Completion by Derived Double Centralizer

Let A be a commutative ring, and let $\mathfrak{a}$ be a weakly proregular ideal in A. (If A is noetherian then any ideal in it is weakly proregular.) Suppose M is a compact generator of the category of cohomologically $\mathfrak{a}$ -torsion complexes. We prove that the derived double centralizer of M is isomorphic to the $\mathfrak{a}$ -adic completion of A. The proof relies on the MGM equivalence from Porta et al. (Algebr Represent Theor, 2013) and on derived Morita equivalence. Our result extends earlier work of Dwyer et al. (Adv Math 200:357–402, 2006) and Efimov (2010).     

The connection between a conjecture of Carlisle and Kropholler,now a theorem of Benson and Crawley-Boevey,and Grothendieck's Riemann-Roch and duality theorems

The research was partly supported by the NSF grant DMS-9204940.     

Real-Space Renormalization Estimates for Two-Phase Flow in Porous Media

We present a spatial renormalization group algorithm to handle immiscibletwo-phase flow in heterogeneous porous media. We call this algorithmFRACTAM-R, where FRACTAM is an acronym for Fast Renormalization Algorithmfor Correlated Transport in Anisotropic Media, and the R stands for relativepermeability. Originally, FRACTAM was an approximate iterative process thatreplaces the L × L lattice of grid blocks, representing the reservoir,by a (L/2) × (L/2) one. In fact, FRACTAM replaces the original L× L lattice by a hierarchical (fractal) lattice, in such a way thatfinding the solution of the two-phase flow equations becomes trivial. Thistriviality translates in practice into computer efficiency. For N=L ×L grid blocks we find that the computer time necessary to calculatefractional flow F(t) and pressure P(t) as a function of time scales as N^1.7 for FRACTAM-R. This should be contrasted with thecomputational time of a conventional grid simulator N^2.3. The solution we find in this way is an accurateapproximation to the direct solution of the original problem.     

Monitoring enzyme activity using a diamagnetic chemical exchange saturation transfer magnetic resonance imaging contrast agent

Chemical exchange saturation transfer (CEST) is a new approach for generating magnetic resonance imaging (MRI) contrast that allows monitoring of protein properties in vivo. In this method, a radiofrequency pulse is used to saturate the magnetization of specific protons on a target molecule, which is then transferred to water protons via chemical exchange and detected using MRI. One advantage of CEST imaging is that the magnetizations of different protons can be specifically saturated at different resonance frequencies. This enables the detection of multiple targets simultaneously in living tissue. We present here a CEST MRI approach for detecting the activity of cytosine deaminase (CDase), an enzyme that catalyzes the deamination of cytosine to uracil. Our findings suggest that metabolism of two substrates of the enzyme, cytosine and 5-fluorocytosine (5FC), can be detected using saturation pulses targeted specifically to protons at +2 ppm and +2.4 ppm (with respect to water), respectively. Indeed, after deamination by recombinant CDase, the CEST contrast disappears. In addition, expression of the enzyme in three different cell lines exhibiting different expression levels of CDase shows good agreement with the CDase activity measured with CEST MRI. Consequently, CDase activity was imaged with high-resolution CEST MRI. These data demonstrate the ability to detect enzyme activity based on proton exchange. Consequently, CEST MRI has the potential to follow the kinetics of multiple enzymes in real time in living tissue.     

Modeling of one-dimensional smoldering of polyurethane in microgravity conditions

Results are presented from a model of forward smoldering combustion of polyurethane foam in microgravity. The transient one-dimensional numerical-model is based on that developed at the University of Texas at Austin. The conservation equations of energy, species, and mass in the porous solid and in the gas phases are numerically solved. The solid and the gas phases are not assumed to be in thermal or in chemical equilibrium. The chemical reactions modeled consist of foam oxidation and pyrolysis reactions, as well as char oxidation. The model has been modified to account for new polyurethane kinetics parameters and radial heat losses to the surrounding environment. The kinetics parameters are extracted from thermogravimetric analyses published in the literature and using Genetic Algorithms as the optimization technique. The model results are compared with previous tests of forward smoldering combustion in microgravity conducted aboard the NASA Space Shuttle. The model calculates well the propagation velocities and the overall smoldering characteristics. Direct comparison of the solution with the experimental temperature profiles shows that the model predicts well these profiles at high temperature, but not as well at lower temperatures. The effect of inlet gas velocity is examined, and the minimum airflow for ignition is identified. It is remarkable that this one-dimensional model with simplified kinetics is capable of predicting cases of smolder ignition but with no self-propagation away from the igniter region. The model is used for better understanding of the controlling mechanisms of smolder combustion for the purpose of fire safety, both in microgravity and normal gravity, and to extend the unique microgravity data to wider conditions avoiding the high cost of space-based experiments.     

p-adic Arakelov theory

We introduce the p-adic analogue of Arakelov intersection theory on arithmetic surfaces. The intersection pairing in an extension of the p-adic height pairing for divisors of degree 0 in the form described by Coleman and Gross. It also uses Coleman integration and is related to work of Colmez on p-adic Green functions. We introduce the p-adic version of a metrized line bundle and define the metric on the determinant of its cohomology in the style of Faltings. We also prove analogues of the Adjunction formula and the Riemann-Roch formula.     

Photoproduction of ω - mesons from 1.2 to 8.2 GeV

The reaction γp→ωp was studied between 1.2 and 8.2 GeV using positron annihilation radiation. Assuming σ ∝ C_OPE · E_γ⁻² + C_DIFF we obtain for the Pomeron exchange cross section (1.5 ± 0.3) μb.     

On the range of accretive operators

The solvability of the nonlinear operator equationw=x+Bx, whereB is accretive in a general Banach spaceX is studied by means of discrete approximations. In particular, ifB is continuous and everywhere defined an algorithm is given for solving the equation. Sponsored by the United States Army under Contract No. DAAG29-75-C-0024. Supported in part by NSF grant MCS 76-10227     

Time-reversal symmetry violation and the oscillating universe

The expressions for the fractional number ofK ⁰'s and¯K ⁰'s in a neutral kaon beam are discussed with reference to time-reversal asymmetry. The suggested relation between the sign of Re ( is the Lee-WuT-violation parameter) and the cosmological arrow of time ifCPT is broken is further clarified.Research sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, U.S. Air Force, under AFOSR grant number EOOAR-68-0010, through the European Office of Aerospace Research.     

Ultimatums in two-person bargaining with one-sided uncertainty: Offer games

In the ultimatum game with complete information a Sender proposes a division of a given amount of surplus (“pie”), which a Receiver can either accept (payoffs are distributed according to the Sender's proposal) or reject (both players earn nothing). We study another version of the ultimatum game under incomplete informaton in which the pie is drawn randomly from a commonly known distribution, the Sender knows the exact size of the pie, but the Receiver only knows her share of the pie, not the residual share requested by the Sender. The basic results are that (1) as the support of the pie distribution increases in a mean-preserving spread, the Senders make lower offers that the Receivers are less likely to reject, (2) for a given support, Senders tend to offer a lower proportion of the pie to the Receivers as the pie size grows larger, and (3) although knowing only their share of the pie, Receivers estimate its size quite accurately.