Distributional control and generalized analyticity

Let S be a strongly continuous, separation-preserving representation of a locally compact abelian group G in L^p(), where 1p<, and is an arbitrary measure. We show that S is uniformly bounded with respect to the L^p-and L-norms if and only if it satisfies a certain boundedness condition for distribution functions. These equivalent conditions facilitate the transference from L^p(G) to L^p() of the a.e. convergence for a wide class of sequences of convolution operators. The result unifies and generalizes various aspects of ergodic theory--in particular, the ergodic singular integral operators and ergodic Hardy spaces.     

Mean-boundedness and Littlewood-Paley for separation-preserving operators

Suppose that is a -finite measure space, , and is a bounded, invertible, separation-preserving linear operator such that the linear modulus of is mean-bounded. We show that has a spectral representation formally resembling that for a unitary operator, but involving a family of projections in which has weaker properties than those associated with a countably additive Borel spectral measure. This spectral decomposition for is shown to produce a strongly countably spectral measure on the ``dyadic sigma-algebra' of , and to furnish with abstract analogues of the classical Littlewood-Paley and Vector-Valued M. Riesz Theorems for .

     

Accelerated stochastic simulation of the stiff enzyme-substrate reaction

The enzyme-catalyzed conversion of a substrate into a product is a common reaction motif in cellular chemical systems. In the three reactions that comprise this process, the intermediate enzyme-substrate complex is usually much more likely to decay into its original constituents than to produce a product molecule. This condition makes the reaction set mathematically "stiff." We show here how the simulation of this stiff reaction set can be dramatically speeded up relative to the standard stochastic simulation algorithm (SSA) by using a recently introduced procedure called the slow-scale SSA. The speedup occurs because the slow-scale SSA explicitly simulates only the relatively rare conversion reactions, skipping over occurrences of the other two less interesting but much more frequent reactions. We describe, explain, and illustrate this simulation procedure for the isolated enzyme-substrate reaction set, and then we show how the procedure extends to the more typical case in which the enzyme-substrate reactions occur together with other reactions and species. Finally, we explain the connection between this slow-scale SSA approach and the Michaelis-Menten [Biochem. Z. 49, 333 (1913)] formula, which has long been used in deterministic chemical kinetics to describe the enzyme-substrate reaction.     

In vivo EXPOSURE TO ULTRAVIOLET RADIATION ENHANCES PATHOGENIC EFFECTS OF MURINE LEUKEMIA VIRUS, LP-BMS, IN MURINE ACQUIRED IMMUNODEFICIENCY SYNDROME

LP-BM5 murine leukemia virus (MuLV) induces an immunodeficiency syndrome (MAIDS) in C57BL/6 mice which resembles immunological abnormalities observed in early stages of human AIDS. In our study, MAIDS virus-infected mice were exposed to low doses of ultraviolet radiation (UVR) before and after virus inoculation and compared with MAIDS-infected but not UVR-exposed mice. In all tested parameters (blood IgM levels; mitogenic responses to PHA, ConA, LPS and anti-mu; MLR; antigenic response to SRBC; enlargement and histopathologic changes of the spleen) we observed the same trend: changes due to MAIDS infection were more pronounced in the UVR-exposed group than in the unexposed group. Statistically significant differences between these two groups were seen for mitogenic responses at two different time points after virus inoculation. These results demonstrate that in vivo UVR exposure enhances the immunosuppressive effects of a retroviral infection. UVR exposure may affect the progression of AIDS in a similar manner.     

Thermodynamic quantities for the interaction of H+ and Na+ with C2H3O 2 − and Cl− in aqueous solution from 275 to 320°C

The aqueous reactions, {ie865-1}were studied as a function of ionic strength at 275, 300, and 320°C using a flow calorimetric technique. Log K, H and S values were determined from the fits of the calculated and experimental heats while Cp values were calculated from the variation of H values with temperature. The log K and H values for the first two reactions agree well with literature values at these temperatures. No previous results have been reported for the third reaction. The use of equations containing identical numbers of positive and identical numbers of negative charges on both sides of the equal sign (isocoulombic reaction principle) was applied to the log K values determined in this study. The resulting plots of log K for the isocoulombic reactions vs. I/T were approximately linear, which demonstrates that the Cp values for these reactions are approximately zero.Deceased 5 September 1987