An old question of T. Jech and K. Prikry asks if an existence of a precipitous ideal implies necessary existence of a normal precipitous ideal. The aim of the paper is to prove some results in the positive direction. Thus, it is shown that under some mild assumptions, an existence of a precipitous ideal over א1 implies an existence of a normal precipitous ideal over א1 once a Cohen subset is ad...

the rings considered in this article are commutative with identity $1neq 0$. by a proper ideal of a ring $r$,  we mean an ideal $i$ of $r$ such that $ineq r$.  we say that a proper ideal $i$ of a ring $r$ is a  maximal non-prime ideal if $i$ is not a prime ideal of $r$ but any proper ideal $a$ of $r$ with $ isubseteq a$ and $ineq a$ is a prime ideal. that is, among all the proper ideals of $r$,...

The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

INTRODUCTION Iterative Decomposition of Water and Fat with Echo Asymmetry and Least-Squares Estimation (IDEAL) is a promising MRI technique for robust fat and water separation (1). It was found with higher fluid/cartilage contrast-to-noise ratio efficiency and fat-suppression quality than FSE imaging in ankle. The goal of this study is to assess image quality, fat suppression and fat-water sepa...

OBJECTIVE To provide evidence on recent trends in: (1) market exclusivity periods (MEPs, the time between launch of a brand-name drug and its first generic competitor) for new molecular entities (NMEs); (2) the likelihood and timing of patent challenges under Paragraph IV of the Hatch-Waxman Act; and (3) generic drug penetration. METHODS IMS Health National Sales Perspectives data were used t...

OBJECTIVE To provide updated evidence on US trends in: market exclusivity periods (MEPs, time between brand-name drug launch and first generic competitors) for new molecular entities (NMEs); likelihood, timing and number of Hatch-Waxman Act Paragraph IV patent challenges; and generic drug penetration. METHODS This study used IMS Health National Sales Perspectives(TM) US data to calculate MEPs...