Phase sensitive demodulation in multiphoton microscopy.

Multiphoton laser scanning microscopy offers advantages in depth of penetration into intact samples over other optical sectioning techniques. To achieve these advantages it is necessary to detect the emitted light without spatial filtering. In this nondescanned (nonconfocal) approach, ambient room light can easily contaminate the signal, forcing experiments to be performed in absolute darkness. For multiphoton microscope systems employing mode-locked lasers, signal processing can be used to reduce such problems by taking advantage of the pulsed characteristics of such lasers. Specifically, by recovering fluorescence generated at the mode-locked frequency, interference from stray light and other ambient noise sources can be significantly reduced. This technology can be adapted to existing microscopes by inserting demodulation circuitry between the detector and data collection system. The improvement in signal-to-noise ratio afforded by this approach yields a more robust microscope system and opens the possibility of moving multiphoton microscopy from the research lab to more demanding settings, such as the clinic.     

Homoclinic orbits on compact hypersufaces in 293-1293-1293-1, of restricted contact type

Consider a smooth Hamiltonian system in ^2N , , the energy surface ={x/H(x)=H(0)} being compact, and 0 being a hyperbolic equilibrium. We assume, moreover, that {0} is of restricted contact type. These conditions are symplectically invariant. By a variational method, we prove the existence of an orbit homoclinic, i.e. non-constant and doubly asymptotic, to 0.     

Logarithmic correction to the probability of capture for dissipatively perturbed Hamiltonian systems

Hamiltonian systems are analyzed with a double homoclinic orbit connecting a saddle to itself. Competing centers exist. A small dissipative perturbation causes the stable and unstable manifolds of the saddle point to break apart. The stable manifolds of the saddle point are the boundaries of the basin of attraction for the competing attractors. With small dissipation, the boundaries of the basins of attraction are known to be tightly wound and spiral-like. Small changes in the initial condition can alter the equilibrium to which the solution is attracted. Near the unperturbed homoclinic orbit, the boundary of the basin of attraction consists of a large sequence of nearly homoclinic orbits surrounded by close approaches to the saddle point. The slow passage through an unperturbed homoclinic orbit (separatrix) is determined by the change in the value of the Hamiltonian from one saddle approach to the next. The probability of capture can be asymptotically approximated using this change in the Hamiltonian. The well-known leading-order change of the Hamiltonian from one saddle approach to the next is due to the effect of the perturbation on the homoclinic orbit. A logarithmic correction to this change of the Hamiltonian is shown to be due to the effect of the perturbation on the saddle point itself. It is shown that the probability of capture can be significantly altered from the well-known leading-order probability for Hamiltonian systems with double homoclinic orbits of the twisted type, an example of which is the Hamiltonian system corresponding to primary resonance. Numerical integration of the perturbed Hamiltonian system is used to verify the accuracy of the analytic formulas for the change in the Hamiltonian from one saddle approach to the next. (c) 1995 American Institute of Physics.     

Dispersion relations in string theory

We analyze the analytic continuation of the formally divergent one-loop amplitude for scattering of the gravitonmultiplet in the Type II superstring. In particular we obtain explicit double and single dispersion relations, formulas for all the successive branch cuts extending out to +, as well as for the decay rate of a massive string state of arbitrary mass2N into two string states of lower mass. We compare our results with the box diagram in a superposition of ³-like field theories. The stringy effects are traced to a convergence problem in this superposition.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98. No. 3, pp. 442–455, March, 1994.     

Results and estimates on pseudopowers

Let be a positive integer. We say looks like a power of 2 modulo a prime if there exists an integer such that . First, we provide a simple proof of the fact that a positive integer which looks like a power of modulo all but finitely many primes is in fact a power of . Next, we define an -pseudopower of the base to be a positive integer that is not a power of , but looks like a power of modulo all primes . Let denote the least such . We give an unconditional upper bound on , a conditional result (on ERH) that gives a lower bound, and a heuristic argument suggesting that is about for a certain constant . We compare our heuristic model with numerical data obtained by a sieve. Some results for bases other than are also given.

     

Weak decoherence and quantum trajectory graphs

Griffiths' quantum trajectories formalism is extended to describe weak decoherence. The decoherence conditions are shown to severely limit the complexity of histories composed of fine-grained events.     

Improved oxygen delivery in a continuous-roller-bottle reactor

Variations to the original aeration system in a continuous roller bottle reactor of novel design have been tested and compared for optimal oxygen (O) delivery. Reactor operating parameters that affect O transfer are rotation rate, liquid-volume level, fresh-feed rate, and supplementary-aeration rate. Design modifications to enhance gas-liquid O transfer include the addition of wall baffles and center baffles. The number and location of each of these baffles are compared for their effect on k_La values in the reaction chamber. The liquid feed into the system has been modified to improve the axial liquid mixing and O transfer.     

Development of a tandem cyclization mediated by samarium(II) iodide: sequential intramolecular conjugate addition/nucleophilic acyl substitution

The development of a one-pot tandem intramolecular conjugate addition/nucleophilic acyl substitution using samarium(II) iodide is reported. The reaction relies on the reagent’s unique ability to mediate both radical and anionic pathways, which are likely integral to the mechanism of this transformation. The tricyclic hemiacetal product was formed in good yield, with excellent diastereoselectivity, and its structure was verified by X-ray crystallographic analysis.     

Electrospray/mass spectrometric identification and analysis of 4-hydroxy-2-alkylquinolines (HAQs) produced by <Emphasis Type="Italic">Pseudomonas aeruginosa</Emphasis>

The opportunistic pathogen Pseudomonas aeruginosa produces a large array of 4-hydroxy-2-alkylquinolines (HAQs). These compounds were analyzed by LC/MS, using positive electrospray ionization, in the culture supernatant of strain PA14. Fifty-six HAQs and related compounds were detected and their [M + H](+) ions were further analyzed by collision induced dissociation (CID). These HAQs were grouped into five different series based on the presence of an hydrogen or hydroxyl group at the 3 position, an N-oxide group in place of the quinoline nitrogen, and an unsaturation on their alkyl side chain. Two new analogs of 3,4-dihydroxy-2 heptylquinoline, the Pseudomonas quinolone signal (PQS), were found with an alkyl chain longer by one and two methylene groups. Moreover, two additional series of compounds were identified in which a saturated or unsaturated alkyl side chain is located at the 3 position along with an hydroxyl group at the 3 position and a ketone at the 2 position. No HAQ N-oxides, nor any compounds from the latter two series, were detected in a pqsL mutant derivative of PA14, indicating that this gene is involved in the biosynthesis of these compounds. This work demonstrates the large repertoire of HAQ and HAQ-related compounds produced by P. aeruginosa, and provides insight into N-oxides biosynthesis and confirm the hypothesis that N-oxides are the precursors of compounds from Series 6 and 7.