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51.
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. 相似文献
52.
Eric Bach Richard Lukes Jeffrey Shallit H. C. Williams. 《Mathematics of Computation》1996,65(216):1737-1747
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.
53.
Eric Berson R. Mane Trupti V. Kurt Svihla C. Hanley Thomas R. 《Applied biochemistry and biotechnology》1998,(1):615-627
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 kLa values in the reaction chamber. The liquid feed into the system has been modified to improve the axial liquid mixing and
O transfer. 相似文献
54.
55.
Lépine F Milot S Déziel E He J Rahme LG 《Journal of the American Society for Mass Spectrometry》2004,15(6):862-869
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. 相似文献
56.
We describe the properties of a series of oligomeric polyfluorophores assembled on the DNA backbone. The 11 oligomers (oligodeoxyfluorosides, ODFs), 4-7 monomers in length, were composed of only two fluorescent monomers and a spacer in varied sequences, and were designed to test how fluorescent nucleobases can interact electronically to yield complexity in fluorescence emission. The monomer fluorophores were deoxyribosides of pyrene and perylene, which emit light in violet and blue wavelengths, respectively. The experiments show that simple variation in sequence and spacing can dramatically change fluorescence, yielding emission maxima ranging from 380 to 557 nm and visible colors from violet to orange-red. Fluorescence lifetime data, excitation spectra, and absorption data point to a number of multi-fluorophore electronic interactions, including pyrene-pyrene and perylene-perylene excimers, pyrene-perylene exciplexes, as well as monomer dye emissions, contributing to the final spectral outcomes. Thus, two simple fluorophores can be readily combined to give emissions over much of the visible spectrum, all requiring only a single excitation. The results demonstrate that fluorescent nucleobases in oligomeric form can act cooperatively as electronic units, and that fluorophore sequence in such oligomers is as important as fluorophore composition in determining fluorescence properties. 相似文献
57.
Russell SC Czerwieniec G Lebrilla C Tobias H Fergenson DP Steele P Pitesky M Horn J Srivastava A Frank M Gard EE 《Journal of the American Society for Mass Spectrometry》2004,15(6):900-909
The appearance of informative signals in the mass spectra of laser-ablated bio-aerosol particles depends on the effective ionization probabilities (EIP) of individual components during the laser ionization process. This study investigates how bio-aerosol chemical composition governs the EIP values of specific components and the overall features of the spectra from the bio-aerosol mass spectrometry (BAMS). EIP values were determined for a series of amino acid, dipicolinic acid, and peptide aerosol particles to determine what chemical features aid in ionization. The spectra of individual amino acids and dipicolinic acid, as well as mixtures, were examined for extent of fragmentation and the presence of molecular ion dimers, which are indicative of ionization conditions. Standard mixtures yielded information with respect to the significance of secondary ion plume reactions on observed spectra. A greater understanding of how these parameters affect EIP and spectra characteristics of bio-aerosols will aid in the intelligent selection of viable future biomarkers for the identification of bio-terrorism agents. 相似文献
58.
Eric Magnusson 《Journal of computational chemistry》1993,14(1):54-66
Energy optimization calculations have been carried out to determine the variability of optimum p, d, and f polarization function exponents in molecules containing first- and second-row elements and in normal valency and hypercoordinate species. Optimum exponents were determined for single sets of higher-order functions at both Hartree–Fock and correlated (Moller–Plesset) levels of theory using the Dunning–Hay double zeta and the McLean–Chandler triple zeta basis sets. More detailed calculations were used to test the response to nonoptimum d and f function exponents of the total energy, the optimum geometry, and harmonic stretching frequencies. The variability in optimum exponents and the size of the energy penalties incurred by adopting nonoptimum values reduces the utility of standard exponents for p, d, and f polarization functions. © 1993 John Wiley & Sons, Inc. 相似文献
59.
Nonribosomal peptide synthetases (NRPS) are multimodular biocatalysts that bacteria and fungi use to assemble many complex peptides with broad biological activities. The same modular enzymatic assembly line principles are found in fatty acid synthases (FAS), polyketide synthases (PKS), and most recently in hybrid NRPS/PKS multienzymes. FAS as well as PKS are known to function as homodimeric enzyme complexes, raising the question of whether NRPS may also act as homodimers. To test this hypothesis, biophysical methods (size exclusion chromatography, analytical equilibrium ultracentrifugation, and chemical crosslinking) and biochemical methods (two-affinity-tag-system and complementation studies with enzymes being inactivated in different catalytic domains) were applied to NRPS subunits from the gramicidin S (GrsA-ATE), tyrocidine (TycB(1)-CAT and TycB(2-3)-AT.CATE), and enterobactin (EntF-CATTe) biosynthetic systems. These methods had revealed the dimeric structure of FAS and PKS previously, but all three NRPS systems investigated are functionally active as monomers. 相似文献
60.
6-Diazopenicillanates react with allylic sulphides, selenides and bromides, to give 6,6-disubstituted penicillanates [2,3]-sigmatropic rearrangements. 相似文献