How Fast can a Subharmonic Function Decay Along a Ray?

Much is known about the connection between the growth and decayof subharmonic functions. The results indicate that there isa general principle: asubharmonic function cannot decay ‘toofast’ relative to its growth.Three theorems are provedwhich, together with work previously published elsewhere, givea fairly complete account of how this principle works out fora subharmonic function having extremal decay along a ray. 1991Mathematics Subject Classification: 30D20, 31A05.     

A silicon tether approach for addition of functionalized radicals to chiral alpha-hydroxyhydrazones: diastereoselective additions of hydroxymethyl and vinyl synthons

Stereocontrolled additions of hydroxymethyl and vinyl groups to chiral alpha-hydroxyhydrazones can be achieved by radical cyclizations using bromomethyl or vinyl radical precursors tethered via a temporary silicon connection. Tin-mediated 5-exo radical cyclization of alpha-hydroxyhydrazones using a silicon-tethered bromomethyl group, followed by oxidative removal of the tether, provides anti-2-hydrazino 1,3-diols in good yield. Tandem thiyl radical addition-cyclization of alpha-hydroxyhydrazones using a silicon-tethered vinyl group, followed by treatment with potassium fluoride, affords acyclic allylic anti-hydrazino alcohols in good yield. The thiyl addition-cyclization method has been successfully extended to the use of alpha,beta-dihydroxyhydrazones without prior protection or hydroxyl differentiation. Diastereoselection in both reaction types increases with increasing A values of the appended groups, consistent with prediction by the Beckwith-Houk model for stereocontrol in 5-hexenyl radical cyclizations.     

Qualitative properties of modified equations

Suppose that a consistent one-step numerical method of orderr is applied to a smooth system of ordinary differential equations.Given any integer m 1, the method may be shown to be of orderr + m as an approximation to a certain modified equation. Ifthe method and the system have a particular qualitative propertythen it is important to determine whether the modified equationsinherit this property. In this article, a technique is introducedfor proving that the modified equations inherit qualitativeproperties from the method and the underlying system. The techniqueuses a straightforward contradiction argument applicable toarbitrary one-step methods and does not rely on the detailedstructure of associated power series expansions. Hence the conclusionsapply, but are not restricted, to the case of Runge-Kutte methods.The new approach unifies and extends results of this type thathave been derived by other means: results are presented forintegral preservation, reversibility, inheritance of fixed points.Hamiltonian problems and volume preservation. The techniquealso applies when the system has an integral that the methodpreserves not exactly, but to order greater than r. Finally,a negative result is obtained by considering a gradient systemand gradient numerical method possessing a global property thatis not shared by the associated modified equations.     

Transient hydrodynamics of in-line valves in viscoelastic pressurized pipes: long-period analysis

The literature contains few reports devoted to the analysis of the effects of a partially closed in-line valve on the characteristics of transients in viscoelastic pressurized pipes. In this paper a contribution to the analysis of the long-period behavior of pressure is offered from both the experimental and numerical modeling point of view. In the first part, laboratory tests and the related results??noticeably extensive with respect to the existing literature??are examined. More precisely, the dependance of the damping of the dimensionless pressure maximum values on the initial conditions and in-line valve local head loss coefficient is shown. In the second part, a 1-D numerical model is developed by determining its parameters within a physically based procedure. Model parameters are obtained by considering transients in a constant-diameter pipe (single pipe) and then exported to the case of pipes with a partially closed in-line valve (in-line valve pipe). Moreover, particular attention is devoted to the modalities of specifying boundary conditions. In particular, the quasi-steady-state approach is followed for determining the transient local head loss due to the partially closed in-line valve and the actual supply conditions and characteristics of the maneuver are taken into account. Finally, the effect of unsteady friction and viscoelasticity is examined in both single and in-line valve pipes.     

The influence of aqueous versus glassy solvents on protein dynamics: vibrational echo experiments and molecular dynamics simulations

Spectrally resolved infrared stimulated vibrational echo measurements are used to measure the vibrational dephasing of the CO stretching mode of carbonmonoxy-hemoglobin (HbCO), a myoglobin mutant (H64V), and a bacterial cytochrome c(552) mutant (Ht-M61A) in aqueous solution and trehalose glasses. The vibrational dephasing of the heme-bound CO is significantly slower for all three proteins embedded in trehalose glasses compared to that of aqueous protein solutions. All three proteins exhibit persistent but notably slower spectral diffusion when the protein surface is fixed by the glassy solvent. Frequency-frequency correlation functions (FFCFs) of the CO are extracted from the vibrational echo data to reveal that the structural dynamics, as sensed by the CO, of the three proteins in trehalose and aqueous solution are dominated by fast (tens of femtoseconds), motionally narrowed fluctuations. MD simulations of H64V in dynamic and "static" water are presented as models of the aqueous and glassy environments. FFCFs are calculated from the H64V simulations and qualitatively reproduce the important features of the experimentally extracted FFCFs. The suppression of long time scale (picoseconds to tens of picoseconds) frequency fluctuations (spectral diffusion) in the glassy solvent is the result of a damping of atomic displacements throughout the protein structure and is not limited to structural dynamics that occur only at the protein surface. The analysis provides evidence that some dynamics are coupled to the hydration shell of water, supporting the idea that the bioprotection offered by trehalose is due to its ability to immobilize the protein surface through a thin, constrained layer of water.