Topology and Factorization of Polynomials

For any polynomial $P \in \mathbb{C}[X_1,X_2,...,X_n]$, we describe a $\mathbb{C}$-vector space $F(P)$ of solutions of a linear system of equations coming from some algebraic partial differential equations such that the dimension of $F(P)$ is the number of irreducible factors of $P$. Moreover, the knowledge of $F(P)$ gives a complete factorization of the polynomial $P$ by taking gcd's. This generalizes previous results by Ruppert and Gao in the case $n=2$.Comment: Accepted in Mathematica Scandinavica. 8 page

Pengaruh Suplementasi Seng Dan Probiotik Pasca Perawatan Diare Akut Cair Anak Terhadap Kejadian Diare Berulang

Background. Diarrhea remains a major health problem among children under five years old in developing countries due to its high morbidity. Prevention of diarrhea is needed to reduce the high incidence. Zinc has a function to shorten duration of diarrhea and the use of probiotics preventing and treat acute diarrhea. Objective. To prove effect of zinc and probiotic suplementation on the incidence of recurrent acute watery diarrhea in children aged 6-24 months post-hospitalization. Method. Seventy five subjects aged 6-24 months with acute diarrhea in Dr. Kariadi Hospital, the subject of study I, was observed. The subjects were randomly divided into four groups and received treatment in the form of zinc supplementation, supplementation with probiotics, or a combination of zinc and probiotics and one group as control. Each group received the standard form of rehydration therapy and dietetic. Survival analysis was used to analyze the incidence of recurrent diarrhea and Kruskal wallis was used to analyze the difference of frequency and duration of recurrent diarrhea between four groups. Result. The group who received zinc in conjunction with probiotics had mean recurrent of diarrhea longer than the other three groups (10.94 weeks 95% CI 9.24 - 12.65). There was no statistically significant difference in the mean survival of diarrhea in the four groups (p = 0.892). No significant differences in frequency and duration of recurrent diarrhea in four groups at first, second and third month postsupplementation. Conclussion. There were no significant differences between groups of zinc, probiotics and a combination of zinc and probiotics on the average recurrent diarrhea, duration and frequency of diarrhea. Keyword : acute watery diarrhea, recurrent diarrhea, zinc, probiotic

Recent perspectives on the relations between faecal mutagenicity, genotoxicity and diet

Peer reviewedPublisher PD

Singularity \& Regularity Issues for Simplified Models of Turbulence

We consider a family of Leray-$\alpha$ models with periodic boundary conditions in three space dimensions. Such models are a regularization, with respect to a parameter $\theta$, of the Navier-Stokes equations. In particular, they share with the original equation (NS) the property of existence of global weak solutions. We establish an upper bound on the Hausdorff dimension of the time singular set of those weak solutions when $\theta$ is subcritical. The result is an interpolation between the bound proved by Scheffer for the Navier-Stokes equations and the regularity result proved in \cite{A01}