Small random perturbations of finite- and infinite-dimensional dynamical systems: Unpredictability of exit times

We apply previous results on the pathwise exponential loss of memory of the initial condition for stochastic differential equations with small diffusion to the problem of the asymptotic distribution of the first exit times from an attracted domain. We show under general hypotheses that the suitably rescaled exit time converges in the zero-noise limit to an exponential random variable. Then we extend the results to an infinite-dimensional case obtained by adding a small random perturbation to a nonlinear heat equation.     

TRANILAST ^1H^13CNMR谱分析及其结构的鉴定

本文用COSY,CHCOR等二维核磁共振技术对TRANILAST,2[]3-(3.4-二甲基苯基)1-氧代-2-丙烯基]氨基]苯甲到进行了~1H、~(13)C NMR谱数据分析及归属,并结合~(13)C弛豫时间T_1 及变温实验对合成产品进行了结构鉴定.     

Nano-crater formation on a Si(1 1 1)-(7 × 7) surface by slow highly charged ion-impact

Using scanning tunneling microscopy (STM) and time of flight secondary ion mass spectrometry (TOF/SIMS), we observed radiation effects on a Si(1 1 1)-(7 × 7) surface in the collision of a single highly charged ion (HCI) with a charge state q up to q = 50. The STM observation with atomic resolution revealed that a nanometer sized crater-like structure was created by a single HCI impact, where the size increased rapidly with q. The secondary ion yields also increased with q in which multiply charged Si ions (Siⁿ⁺) were clearly observed in higher q HCI-collisions. The sputtering mechanism is briefly discussed, based on the so-called Coulomb explosion model.     

Fluorescence and Rotational Dynamics of Dityrosine

We have examined the lifetimes and rotational correlation times of dityrosine emission by time-correlated single-photon counting. We first noticed dityrosine fluorescence in samples of tyrosine and tyrosine dipeptides by its characteristic red-shifted emission at 400 to 430 nm. The longer rotational correlation time relative to tyrosine proved that this fluorescence emanated from a distinct species. Comparison with the fluorescence properties of synthesized dityrosine established the identity of the emitting species. Fluorescence intensity decays of dityrosine are generally characterized by two decay components, one with a lifetime in the range of 150 to 800 ps and another between 2.5 and 4.5 ns. We found no evidence for an excited-state reaction, since a rising phase (negative-amplitude component) was not observed. In the pH range from 4 to 10, two ground-state species exist in equilibrium with pK _a 7. Both species exhibit two fluorescence decays. The average fluorescence lifetime increases gradually with pH over the pH range from 4 to 10 and decreases at pH 2. Anisotropy decays were measured for dityrosine and the alanine–dityrosine–alanine and leucine–dityrosine–leucine dipeptides. The rotational correlation times of dityrosine and dityrosine dipeptides increase linearly with van der Waals volumes. The slope indicates a stronger solute–solvent interaction than predicted with stick boundary conditions. It is suggested that these interactions result from the presence of two zwitterionic pairs.     

Dynamics of Random One-Dimensional ±J Systems

Finite chains of a two-state random Potts spin model with periodic boundary conditions are studied within Glauber dynamics. The spin exchange is assumed random with frustration between ferro and antiferromagnetic values (±J). Time-dependent fluctuations are induced by periodic temperature oscillations. Master type differential equations for spin correlation functions are solved within linear response theory. The spectrum of relaxation times are calculated at different temperatures. The ±J Potts glass chains undergo a zero temperature phase transition. The barriers against inversion of the spin chain take only two values; 0 and 2|J|. The temperature behaviour of specific heat is characterized by rounded peaks. The frequency dependence displays two plateaus for the real part of specific heat and two corresponding peaks for the imaginary part. The dynamic specific heat is not affected by the longest relaxing mode like susceptibility. The time separation of the modes is demonstrated by the Cole-Cole plots.     

Local times of continuous N-parameter strong martingales

Let M be a 4N-integrable, real-valued continuous N-parameter strong martingale. By extending Itô-type formulas for M to a function whose 2Nth derivative is Dirac's δ-distribution, Tanaka-type formulas for M are obtained. They represent local time of M with respect to occupation time scaled by the N-fold product of the Stieltjes measure defined by the quadratic variation of M and its kth derivatives in space, where k ≤ N − 1. Applications of Doob's and Burkholder's inequalities give continuity properties: space time continuity for local time, space continuity for the derivatives. In case N is even, for the continuity of the (N − 1)st derivative an additional condition on M is needed which may have a relation to the existence of local times of M w.r.t. different occupation time scales.     

Shifting of gas chromatographic retention times due to solvent effects — a study using sulfur chemiluminescence detection

Gas chromatrography (GC) with sulfur chemiluminescence detection (SCD) is an outstanding combination for selectively determining trace concentrations of sulfur compounds in hydrocarbon samples. GC peaks can be identified by retention times when reproducible, automated injection techniques are used. However, as described in this work, analysts should be on the look out for retention shifting due to solvent effects from sample components. Three examples of retention shifting are presented: (1) thiophene by benzene; (2) methylthiophenes by toluene; and (3) dibenzothiophene by gas oil. Depending on samples and analysis conditions, retention shifts from a few hundredths to 1.5 min have been observed. Such retention shifts are likely to cause errors in peak identifications. Therefore, when using SCD, simultaneous FID monitoring is recommended as an aid in evaluating chromatograms for possible retention shifting due to solvent effects.     

A note on the spectrum of an upper triangular operator matrix

Let be a upper triangular operator matrix acting on the Banach space . We investigate the set of the operators for which , where denotes the spectrum.

     

A characterization for mixtures of semi-Markov processes

Mixtures of recurrent semi-Markov processes are characterized through a partial exchangeability condition of the array of successor states and holding times. A stronger invariance condition on the joint law of successor states and holding times leads to mixtures of Markov laws.     

Closed‐form formulas for Kirchhoff index

We find closed‐form expressions for the resistance, or Kirchhoff index, of certain connected graphs using Foster's theorems, random walks, and the superposition principle. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 135–140, 2001