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31.
LetX be a Brownian motion defined on the line (withX(0)=0) and letY be an independent Brownian motion defined on the nonnegative real numbers. For allt0, we define theiterated Brownian motion (IBM),Z, by setting
. In this paper we determine the exact uniform modulus of continuity of the process Z.Research supported by NSF grant DMS-9122242. 相似文献
32.
Thomas M. Lewis 《Journal of Theoretical Probability》1993,6(2):209-230
LetX, X i ,i≥1, be a sequence of independent and identically distributed ? d -valued random vectors. LetS o=0 and \(S_n = \sum\nolimits_{i = 1}^n {X_i } \) forn≤1. Furthermore letY, Y(α), α∈? d , be independent and identically distributed ?-valued random variables, which are independent of theX i . Let \(Z_n = \sum\nolimits_{i = 0}^n {Y(S_i )} \) . We will call (Z n ) arandom walk in random scenery. In this paper, we consider the law of the iterated logarithm for random walk in random scenery where deterministic normalizers are utilized. For example, we show that if (S n ) is simple, symmetric random walk in the plane,E[Y]=0 andE[Y 2]=1, then $$\mathop {\overline {\lim } }\limits_{n \to \infty } \frac{{Z_n }}{{\sqrt {2n\log (n)\log (\log (n))} }} = \sqrt {\frac{2}{\pi }} a.s.$$ 相似文献
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D.J.T. Hill D.A. Lewis J.H. ODonnell P.W. OSullivan P.J. Pomery 《European Polymer Journal》1982,18(1):75-80
Styrene-acrylonitrile copolymers, like many other copolymers containing styrene, exhibit both normal and excimer fluorescence. We have shown that the ratio of the excimer to monomer fluorescence intensities in random styrene-acrylonitrile copolymers is linearly dependent upon the concentration of styrene-styrene bonds in the copolymer. This observation is consistent with a photophysical model which allows the energy absorbed by styrene units to migrate freely along the copolymer chain. Some of the energy is emitted in the form of normal fluorescence; some of the energy, trapped by neighbouring styrene-styrene pairs suitably oriented to allow excimer formation, is emitted as excimer fluorescence. The fluorescence characteristics of acrylonitrile-styrene copolymers are contrasted with those of methyl methacrylate-styrene copolymers, in which the methylmethacrylate sequences are believed to present partial barriers to energy migration along the copolymer chains. 相似文献
36.
The syntheses, structures, and spectroscopy of a series of oligomeric tertiary oligophenylureas possessing one to five phenyl rings are reported. A convergent synthetic method employing tertiary monoamine and diamine building blocks is employed. NMR and molecular modeling are indicative of folded structures for all of the oligophenylureas in which adjacent phenyl rings have a splayed face-to-face geometry. NMR chemical shifts, absorption and emission maxima, and electrochemical oxidation potentials are all dependent upon the number of phenyl rings. The addition of a first inner phenyl has a pronounced effect on the chemical shifts, while a second and third inner phenyl have diminished effects. The oxidation potentials of the oligophenylureas display an abrupt decrease upon the addition of the second inner phenyl. The absorption and emission spectra are relatively insensitive to the addition of one to three inner phenyl rings. The electronic structures of the oligophenylureas possessing one to eight rings have been analyzed using ZINDO calculations. The frontier orbitals of the ureas with one to three phenyl rings are localized on a single phenyl ring (the inner ring for the three-ring urea), whereas the frontier orbitals of the higher oligomers are delocalized over two phenyl rings. In all cases, urea-localized n,pi* transitions are lower in energy than the phenyl-localized pi,pi* transitions. The changes in properties with added phenyl rings parallel those previously observed for multilayered cyclophanes; however, they are less pronounced because of weaker coupling between the phenyl rings of the oligophenylureas. 相似文献
37.
Optical absorbance changes are commonly used to characterize intermediates which appear in the bleaching sequence of rhodopsin and in the photocycle of bacteriorhodopsin. Absorbance changes can be caused by an intermediate's rotational diffusion, and when this occurs it can distort absorbance changes due to the structural evolution of intermediates. Linear polarization of an optical probe source at 54.7 degrees (the magic angle) relative to the polarization direction of a linearly polarized actinic source has often been used to eliminate signals due to rotational diffusion. We used Jones calculus to investigate the validity of the magic-angle strategy. Taylor expansion of the result in powers of the absorbances of the bleached ground state and of the intermediates leads to a relatively simple expression which can be used to determine whether rotational contributions are likely under various experimental conditions. This expression shows that in first order no dichroism-dependent term appears in the absorbance measured at magic angle. In second order, however, linear dichroism contributes to signals. For the sequence of rhodopsin intermediates: rhodopsin hv----bathorhodopsin in equilibrium BSI----lumirhodopsin, where BSI is a recently discovered blue-shifted intermediate, we determined the magnitude of the dichroism signals to be, on average, less than 2% of the true absorbance change due to the intermediates themselves (and hence undetectable). Freedom from dichroism artifacts in this case results from the fact that the transition dipoles of these intermediates are similar to that of rhodopsin. Larger and certainly detectable dichroism signals are predicted to occur, even at the magic angle, for later intermediates which have transition dipole moments which differ significantly from that of rhodopsin.(ABSTRACT TRUNCATED AT 250 WORDS) 相似文献
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Rashid MA Gustafson KR Crouch RC Groweiss A Pannell LK Van QN Boyd MR 《Organic letters》2002,4(19):3293-3296
Poecillastrin A (1), a new polyketide-derived macrolide lactam, was isolated from a deep-water collection of the marine sponge Poecillastra species. The structure of poecillastrin A (1) was assigned using NMR data acquired at 500 MHz with an inverse-detection cryogenic probe and at 800 MHz with a room-temperature probe. 相似文献
40.
C. R. Lewis 《Journal of polymer science. Part A, Polymer chemistry》1983,21(5):1543-1550
Metals may be chemically incorporated into organic lithographic resists that contain or can be functionalized with ? OH groups. A wide range of metal incorporation (0.04–12% of total solids by weight) has been demonstrated for AZ-1370 (Shipley), a diazo-type photo- and electron resist. The novolac component of the resist is reacted with an organometallic halide, RyMX (R = alkyl, aryl; M = transition or main group metal; X = CI, Br; 1 ≤ y ≤ 4, depending on M) to introduce the corresponding organometallic function into the resist. 相似文献