The patch topology and the ultrafilter topology on the prime spectrum of a commutative ring

Let R be a commutative ring and let Spec(R) denote the collection of prime ideals of R. We define a topology on Spec(R) by using ultrafilters and demonstrate that this topology is identical to the well known patch or constructible topology. The proof is accomplished by use of a von Neumann regular ring canonically associated with $R$.Comment: A Remark was added at the end of the paper. To appear in Comm. Algebr

Nagata Rings, Kronecker Function Rings and Related Semistar Operations

In 1994, Matsuda and Okabe introduced the notion of semistar operation. This concept extends the classical concept of star operation (cf. for instance, Gilmer's book \cite{G}) and, hence, the related classical theory of ideal systems based on the works by W. Krull, E. Noether, H. Pr\"{u}fer and P. Lorenzen from 1930's. In \cite{FL1} and \cite{FL2} the current authors investigated properties of the Kronecker function rings which arise from arbitrary semistar operations on an integral domain $D$. In this paper we extend that study and also generalize Kang's notion of a star Nagata ring \cite{Kang:1987} and \cite{Kang:1989} to the semistar setting. Our principal focuses are the similarities between the ideal structure of the Nagata and Kronecker semistar rings and between the natural semistar operations that these two types of function rings give rise to on $D$.Comment: 20 page

An historical overview of Kronecker function rings, Nagata rings, and related star and semistar operations

An historical overview of Kronecker function rings, Nagata rings, and related star and semistar operationsComment: "Multiplicative Ideal Theory in Commutative Algebra: A tribute to the work of Robert Gilmer", Jim Brewer, Sarah Glaz, William Heinzer, and Bruce Olberding Editors, Springer (to appear

Cancellation properties in ideal systems: A classification of e.a.b.\boldsymbol{e.a.b.} semistar operations

We give a classification of {\texttt{e.a.b.}} semistar (and star) operations by defining four different (successively smaller) distinguished classes. Then, using a standard notion of equivalence of semistar (and star) operations to partition the collection of all {\texttt{e.a.b.}} semistar (or star) operations, we show that there is exactly one operation of finite type in each equivalence class and that this operation has a range of nice properties. We give examples to demonstrate that the four classes of {\texttt{e.a.b.}} semistar (or star) operations we defined can all be distinct. In particular, we solve the open problem of showing that {\texttt{a.b.}} is really a stronger condition than {\texttt{e.a.b.}

Prostate Cancer Care Before and After Medicare Eligibility.

Prior studies suggest Medicare eligibility confers significant and substantial reductions in mortality and beneficial increases in health service utilization. We compared 13,882 patients diagnosed with prostate cancer at ages 63 to 64 years with 14,774 patients diagnosed at ages 65 to 66 (controls) in 2004 to 2007. Compared with controls, patients diagnosed with prostate cancer before Medicare eligibility had no statistically significant or meaningful differences in cancer stage, time to treatment, or type of treatment

Lung Cancer Care Before and After Medicare Eligibility.

Uninsured and underinsured near-elderly may not have timely investigation, diagnosis, or care of cancer. Prior studies suggest Medicare eligibility confers significant and substantial reductions in mortality and increases in health service utilization. We compared 2245 patients diagnosed with lung cancer at ages 64.5 to 65 years and 2512 patients aged 65 to 65.5 years, with 2492 patients aged 65.5 to 66 years (controls) in 2000 to 2005. Compared with controls, patients diagnosed with lung cancer before Medicare eligibility had no statistically significant differences in cancer stage, time to treatment, type of treatment, and survival. Study power was sufficient to exclude mortality reductions and health service utilization changes of the magnitude found in prior work, suggesting that typically, appropriate lung cancer care may be sought and delivered regardless of insurance status

Kinetics of the Wako-Saito-Munoz-Eaton Model of Protein Folding

We consider a simplified model of protein folding, with binary degrees of freedom, whose equilibrium thermodynamics is exactly solvable. Based on this exact solution, the kinetics is studied in the framework of a local equilibrium approach, for which we prove that (i) the free energy decreases with time, (ii) the exact equilibrium is recovered in the infinite time limit, and (iii) the folding rate is an upper bound of the exact one. The kinetics is compared to the exact one for a small peptide and to Monte Carlo simulations for a longer protein, then rates are studied for a real protein and a model structure.Comment: 4 pages, 4 figure