A bracket power characterization of analytic spread one ideals

The main theorem characterizes, in terms of bracket powers, analytic spread one ideals in local rings. Specifically, let be regular nonunits in a local (Noetherian) ring and assume that , the integral closure of , where . Then the main result shows that for all but finitely many units in that are non-congruent modulo and for all large integers and it holds that for and not divisible by , where is the -th bracket power of . And, conversely, if there exist positive integers , , and such that has a basis such that , then has analytic spread one.

     

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Identification of tyrosine nitration in UCH-L1 and GAPDH

Protein tyrosine nitration is a post-translational modification commonly used as a marker of cellular oxidative stress associated with numerous pathophysiological conditions. We focused on ubiquitin carboxyl terminal hydrolase-L1 (UCH-L1) and glyceraldehyde-3-phosphate (GAPDH) which are high-abundant brain proteins that have been identified to be highly susceptible to oxidative modification. Both UCH-L1 and GAPDH have been linked to the pathogenesis of Alzheimer's and Parkinson's disease, however specific nitration sites have not been elucidated. Identification of specific nitration sites and quantitation of endogenous nitrated proteins are important in correlating this modification to disease pathology. In this study, purified UCH-L1 and GAPDH were nitrated in vitro with peroxynitrite and the presence of nitrated proteins was confirmed by anti-3-nitrotyrosine Western blots. Data-dependent LC-MS/MS analysis identified several distinct tyrosine nitration sites in UCH-L1 (Tyr-80) and GAPDH (Tyr-47, Tyr-92, and Tyr-312). Subsequent validation with synthetic peptides was conducted for selected nitropeptides. An LC-MS/MS method was developed for semi-quantitative determination of the synthetic nitropeptides: KGQEVSPKVY(*) (UCH-L1) and mFQY(*) DSTHGKF (GAPDH). The nitropeptides were detectable in the mid-attomole range and the peak area response was linear over three orders of magnitude. Targeted analysis of endogenous UCH-L1 and GAPDH nitration was then conducted in an in vivo second-hand smoke rat model to evaluate the utility of this approach.     

Product branching from the CH2CH2OH radical intermediate of the OH + ethene reaction

Using a crossed laser-molecular beam scattering apparatus and tunable photoionization detection, these experiments determine the branching to the product channels accessible from the 2-hydroxyethyl radical, the first radical intermediate in the addition reaction of OH with ethene. Photodissociation of 2-bromoethanol at 193 nm forms 2-hydroxyethyl radicals with a range of vibrational energies, which was characterized in our first study of this system ( J. Phys. Chem. A 2010 , 114 , 4934 ). In this second study, we measure the relative signal intensities of ethene (at m/e = 28), vinyl (at m/e = 27), ethenol (at m/e = 44), formaldehyde (at m/e = 30), and acetaldehyde (at m/e = 44) products and correct for the photoionization cross sections and kinematic factors to determine a 0.765:0.145:0.026:0.063:<0.01 branching to the OH + C(2)H(4), H(2)O + C(2)H(3), CH(2)CHOH + H, H(2)CO + CH(3), and CH(3)CHO + H product asymptotes. The detection of the H(2)O + vinyl product channel is surprising when starting from the CH(2)CH(2)OH radical adduct; prior studies had assumed that the H(2)O + vinyl products were solely from the direct abstraction channel in the bimolecular collision of OH and ethene. We suggest that these products may result from a frustrated dissociation of the CH(2)CH(2)OH radical to OH + ethene in which the C-O bond begins to stretch, but the leaving OH moiety abstracts an H atom to form H(2)O + vinyl. We compare our experimental branching ratio to that predicted from statistical microcanonical rate constants averaged over the vibrational energy distribution of our CH(2)CH(2)OH radicals. The comparison suggests that a statistical prediction using 1-D Eckart tunneling underestimates the rate constants for the branching to the product channels of OH + ethene, and that the mechanism for the branching to the H(2)O + vinyl channel is not adequately treated in such theories.     

Notes on a new chain condition for prime ideals

A chain condition intermediate to the catenary property and the chain condition for prime ideals (c.c.) is studied. Like the c.c., the condition is inherited from a semi-local domain R by integral extension domains, by local quotient domains, and by factor domains, and a semi-local ring that satisfies the condition is catenary. (Unlike the c.c., none of these statements is true when R is not semi-local.) A number of characterizations of a semi-local domain that satisfies the condition are given in terms of: integral (respectively, algebraic, transcendental) extension domains, Henselizations, completions, Rees rings, associated graded rings and certain discrete valuation over-rings. Then four of the catenary chain conjectures are characterized in terms of this condition.     

Characterizations of taut semi-local rings

Summary It is proved that the following statements are equivalent for semi-local domain R:1) R is taut (i.e., for each non-maximal prime ideal P in R, height P+depth P=altitude R).2) Every integral domain which contains and is integral over R is taut.3) R[1/b]. satisfies the second chain condition for prime ideals (s.c.c.), for each non-zero b in the Jacobson radical J of R.4) R[1/b] satisfies the first chain condition for prime ideals (f.c.c.), for some non-zero b in J.5) For each depth one prime ideal P in R, R_P satisfies the s.c.c. and height P=altitude R−1.6) R(X) is taut, where X is an indeterminate.7) For each pair of analytically independent elements b, c in R, R(c/b) is taut and altitude R(c/b)=altitude R−1.8) Each maximal set of analytically independent elements in R contains either one element or altitude R elements. Much of the theorem is then generalized (with suitable modifications) to rings which contain and are integral over a taut semi-local ring. Entrata in Redazione il 5 dicembre 1975. Research on this paper was supported in part by the National Science Foundation grant NSF GP-28939-1.