a new Morse-Sard-type theorem for the asymptotic critical values of semi-algebraic mappings and a new fibration theorem at infinity for C-2 mappings. We show the equivalence of three different types of regularity conditions which have been used in the literature in order to control the asymptotic behaviour of mappings. The central role of our picture is played by the p-regularity and its bridge toward the rho-regularity which implies topological triviality at infinity.

Kurzweil integral for Riesz space-valued functions: Uniform convergence theorem

Our objective here is to prove that the uniform convergence of a sequence of Kurzweil integrable functions implies the convergence of the sequence formed by its corresponding integrals.

High dosage folic acid supplementation, oral cleft recurrence and fetal growth

Objectives: To evaluate the effects of folic acid supplementation on isolated oral cleft recurrence and fetal growth. Patients and Methods: The study included 2,508 women who were at-risk for oral cleft recurrence and randomized into two folic acid supplementation groups: 0.4 and 4 mg per day before pregnancy and throughout the first trimester. The infant outcome data were based on 234 live births. In addition to oral cleft recurrence, several secondary outcomes were compared between the two folic acid groups. Cleft recurrence rates were also compared to historic recurrence rates. Results: The oral cleft recurrence rates were 2.9% and 2.5% in the 0.4 and 4 mg groups, respectively. The recurrence rates in the two folic acid groups both separately and combined were significantly different from the 6.3% historic recurrence rate post the folic acid fortification program for this population (p = 0.0009 when combining the two folic acid groups). The rate of cleft lip with palate recurrence was 2.9% in the 0.4 mg group and 0.8% in the 4 mg group. There were no elevated fetal growth complications in the 4 mg group compared to the 0.4 mg group. Conclusions: The study is the first double-blinded randomized clinical trial (RCT) to study the effect of high dosage folic acid supplementation on isolated oral cleft recurrence. The recurrence rates were similar between the two folic acid groups. However, the results are suggestive of a decrease in oral cleft recurrence compared to the historic recurrence rate. A RCT is still needed to identify the effect of folic acid on oral cleft recurrence given these suggestive results and the supportive results from previous interventional and observational studies, and the study offers suggestions for such future studies. The results also suggest that high dosage folic acid does not compromise fetal growth

A uniqueness theorem for the determination of sources in the Germain–Lagrange plate equation

We prove a uniqueness result related to the Germain–Lagrange dynamic plate differential equation. We consider the equation {∂2u∂t2+△2u=g⊗f,in ]0,+∞)×R2,u(0)=0,∂u∂t(0)=0, where uu stands for the transverse displacement, ff is a distribution compactly supported in space, and g∈Lloc1([0,+∞)) is a function of time such that g(0)≠0g(0)≠0 and there is a T0>0T0>0 such that g∈C1[0,T0[g∈C1[0,T0[. We prove that the knowledge of uu over an arbitrary open set of the plate for any interval of time ]0,T[]0,T[, 0