Hamiltonian constants for several new entire solutions

Using the Hamiltonian identities and the corresponding Hamiltonian constants for entire solutions of elliptic partial differential equations, we investigate several new entire solutions whose existence were shown recently, and show interesting properties of the solutions such as formulas for contact angles at infinity of concentration curves.      

The distribution of the number of arrivals in a subinterval of a busy period of a single server queue

In the course of attempting to estimate the arrival rate of a single server queue using an active probing experiment, the authors found it necessary to derive the distribution of the number of arrivals between two probes under the conditions that the busy period of the queue lasts this long. In this paper we derive this distribution. The key building blocks in the derivation of the distribution are the classical ballot theorem and its generalized forms.     

带启动时间的多重休假的GI/Geom/1离散时间排队

本文通过矩阵几何解方法分析了带启动时间的多重休假的GI／Geom／1离散时间排队，得到了稳态队长和等待时间的分布、母函数及随机分解结果，推广了以前的结论。此外，本文考虑的休假都是服从几何分布．我们还可讨论更一般的分布。     

Comparison of single and double cladding long period fiber grating sensor using an intensity modulation interrogation system

The performance of long period fiber grating (LPFG) sensors written in single cladding and double cladding fibers have been compared by using a fast responding interrogation system based on intensity modulation. Temperature and dynamic strain monitoring using this system have been demonstrated. This system is capable of resolving strain to 0.2 and 0.4 με at a loading frequency of 20 Hz, and temperature resolution to 0.02 and 0.19 °C by using LPFG in the single cladding (SC-LPFG) and double cladding (DC-LPFG), respectively.     

稳恒超导载流态正常─超导界面层的作用

研究了稳恒超导载流态条件下 ,正常超导界面层对超导载流子的作用。指出在正常超导界面层内存在着“类感应电场力”,其本质上是束缚电子对所受 Lorentz力沿超导体对称轴线的分量之和。在“类感应电场力”的作用下 ,束缚电子对质心定向运动速度由零增大到 1 0 3 - 1 0 4 ms- 1,使超导电流的熵小于正常电流的熵。正常超导界面层是熵变区。     

Tail Behaviour of the Area Under the Queue Length Process of the Single Server Queue with Regularly Varying Service Times

This paper considers a stable GI∨GI∨1 queue with a regularly varying service time distribution. We derive the tail behaviour of the integral of the queue length process Q(t) over one busy period. We show that the occurrence of a large integral is related to the occurrence of a large maximum of the queueing process over the busy period and we exploit asymptotic results for this variable. We also prove a central limit theorem for ∫₀^t Q(s) ds.AMS subject classification: 60K25, 90B22.     

Substituent effect on the diastereoselectivity in the chelation-controlled radical reactions of γ-(p-substituted-benzyloxy)-α-methylene esters with alkyl iodides

A pronounced substituent effect on the diastereoselectivity in the chelation controlled radical reactions of ethyl γ-(p-substituted-benzyloxy)-α-methylenecarboxylates with alkyl iodides was observed. The syn-selectivity increased in the order of electron-donating ability NO₂<CN<CF₃<F<H<i-Pr, Me, OMe of the p-substituent, and the plot of the log(syn/anti) versus Hammett sigma constants gave a linear correlation. The complexation experiments of the substrates with Lewis acid using ¹H NMR spectroscopy and the competition experiments between p-isopropylbenzyloxy and p-trifluoromethylbenzyloxy esters showed that the electron-donating p-isopropyl group stabilized the seven-membered chelate ring to give high syn-selectivity.     

Titanium fluoride complexes as catalysts for the enantioselective addition of Me3Al to aldehydes

We report a Ti(IV) catalyst prepared in situ from TiF₄ for the asymmetric addition of trimethylaluminum to aldehydes. The process we detail herein does not necessitate the use of excess trimethylaluminum or Ti(IV) reagent. Good enantioselectivities are achieved with a variety of aromatic and heteroaromatic aldehydes with the products isolated in high yield.     

On the quasi-stationary distribution of a stochastic Ricker model

We model the evolution of a single-species population by a size-dependent branching process Z_t in discrete time. Given that Z_t = n the expected value of Z_t+1 may be written nexp(r − γn) where r> 0 is a growth parameter and γ > 0 is an (inhibitive) environmental parameter. For small values of γ the short-term evolution of the normed process γZ_t follows the deterministic Ricker model closely. As long as the parameter r remains in a region where the number of periodic points is finite and the only bifurcations are the period-doubling ones (r in the beginning of the bifurcation sequence), the quasi-stationary distribution of γZ_t is shown to converge weakly to the uniform distribution on the unique attracting or weakly attracting periodic orbit. The long-term behavior of γZ_t differs from that of the Ricker model, however: γZ_t has a finite lifetime a.s. The methods used rely on the central limit theorem and Markov's inequality as well as dynamical systems theory.     

Anomalous Pulsation

Subordinating regular diffusion – namely, Brownian motion – to random time flows generated by Lévy noises may result in anomalous diffusion. Motivated by this phenomena, and by the recent interest in the phenomena of blinking in various physical systems, we explore the subordination of regular stochastic pulsation – namely, Poisson process – to random time flows generated by Lévy noises. We show that such subordination may yield, analogous to the case of diffusion, anomalous pulsation. Anomalous pulsation displays the following anomalous behaviors, which are impossible in the case of regular pulsation: (i) simultaneous emission of multiple pulses; (ii) non-linear local pulsation rates; (iii) clustering of pulsation epochs.